The Impact of Protostellar Jets on their Environment

The Impact of Protostellar Jets on theirEnvironment

by

Barry F. O’Connell

A thesis submitted for the degree ofDoctor of Philosophy

Department of Physics

Faculty of ScienceTrinity College Dublin

Dublin, Ireland

January 2005

DECLARATION

This thesis has not been submitted as an exercise for a degree at any other university.

Except where stated, the work described therein was carried out by me alone.

I give permission for the Library to lend or copy this thesis upon request.

SIGNED:

Dedicated to my parents, Frank and Una

Summary

The nature of the accelerated and heated gas along collimated outflows emanating from

deeply embedded protostars is investigated. By analysing the shock structures and exci-

tation conditions it is possible to deduce information concerning the flow dynamics and

environmental structure governing the morphology of outflows. Narrow-band imaging

at near-infrared wavelengths and various spectroscopic techniques are employed in con-

junction with bow shock modeling to uncover the underlying gas dynamics and excitation

structure.

The L 1634 globule contains two series of aligned molecular shock waves associated

with the Herbig-Haro flows HH 240 and HH 241. Near-infrared spectroscopy and narrow-

band imaging in the (1,0) S(1) and (2,1) S(1) emission lines of molecular hydrogen yield

the spatial distributions of both the molecular excitation and velocity, which demonstrate

distinct properties for the individual bow shocks. Bow shock models are applied to in-

fer the shock physics, geometry, speed, density and magnetic field properties. The ad-

vancing compact bow HH240C is interpreted as a J-type bow (frozen-in magnetic field)

with the flanks in transition to C-type (field di!usion). It is a paraboloidal bow of speed

! 42 km s!1 entering a medium of density ! 2 " 104 cm!3. The following bow HH240A

can be fit by a C-type model. It has a higher bow speed in spite of a lower excitation,

and is propagating through a lower density medium. It is concluded that, while the CO

emission originates from cloud gas directly set in motion, the H2 emission is generated

from shocks sweeping through an outflow.

The HH211 outflow is of considerable interest because of its ascribed youth. The

outflow is explored through imaging and spectroscopy in the near-infrared. The detec-

i

Summary

tion of a near-infrared continuum of unknown origin is confirmed. It is proposed that

the continuum is emitted by the driving protostellar source, escapes the core through the

jet-excavated cavity, and illuminates the features aligning the outflow. In addition, [Fe II]

emission at 1.644 µm has been detected but is restricted to isolated condensations. The or-

dered structure of the western outflow is modeled as a series of C-type shocks with J-type

dissociative apices. Essentially the same conditions are predicted for each bow except

for a systematic reduction in speed and density with distance from the driving source. In-

creased K-band extinctions are found in the bright regions, as high as 2.9 magnitudes, and

suggest that the bow shocks become visible where the outflow impacts on dense clumps

of cloud material.

Integral field spectroscopy was performed on the highly symmetric HH212 outflow.

Narrow-band images and spectra were simultaneously obtained between 1.5 to 2.5 µm.

Images in H2 and [Fe II] transition lines were compared in order to extract the excitation

and extinction conditions. Collisional excitation was confirmed as the process leading to

the radiation from the inner knots and bows. Lower excitation and extinction are found for

the bows which appear to have exited from the dense inner gas. The peak flux positions

are compared for all the transition lines detected. For the knots, a trend is found between

the measured o!sets and the upper level temperatures both along the outflow direction

and transverse to the jet axis. An underlying shock structure is implied.

A timescale for the Class O evolutionary stage is suggested which relates the envelope

mass to the mass accretion rate as inferred from the outflow luminosity. The deduced

timescales are in general agreement with the Class O lifetimes estimated from statistical

surveys. It is proposed that in order to investigate the relationship between outflows and

protostellar evolution, the individual environmental factors for each outflow need to be

examined. Only then can the intrinsic luminosities be revealed and related to the evolution

which may be di!erent for each source.

ii

Acknowledgments

In the three years I have spent at the Armagh Observatory my mind has opened to new

possibilities and new horizons. I have had the invaluable opportunity of applying the

concepts which I studied as an undergraduate. It is the application of concepts and their

interaction through people which gives them weight. I would like to thank all of those

people.

The supervisor who has led me through the myriad of intricate ideas is Dr. Michael

Smith. I am especially grateful for the boundless enthusiasm which he expressed during

our many discussions on star formation. He taught me how to test and apply a notion as

well as patiently encouraging me to follow my own research instinct.

All the sta! at the Observatory deserve special appreciation. They provided not only

the means but also the friendly atmosphere in which to pursue this research.

Dr. Chris Davis showed me how to carry out observations on a 3.8 meter telescope.

His benevolence didn’t end there. He provided constant support and help when it came to

dealing with and interpreting the data. I am also grateful to Dr. Tigran Khanzadyan for

guiding me through the data reduction steps.

A number of people at the Dublin Institute for Advanced Studies also participated in

this project. My co-supervisor Prof. Tom Ray was always available to provide beneficial

assistance when necessary. A large volume of research was carried out in collaboration

with Dr. Dirk Froebrich. I thank him for his patience and for pushing me to complete

things when time was slipping by.

I wish to thank Dr. Klaus Hodapp for supplying some of the data which I used to

construct much of my interpretation. Dr. Jochen Eislo!el was also a collaborator and his

iii

Acknowledgments

positive criticism is greatly appreciated.

I would like to thanks those in the Physics Department in Trinity College Dublin

who taught me almost everything I know about the fundamentals of physics, especially

Dr. Sara McMurry who also helped me to organise this project. Thanks to Dr. Brian

Espey and Dr. Roland Gredel for taking the time to read this thesis carefully and for

pointing out where improvements were possible. I learned much from their observations

and suggestions.

My parents Frank and Una laid out a solid foundation for me to stand on. Their

steadfast support and understanding fills me with the deepest appreciation. This thesis is

dedicated to them.

Big thanks to Marijana Pilipovic. Her love and support have propelled me forward

and given me a deeper perspective on life.

And certainly not least, I am extremely happy to have had the pleasure of partaking

in the social life at the observatory. Shared moments with all the students encouraged me

in di!erent ways and nothing could have been accomplished without friends. My o"ce

mates Amir and Ignacio provided the entertainment and much appreciated diversion from

work. The eccentric laughter resonates constantly in my mind. Thanks to Jonathan for

live music and for always expressing his thoughts. Much valued. And thanks to Georgi

for sharing many good times with me. I hope we all stay in contact.

iv

Publications

A list of publications resulting from work presented in this thesis is given below.

Refereed Publications1. A near-infrared study of the bow shocks within the L1634 protostellar outflowO’Connell B. F., Smith M. D., Davis C. J., Hodapp K. W., Khanzadyan T., and RayT., 2004, Astronomy and Astrophysics, 419, 975

2. The near-infrared excitation of the HH211 protostellar outflowO’Connell B. F., Smith M. D., Froebrich D., Davis C. J., Eislo!el J., 2005, Astron-omy and Astrophysics, 431, 223

In Preparation1. Integral Field Spectroscopy of the HH212 protostellar OutflowO’Connell B. F., Smith M. D., Davis C. J.

v

Table of Contents

Summary i

Acknowledgments iii

Publications v

Table of Contents vi

List of Tables ix

List of Figures xii

Introduction 1

1 The Birth of Stars: A Review 41.1 Molecular Clouds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.1.1 The Structure and Lives of Molecular Clouds . . . . . . . . . . . 61.1.2 The Chemistry of Molecular Clouds . . . . . . . . . . . . . . . . 81.1.3 Towards Stellar Birth . . . . . . . . . . . . . . . . . . . . . . . . 11

1.2 Protostellar Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171.2.1 Molecular Cloud Cores . . . . . . . . . . . . . . . . . . . . . . . 171.2.2 The Protostars . . . . . . . . . . . . . . . . . . . . . . . . . . . 191.2.3 Accretion Disks . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

1.3 Outflows from Young Stars . . . . . . . . . . . . . . . . . . . . . . . . . 231.3.1 The Jet Launch Mechanism . . . . . . . . . . . . . . . . . . . . 241.3.2 HH Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261.3.3 The Formation and Structure of Bow Shocks . . . . . . . . . . . 281.3.4 Numerical Simulations of Jets and Outflows . . . . . . . . . . . . 29

2 The Framework of the Study 342.1 Observing Outflows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

2.1.1 The H2 Molecule . . . . . . . . . . . . . . . . . . . . . . . . . . 352.1.2 Excitation Mechanisms of H2 . . . . . . . . . . . . . . . . . . . 37

vi

TABLE OF CONTENTS

2.2 Interstellar Shocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422.2.1 Hydrodynamic Flows: The Basic Equations . . . . . . . . . . . . 432.2.2 J-shocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452.2.3 Shock-driven Chemistry . . . . . . . . . . . . . . . . . . . . . . 492.2.4 The Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 512.2.5 Magnetohydrodynamic (MHD) Flows . . . . . . . . . . . . . . . 562.2.6 C-type Shocks . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

2.3 Modelling Bow Shocks . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

3 The Bow Shocks within the L 1634 Protostellar Outflow 673.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 683.2 Observations and data reduction . . . . . . . . . . . . . . . . . . . . . . 70

3.2.1 Near-Infrared Imaging . . . . . . . . . . . . . . . . . . . . . . . 703.2.2 Position-Velocity (P-V) Spectroscopy . . . . . . . . . . . . . . . 72

3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 733.3.1 Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 733.3.2 Near-Infrared Echelle Spectroscopy . . . . . . . . . . . . . . . . 77

3.4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 803.4.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 803.4.2 Modelling HH240A as a C-type Bow . . . . . . . . . . . . . . . 813.4.3 Modelling the HH240C image and power . . . . . . . . . . . . . 873.4.4 Modelling with J-type shocks . . . . . . . . . . . . . . . . . . . 89

3.5 Modelling the velocity distribution . . . . . . . . . . . . . . . . . . . . . 913.5.1 C-type bows . . . . . . . . . . . . . . . . . . . . . . . . . . . . 913.5.2 J-type bows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 933.5.3 The HH 241 system of shocks . . . . . . . . . . . . . . . . . . . 95

3.6 Column density distributions . . . . . . . . . . . . . . . . . . . . . . . . 953.6.1 Extinction modelling . . . . . . . . . . . . . . . . . . . . . . . . 953.6.2 Bow shock models . . . . . . . . . . . . . . . . . . . . . . . . . 98

3.7 CO structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 993.8 Optical structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1023.9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

4 The HH211 Protostellar Outflow 1084.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1094.2 Observations and data reduction . . . . . . . . . . . . . . . . . . . . . . 111

4.2.1 KSPEC observations . . . . . . . . . . . . . . . . . . . . . . . . 1114.2.2 MAGIC observations . . . . . . . . . . . . . . . . . . . . . . . . 1124.2.3 UFTI observations . . . . . . . . . . . . . . . . . . . . . . . . . 113

4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

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TABLE OF CONTENTS

4.4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1214.4.1 Modelling the bow shocks . . . . . . . . . . . . . . . . . . . . . 1214.4.2 The outflow continuum emission and excitation . . . . . . . . . . 129

4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1314.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

5 Integral Field Spectroscopy of HH212 1375.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1385.2 Observations and Data Reduction . . . . . . . . . . . . . . . . . . . . . . 1445.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

5.3.1 Inner knots: NK1 and SK 1 . . . . . . . . . . . . . . . . . . . . 1465.3.2 Inner Bows: NB1/NB2 and SB 1/SB 2 . . . . . . . . . . . . . . 154

5.4 Analysis, Discussion and Speculation . . . . . . . . . . . . . . . . . . . 1605.5 Summary of Findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168

6 Discussion 170

Conclusions and Future Prospects 175

Bibliography 184

Appendices 193

A Model Parameter Dependence 194

B Equations 201B.1 Gravitational Instability . . . . . . . . . . . . . . . . . . . . . . . . . . . 202B.2 Rankine–Hugoniot Jump Conditions . . . . . . . . . . . . . . . . . . . . 204

C CO Outflows and Protostellar Cores 207

D Evolution Model 214

viii

List of Tables

1.1 Tbol limits used to infer YSO Class divisions. . . . . . . . . . . . . . . . 22

2.1 Interstellar extinction law . . . . . . . . . . . . . . . . . . . . . . . . . . 412.2 List of input parameters and variables for the J-BOW and C-BOW models 64

3.1 Photometric results for HH240 . . . . . . . . . . . . . . . . . . . . . . . 763.2 Model parameters derived to fit HH240 bows with C-type shocks . . . . 813.3 Observed and predicted luminosities for the HH240 bows . . . . . . . . 823.4 Model parameters derived with J-type shocks for the HH240 bows . . . . 903.5 Predicted IR line fluxes for HH240A and HH240C . . . . . . . . . . . . 95

4.1 KSPEC relative fluxes for HH211 . . . . . . . . . . . . . . . . . . . . . 1124.2 Photometric results for HH211 . . . . . . . . . . . . . . . . . . . . . . . 1184.3 K-band extinction for HH211 . . . . . . . . . . . . . . . . . . . . . . . 1194.4 Observed and predicted luminosities and excitation ratios for HH211 . . 1244.5 Model parameters constrained for the HH211 bows . . . . . . . . . . . . 125

5.1 Photometric results for the NK1 knot in HH212 . . . . . . . . . . . . . . 1475.2 Photometric results for the SK 1 knot in HH212 . . . . . . . . . . . . . . 1485.3 Photometric results for the NB1 bow in HH212 . . . . . . . . . . . . . . 1545.4 Photometric results for the NB2 bow in HH212 . . . . . . . . . . . . . . 1555.5 Photometric results for SB 1/SB2 . . . . . . . . . . . . . . . . . . . . . 156

6.1 Observed properties of the three outflows investigated . . . . . . . . . . . 1726.2 Present accretion rates and Class 0 timescales . . . . . . . . . . . . . . . 173

ix

List of Figures

1.1 Orion A and B giant molecular cloud complexes . . . . . . . . . . . . . . 71.2 Molecular cloud hierarchical structure . . . . . . . . . . . . . . . . . . . 81.3 1.3 mm continuum maps of prestellar and protostellar cores . . . . . . . . 181.4 Evolutionary sequence for protostars . . . . . . . . . . . . . . . . . . . . 201.5 HST images of circumstellar disks . . . . . . . . . . . . . . . . . . . . . 231.6 The HH30 jet and edge-on disk system . . . . . . . . . . . . . . . . . . 241.7 Schematic of the structure of a bow shock . . . . . . . . . . . . . . . . . 291.8 Simulated outflow similar to HH240 . . . . . . . . . . . . . . . . . . . . 301.9 Simulated outflow similar to HH211 . . . . . . . . . . . . . . . . . . . . 321.10 Simulated jet possessing similarities to HH212 . . . . . . . . . . . . . . 32

2.1 Potential energy curves of H2 . . . . . . . . . . . . . . . . . . . . . . . . 362.2 Radiative shock structure . . . . . . . . . . . . . . . . . . . . . . . . . . 422.3 Pre-shock and post-shock variables . . . . . . . . . . . . . . . . . . . . . 462.4 Shock structure in presence of magnetic field . . . . . . . . . . . . . . . 582.5 Bow shock model geometry . . . . . . . . . . . . . . . . . . . . . . . . 62

3.1 HH240 H2 (1,0) S(1) image . . . . . . . . . . . . . . . . . . . . . . . . 743.2 HH240A and HH240C structure . . . . . . . . . . . . . . . . . . . . . . 753.3 H2 (2,1)/(1,0) S(1) profiles for HH240A and HH240C . . . . . . . . . . 773.4 HH241 spectroscopic slit positions . . . . . . . . . . . . . . . . . . . . . 783.5 Position-velocity diagrams for HH240 and HH241 . . . . . . . . . . . . 793.6 C-bow models for HH240A: varying magnetic field . . . . . . . . . . . . 833.7 C-bow models for HH240A: varying bow velocity . . . . . . . . . . . . 843.8 C-bow models for HH240A: varying orientation . . . . . . . . . . . . . 853.9 Dependence on shape parameter s . . . . . . . . . . . . . . . . . . . . . 853.10 Dependence on magnetic field direction . . . . . . . . . . . . . . . . . . 863.11 C-bow model for HH 240C . . . . . . . . . . . . . . . . . . . . . . . . . 883.12 J-type bow model for HH240A and HH240C . . . . . . . . . . . . . . . 893.13 Model P-V diagrams for HH240A and HH240C: C-type . . . . . . . . . 913.14 Model P-V diagrams for HH240A and HH240C: J-type . . . . . . . . . 943.15 CDR diagrams for HH240C . . . . . . . . . . . . . . . . . . . . . . . . 97

x

LIST OF FIGURES

3.16 CDR diagram for HH240A . . . . . . . . . . . . . . . . . . . . . . . . . 983.17 CDR diagram for HH240A . . . . . . . . . . . . . . . . . . . . . . . . . 993.18 Model CO J = (1,0) emission for HH240A . . . . . . . . . . . . . . . . 1003.19 S II optical image of HH240 with H2 contours . . . . . . . . . . . . . . . 103

4.1 HH211 imaged at 2.122 µm . . . . . . . . . . . . . . . . . . . . . . . . 1094.2 Broad-band K image of HH211 . . . . . . . . . . . . . . . . . . . . . . 1154.3 HH211 imaged at 2.248 µm . . . . . . . . . . . . . . . . . . . . . . . . 1164.4 HH211 at 1.644 µm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1174.5 Column density ratio diagrams for HH211 . . . . . . . . . . . . . . . . . 1204.6 HH211 western outflow in H2 (1,0) S(1), H2 (2,1) S(1) and Fe II . . . . . 1224.7 Bow shock model for HH 211 bow-de . . . . . . . . . . . . . . . . . . . 1264.8 Bow shock model for HH 211 bow-bc . . . . . . . . . . . . . . . . . . . 1274.9 Bow shock model for HH 211 bow-a . . . . . . . . . . . . . . . . . . . . 1284.10 Map of HH211 showing the 2.248 µm to 2.122 µm flux ratio . . . . . . . 129

5.1 HH212 outflow at 2.122 µm . . . . . . . . . . . . . . . . . . . . . . . . 1395.2 Schematic of the Integral Field Unit . . . . . . . . . . . . . . . . . . . . 1455.3 NK1 (1,0) S(1) binned image . . . . . . . . . . . . . . . . . . . . . . . . 1495.4 NK1 spectrum between 1.5 and 2.5 µm . . . . . . . . . . . . . . . . . . 1505.5 SK 1 spectrum between 1.5 and 2.5 µm . . . . . . . . . . . . . . . . . . . 1515.6 Extracted line emission images for NK1 . . . . . . . . . . . . . . . . . . 1525.7 Extracted line emission images for SK 1 . . . . . . . . . . . . . . . . . . 1535.8 NB1 spectrum between 1.5 and 2.5 µm . . . . . . . . . . . . . . . . . . 1575.9 SB 1 spectrum between 1.5 and 2.5 µm . . . . . . . . . . . . . . . . . . . 1585.10 Extracted line emission images of NB1 and NB2 . . . . . . . . . . . . . 1595.11 Extracted line emission images of SB 1/SB 2. . . . . . . . . . . . . . . . 1595.12 Column density ratio diagrams for NK1 . . . . . . . . . . . . . . . . . . 1615.13 Column density ratio diagrams for SK 1 . . . . . . . . . . . . . . . . . . 1615.14 Column density ratio diagrams for NB1 and NB2 . . . . . . . . . . . . . 1625.15 Column density ratio diagram for SB 1 . . . . . . . . . . . . . . . . . . . 1625.16 (1,0) S(1) image of NK1 overlaid with FeII contours . . . . . . . . . . . 1635.17 (1,0) S(1) image of SK 1 overlaid with FeII contours . . . . . . . . . . . . 1635.18 Relative peak flux positions for NK1 . . . . . . . . . . . . . . . . . . . . 1655.19 Relative peak flux positions for SK 1 . . . . . . . . . . . . . . . . . . . . 1655.20 Relative peak flux positions for NB1 . . . . . . . . . . . . . . . . . . . . 1665.21 Relative peak flux positions for SB 1 . . . . . . . . . . . . . . . . . . . . 1665.22 Bow shock schematic for the HH212 knots . . . . . . . . . . . . . . . . 168

A.1 Dependency of bow appearance on molecular fraction . . . . . . . . . . . 195A.2 Dependency of bow appearance on magnetic field direction . . . . . . . . 196

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LIST OF FIGURES

A.3 Dependency of bow appearance on velocity and angle to the line of sight . 197A.4 Dependency of bow appearance on density and velocity . . . . . . . . . . 198A.5 Dependency of bow appearance on magnetic field strength and ion fraction 199A.6 Dependency of bow appearance on shape parameter and velocity . . . . . 200

C.1 CO J = (1,0) emission maps of the HH240/241 outflow . . . . . . . . . . 208C.2 Integrated intensity maps of SFO 16 in HCO+ and CO emission . . . . . . 209C.3 Velocity structure of SFO 16 . . . . . . . . . . . . . . . . . . . . . . . . 210C.4 CO J = (2,1) emission maps of HH211 . . . . . . . . . . . . . . . . . . . 211C.5 H13CO+ J = (1,0) integrated emission from HH211 . . . . . . . . . . . . 212C.6 CO J = (1,0) emission map of the HH212 outflow . . . . . . . . . . . . . 213

D.1 Theoretical protostellar evolutionary model . . . . . . . . . . . . . . . . 215

xii

Introduction

The birth of a star is naturally a fundamentally important process for astrophysicists to

grasp. Elements heavier than H and He are produced in the interiors of stars by nuclear

fusion. The elements of the Earth and Solar System went through many cycles of stellar

birth and death to reach the abundances which we observe today. It seems fitting that we

should strive to understand how stars come into being. We are, after all, composed of

material which was assembled in the innards of a star.

Before their arrival on the main sequence stars undergo an incubation period within

molecular cloud cores. During this period they accumulate their mass from the dense sur-

rounding gas which also acts to hide them from us. As they accrete mass they gradually

warm up the cloud cores which house them. The warm cores are detected at far-infrared

and submillimetre wavelengths but the events taking place close to the protostars them-

selves evade direct analysis at optical wavelengths. The processes involved also have

implications beyond their parental cores; some of the in-falling material is ejected away

from the protostars at high velocity in the form of bipolar highly collimated jets. The con-

sequences of this outward bound material are multi-fold. Excess angular momentum can

be shed preventing the protostar from spinning to break-up velocity. Enveloping material

can be dissipated allowing the new star to break free of its parental cloud. The surround-

ing environment is disrupted and excited to form spectacular protostellar outflows. The

interstellar medium with which they interact becomes observable at optical and near-

infrared wavelengths and can be scrutinised in emission lines from atoms, molecules and

ions. A unique window of opportunity is provided to study the physics of shocked gas,

the properties of magnetised plasmas, and the chemistry of the interstellar medium. It is

1

Introduction

these outflows which constitute the subject of this thesis. A vast amount of knowledge

has already been acquired but, as always, there are many unsolved questions and debated

issues.

The aim of this study is to conduct an examination of protostellar outflows, to deter-

mine the nature of the shock waves which are exciting the otherwise cold gas and to learn

about the environment through which they propagate. The relationship between outflows

and the evolution of their driving protostars is vaguely understood. By elucidating the

nature of the jet environment interaction it may become possible to better constrain the

nature of this relationship.

In order to proceed with the study three outflows were selected: HH240/241, HH 211

and HH212. They are all young sources for which good data is available in the literature.

Near-infrared observations were obtained including narrow-band images, K-band spec-

troscopy, position-velocity spectroscopy, and integral field spectroscopy. Emission lines

of molecular hydrogen and ionised iron were analysed in conjunction with other pub-

lished observations at various wavelengths which trace the outflow gas at various levels

of excitation. Steady-state models are used to interpret the bow-shape shock structures

which regularly form along with the outflowing gas.

In the first chapter a general review of star formation is provided. Structures are

described which range in size from giant molecular clouds to outflows and protostars.

The framework of the study is laid out in the second chapter. The energy levels and

excitation processes of molecular hydrogen are described as well as the e!ects of inter-

stellar extinction. The essential chemical network is presented as well as the mechanisms

which allow the heated gas to cool. Hydrodynamic interstellar shocks are first described.

The influence of magnetic fields is the included in the magnetohydrodynamic case. After

presenting the necessary equations the method of modeling the bow shocks is described.

The third, fourth and fifth chapters focus on the protostellar outflows HH240/241,

HH211 and HH212, respectively. Each object is introduced and the observations are

presented and discussed.

In the sixth chapter the evolution of protostars is discussed in relation to the findings

2

Introduction

of the thesis.

Finally, the main conclusions which have been reached in this work as well as the

implications are presented.

The appendices contain some important and relevant material. Appendix A contains

figures which illustrate how sensitive the bow shock model is to changes in the set of input

parameters and variables. Appendix B contains the Jeans description of gravitational col-

lapse and the derivation of the Rankine–Hugoneot conditions which describe the changes

experienced as material passes through a shock front. In Appendix C millimetre CO maps

of HH240/241, HH211 and HH212 are presented. A theoretical protostellar evolutionary

scheme is given in Appendix D.

3

Chapter 1

The Birth of Stars: A Review

4

Chapter 1. The Birth of Stars: A Review

The birth of a star takes place inside the densest regions of molecular clouds. During the

period of gestation, material is accreted onto the star via gravitational collapse. These

early stages in the life of a star are also curiously associated with the violent and col-

limated ejection of material into the parental cloud from the immediate vicinity of the

youthful star. The process is heralded by a dramatic display. The star formation engine

brings about a severe transformation of the cloud material. Gas and dust with a mean

density of 10!20 – 10!19 g cm!3 (in hot dense cores) and temperature of 10 – 20 K un-

dergoes a drastic density and temperature increase to eventually reach 1 – 100 g cm!3

and 5 " 105 – 106 K (Chabrier et al., 2000) in order to enable thermonuclear fusion via

deuterium burning. These changes take place over a period of a few million years which

is relatively short compared with the lifespan of a typical 1 M" star of 1010 yr. Besides an

understanding of this important episode in the life of any star it is also necessary to study

the complex system of star formation on a large size and time scale. In this chapter I will

briefly summarise the current state of knowledge on this intriguing subject. In Section 1.1

the structure and composition of molecular clouds is discussed as well as the collapse of

cloud cores which form stars. The various stages of protostellar evolution are presented

in Section 1.2 and in Section 1.3 the main topic of this thesis is launched: protostellar jets

and outflows.

1.1 Molecular Clouds

Besides being littered with stars the night sky contains dark patches of obscuration along

the band of the Milky Way. These are clouds of gas and dust which block the light from

distant stars. Due their predominantly molecular content they are referred to as molecular

clouds and observations reveal that all present-day star formation taking place within our

galaxy and others is associated with such clouds (Blitz & Williams, 1999). They are

described as “self-gravitating, magnetised, turbulent, compressible fluids” by Williams

et al. (2000) and the investigation into star formation explores these properties through a

range of hierarchical scales in both space and time.

5


1.1.1 The Structure and Lives of Molecular Clouds

The largest molecular structures in the galaxy are Giant Molecular Clouds (GMCs). They

are found in a range of sizes (10 – 100 pc) and masses (104 – 106 M"). Their main

constituent is H2 but they cannot be mapped in H2 emission due to the high temperatures

required to excite detectable emission. The COmolecule is the perfect tracer of molecular

cloud structure because (1) it is relatively abundant ([CO] / [H2] ! 10!4) (2) it can be

excited at the low temperatures which characterise such environments and (3) its high

dissociation energy (11.09 eV) means that it tends to remain in molecular form.

Fig. 1.1 displays the CO J = (1,0) map of the Orion complex which spans a huge

portion of the sky (15 degrees). It has a total mass of ! 105 M" and lies at a distance

of 450 pc (Genzel & Stutzki, 1989). Other GMCs show similar structure: they are elon-

gated, inhomogeneous, filamentary and have density enhancements corresponding to star

formation regions. The famous Orion nebula is situated in the Trapezium Cluster and is

caused by reflected light from newly formed massive stars which are extremely luminous

(104 – 105 L").

Besides the physical structure of GMCs it is important to discuss their lifetime. CO

emission in the outer galaxy is confined almost exclusively to the spiral arms with a ratio

of emission in the arm to inter-arm regions of 28:1 (Heyer & Terebey, 1998; Digel et al.,

1996) suggesting that giant molecular clouds have lifetimes ! 107 years (the arm crossing

time) and form out of the vast reservoir of atomic gas which comprises 99% of the galactic

volume. Only where this gas is sheltered from ultra-violet (UV) radiation can molecules

form and clouds grow; such conditions are to be found in the pressure enhanced higher

density spiral arms. Similar conclusions have been reached concerning the distribution

of CO emission in other galaxies such as M31 (Loinard et al., 1996). This condition,

however, may not apply to the inner regions of the Galaxy where the spiral structure loses

consistency.

Larger molecular clouds have shorter lifetimes. This is due to the self-destructive

mechanism of photoevaporation by which high energy Extreme UV (EUV) photons (h!

> 13.6 eV) produced by O and B stars ionise and destroy their molecular surroundings.

6


Figure 1.1: The Orion A and B giant molecular cloud complexes mapped in CO J = (1,0)(Maddalena et al., 1986) together with their associated young star clusters (Blaauw et al.,1991).

Large clouds tend to produce rich associations of such stars and absorb all the result-

ing high energy photons. Disruptive ionisation shock fronts form as a result and sweep

through the clouds. Williams & McKee (1997) have shown that high mass clouds (M >

3 " 105 M") would be destroyed by a large number of small OB associations in a time

! 30 – 40 Myr by the formation of ‘blister H II regions’. Smaller clouds (M < 105 M")

may avoid this fate; the ionizing photons escape through the formation of ‘cometary H II

regions’. However, the lifetimes of smaller clouds may be reduced as they agglomerate

into larger complexes.

7


Figure 1.2: From cloud to clump to core. The three panels show the hierarchical catagori-sation of molecular clouds. The entire Rosette molecular cloud (left panel) is traced inCO. Adopting a distance of 1600 pc (Perez et al., 1987) the image covers an area of 55 pc" 55 pc. At higher resolution star forming clumps are observed in optically thin lines suchas C18O (middle panel). Dense core structures are revealed with a high density tracer suchas CS (right panel). The image resolution in the panels is 90##, 50## and 10## respectively.Image taken from Blitz & Williams (1999).

The e!ect of cloud destruction is demonstrated in Fig. 1.1. Region 1a contains the

first batch of stars, formed 12 Myr ago. This region is already devoid of circumstellar

material. Star formation is ongoing since 7 Myr ago in region 1b where the new stellar

group is partly free of cloud material. Finally, in region 1c, these 3 Myr old stars are still

embedded in their parental cloud.

In recent years the complicated density structure of GMCs has been described as

scale-free and fractal (Falgarone et al., 1991). At this point it is unsure to what extent

this condition applies. Here, I present the observational classification of molecular clouds

into clumps and cores as illustrated in Fig. 1.2. Star forming clumps are the large gravita-

tionally unbound regions which form stellar clusters. Dense cores are the gravitationally

bound high density regions where individual stars (or multiple systems) are born. They

have masses in the range 1 – 10 M" and are 0.1 – 0.4 pc in diameter with a mean gas

density of 104 – 105 cm!3 (Saraceno & Orfei, 2001). It is the gravitational collapse of

these dense cores which eventually leads to stars.

1.1.2 The Chemistry of Molecular Clouds

Molecular Clouds contain atoms, ions, molecules, electrons, and dust (and stars). The

dominant elements are hydrogen (! 90 %) and helium (! 9 %). The abundance of other

8


elements (refered to as metals by astrophysicists) varies considerably and depends on

the enrichment history of the region. Over 120 di!erent molecular species have been

identified from thousands of spectral lines across a broad range of wavelengths. The

subject of astrochemistry deals with the complex chemical interactions in the ISM. The

subject is indeed diverse and only the principal species and reactions are discussed here.

Formation of Molecules

The density of molecular clouds is insu"cient to accommodate the formation of its main

constituent, H2, via collisions. The time spent during collisions (! 10!13 s) is too short

compared to the radiation time scale (! 10!8 s) and three-body collisions in which the third

party carries away the binding energy (4.48 eV) are too rare. The most e"cient method

of H2 formation in the ISM involves dust grains which act as catalysts (Hollenbach &

Salpeter, 1971). The grains consist mainly of graphitic carbon and silicates. Successive

atoms collide with a grain, stick to the surface, and form a molecule. The release of

the binding energy on to the grain is su"cient to allow the newly formed molecule to

evaporate into space.

H + (grain + H)! H2 + (grain) (1.1)

In order for this process to be e"cient low dust temperatures (< 20 K) are essential.

Once enough H2 has formed (and su"cient shielding from EUV photons is in place),

it collisionally induces the subsequent formation of a variety of molecules. Firstly, H2 is

converted to H+2 and H+3 by cosmic ray ionisation. Cosmic rays are abundant high energy

(up to 1020 eV) particles, mainly electrons and protons. At low temperatures they enable

a chain of molecule formation as follows:

H2 + cosmic ray! H+2 + e!

H+2 + H2! H+3 + H(1.2)

H+3 ions can now react with oxygen. The energy barrier is small and H+3 readily donates a

9


proton to form OH+,

O + H+3 ! OH+ + H2 (1.3)

OH+ reacts with H2 in hydrogen abstraction reactions,

OH+H2#####$ OH+2

H2#####$ OH+3 (1.4)

OH and H2O are formed by dissociative recombinations with electrons,

OH+3 + e!! OH + H2

OH+3 + e!! H2O + H(1.5)

The CO molecule plays a vital role in interstellar processes; the reactions leading to its

formation are as follows:

C+ + OH! CO+ + H

CO+ + H2! HCO+ + H

C+ + H2O! HCO+ + H

HCO+ + e! ! H + CO

(1.6)

These are just some of the important molecules which are discussed in this thesis.

There will be a substantial build-up of molecules in regions where the formation rate

is significantly higher than the destruction rate. Photo dissociation by UV radiation is the

principle destruction method. Molecules which are exposed to the interstellar UV flux of

! 106 cm!2 s!1 nm!1 have a mean lifetime of a few hundred years. Clearly, molecular

clouds need to be shielded from these dangerous photons. For a more thorough review on

molecule formation and destruction see Flower (1990) and Dyson & Williams (1997).

10


The Cooling of Molecular Clouds

Molecular clouds have many sources of heat: Far UV photons (photoelectric heating),

cosmic ray ionisation, X-rays, as well as gas motions including turbulent compression

and shocks. In order to form stars molecular cloud material must collapse at some stage.

This can only occur when the collapsing material rids itself of the resulting gain in ki-

netic energy. Atoms, ions and molecules are excited through collisions. After some time

the excited system releases a photon by spontaneous de-excitation. The escape of these

photons from the cloud allows it to attain lower temperatures. Di!erent coolants become

e!ective in various temperature regimes.

CO dominates the cooling at low temperatures, especially in dense clouds with molec-

ular hydrogen density n (H2) > 104 cm!3. The large permanent dipole moment of CO al-

lows rotational transitions to occur (unlike H2). The energy di!erence between the J = 0

and J = 1 rotational levels is equivalent to 5.5 K so CO is an e!ective coolant down to very

low temperatures. However, in higher density regions where the CO column is high, the

photons are reabsorbed by CO. In this case other coolants such as H2O and OH become

important. Dust grains also act as important coolants, especially in dense molecular cloud

cores. After gas grain collisions they radiate energy in the infrared and submillimetre

which escapes from the cloud.

1.1.3 Towards Stellar Birth

A big leap is now necessary. Which conditions must be attained in order for star formation

to proceed? How do molecular clouds provide these critical conditions? For an excellent

review read Mac Low & Klessen (2004).

Classical Theory

It is the gravitational contraction of molecular cloud material which leads to star forma-

tion. The classical dynamical theory, originally proposed by Jeans, involves the gravita-

tional collapse due to self gravity acting against thermal and micro-turbulent pressure. In

11


order for inevitable collapse to ensue, certain conditions must be met. These are described

in terms of the Jeans length "J or the Jeans mass MJ as follows:

" > "J =!# c2sG $

"1/2(1.7)

M > MJ =4 #3

!"J2

"3$ =#

6

! #G

"3/2c3s $!1/2 (1.8)

where cs is the sound speed and $ is the mass density (see Appendix B).

The main failure of the theory was the huge star formation rate which it predicted on

time-scales much shorter than the ages of typical galaxies (1010 years). The free-fall time

for a typical cloud is

% f f =! 3 #32G $

"1/2= 1.4 " 106

! n103 [cm!3]

"[yr] (1.9)

where G is the Newton gravitational constant, n is the H nuclei number density, $ is the

mass density (which is taken as 2.32 " 10!24 " n [g], i.e. 90% H and 10% He). Besides

this mismatch in time-scales, the theory was unable to account for the fact that the angular

momentum of clouds is much larger than that found in any star. There was another prob-

lem: When the extent of the interstellar magnetic field was realised by Chandrasekhar &

Fermi (1953) it was believed that magnetic pressure would halt gravitational contraction

unless a certain critical mass would be exceeded. According to the virial theorem, the

critical mass is the magnetic mass, i.e.,

M > M! % 0.4G!1/2 BR2 = 200M"#

B3 [µG]

$ #R

1 [pc]

$2(1.10)

where B is the magnetic field strength and R is the radius. Such a large critical mass and

the lack of any fragmentation process during collapse posed a huge problem in trying to

account for the observed collapsing protostellar cores described in Section 1.1.1. A new

theory was needed, one which accounted for the loss of angular momentum and allowed

12


for a prolonged collapse without halting it completely.

Standard Theory (Ambipolar Di!usion)

The standard theory of isolated star formation arose when Mestel & Spitzer (1956) noted

that the magnetic field was not necessarily fixed to the cloud gas. Although the ions are

coupled to the magnetic field, the neutrals may drift across the field lines in a process

called ambipolar di!usion. In this way cloud matter can gravitationally condense without

compressing the magnetic field, e!ectively decreasing the critical mass for gravitational

collapse. The neutrals are decoupled from the ions when the ion fraction is extremely low.

Elmegreen (1979) showed that at densities above 104 cm!3 the ionisation fraction due to

cosmic ray ionisation is roughly

& & (5 " 10!8)! n105 [cm!3]

"1/2(1.11)

The crucial time-scale on which ambipolar di!usion operates, %AD, can be derived (Spitzer,

1968) considering the relative drift velocity between the neutrals and ions, #$vD = #$vi - #$v n,

and the magnetic field #$B . The interaction of neutrals and ions during di!usion results in

friction. The resulting drag force per unit volume can be described as

fd = 'd $i $n (vi # vn) (1.12)

(Shu, 1991) where 'd is the drag coe"cient (% 3.5 " 1013 cm3 g!1 s!1) (Draine et al.,

1983), $i, $n and vi, vn are the density and velocity of the ions and neutrals respectively.

The drag force induces a compensating Lorentz force due to the movement of ions through

the magnetic field,

fL =14#%' " #$B

&" #$B (1.13)

13


Equating Eqs. 1.12 and 1.13 gives us an expression for the drift velocity,

vd ( vi # vn =1

4# 'd $i $n

'%' " #$B

&" #$B(

(1.14)

And following Mac Low & Klessen (2004) the approximate time-scale is the size of the

system divided by the drift speed,

%AD =Rvd=4# 'd $i $n R)' " #$B* " #$B

% 4# 'd $i $n R2

B2

= 2.5 " 107! B3 [µG]

"!2 ! n102 [cm!3]

"2 ! R1 [pc]

"2 ! &10!6"[yr](1.15)

In this way collapse may proceed at a slower rate and not be completely opposed by mag-

netic support. As well as predicting the correct star formation rate the theory also seemed

to solve the angular momentum problem by the process of magnetic braking. In collaps-

ing cores with strong magnetic fields the outgoing Alfven waves from the rotating gas

couple to the surrounding gas and e!ectively remove angular momentum on a time-scale

less than % f f . Magnetic di!usion was believed to be the dominant physical process con-

trolling star formation. The self-similar collapse of quasi-static isothermal spheres was

proposed by Shu (1977). In a magnetically sub-critical cloud core (M < M!) ambipolar

di!usion would lead to the build-up of a quasi-static 1/r2 density structure which contracts

on a time-scale of %AD. Eventually, the system becomes unstable and undergoes final col-

lapse when enough mass has built up at the centre. Although it was widely accepted in the

80s, the standard theory of star formation does seem to fail on many fronts with the advent

of improved instrumentation and computer modeling techniques. Some of the objections

are as follows:

• Although the debate is ongoing, observations suggest that protostellar cores are

supercritical, i.e. the magnetic fields are too weak to postpone the gravitational

collapse of cores.

• Detected protostellar infall motions contradict the long lasting, quasi-static phase

which is expected in the standard theory. Mass infall rates are typically a few 10!6

14


to a few 10!5 M" yr!1, as measured in CS emission (Myers et al., 2000; Lee et al.,

1999, 2001).

• Density structures in starless cores do not match the 1/r2 profiles which the theory

assumes. Instead, the inner prestellar cores have flat profiles (Andre et al., 2000).

• The time required to reach observed chemical abundances under certain conditions

can be used to define a chemical age for the cloud material. Substructures within

molecular clouds have estimated chemical ages of about 105 years, much shorter

than the ambipolar di!usion time-scale (Bergin & Langer, 1997; Langer et al.,

2000).

• A high fraction of cores which contain embedded protostellar objects is observed.

If cores evolved on ambipolar di!usion time-scales we would expect to find a sig-

nificantly larger number of starless cores (Beichman et al., 1986a)

• The standard theory cannot account for the formation of stellar clusters and high-

mass stars. High mass stars in isolation would halt their own accretion by radiation

pressure limiting their size to < 10 M" (Wolfire & Cassinelli, 1987).

It became obvious that a new interpretation was required, one which solved all the above

contradictions and provided the environments which could harbour high-mass stars.

Interstellar Turbulence

In the last decade a new perception of star formation has arisen. Supersonic turbulence

is now seen as the central process controlling star formation. The random supersonic

motions (described byM = vrms/cs whereM is the Mach number, vrms =)*v+ is the

root mean square velocity of the flow or the average speed of the random motions and cs

is the sound speed) in the interstellar medium describe a turbulent structure which is very

di!erent to terrestrial turbulence. Laminar flows interact to produce enhanced density

contrasts in the highly compressible gas with strong cooling. Where the flows meet,

sheet-like shock layers form which propagate, collide, fragment and disappear.

15


Because of the lack of a consistent theory for turbulence in compressible gas, most

progress has been achieved via three dimensional computer simulations, see for example

Pavlovski (2003). To begin with, there is ample observational evidence that molecular

clouds contain random supersonic motions (Crawford & Barlow, 2000, 1996; Munoz-

Tunon et al., 1995; Zuckerman & Palmer, 1974). The importance of such motions was

not realised until recently because molecular clouds were thought of as long-lived and

turbulence decays quickly. Today a new picture has emerged: Molecular clouds have

much shorter lifespans, they are dynamic and ephemeral, and the violent events occurring

in interstellar space are capable of supplying turbulence as quickly as it dissipates.

The turbulent kinetic energy density is given by e = (1/2) $ v2rms, and, when in equi-

librium, the dissipation rate is given by

e & #(1/2) $v3rms (Ld)!1

= #3 " 10!27#

n1 [cm!3]

$ #vrms

10 [km s!1]

$3# Ld100 [pc]

$!1 +erg cm!3 s!1

, (1.16)

where Ld is the driving scale (Mac Low, 1999, 2003). The dissipation time for turbulent

kinetic energy is then

%d = e/e &Ldvrms= (3Myr)

! Ld50 [pc]

" ! vrms6+km s!1

,"!1

(1.17)

The supersonic turbulence contained within a large cloud would dissipate in a lifetime

which is comparable to the free-fall time-scale (Eq. 1.9) if there was no recurring injection

of energy into the large scale motions. Although it is debated which mechanism (or

combination of mechanisms) could supply the driving energy capable of maintaining the

turbulent motions, there are several candidates. They are listed here along with their

estimated energy contribution rates for comparison with Eq. 1.16:

• galactic rotation and shear (3 " 10!29 erg cm!3 s!1)

• gravitational instabilities (4 " 10!29 erg cm!3 s!1)

• protostellar outflows (2 " 10!28 erg cm!3 s!1)16


• HII region expansion (3 " 10!30 erg cm!3 s!1)

• supernova explosions (3 " 10!26 erg cm!3 s!1)

These values are taken from Mac Low & Klessen (2004). Such energy input arguments

suggest that it is the supernovae events which supply the turbulence observed in molecular

clouds. The above energy estimate is based on a supernova rate of (50 yr)!1 with each

event providing 1051 erg. Indeed it is also possible that such powerful events may be

responsible for molecular cloud formation by sweeping gas up in their turbulent wake. At

this stage a strong link between supernova events and star formation is obvious although

the exact nature of this link remains to be uncovered. It is not so obvious whether or

not protostellar outflows play any significant role in the star formation process. They

seem capable of providing some support locally (over a few parsecs) but they are a minor

contribution compared to the energetic supernova explosions.

Supersonic turbulence supports clouds against gravitational collapse, increasing their

lifetime by a few %! . But how do stars form in such an environment? The highly com-

pressible turbulence also promotes local collapse through the formation of density en-

hancements. Passing shock fronts may compress the gas and create a Jeans unstable

clump which gravitationally contracts and decouples from the turbulent flow. With con-

tinued contraction the ability to survive successive shock fronts increases. Accretion from

the surrounding gas eventually leads to high density cores and ultimately stars. For a re-

view of the initial conditions leading to star formation see Bouvier & Zahn (2002).

1.2 Protostellar Evolution

1.2.1 Molecular Cloud Cores

Molecular cloud cores are the potential sites where individual stars or multiple systems

are born. They can be mapped in line emission frommolecules with large dipole moments

such as CS, NH3, H2CO and HCN. However, in the dense, cold, inner core regions these

molecules tend to freeze out onto dust grains (Walmsley et al., 2002). Their density

17


Figure 1.3: Dust continuum maps of a prestellar core L1544 (a) and a protostellar coreIRAM 04191 (b) at 1.3 mm. The direction of the magnetic field measured in L1544 isindicated in (a) and the collimated CO outflow from IRAM 04191 is overlayed in (b).From Andre (2002)

structure is best traced either in the optically thin submillemetre continuum emission from

cold dust in the cores or in absorption of the background infrared emission by dust grains.

They can be roughly divided into two categories: prestellar or starless cores and pro-

tostellar cores. Prestellar cores are cores which have condensed out of the parent cloud

but do not show any signs of possessing a central protostellar object (i.e. M$ = 0) (see

Fig. 1.3 (a)). Their density structure cannot be modeled by a single scale-free power law,

but instead they have flat inner radial density profiles suggestive of slow contraction by

ambipolar di!usion (Mouschovias, 1991; Ciolek & Basu, 2001). Statistical surveys of

cores suggest the lifetime of the prestellar phase to be ! 3 " 105 # 2 " 106 yr (Beichman

et al., 1986a).

Protostellar cores (see Fig. 1.3 (b)) display modified characteristics, some of which

can be identified with the emergence of a young stellar object (YSO). These characteris-

tics of these cores are:

• They have smaller FWHM sizes as observed in the 800 µm dust emission (Ward-

Thompson et al., 1994),

• their more compact density structure more closely resembles a centrally peaked

18


$(r) , r!2 profile,

• their velocity structure shows distinct signatures of infalling material as well as

increased turbulence indicating protostellar activity such as jet formation,

• indirect evidence of a YSO, such as compact centimeter radio continuum emission

or the detection of a collimated outflow.

1.2.2 The Protostars

As molecular cloud cores undergo gravitational collapse the thermal energy density tends

to increase. The subsequent radiative cooling results in a runaway isothermal collapse,

a strong central concentration of matter ($(r) , r!2) and eventually the formation of an

opaque, hydrostatic protostellar object which is thermally enclosed (i.e. photons cannot

escape from within a central sphere but are indirectly radiated from its photosphere). This

moment is often considered the point of stellar conception and can be termed Age Zero.

The accretion of circumstellar matter will proceed until the protostar becomes a star and

can be located on the Hertzsprung-Russell (H-R) diagram.

Analysing protostars represents a major challenge to observers. They are still con-

tained within their shells of obscuring material out of which they are growing. At optical

wavelengths they are completely hidden. At longer wavelengths such as the near-infrared

(NIR) the obscuration caused by dust grains is considerably less. But the protostars are

still too deep to be directly observed. The surrounding circumstellar material is heated by

the accretion process and radiation from the protostar which it re-emits at longer wave-

lengths, in the far-infrared (FIR) and submillimetre. So, until their circumstellar skin is

shed, protostars remain extremely di"cult to be directly detected.

Classification of Protostars

Protostars can be classified according to their spectral energy distribution (SED). As men-

tioned above, the warm circumstellar material emits radiation which peaks longward of

100 µm. As a protostar evolves it frees itself of surrounding material. As it does so its

19


1 000 000 yr-

Class 0

Class III

Class II

Class I

Black Body

Disk

Disk?

Infrared Excess

Cold Black Body

Stellar Black Body

Cold Black Body

Fragment

Classical T Tauri Star

Pre-Stellar Dense Core

Weak T Tauri Star

Time

t ~ 0 yr

< 30 000 yr

~ 10 000 000 yr

~ 1 000 000 yr

~ 200 000 yr

Pre-

Stel

lar

Phas

ePr

e-M

ain

Sequ

ence

Pha

sesubmm

submm

Pre-main sequence starsBirthline for

Debris + Planets ?

Protoplanetary Disk ?

Core

Parent Cloud

Formation of the central protostellar object

bol

Young Accreting Protostar

Disk

Disk

env

Prot

oste

llar

Phas

e

T ~ 650-2880 K, M ~ 0.01 Mbol

T > 2880 K, M < Mbol Jupiter

bol

*T ~ 10-20 K, M = 0bol

env

Evolved Accreting Protostar

T < 70 K, M << M*

T ~ 70-650 K, M > M*

Figure 1.4: The protostellar evolutionary sequence from a prestellar cloud to a Class IIIYSO based on the shape of the SED, the bolometric temperature and the mass of circum-stellar material. From Lada (1987); Andre et al. (1993); Chen et al. (1995).

SED changes shape, peaking at shorter and shorter wavelengths. The main protostellar

classification system, first proposed by Lada &Wilking (1984), is based on the SED shape

and is illustrated in Fig. 1.4. Protostars are thought to evolve through four main phases

or classes: 0, I, II and III. The infrared spectral index, (IR is the logarithmic slope of the

20


spectrum between 2 and 20 µm, i.e.

(IR =d)log "F"

*

d)log "* (1.18)

where F" is the luminosity within each unit wavelength interval. The youngest proto-

stars, Class 0 and Class I (which are of major interest in this thesis), possess a positive

infrared spectral index ((" > 0) reflecting the large contribution of circumstellar material

to their SED. Class II objects have #1.5 < (IR < 0 and Class III have (IR < #1.5. A fur-

ther constraint is introduced in order to identify the youngest protostars, i.e. to separate

Class 0 from Class I. The protostellar core can be observed in submillimetre radiation

longward of 350 µm, Lsmm, which is emitted by the envelope of cold dust surrounding

the central object. The bolometric luminosity, Lbol, is the total luminosity summed over

all wavelengths. A high ratio of submillimetre to bolometric luminosity suggests that the

envelope mass now exceeds the central protostellar mass. Class 0 objects are defined as

having an envelope mass which is greater than the protostellar mass or Lsmm/Lbol > 0.005

(Andre et al., 1993).

The bolometric temperature, Tbol, is the temperature of a blackbody whose spectrum

has the same mean frequency as the observed YSO spectra,

Tbol = 1.25! < ! >

100 [GHz]

"[K] (1.19)

As the system evolves, the SED peaks at higher frequencies and Tbol increases, thus indi-

cating the age and defining an evolutionary sequence. In order to determine Tbol a range

of measurements over di!erent wavelengths using di!erent instruments is necessary, e.g.

Froebrich (2005)1. As an analog to the H-R diagram for optically visible stars, Myers &

Ladd (1993) have proposed the Lbol/Tbol diagram for embedded YSOs. The class divisions

are defined using Tbol limits as given in Table 1.1. It is important to note that this system

of classification only serves as a rough indication at present.1See http://www.dias.ie/protostars/ for a compiled list of Class 0 observations between 1 µm and 3.5

mm.

21


Table 1.1: Tbol limits used to infer YSO Class divisions.

Class TbolO < 70KI 70K # 650KII 650K # 2880KIII > 2880K

1.2.3 Accretion Disks

So far in our story of how molecular cloud material gravitationally contracts to form a

protostar we have neglected to mention a vital physical process. The angular momentum

of infalling cloud material inevitably gives rise to the formation of a rotating disk. In-

falling envelope material then accumulates on the disk surface and from there spirals into

the protostar. Accretion disks were first suggested by Walker (1972) in order to explain

the P Cygni profiles and strong UV excess of YYOrionis stars and later by Lynden-Bell &

Pringle (1974) to explain the infrared continuum excesses in T Tauri stars (TTSs). Since

that time the evidence has steadily accreted and circumstellar disks around optically visi-

ble Classic T Tauri stars (CTTSs) (Class II YSOs) have now been directly observed by the

Hubble Space Telescope, Fig. 1.5. Such a disk played an important role in the formation

of the Solar System. They seem to be necessary for planet formation and are referred to

as protoplanetary disks. For a review from the observational perspective see Menard &

Bertout (2002). The infrared excess which is observed in Class II YSOs is thought to arise

from radiation which is emitted by a thin circumstellar disk. In this way the star can then

be observed in the optical as the circumstellar obscuration is minimised in the star-disk

configuration (as opposed to a spherical distribution which would completely obscure the

star in the optical).

22


Figure 1.5: Dramatic confirmation of circumstellar disks by the Hubble Space Telescope.Left: A resolved circumstellar disk around a Class II YSO seen in silhouette against theOrion nebula (McCaughrean & O’dell, 1996). The field of view is 4.1## " 4.1##. Right:The pre-main sequence binary star HKTau (Stapelfeldt et al., 1998). The southern com-panion is seen only in scattered emission from circumstellar material and the dark lane isinterpreted as an edge-on disk. The field of view is 5.2## " 3.6##.

1.3 Outflows from Young Stars

During the accretion of infalling material onto the protostar something curious is seen to

happen: some of the material is ejected at high velocity (of order 100 – 200 km s!1) away

from the protostar. This outward bound material is collimated and accelerated in a direc-

tion perpendicular to the accretion disk. The resulting bipolar jets shock excite and sweep

up the surrounding ambient material to form much larger outflows. The strong impact of

such outflows on our imagination has gained them considerable attention since they were

first discovered in the early 1950’s. They were originally observed in the visible region

of the spectrum and termed Herbig-Haro (HH) objects by their discoverers Herbig (1950,

1951); Haro (1952, 1953). More than 600 HH objects have been found to date thanks

to modern wide angle imagers. A general catalogue of all known HH objects discovered

to date has been compiled by Reipurth (1999)2. Wherever we find star formation to be

taking place, they are present. Their triggering during protostellar evolution seems to be2http://www.casa.colorado.edu/hhcat

23


Figure 1.6: Three images of the HH30 jet as observed by the HST over a 5 year period.Shocked material traced by H( emission is seen to be ejected perpendicular to the edge-ondisk system. Credits: NASA, AlanWatson (Universidad Nacional Autonoma de Mexico),Karl Stapelfeldt (Jet Propulsion Laboratory), John Krist and Chris Burrows (EuropeanSpace Agency/Space Telescope Science Institute)

unavoidable. They dramatically announce the arrival of new stars. Because protostars

are highly obscured it is thought that, by studying the outflows, important insight can

be gained about the evolution of the protostars themselves. Before describing some im-

portant observations, our short discussion will begin in the close vicinity of the protostar

where they originate.

1.3.1 The Jet Launch Mechanism

Various theories have been formulated in an attempt to explain how infalling circumstel-

lar material ends up being launched outwards. Importantly, a strong link between outflow

activity and accretion disks is found. The jet-disk connection is based on various obser-

vations as follows:

• Jets and outflows are commonly found in protostellar objects alongside circumstel-

lar disks and envelopes,

24


• the outflow mechanical luminosity is correlated with the bolometric luminosity of

the source (which is dominated by accretion processes during the early stages)

(Bally & Lada, 1983; Lada, 1985; Richer et al., 2000),

• accretion indicators are correlated with outflow indicators for T-Tauri stars and sug-

gest that the ouflow rate is proportional to the accretion rate (Cohen et al., 1989;

Cabrit et al., 1990),

• jet and outflow axes are found to lie perpendicular to disk planes, e.g. HH30 as

observed by the HST (Fig. 1.6).

The launching of protostellar jets is almost certainly a product of the accretion process

and the most favored mechanism involves magnetocentrifugal acceleration from the cir-

cumstellar disk in a Magnetised Accretion-Ejection Structure (MAES). These systems are

thought to account for observations where collimated mass ejections are detected along-

side accretion. Besides jets from YSOs, the MAES system applies to various astrophysi-

cal phenomenon including neutron stars, low-mass X-ray binaries and active galactic nu-

clei which host enormous relativistic jets and outflow lobes which are seen in synchrotron

emission. In the case of YSOs the ejected mass and momentum fluxes are too great to be

driven by radiation pressure from the central source. The strongest argument in favour of

disk-driven jets is the observed correlation between signatures of accretion and ejection

which in the MAES description are interdependent processes (Ferreira, 1997).

In the MHD models of YSO jets the ejected material may originate in winds from the

stellar surface, winds from the surface-disk interaction zone or in disk winds. The details

involved in the theories are rather plentiful and beyond the scope of this introduction. I

will summarise the main ideas here; for an in-depth discussion see Ferreira (2002).

The basic idea is that a poloidal magnetic field is frozen into the rotating accretion

disk. If the field lines are inclined to the rotation axis by more than 30% then material can

be thrown out along the field lines and away from the disk plane. The field lines (which

are driven by the rotating accretion disk) rotate at constant angular velocity and as the gas

moves outwards towards larger radii it is accelerated by magnetocentrifugal acceleration.

25


Further out the field lines become increasingly wound up and a strong toroidal component

is generated which is responsible for collimating the flow of gas along the rotation axes.

Such models predict that the mass outflow rate is a constant fraction of the mass accretion

rate, i.e.

Mout = ) Macc (1.20)

The value of ) is typically taken to be ! 0.1. In recent years, numerical simulations

have been showing that jet formation through magnetocentrifugal acceleration appears to

be unavoidable for a rotating accretion disk with an embedded magnetic field and central

protostar, e.g. Konigl & Pudritz (2000). It must be pointed out, however, that a conclusive

theory has not yet been reached. Attempts are also being made to explain jet launching

by purely hydrodynamical e!ects (Raga & Canto, 1989; Smith, 1986; Canto et al., 1988).

1.3.2 HH Flows

High velocity jets from YSOs dramatically interact with their surroundings; they flow at

supersonic speeds, sweep up material, excavate cavities, and shock excite slower moving

or stationary material. Variable accretion rates give rise to non-uniform ejection rates

and the jet may take the form of a series of bullets which are often symmetrically placed

on both sides of the bipolar jet, i.e. equidistant from the protostar. HH objects are the

resulting shock excited regions which are seen in optical emission. At longer wavelengths

the extinction is greatly reduced and observations of H2 and CO transitions reveal the

accentuated morphology of HH flows. At the terminal working surface the supersonic

flow ploughs directly into the undisturbed medium. Velocity di!erences along the outflow

also give rise to shocks, called internal working surfaces, which propagate away from the

protostar. Their proper motions (measured from high resolution images over a time-base

of a few years) often exceed their shock velocities as they propagate within gas which is

already set in motion. The working surfaces actually contain two shocks: a forward shock

which accelerates the slower gas upstream and a reverse shock which decelerates the

26


supersonic flow. The forward shock often takes the form of a bow shock, a curved, bullet-

shaped structure which points away from the protostar. Some bow shocks even point back

towards the protostar. They form when the supersonic flow encounters stationary compact

material. In chapter 2 the physics of interstellar shocks will be discussed in greater detail.

For now we focus our attention on the observed morphologies of HH flows.

Observed features of Outflows

The passage of a shock wave has the e!ect of heating the gas. The study of outflows is

most often a study of the emission from collisionally excited transitions of various species

within the gas which has been shock-heated following the ejection process. Excitation

by high energy photons may also become important for strong shocks or for outflows

which are exposed to the radiation field of bright stars. The high abundance of H2 and

the fact that its vibrational-rotational transitions occur in the NIR make it an excellent

tracer of outflow morphology (the extinction due to dust grains is about ten times lower

in the NIR than in the optical). The strongest line is the (1,0) S(1) line at 2.121 µm

(upper energy level of 6953 K) and was first detected in the HH objects around T Tauri

by Beckwith et al. (1978). Outflows have been primarily detected and studied at this

wavelength. Whereas the high excitation H2 emission traces the current shock structure,

the low excitation CO emission traces the bulk mass swept up by the flow. The main

observed features characterising outflows in a general sense are listed here.

• Sizes range from less than 0.1 pc to parsec-scale outflows covering ! 8 pc, e.g.

Reipurth et al. (1997).

• Outflow lifetimes are of the order of about 2 " 105 yr as estimated from statistical

studies (Parker et al., 1991; Fukui et al., 1993). Dynamical ages, %d, are determined

by dividing the outflow extent by the velocity and are much less than 105 yr (! 1 –

5 " 104 yr). The reason for this underestimate in the age is because the observed

outflow extent does not always represent the complete ejection history as the outer

flow regions may have exhausted their momentum or broken free from their dense

27


clouds, becoming too weak to be detected.

• Flow velocities range from a few km s!1 to a few 100 km s!1. The high velocity gas

is seen closest to the source in the form of a highly collimated jet or series of knots

or bullets.

• The masses of outflowsMCO, as determined through millimetre observations of CO,

are of the same order or exceed the masses of their driving sources which implies

that the bulk of the mass is not accelerated close to the central YSO. The bulk of the

material is swept up and entrained by the interaction of the jet with ambient cloud

material.

• The mechanical luminosity of outflows Lmech, as observed in CO emission, is equiv-

alent to the total kinetic energy divided by the dynamical time-scale. A comparison

with driving source luminosities, Lbol shows that YSO radiation pressure is too weak

to power the outflows (Bally & Lada, 1983).

• Outflow energetics are correlated with Lbol. In particular, the mean momentum

deposit rate FCO (=MCOvCO/%d where MCO is the mass and vCO is the velocity of

CO) is a function of Lbol for Class I objects. For Class 0 objects a correlation

is also found but lies an order of magnitude above the Lbol vs. FCO relation, i.e.

Class 0 objects power more energetic CO outflows. In addition, a strong correlation

between FCO and the circumstellar envelope mass Menv is found for both Class 0

and Class I YSOs indicating a more or less steady decline in outflow activity as the

accretable mass is consumed (Richer et al., 2000).

1.3.3 The Formation and Structure of Bow Shocks

Bow-shaped shocks are the recurring structures which are seen in outflows. They form

when a collimated flow or bullet ploughs into the ambient cloud gas. Fig. 1.7 shows a

2–D schematic which illustrates the defining 3–D structure. Where the ambient gas op-

poses and decelerates the flow a reverse shock or Mach disk forms. In the rest frame of

28


Mach Disk

Ejected Material

Slow Shock

Fast Shock

Ambient Shock

Ambient Medium

Figure 1.7: Schematic of the structure of a bow shock. In the rest frame of the bow shock,high speed material entering from the left is decelerated at the Mach disk. The ambientmedium is decelerated and forms a second shock front at the leading cap. Between bothshocks material is compressed and forced out sideways, shocking the ambient gas to formthe bow wings.

the bow shock, upstream material is decelerated in the ambient shock front. Material is

compressed between the Mach disk and bow front to form a dense clump from which

pressurised material is ejected out sideways to interact with the ambient medium, com-

pleting the bow-shaped ambient shock. The strongest shock is experienced at the shock

front (or apex) and weakens as the surface becomes more oblique towards the ambient

flow leading to a range of excitation conditions. As a result, the observed emission at dif-

ferent wavelengths and from various species can be analysed to yield valuable insight into

outflow dynamics and chemical make-up. The model aided interpretation of these struc-

tures forms the crux of this thesis; the details, including chemistry and shock structure,

leading to our analysis, are described in the next chapter.

1.3.4 Numerical Simulations of Jets and Outflows

A substantial amount of insight could be gained through three dimensional numerical

simulations of jets and outflows. A large e!ort to reproduce the observed characteris-

tics of outflows is being undertaken by Michael Smith (Armagh Observatory) and Alex

Rosen (Dublin City University). The employed code is ZEUS–3D, a computational fluid

dynamics code developed at the Laboratory for Computational Astrophysics (NCSA, Uni-

29


Figure 1.8: Simulated outflow similar to HH240. The slow precessing (period = 400 yr;half-angle = 10%) and pulsed jet (period = 60 yr; amplitude = ± 30%) has a speed of 100km s!1 along the axis and 70 km s!1 along the perimeter. The ambient density is 104 cm!3and the jet to ambient density ratio is 10. The outflow is shown at 3 di!erent epochs:A – 150 yr; B – 250 yr; C – 350 yr. Published in Smith & Rosen (2005)

versity of Illinois at Urbana-Champaign) for the simulation of astrophysical phenomena.

The code has been modified to solve the equilibrium chemistry as well as the complete

cooling which will be described in Chapter 2. Until now the simulations are restricted

to purely hydrodynamic flows. The results are very encouraging and pave the way to-

wards a richer understanding of the relationship between outflows and the evolution of

their driving protostars.

Bipolar outflows often display collimated but twisted structures where the flow direc-

tion varies with distance from the central object. One such object is HH 240 (presented in

Chapter 3 – Fig. 3.1) which can be described as having an S-shaped structure. The out-

flow directional variation is likely to be caused by changes in the jet launch direction. Jet

precession could be caused by orbital forces in a close binary system (Fendt & Zinnecker,

30


2000) or even magnetically driven warping of the accretion disk (Lai, 2003). Simulations

which include such precession produce extremely convincing results.

As an example, Fig. 1.8 from Smith & Rosen (2005)3 shows a simulated pulsed jet

of hydrogenic nucleon density 105 cm!3 driven into ambient gas of density 104 cm!3.

The jet is precessing slowly with respect to the kinematic and pulse timescales with a

precession half-angle of 10%. Shear is introduced by varying the jet velocity from 100 km

s!1 at the centre to 70 km s!1 at the edges. The H2 (1,0) S(1) structure (at B) bears close

resemblance to the observed structure of HH240. The extent of the simulated outflow is

an order of magnitude smaller than the observed structure. The shock cooling length is

highly influenced by the density; to achieve higher resolution the densities are relatively

low.

In the analysis of observed outflows it is generally assumed that the shock structures

are older with increased distance from the driving source. Simulations often show new

shock structures associated with new ejecta overtaking the older structures which slow

down as they expand and entrain ambient material. Therefore, the sequence of bows may

not necessarily represent the jet ejection history. The time sequence assumed for outflows

in general should certainly be considered with caution.

Fig. 1.9 shows a simulated outflow in H2 (1,0) S(1) which bears some likeness to the

HH211 outflow (presented in Chapter 4 – Fig. 4.1). In this case the outflow precession

is limited to 1%. The bows tend to form limb-brightened structures and the advancing

structure appears point-like. A mid-plane cross section of the density is also shown.

The puzzling appearance of double bow shocks in HH212 (presented in Chapter 5 –

Fig. 5.1) can possibly be explained by the velocity variations of the jet. Fig. 1.10 shows a

simulation where such structures can indeed be found in the (1,0) S(1) emission. A faster

precession is explored with an angle of 1.75%. The velocity structure of this HAMMER

(High AMplitudeMultiple ERuptions) jet is shown. Small double bows form in a sequence

along the jet, they gradually widen to form larger bows at the end of the jet. The shocked

structures grow drastically in the outer regions in a similar manner to the HH212 outer3The simulated outflow movies are available at http://star.arm.ac.uk/mds/

31


Figure 1.9: Simulated outflow similar to HH211. The pulsed jet (period = 60 yr; ampli-tude = ± 30%) has a velocity of 100 km s!1. The ambient density is 104 cm!3 and thejet to ambient density ratio is 10. The outflow is shown at 3 di!erent epochs: A – 170yr; B – 270 yr; C – 470 yr. The midplane cross section of density is shown in the lowerpanel. Low density gas is represented by light shading. The low density cocoon whichhas formed around the jet is ! 104 times less dense than the ambient density. Publishedin Rosen & Smith (2004a)

Figure 1.10: Simulated jet possessing similarities to HH212. The ambient velocity is 1.4"10 4 cm!3 and the jet to ambient density ratio is 10. The precessing jet (period = 26 yr;angle = 1.75%) is pulsed with the velocity variation structure shown in the lower panel. Jetshear is also included; the perimeter speed is 50% of the axis speed. Published in Volkeret al. (1999)

bows.

The simulations predict that about 1% of the input jet mechanical power is converted

to H2 (1,0) S(1) emission and that the conversion is more e"cient for lighter jets (i.e.

ratio of jet-to-ambient mass density ratio * = 0.1) associated with slower and wider bow

shocks. Class 0 protostars are known to display (non extinction corrected) outflows which

32


are about an order of magnitude more powerful than those driven by Class I protostars

(Stanke et al., 2002). Therefore, the evolution from Class 0 to Class I may involve a

decrease in the jet power or simply the evolution from light to heavy (* = 10) jets, see

Rosen & Smith (2004b).

The near future for numerical simulations of outflows is extremely promising. The

goal will be to include the e!ects imposed by magnetic fields by solving the complete set

of MHD equations. Another obvious step will be to increase the resolution as compu-

tational power becomes more readily attainable. The atomic cooling lengths associated

with shock speeds exceeding ! 25 km s!1 are are of order 1013 – 1014 cm. At present

the 3–D grid is divided into zones of ! 1014 cm so the cooling and chemistry are poorly

resolved due to the stringent demands of performing three dimensional simulations. An-

other task about to be undertaken is the addition of a realistic ambient medium. Current

simulations assume a uniform density whereas the environment of molecular clouds is

characterised by density gradients and higher density clumps. It will be fascinating to

simulate 3–D outflows with C-type physics ploughing through such an environment with

higher resolution.

33

Chapter 2

The Framework of the Study

34

Chapter 2. The Framework of the Study

This study represents an attempt to understand some new aspect of how stars are born

as well as a personal voyage of learning. As with any study, it is built upon seemingly

solid foundations. Although some of the details here may be skipped over, a basic under-

standing of the ideas is essential. In this chapter I will lay out and present the necessary

knowledge and groundwork which form the basis of this thesis.

2.1 Observing Outflows

Near-infrared emission lines from the H2 molecule contain a wealth of information about

HH flows. As this thesis is chiefly concerned with the deciphering of this information it

seems beneficial to describe the H2 molecule and the relevant processes which result in

observable near-infrared emission lines.

2.1.1 The H2Molecule

It is not surprising that H2 is the most common interstellar molecule to be found; it is the

simplest molecule which can be made. It consists of two protons and two electrons bound

together in a covalent bond. The formation mechanisms of H2 in the interstellar medium

have already been discussed in 1.1.2. Fig. 2.1 illustrates the potential energy of the H2

molecule as a function of the internuclear separation. Only the first few potential energy

curves are shown, each one corresponds to a di!erent electronic configuration. Each

electronic state can be subdivided into a set of vibrational and rotational levels, which

form as a result of the motions of the nuclei. There are 14 vibrational energy levels in the

electronic ground state and a number of rotational levels which are characterised by the

vibrational and rotational quantum numbers V and J. The binding energy of H2 is 4.48

eV which corresponds to a kinetic velocity of ! 24 km s!1 (Kwan, 1977).

The first allowed electronic dipole transitions occur at UV wavelengths (" ! 0.1µm).

They take place between the ground state X1#+g and the B1#+u state at 11.2 eV (Lyman

bands) and the C1$u state at 12.3 eV (Werner bands).

But it is the rotational–vibrational transitions occurring within the electronic ground

35


1966ARA&A...4..207F

Figure 2.1: The potential energy curves of the lowest excited states and ground state ofthe hydrogen molecule. Taken from Field et al. (1966).

state which we focus our attention on in this work. Certain restrictions are imposed which

limit the array of transitions which may take place. The H2 molecule does not possess a

permanent dipole moment and for this reason dipole transitions between di!erent levels of

V and J within the electronic ground state are forbidden. Electric quadrupole transitions,

however, are permitted because H2 has a permanent quadrupole moment. Consequently,

there are no restrictions imposed on transitions between di!erent V states but transitions

between di!erent J states must satisfy %J = 0, ± 2, with J = (0, 0) also forbidden (note

that in this thesis the notation (a,b) is equivalent to a $ b).

The rotational–vibrational transitions are labelled by giving the vibrational transition,

the rotational quantum number J of the final state, and the di!erence in J as indicated by

the letters O, Q and S which indicate %J = +2, 0 and -2 respectively. For example, the

H2 (1,0) S(1) line at 2.121 µm is characterised by a transition from V = 1 to V = 0 and

from J = 3 to J = 1. Importantly, narrow band filters can be used to capture the emission

at specific wavelengths thus making it possible to make and compare observations from

various transition lines.

36


2.1.2 Excitation Mechanisms of H2

Local Thermodynamic Equilibrium

Within dense molecular clouds the collision time-scales are of order a few days or more

whereas most atomic and molecular radiative processes occur on much shorter (atomic

and CO) or comparable (H2) time-scales. Therefore, after becoming collisionally excited,

atoms and molecules usually radiate any excess internal energy they have gained and re-

turn to their ground state. Here in the earth’s atmosphere, where the particle density is !

1015 times higher, the situation is quite di!erent. Every possible atomic state is being pop-

ulated by collisions as fast as it is being depleted by other collisions; there is a dynamical

balance between energetic states and collision processes. This condition is known as local

thermodynamic equilibrium (LTE) and the number density of atoms or molecules in any

excited state (m) relative to another state (l) is described by the Boltzmann distribution:

Nm

Nl=gmglexp!Tl # Tm

Tex

"(2.1)

where gm and gl are the degeneracies of each state; Tm and Tl are the upper level energy

equivalent temperatures; and Tex is the excitation temperature or gas temperature. Di!use

astrophysical plasmas rarely follow the Boltzmann distribution and they are described as

being in a non-LTE (NLTE) state.

The lower rotational–vibrational transitions of H2 require excitation temperatures of

a few 103 K to become populated. However, molecular clouds are, on average, cold. A

discussion of the various excitation mechanisms and methods of distinguishing between

them is given by Wolfire & Konigl (1991). The dominant mechanisms are as follows:

Collisional Excitation

Temperatures of several 103 K are easily attained in the post-shock gas of typical HH

flows. Under such conditions the lower ground state rotational–vibrational levels of H2

become populated through collisions with other H2 molecules, atoms and electrons. At

37


higher temperatures (through stronger shocks) the molecules become dissociated.

The excitation temperature between two H2 transition lines (l and m) is a useful diag-

nostic quantity which is defined (from Eq. 2.1) as follows:

Tex =Tm # Tl

ln (+mgm/+lgl) # ln (Nm/Nl)[K] (2.2)

where + is the mass fraction, which is related to the ortho to para ratio ,: + = ,/(1 + ,)

for ortho transitions and + = 1/(1 + ,) for para transitions. , can be assumed to be 3 for

post-shock collisional excitation (Smith et al., 1997a). Nm/Nl is the ratio of the columns

of gas in the upper level of each transition which can be determined observationally using

Nm

Nl= 100.4"

"m Zl"l Zm

"#FmFl

$(2.3)

where "m and "l are the wavelengths associated with each transition, Zm and Zl are the

electric quadrupole transition probabilities, % is the di!erential extinction between the

two lines (% = Am # Al) and Fm/Fl is the observed flux ratio, or excitation ratio between

the two transition lines. Note that Tex is determined by assuming a Boltzmann distribution

of energy states under LTE which may or may not be the case (Eislo!el et al., 2000).

In this thesis we will explore the vibrationally excited emission between the H2 (2,1)

S(1) (" = 2.247 µm, Z = 4.98 " 10!7 s!1) and the (1,0) S(1) (" = 2.121 µm, Z = 3.47 "

10!7 s!1)1 lines. Both lines are ortho transitions with equal upper level degeneracies and

the excitation temperature, Tex, is simply given by

Tex =5 597

0.30 + (0.92%) # ln (F2/F1)[K] (2.4)

A useful indicator of collisional excitation due to shock heating is the absence of emission

following transitions from higher vibrational levels, i.e. F2/F1 & 0.1# 0.2 corresponding

to Tex & 2 000 - 3 000 K.

Another indicator of collisional excitation is the ortho to para ratio, ,. The hydrogen1The electric quadrupole transition probabilities for H2 have been calculated byWolniewicz et al. (1998)

38


molecule is characterised by the alignment of the nuclear spins of each hydrogen atom.

In the ortho configuration the spins are aligned and in the para configuration they are

opposed. The ratio of the ortho to para configurations based on the statistical weights

is 3:1. For grain assisted conversion to H2 this is the expected ratio. , can, however,

be lowered through conversion on grains for collisions with protons or H atoms at low

densities, yielding an equilibrium ratio of 9 exp(-170 K/T ) (Flower & Watt, 1984; Martin

et al., 1996). The value of , = 3.0 ± 0.4 was measured for OMC–1 by Smith et al.

(1997a) (indicating collisional excitation) and the method of extracting , is described in

detail therein.

Excitation by UV Photons

A second means of exciting H2 is UV pumping. UV photons with " > 912 Å (energy

less than 13.6 eV) are not energetic enough to ionise hydrogen and can be absorbed into

the H2 Lyman and Werner band systems from the ground state (provided that " < 1108

Å, see Fig. 2.1). 90% of such absorptions are followed by fluorescence to the excited

vibrational–rotational levels of the ground state, whereas the remaining 10% result in

molecule dissociation. A thorough investigationwas carried out by Black & van Dishoeck

(1987). The excited molecules then decay via electric quadrupole transitions on time-

scales of 106 s (Black & Dalgarno, 1976) resulting in infrared line emission. Excitation

by UV fluorescence provides larger populations in vibrational levels with v - 2 than

collisional excitation and can be identified by a higher F2/F1 ratio (! 0.5).

The ortho to para ratio can be used to distinguish between collisional excitation and

excitation by UV radiation. Ratios of below 2:1 have been measured and are consistent

with thermodynamic equilibrium below temperatures of ! 100 K. A low ortho to para

ratio indicates low temperatures and photon excitation as the source leading to radiation.

Other Important Species

Interstellar gas contains a rich laboratory of both active and dormant chemical species.

The majority of these species remain inactive; they are either unexcited by their cold

39


surroundings or locked up on the icy mantles of interstellar dust grains. They are, how-

ever, awoken in the vicinity of stellar birth. Molecular and atomic abundances can be

greatly enhanced behind the shock waves produced by outflows. The resulting com-

pression and heating trigger reactions such as the formation of the reactive OH radical:

O + H2 $ OH + H (energy barrier of 3 160 K), and the subsequent formation of water:

OH + H2 $ H2O + H (energy barrier of 1 660 K) (Bergin et al., 1998).

Shocks also release agents from dust grains. Soft shocks can evaporate volatile species

from the grain mantles whereas violent shocks destroy the grain cores and release refrac-

tory elements such as Si and Fe into the gas phase (Flower et al., 1996). The entrance

of this fresh material together with a high abundance of OH produces oxides such as SiO

and SO (Bachiller, 1996; van Dishoeck & Blake, 1998).

The plethora of reactions is rich and complex and the details are still poorly under-

stood. Within the context of this thesis is is important to mention that there are significant

di!erences in the spacial distribution of the various species along an outflow. This gradi-

ent of chemical abundances is related to the time-dependence of the shock chemistry.

[Fe II] versus H2 emission

Recently, the understanding of shocked flows has been greatly advanced through imaging

in the 4F9/2 # 4D7/2 transition line of [Fe II] at 1.644 µm (upper energy level of 11 300

K) (Allen & Burton, 1993; Tedds et al., 1999; Reipurth, 2000). Comparative studies of

shock excited H2 and [Fe II] emission have lead to important insights into the outflow

phenomenon (Reipurth, 2000; Khanzadyan et al., 2004). The presence of [Fe II] emission

seems to depend on the shock type involved: Strong dissociative Jump–Shocks (J-type

shocks) tend to induce high post-shock temperatures, dissociate molecules, disrupt dust

grains, and ionise gas. It is the passage of these abrupt shocks which give rise to [Fe II]

emission. A second type of shock called a Continuous–Shock (C-type shocks) is less

extreme and less likely to induce detectable amounts of [Fe II] emission. Both shock

types are discussed in detail in 2.2. The location within the shock front is also an important

factor. For bow shocks the atomic component is expected (and usually found) at the front

40


of the bow where the velocity component normal to the shock surface is the greatest and

the highest excitation conditions are reached.

Interstellar Extinction

Dust grains in the interstellar gas scatter and absorb light. The resulting reduction in light

intensity is called extinction. Due to the comparable sizes of the dust grains, UV and

optical wavelengths are more a!ected by extinction than IR wavelengths. For this reason

the dense inner regions of molecular clouds are probed at IR and longer wavelengths. The

amount of extinction is proportional to the column of interstellar gas through which the

light passes in a surprisingly uniform relationship:

AV [mag] =NH

1.9 " 1021 [cm!2] (2.5)

where AV is the extinction in the V band expressed in magnitudes and NH is the total

column density of H nuclei per cm2 (Bohlin et al., 1978). Eq. 2.5 assumes that the mean

ISM selective to total extinction (E(B # V)/AV) is equal to 3.1, as in Glass (1999).

Extinction is wavelength dependent. From a study of highly reddened cool stars near

the galactic centre, Rieke & Lebofsky (1985) determined the Interstellar Extinction Law

from 1 to 13 µm which is frequently used to estimate the extinction for di!erent wave-

bands, see table 2.1. Methods of estimating the extinction a!ecting HH flows will be

discussed in Chapters 3 and 4. Bow shocks are extended objects and the measured ex-

tinction has two sources: intrinsic extinction due to the dust which is located within the

Table 2.1: A" values according to the work of Rieke & Lebofsky (1985).

Band " [µm] A"/AVV 0.55 1.0J 1.21 0.282H 1.65 0.175K 2.2 0.112L 3.45 0.058M 4.8 0.023

41


observed structure and intervening extinction which is due to dusty gas which is located

along the line of sight to the object and dominated by the gas within the object parental

cloud. The proportionality of both sources of extinction depends on the density structure

of the cloud.

2.2 Interstellar Shocks

The ejection of material into the interstellar medium by a protostellar jet results in the

build-up of pressure as the outflowing material compresses the gas which it encounters.

A disturbance propagates. As long as the velocity of the disturbance remains below the

sound speed, the sound waves will propagate forward, resulting in a smooth and continu-

ous density gradient. As the velocity of the disturbance increases, the forward propagating

sound waves converge closer and closer together until they merge. The information which

was carried by the separate sound waves is lost at this point, equating to an increase in

Figure 2.2: The structure of a radiative shock showing the temperature T, density $ andvelocity v relative to the shock velocity vs. $1 is the pre-shock density and T2 is theimmediate temperature behind the shock front. From Draine & McKee (1993).

42


entropy, i.e. an irreversible process. A discontinuity in the flow variables occurs and the

structure is called a shock.

Fig. 2.2 illustrates the basic structure where the temperature, density and velocity are

plotted against distance relative to the shock front. Our analysis takes place within the

rest frame of the shock. The pre-shock gas, which enters the shock from the left, is

compressed, heated and its flow velocity is reduced. The shocked gas cools by emitting

photons in the radiative zone. Some of the emitted photons penetrate ahead of the shock

and may heat and ionise the pre-shock gas; a radiative precursor forms as a result. A basic

understanding of the physical mechanisms governing the nature of shocks is necessary in

order to appreciate and follow this study. Our aim is to compare observations of bow

shocks with model generated images so the following discussion will proceed along the

logical steps which the bow shock model code is based on. The available literature on

interstellar shocks is extremely rich and challenging. A detailed review has been provided

by Draine &McKee (1993) as well as Dopita & Sutherland (2003) and Dyson &Williams

(1997).

2.2.1 Hydrodynamic Flows: The Basic Equations

Initially we will restrict our description to hydrodynamic flows (HD flows), i.e. we will

not include the e!ects imposed by magnetic fields as the e!ects are small compared to the

purely hydrodynamic changes for certain shocks. The time-dependent one-dimensional

equations governing the fluid motion are derived by considering the conservation of mass,

momentum and energy between di!erent points within the flow. They are

-$

-t+-($v)-x= 0 mass flux conservation (2.6)

-($v)-t+-($v2 + p)-x

= 0 momentum flux conservation (2.7)

-e-t+-(ev)-x+ p-v-x+ L(T, n, f ) = 0 specific total energy conservation (2.8)

43


where v is the velocity and e is the internal energy per unit volume which is related to the

pressure by

e =p

(' # 1) (2.9)

' is the specific heats ratio, p is the pressure and $ is the mass density. L is the net rate of

energy removal per unit volume due to radiative cooling (heating is also included here).

f is the molecular hydrogen fractional abundance, i.e. n(H2) = f n, where n is the total

number density of hydrogen nuclei. The most abundant element after H is helium He

which has an abundance of ! 10% which is equivalent to 0.1n and we will include its

contribution in our shock treatment.

n(H nuclei) = 2 " n(H2) + n(H atoms) = 2 f n + n(H)

=. n(H) = (1 # 2 f ) n(2.10)

The average number of particles per unit volume *n+ is given by

*n+ ( total number of particlesvolume

*n+ = n(H) + n(H2) + n(He)

= (1 # 2 f ) n + f n + 0.1n

= (1.1 # f ) n

(2.11)

and the average mass per particle *m+ is given by

*m+ ( 1*n+! total massvolume

"

=1*n++n(H) " m (H) + n(H2) " m (H2) + n(He) " m (He)

,

=1*n++(1 # 2 f ) n " m (H) + f n " 2m (H) + 0.1n " 4m (H),

=1.4m (H)(1.1 # f )

(2.12)

44


The specific heat cV of the gas mixture is given by the sum of the specific heats of the

components,

cV = cV (H) + cV (H2) + cV (He)

=32kBn(H)*n+ +

52kBn(H2)*n+ +

32kBn(He)*n+

(2.13)

H and He possess 3 degrees of freedom (translational) whereas H2 is taken to possess 5 de-

grees of freedom (3 translational plus 2 rotational). The vibrational degrees of freedom are

ignored here because at the high temperatures required for their inclusion, T > 6 000K,

H2 is largely dissociated. We can now write cV in terms of the H2 fraction using Eq. 2.11,

cV =3.3 # f2.2 # 2 f kB (2.14)

and the specific heats ratio, ', is then simply given by

' =cPcV=cV + kBcV

=5.5 # 3 f3.3 # f (2.15)

In order to complete our set of relevant HD equations, the dissociation and reformation of

H2 molecules needs to be accounted for as follows

-( f n)-t+-( f nv)-x

= R(T, n, f ) # D(T, n, f ) (2.16)

where R and D are the molecular hydrogen reformation and dissociation rates as described

in 2.2.3

2.2.2 J-shocks

We will now consider the case in which the shock can be seen as a discontinuous jump

in the flow variables (as opposed to a gradual change which will be discussed in Sec-

tion 2.2.5). This type of shock is called a Jump Shock or J-shock. The neutrals and ions

are coupled by their relatively frequent collisions and behave as a single fluid. If we as-

45


Figure 2.3: The pre-shock and post-shock variables (velocity v, density $, pressure p,molecular fraction f , specific heats ratio ' and temperature T ) on both sides of the shock.The flow is relative to the rest frame of the shock.

sume (appropriately for our case) that the time-scale for variations is long compared to

the time required to flow across the shock front then the shock is considered as steady-

state and our analysis is greatly simplified. The partial time derivatives are dropped and

Eqs. 2.6, 2.7, and 2.8 may be integrated to obtain the jump conditions which are also

called the Rankine-Hugoniot conditions, see Hollenbach & McKee (1979).

$0v0 = $1v1 = µ (2.17)

p0 + $0v20 = p1 + $1v21 = # (2.18)

v202+'0'0 # 1

p0$0=v212+'1'1 # 1

p1$1= ) (2.19)

where the prefixes ‘0’ and ‘1’ represent the pre-shock and post-shock quantities respec-

tively (see Appendix B.2). In order to derive some useful expressions from the jump

conditions we need to make an essential approximation: no inelastic processes occur in

the shock front itself (Hollenbach & McKee, 1979). Therefore, certain quantities in the

immediate post-shock remain unchanged: f0 = f1 = f (since molecular dissociation

and reformation require a finite time which is unavailable within the shock front) and

46


'0 = '1 = ' . The Mach number is given by

M2 =v2

c2s=$v2

'p(2.20)

For the pre-shock flow: v = v0, p = p0 andM =M0. In the post-shock regime: v = v1,

p = p1 andM =M1. By dividing Eq. 2.18 by Eq. 2.17 and using Eq. 2.20 we obtain

M!2 + ' =#

µ

'

v(2.21)

and from Eqs. 2.18 and 2.17 we can also derive

p$= v!#µ# v"

(2.22)

By substituting Eq. 2.22 into Eq. 2.19 we obtain the quadratic equation for the velocity of

the flow,

v2!12# '

' # 1"+ v! '' # 1

#

µ

"# ) = 0 (2.23)

which has two roots v0 and v1, the pre-shock and post-shock velocities. Due to the

quadratic nature of Eq. 2.23,

v0 + v1 =2'1 + '

#

µ(2.24)

Using v = v0 and M = M0 in Eq. 2.20 and combining with Eq. 2.24 we are left with

an expression for the velocity and density jump conditions. The compression factor S is

given by

$1$0=v0v1=

('0 + 1)M20

('0 # 1)M20 + 2

( S (2.25)

47


The jump conditions for pressure and temperature are obtained from Eq. 2.19 using

Eq. 2.25 and the ideal gas equation,

p1p0= 1 +

!1 # 1S

"M2

0 (2.26)

T1T0=

p1Sp0

(2.27)

We now need to describe the changes which occur after the initial jump in flow variables,

i.e. in the post-shock radiative layer. In this region the inelastic processes, which we

ignored across the shock front, become important and must be accounted for. The down-

stream variables at any point, $ and v, are related to the immediate post-shock quantities,

$1 and v1, by

$v = $1v1 (2.28)

p + $v2 = p1 + $1v21 (2.29)

The conservation of energy throughout the flow, Eq. 2.8, together with the expression for

the internal energy, Eq. 2.9, becomes

v-[p/(' # 1)]-x

+'

' # 1 p-v-x= #L(n, T, f ) (2.30)

We are interested in monitoring the changing conditions in the radiative layer with in-

creasing distance from the shock front. To accommodate this, we define expressions for

-'/-x and - f /-x using Eqs. 2.15 and 2.16,

-'

-x=

#4.4(3.3 # f )2

- f-x

(2.31)

- f-x=1.4m (H) (R # D)

$1v1(2.32)

The above equations describe the initial jump in the flow variables as the gas passes

through the shock front as well as the gradual changes which follow in the downstream

48


gas.

2.2.3 Shock-driven Chemistry

A rich network of chemical reactions is induced by shock heating and compression of

the gas which contains atoms and molecules as well as chemically rich dust grains. In the

post-shock radiative layer di!erent reactions and cooling mechanisms dominate at various

temperatures and locations. Free atomic and molecular abundances are not fixed but vary

depending on the behaviour of the downstream gas. To facilitate a comparison between

the observed shock regions in protostellar outflows and shock models we must take into

account the relevant and dominant chemical reactions which are described in Appendix B

of Smith & Rosen (2003). The most important characteristic of fast shocks is their ability

to dissociate the most abundant species: molecular hydrogen. Atomic hydrogen then

enables almost all other reactions taking place in the post-shock zone (Hollenbach &

McKee, 1989). The reactions involving H2 are:

H + (grain + H)! H2 + (grain) (2.33)

H2 + H! 3H (2.34)

H2 + H2! 2H + H2 (2.35)

The synthesis of molecular hydrogen, Eq. 2.33, takes place on grain surfaces with the

rate,

kR =3 " 10!18#

T 1/2 fa1 + 0.04 (T + Tdust)1/2 + 2 " 10!3 T + 8 " 10!6 T 2

$+cm3 s!1

,(2.36)

fa =+1 + 10 000 exp (#600/Tdust)

,!1 (2.37)

(Hollenbach & McKee, 1979) where Tdust is fixed at 20 K for our modelling purposes.

The collisional dissociation rates for Eqs. 2.34 and 2.35 determined by Shapiro & Kang

49


(1987) are

kD,H = 1.2 " 10!9 exp (#52 400/T )+0.0933 exp (#17 950/T ),# +cm3 s!1

,(2.38)

kD,H2 = 1.3 " 10!9 exp (#53 300/T )+0.0908 exp (#16 200/T ),# +cm3 s!1

,(2.39)

where the exponent . depends on the critical densities for dissociation of molecular hy-

drogen by collisions with atomic hydrogen n1 and molecular hydrogen n2:

. =

-1.0 + n

.2 f! 1n1# 1n2

"+1n1

/ 0!1(2.40)

n1 = exp+ln 10 " )4.0 # 0.416x # 0.327x2*, +cm!3, (2.41)

n2 = exp+ln 10 " )4.845 # 1.3x + 1.62x2*, +cm!3, (2.42)

with x = log)T/104

*.

The following reversible reactions are used to determine the equilibrium abundances

of O, OH, CO and H2O:

O + H2 " OH + H (2.43)

OH + C" CO + H (2.44)

OH + H2 " H2O + H (2.45)

The forward and reverse rates for these reactions are given by Hollenbach & McKee

(1989) as:

k&(2.43) = 2.32 " 10!12#T300

$1.93exp (#3 940/T ) [cm3 s!1] O $ OH (2.46)

k'(2.43) = 6.90 " 10!13#T300

$1.93exp (#2 970/T ) [cm3 s!1] OH $ O (2.47)

k&(2.44) = 1.11 " 10!10#T300

$0.5[cm3 s!1] OH $ CO (2.48)

50


k'(2.44) = 1.11 " 10!10#T300

$0.5exp (#77 700/T ) [cm3 s!1] CO $ OH (2.49)

k&(2.45) = 8.80 " 10!13#T300

$1.95exp (#1 429/T ) [cm3 s!1] OH $ H2O (2.50)

k'(2.45) = 7.44 " 10!12#T300

$1.57exp (#9 140/T ) [cm3 s!1] H2O $ OH (2.51)

The resulting ratio between the equilibrium abundances of O and OH is then

f (O)f (OH)

= 0.28#T300

$!0.4exp (970/T ) n(H)

n(H2)(2.52)

and for the CO equilibrium,f (CO)f0(C)

=/ f (OH)

1 + / f (OH)(2.53)

where

/ = exp#77 700T

$n

n(H)(2.54)

f0(C) is the fractional abundance of carbon nuclei present (in atomic as well as molecular

form, i.e. a fixed quantity).

Eqs. 2.50 and 2.51 yield the equilibrium water abundance of

f (OH)f (H2O)

= 8.45#T300

$exp##7 711

T

$n(H)n(H2)

(2.55)

2.2.4 The Cooling

The behaviour of the radiation emitting post-shock region is dominated by various cooling

(and heating) mechanisms. L, the cooling rate per unit volume in Eqs. 2.8 and 2.30

depends on the densities of the species involved as well as a cooling function & (T ) and

is composed of 13 parts as described in Appendix A of Smith & Rosen (2003),

L =131

i=1Li (2.56)

The various components are as follows:

51


L1 is gas-grain (dust) cooling which is taken from Hollenbach & McKee (1989):

L1 = n2&1 (2.57)

where

&1 =3.8 " 10!33 T 1/2)T # Tdust

*

" +1.0 # 0.8 exp (#75/T ), [erg s!1 cm3](2.58)

Tdust is fixed at 20 K and standard dust properties are assumed; the dust cools very rapidly

after being shocked (Whitworth & Clarke, 1997).

L2 is H2 collisional cooling through vibrational and rotational transitions which is

based on Eqs. (7) – (12) in Lepp & Shull (1983) and found to be consistent with the

detailed description given in Le Bourlot et al. (1999). The cooling is described by:

L2 = n(H2).

Lhv1 + (Lhv/Llv)

+Lhr

1 + (Lhr/Llr)

/(2.59)

where the vibrational coe"cients at high and low density are given by

Lhv =1.10 " 10!18 exp (#6 744/T ) [erg s!1] (2.60)

Llv =8.18 " 10!13 exp (#6 840/T ) "%n(H) k(0,1)H + n(H2) k(0,1)H2

&[erg s!1] (2.61)

the terms k(0,1)H and k(0,1)H2 are the v = (0,1) collisional excitation rates which are converted

to de-excitation rates by the exp (#6 840K/T ) term as follows:

k(0,1)H =

233333343333335

1.4 " 10!13 exp +(T/125) # (T/577)2, T < Tv

1.0 " 10!12 T 1/2 exp (#1 000/T ) T > Tv(2.62)

where Tv = 1635K, and

k(0,1)H2 = 1.45 " 10!12 T!1/2 exp

)#28 728/(T + 1 190)* (2.63)

52


At high density the rotational cooling rate coe"cient is

Lhr =

233333343333335

exp)ln 10 " [#19.24 + 0.474x # 1.247x2]* if T < Tr

3.90 " 10!19 exp (#9 243/T ) if T > Tr(2.64)

where Tr = 1 087K and x = log (T/10 000K). The coe"cient at low density is

LlrQ(n)

=

233333343333335

exp)ln 10 " [#22.90 # 0.553x # 1.148x2]* if T < Tl

1.38 " 10!22 exp (#9243/T ) if T > Tl(2.65)

where Tl = 4 031K and

Q(n) =')n(H2)

*0.77+ 1.2 n(H)0.77

((2.66)

L3 is the atomic cooling:

L3 =)n(H)

*2&3 (2.67)

where the form of &3 is from table 10 of Sutherland & Dopita (1993) (with Fe = 0.5) plus

an additional thermal bremsstrahlung term equal to 1.42 " 10!27 T 1/2 for T > 10 000K.

L4 is water rotational cooling:

L4 =)n(H2) + 1.39 n(H)

*n)H2O*&4 (2.68)

&4 = 1.32 " 10!23 (T/1 000)$ [erg s!1 cm3] (2.69)

( = 1.35 # 0.3 log (T/1 000) (2.70)

where ( fits the values tabulated by Neufeld & Kaufman (1993).

L5 is water vibrational cooling via collisions with H2 (Hollenbach & McKee, 1989),

L5 =)1.03 " 10!26 [erg s!1 cm3]

*n(H2) n(H2O) T exp (#2 325/T ) exp

)#47.5/T 1/3*

(2.71)

53


L6 is water vibrational cooling via collisions with H (Hollenbach & McKee, 1989):

L6 =)7.40 " 10!27 [erg s!1 cm3]

*n(H)&3 n (H2O) T exp (#2 325/T ) exp (#34.5/T 1/3)

(2.72)

L7 is cooling from the dissociation of molecular hydrogen (Shapiro & Kang, 1987):

L7 =)7.18 " 10!12 [erg]*

!)n(H2)

*2 kD,H2 + n(H) n(H2) kD,H"

(2.73)

where 7.18 " 10!12 erg is the 4.48 eV H2 dissociation energy and kD,H and kD,H2 are the

collisional dissociation rates (Eqs. 2.38 and 2.39).

L8 is heating from the reformation of molecular hydrogen (Eq. 2.33):

L8 = #kR n n(H) (1 # .))7.18 " 10!12 [erg]* (2.74)

where kR is the formation rate (Eq. 2.37). The fraction of released energy which is ther-

malised rather than radiated is parametrised by ..

L9 is cooling through rotational modes of CO induced by collisions with molecular

and atomic hydrogen which is based on Eqs. (2.5) — (5.5) of McKee et al. (1982).

L9 = n(CO) nk T 0 vT

1 + na/ncr + 1.5 (na/ncr)1/2(2.75)

where vT is the mean speed of the molecules =68kBT/(#mH2) and the number density

parameters are,

na = 0.5)n(H) +

)2 n(H2)

*(2.76)

ncr = 3.3 " 106! T1 000

"0.75 +cm!3

,(2.77)

and the collisional cross-section is given by,

0 = 3.0 " 10!16! T1 000

"!1/4 +cm!2

,(2.78)

54


L10 is cooling via CO vibrational modes through collisions with molecular hydrogen

(Neufeld & Kaufman, 1993):

L10 =)1.83 " 10!26 +erg s!1 cm3,* n(H2) n(CO) T exp (#3 080/T ) exp

)#68/T 1/3*

(2.79)

L11 is cooling via CO vibrationalmodes through collisions with atomic hydrogen (Neufeld

& Kaufman, 1993):

L11 =)1.28 " 10!24 +erg s!1 cm3,* n(H) n(CO) T 1/2 exp(#3 080/T ) exp )#(2 000/T )3.43*

(2.80)

L12 is cooling through the oxygen fine structure 63 µm line:

L12 =%2.82 " 10!18 +erg s!1,

&n(O)

11/ fH + Z /(rH + rH2)

(2.81)

where Z is the spontaneous transition rate = 8.95 " 10!5 s!1 and

fH =0.6 exp (#228/T )

1 + 0.6 exp (#228/T ) + 0.2 exp (#326/T ) (2.82)

is the fractional occupation of the 3P1 level in LTE. The collisional rates with atomic and

molecular hydrogen provided by D. Flower and including rates determined by Jaquet et al.

(1992) are

rH =)n(H) + 0.48 n(H2)

* '4.37 " 10!12 T 0.66 0.6 exp (#228K/T )

+ 1.06 " 10!12 T 0.80 0.2 exp (#326/T )( (2.83)

rH2 =n(H2)'2.88 " 10!11 T 0.35 0.6 exp (#228/T )

+ 6.68 " 10!11 T 0.31 0.2 exp (#326/T )( (2.84)

L13 is OH cooling (Hollenbach & McKee, 1989):

L13 =%2.84 " 10!28 +erg s!1 cm3,& n2 T 3/2 (2.85)

55


2.2.5 Magnetohydrodynamic (MHD) Flows

In sections 2.2.1 and 2.2.2 the treatment was restricted to purely hydrodynamic flows.

However, the inclusion of a magnetic field may considerably alter the nature of the shock.

For a single-fluid (i.e. the neutrals and ions are coupled together) in which the pre-shock

magnetic field is orientated perpendicular to the shock front there is no change to the

structure of the flow. The inclusion of a pre-shock oblique field with a component B0

parallel to the shock front a!ects the flow parameters by decreasing the compression S

experienced across the shock front. For a detailed description of such MHD shocks see

Smith (1989). Here I will jump ahead to the important modifications to the purely HD

equations which are relevant in this study. Considering the conservation of magnetic

energy and flux across the shock Eq. 2.25 is modified to approximately become:

S ( $1$0( v0v1%

('0 + 1)M20

('0 # 1)M20 + 2'0

#.4 .0M2 )M2 + '20

*('0 + 1)

+M2 ('0 # 1) + 2'0,3

/(2.86)

provided that .0 /M2 where .0 = B20/(8#p0) is the ratio of magnetic to thermal pressures

in the undisturbed medium. In the absence of an oblique field .0 = 0 and S is given by

the purely hydrodynamic value of Eq. 2.25.

The immediate post-shock quantities can then be related to the pre-shock quantities

by

p1p0= 1 +M2 )1 # S!1* + .0

)1 # S2* (2.87)

B1 = S B0 (2.88)

.1

.0= S2

#p0p1

$(2.89)

T1T0=

p1Sp0

(2.90)

which are the jump conditions for J-shocks with magnetic fields. We are now interested

in tracing the density and temperature of the downstream gas within the cooling layer.

The continuity equations describing the flow (Eqs. 2.28 – 2.30) are modified to include

56


the magnetic field B. Eq. 2.28 remains unaltered and Eq. 2.29 becomes

p + $v2 + B2

8#= p1 + $1v21 +

B218#

(2.91)

The energy equation (Eq. 2.30) also remains unchanged and an extra term, the flux-

freezing condition, is added:B$=B1$1

(2.92)

The pressure in the post shock zone can then be calculated by rewriting Eq. 2.91 in terms

of .1 = B21/8#P1,pp1= 1 +

#1 # $$1

2$.1 +

#1 # $1$

2$M2

1 (2.93)

In terms of temperature, the post shock flow can be described by putting p/p1 = $T/$1T1,

to getTT1=

#1 + .1 # .1

! $$1

2" $ $1$

(2.94)

2.2.6 C-type Shocks

So far we have considered shocks where the neutral and ionised components are coupled

and can be regarded as a single fluid. However, when the level of ionisation is low for a

slow (vs # 50 km s!1) shock in a magnetised gas the energy transfer between the ionised

and neutral species may require a time-scale which is considerably long compared to the

characteristic cooling time-scale of the gas. In this case the ions and neutrals become

decoupled and must be considered as two separate fluids (the ions stream through the

neutrals by ambipolar di!usion) which (together) host a shock in which the hydrodynamic

flow variables change continuously. Such a shock is referred to as a continuous orC-shock

for which the conditions were first successfully investigated by Draine (1980).

In a C-shock the shock front is preceded by a compression of the magnetic field called

a magnetic precursor. The magnetic field upstream is a!ected by compressive waves

which propagate in the ion-electron fluid in a direction perpendicular to the magnetic

field. These waves are called ion magnetosonic waves (IMS waves) and they propagate at

57


Figure 2.4: This illustration shows the e!ect of a transverse magnetic field B0 on the shockstructure in partially ionised gas. vn and vi are the velocities of the neutrals and ions. AsB0 increases a magnetic precursor develops (when vims exceeds the shock speed vs) andthe ions are forced to stream ahead of the neutrals. Momentum transfer between the ionsand neutrals takes place and vn begins to follow vi. When B0 > Bcrit the J-shock ceases toexist and vi and vn both change continuously in a C-type shock. From Draine (1980).

the velocity:

vims =#+B2/4# + 5

3)ni + ne

*kB T,/)$i + $e

*

1 + B2/4#)$i + $e

*c2s

$1/2(2.95)

(Spitzer, 1962) where ni and ne are the number density and $i and $e are the mass density

of ions and electrons respectively; cs = (' p /$n)1/2 is the sound speed within the neutral

gas. The nature of the shock depends crucially on whether or not the IMSwaves propagate

faster and ahead of the shock front, i.e. on whether vs > vims or vs < vims. In the first case,

vs > vims, the shock travels faster than any compressive wave resulting in a discontinuous

jump in the flow variables, i.e. a J-shock. This will apply in the limit B $ 0. When

58


vs < vims an interesting situation arises. IMS waves can now propagate ahead of the

shock front and compress the pre-shock magnetic field within a region comparable to

the damping length L, as illustrated in Fig. 2.4. Within the magnetic precursor ions and

electrons are forced to stream through the neutral fluid to which they gradually transfer

their energy via collisions. The neutral gas is heated and compressed before the arrival of

the J-front. In the case where the magnetic field is in excess of some critical value Bcrit

(or the shock speed is small), the discontinuity completely disappears and the variables

change gradually throughout the transition.

Due to the rapid increase in temperature across the shock front molecular hydrogen

is e!ectively dissociated by a J-shock with a velocity above !24 km s!1 (Kwan, 1977).

However, in a well cushioned C-shock molecular hydrogen can survive up to shock ve-

locities of !50 km s!1 (Draine et al., 1983), thus explaining observations of molecular

hydrogen in gas which is being processed by high velocity shocks.

Analytical Treatment of C-shocks

The flow of gas through a steady state C-shock has been investigated in detail by Cherno!

(1987) and Draine et al. (1983). The following is a summary of the approach taken to

understanding the structure of C-shocks. Many of the details have been omitted here but

can be found in the references mentioned.

The streaming velocity between the ions and the neutrals (vn # vi) is the important

quantity which determines the temperature of the disturbed gas. The laws of continuity

and flux conservation are combined to give the momentum equations for the neutral and

ionised gases, respectively:

ddx)mn nn v2n + nn kBTn

*= F (2.96)

ddx

. !vsvi

"2B208#

/= #F (2.97)

59


where F is the drag force resulting from the ion-neutral collisional coupling:

F = *0v+mr nn ni (vn # vi) (2.98)

where mr = mnmi/(mn + mi) is the reduced mass and *0v+ ! 1.5 " 10!9 [cm3 s!1] is

the rate coe"cient for momentum transfer which is of the order of the rate coe"cient for

resonant charge exchange in the orbiting approximation, see Dopita & Sutherland (2003).

The energy equation for the neutral gas becomes

ddx

#mn nn v3n2

+'

' # 1 nn kBTnvn$= Fvn + L(T, n, f ) + ' (2.99)

where ' is the rate of change of internal energy, given by

' =2*0v+mr nn nimn + mi

7 11 # ' kB (Ti # Tn) +

mi

2(vn # vi)2

8(2.100)

For simplicity the structure of the shock is traced via the following dimensionless vari-

ables:

r =vnvs=nn0nn

(2.101)

q =vivs=ni0ni

(2.102)

t =kBTnmnv2s

=TnT0

(2.103)

where vs is the shock speed, nn0 and ni0 are the upstream neutral and ion densities which

have not yet been disturbed by the approaching shock, i.e. & = ni0/nn0. The Alfven waves

(propagating disturbances in the magnetic field) travel at the velocity vA = B964#$ and

the Alfven Mach number of the shock is defined as

M2A =

v2sB209)4 #mn nn0

* (2.104)

A length scale which is related to the actual length scale of the shock structure is defined

60


through

L =mn vs

mr *0v+ ni0(2.105)

Eqs. 2.96 to 2.99 are reduced to give the following relationships:

Lddx

#r +

tr

$=q # rqr

(2.106)

Ldqdx=q2(q # r)

rM2

A (2.107)

Lddx

#r2

2+'t' # 1

$=q # rr# ( tqr

(2.108)

where ( is the ratio of drag to cooling time-scales,

( =mn nn& (Tn)mr ni *0v+ k Tn

(2.109)

By eliminating x, Eqs. 2.107 to 2.109 can be combined to yield

drdq= (' # 1) (r # q) ['r/(' # 1) # q] #( t

rq3 (r # q) (1 # 't/r2)M2A

(2.110)

and introducing the boundary condition r = 1 when q = 1, Eqs. 2.107 and 2.108 integrate

to give

r +tr= 1 +

12M2

A

#1 # 1

q2

$(2.111)

Eqs. 2.110 and 2.111 together with Eq. 2.107 can be solved numerically to yield r(x),

q(x), and t(x), i.e. it is then possible to trace the neutral and ion densities as well as the

temperature through the shock.

2.3 Modelling Bow Shocks

The structure of bow shocks is described in 1.3.3. In this thesis I have set out to study

and interpret observed bow shocks in terms of the physics and chemistry presented in this

chapter. I have used the bow shock models developed initially and described by Smith

& Brand (1990a,b,c); Smith (1991) to generate images in a variety of emission lines.

61


Figure 2.5: The geometry employed by the bow-shock model, moving at velocity vbowwhose surface represents a gradation of velocities transverse to the shock surface. Theangle to the line of sight 1 and magnetic field direction are parameters which must bechosen. The magnetic field direction is relative to the bow direction of motion. Forclarity, if the bow is travelling in a direction parallel to the plane of the sky, then µ adjuststhe magnetic field in a direction parallel with the plane of the sky (perpendicular to theline of sight). In this case , adjusts the magnetic field along a direction out of the planeof the sky.

Through fine tuning of the input parameters (see below) and detailed comparison with

images and spectra of the observed bow shocks it is possible to constrain the conditions

involved; bow shocks can be interpreted through a comparison with model generated

images of bow shocks. The details of the parameter selection and fine tuning process will

be described in 3.4 in relation the bow shocks in the HH240 protostellar outflow. I will

employ two bow shock models: J-BOW and C-BOW, which are geometrically identical

and based on the J-shock and C-shock equations, respectively. The geometry is shown in

Fig 2.5. This model assumes a three dimensional bow surface with a form

62


ZLbow

=1s

! RLbow

"s(2.112)

in cylindrical coordinates (Z,R) where the constant s is the shape parameter and Lbow

fixes the bow size. The bow surface is cut up into an extremely large number of planar

individual shocks called shock elements. Each element is subject to di!erent conditions.

For the shock velocity and magnetic field it is the component perpendicular to the

shock surface which must be considered. The highest shock velocity is experienced at the

front of the bow where v( = vbow. The perpendicular component of velocity v( decreases

out along the bow wings with growing distance from the bow apex. The local angle

of incidence of the shock surface to the flow direction is ( and v( = vbow sin(. The

numerical calculations proceed in steps of d(. At each step (which describes an annulus)

the shock is then divided into segments of azimuthal angle + for which the magnetic field

component is determined. The calculations are greatly reduced when the magnetic field

is aligned with the flow direction. In that case the symmetrical arrangement implies that

every shock element is identical within each d(. As a first approximation this condition

is assumed. Asymmetries can be introduced into the bow appearance afterwards through

adjustment of the angles µ and ,.

The J-BOW and C-BOW (FORTRAN written) codes calculate the relevant densities

and temperatures along the Z direction for each shock element and determine the flux

contribution to a zone in a 3–D image-velocity data cube. The data is adjusted according

to the angle to the line of sight 1 to reproduce the expected 2D image. The planar shock

analysis is only accurate if the cooling length which we are interested in modeling is

considerably less than the bows’ radius of curvature. The input parameters and variables

are listed in Table 2.2 along with typical values which are used throughout this thesis. The

sensitivity to changes in the input parameters and variables is shown in Appendix A.

In order to calculate the line emission properties for a specific transition, the popula-

tion density of the upper level (N j) needs to be determined. J-BOW and C-BOW assume

a non-equilibrium H2 chemistry in which the vibrational level populations are not dis-

tributed according to the Boltzmann distribution (i.e NLTE case). The rotational levels

63


Table 2.2: The list of input parameters and variables for the J-BOW and C-BOW models.As an indication, typical parameter values or ranges used in this thesis are given.

bow speed, vbow 20 # 100 km s!1 Oabundance 5 " 10!4Alfven speed, vA 2 # 8 km s!1 H2Oabundance 0 " 10!4Lbow 1 # 2 " 1016 cm COabundance 1 " 10!4shape parameter, s 1.7 # 2.4 Cabundance 2 " 10!4He fraction 0.1 1initial temperature 100K (J # BOW) (Hdensity, n 2 # 20 " 103 cm!3 +molecular fraction 0.2 # 0.3 (0.5 = fully H2) µion fraction, & 1 # 5 " 10!5(C);> 10!4(J) ,

within each vibrational band are assumed to follow the Boltzmann distribution as they

have much lower radiative transition rates. In NLTE the time in between collisions is long

enough to allow for radiative decays to lower levels via spontaneous radiative transitions.

This possibility reduces the LTE upper level population fraction to new NLTE fraction

which we call *:

* =V j/VG

1 + V j/VG(2.113)

where V j and VG are the populations of the jth and ground vibrational levels and V j/VG

is given by

V j/VG =' exp (#Tv/T )' + Z j

(2.114)

' = 'H2j n(H2) + 'Hj n(H) (2.115)

where Tv is the temperature di!erence between the upper and lower vibrational levels and

Z j is the radiation coe"cient or electric quadrupole transition probability. 'H2j and 'Hj are

the de-excitation rate coe"cients for collisions with H2 and H given by Hollenbach &

64


McKee (1989) and Hollenbach & McKee (1979); Lepp & Shull (1983) as

'H210 = 'H221 = 1.4 " 10!12 T 1/2 exp (#[18 100/(T + 1 200)])

+cm3 s!1

,(2.116)

'H10 = 1.4 " 10!13 exp#! T125

"#! T577

"2$ +cm3 s!1

,T < 1 635 (2.117)

'H10 = 1.0 " 10!12 T 1/2 exp!#1 000

T

" +cm3 s!1

,T > 1 635 (2.118)

'H21 = 4.5 " 10!12 exp##!500T

"2$ +cm3 s!1

,(2.119)

N j is then given by

N j =gj n(H2) * exp (#Tr/T )

Q (T )+cm!3

,(2.120)

where gj is the degeneracy of the level and Tr is the temperature di!erence between the

upper and lower rotational levels within V j. Q (T ) is the molecule partition function which

is taken as Q (T ) = (T/40.75) +1 # exp (#5 987/T ),!1 for H2.

The radiation contribution for each shock element can then be determined from

E =N jZj h c" j

+erg s!1 cm!3

,(2.121)

where h and c are the usual constants and Zj is the spontaneous radiative decay rate. E

is then multiplied by the area of the shock element chosen and used to construct the 3–D

data cube along with the velocity information. The line emission from the whole bow

resulting from the dissipation of thermal energy can then be determined by summing up

the emission from each shock element.

Note, however, that the dissipation of some thermal energy can can also occur in the

turbulent wake of the bow shock. This turbulence arises due to the shear caused by the

passage of a curved shock front, leading to the generation and following dissipation of

vorticity. The energy thus dissipated could be up to 15% of the energy which is converted

to emission in the shock cooling layer (Smith, 1995b). The dissipatation of this energy is

not considered in this analysis as the energy is dissipated through weak shocks which do

not heat the gas to temperatures capable of exciting observable IR emission lines.

65


The bow-shock code serves as first approximation to understanding and interpreting

the observed bow-shaped structures which are regularly seen in outflows because most

of the observable emission is generated in the cooling layer following the ambient shock

front. The code does not include contributions from the turbulence generated in the wake

of the passing bow (mentioned above), the Mach disk, and emission from shocks within

the jet itself and where the outer jet surface interacts with the ambient medium. These

are factors which need to be considered when interpreting the observed line fluxes and

structures of each individual bow shock.

The chemistry network described in Sections 2.2.3 allows for the prediction of line

emission from H, H2, O, OH, H2O, C, and CO. Emission from the [O I] 63µm line is

calculated in the cooling formula Eq. 2.81. In addition, the code includes a set of routines

which handle the iron chemistry, enabling the prediction of the free iron abundance (which

is proportional to the shock velocity as fast shocks sputter the dust grains and release

atoms) and line emission from atomic and ionic Fe. This is the full range of atoms and

species presently considered in this code.

The application of this model has proved remarkably successful at explaining the ob-

served morphology of bow shocks as well as distinguishing between J-type and C-type

conditions, see e.g. Smith et al. (2003b); Khanzadyan et al. (2004).

66

Chapter 3

The Bow Shocks within the L1634

Protostellar Outflow

67

Chapter 3. The Bow Shocks within the L 1634 Protostellar Outflow

3.1 Introduction

Bipolar outflows which sweep up and shock-heat cloud material are often detected as

Herbig-Haro (HH) objects in optical emission lines1 and as molecular hydrogen flows in

the near-infrared provided the outflow has pierced an obscuring parental cloud (Reipurth

& Bally, 2001). A large volume of swept up and disturbed gas, however, may still be

observable at longer wavelengths through emission in CO rotational transitions, and other

molecules. An excellent example of this is associated with the L1634 cloud (Lee et al.,

2000a). This chapter presents a detailed study of the HH objects in L1634 which possess

a particularly striking morphology. The aim is to understand the dominant physical and

dynamical processes in a protostar-environment interaction.

The outflow is driven from IRAS 05173-0555 (Davis et al., 1997), a protostar with

an estimated mass infall rate of 2 – 8 " 10!5 M" yr!1(Beltran et al., 2002), bolometric

luminosity of 17 L" (Reipurth et al., 1993) and bolometric temperature of 77K (Mar-

dones et al., 1997), classifying it as undergoing a transition phase from Class 0 to Class I.

The ratio of submillimetre to bolometric luminosity of 0.014 (Froebrich, 2005), however,

suggests that the protostar still has enough circumstellar mass to classify it as Class 0.

In addition to the east-west outflow there is a weaker northwest-southeast outflow driven

from IRS 7, 40## to the east (Hodapp & Ladd, 1995; Davis et al., 1997). A distance of

460 pc to the molecular cloud which is located in Orion (Bohigas et al., 1993) is adopted.

The main outflow appears to terminate in two regions of shocked gas, identified as

HH240 and HH 241 at visible wavelengths (Cohen, 1980). To the west, HH240A (RNO

40) possesses a high proper motion directed away from the IRAS source and, to the east,

HH 241A (RNO40E) is also identified in optical emission lines (Jones et al., 1984; Bohi-

gas et al., 1993).

The impact regions have been explored in near-infrared H2 emission lines where dis-

tinct and resolved structures have been identified, as displayed in Fig. 3.1. To the west,

several well-defined bow shocks are found (especially HH240A–D) whereas numerous1Note that the term Herbig-Haro (HH) by defi nition only refers to the objects which are detected at

optical wavelengths

68


scattered knots are found to the east (HH 241A–D) (Hodapp & Ladd, 1995). The pro-

jected extent between the two outer D knots is 6.3#, yielding a projected size of 0.84 pc at

a distance of 460 pc. The outer D knots are equidistant from the IRAS source to within

measurement error.

The accelerated gas is observed in CO rotational lines, with most of the blue-shifted

CO lying towards the direction of HH 240 (Davis et al., 1997; De Vries et al., 2002). The

CO J = (1,0) emission map is shown in Appendix C. The blue emission curves around

the giant HH 240A bow shock with a broad range of radial velocities (including some

red-shifted) but there is very little CO emission beyond this location (Lee et al., 2000a).

The CO red wing emission to the east takes the form of a hollow shell which ends near

the cloud edge (Lee et al., 2000a). In the east, however, there is also ample blue-shifted

CO gas. Lee et al. (2000a) favour a jet-driven model with a jet orientation of 30% – 60% to

the line of sight.

Lynds 1634 is a bright-rimmed cloud, SFO16 (see Appendix C), associated with

Barnard’s Loop (Sugitani et al., 1991; De Vries et al., 2002). The C18O cloud struc-

ture suggests an ENE–WSW orientation (De Vries et al., 2002), which may help ex-

plain asymmetries in the outflow. There is a small velocity gradient in the cloud, roughly

perpendicular to the outflow, which o!ers the possibility that the outflow lies along the

cloud’s rotation axis.

This work focuses on the remarkable series of H2 bow shocks. Their shapes suggest

they are being driven away from the IRAS source by a jet or bullets. The origin of the bow

shocks is uncertain. Is each bow the result of a distinct protostellar outburst event? Could

they form through fluid dynamic instabilities in the jet? Or, are they the consequence of a

jet interaction with a non-uniform environment?

High resolution spatial and velocity data permit an exploration of the bow shock’s

characteristics through detailed geometric and physical modelling. It is then possible to

(1) determine the necessary driving power, (2) resolve the debate concerning the shock

physics (e.g. C-type or J-type) and (3) limit the speeds of the bow shocks. Recent 1 –

2.5 µm long-slit spectra yield a high molecular excitation for HH240C, and excitation of

69


atomic lines consistent with a shock speed of ! 80 km s!1 (Nisini et al., 2002a). The

excitation imaging presented here should reveal if the slit spectra are representative of the

entire bow shock.

Only a few interstellar bow shocks have been previously imaged in H2 lines from

transitions originating above the first vibrational level. One recent such study of HH 7

concluded that C-type shock physics with paraboloidal bow shocks is responsible (Smith

et al., 2003b). Here, after presenting and discussing the new data in Section 3.3, the bow

shock models developed in order to model the HH240 bow shocks are adopted employing

both C-type and J-type physics (in Section 3.4). The modeling results are compared with

the narrow-band H2 imaging and position-velocity spectroscopy in Section 3.5 as well as

with previously published 1 - 2.5 µm spectroscopy in Section 3.6 and CO J = (1,0) imag-

ing and spectroscopy in Section 3.7. In Section 3.8 the findings are discussed in relation

to previously published optical data before making several conclusions (in Section 3.9)

based on this large reservoir of data.

3.2 Observations and data reduction

3.2.1 Near-Infrared Imaging

On November 12th 2001 I observed HH240 in the near-infrared with the Fast Track Im-

ager camera UFTI on the 3.8–m U.K. Infrared Telescope UKIRT, on the summit of Mauna

Kea, Hawaii. The camera is fitted with a 1024 x 1024 HgCdTe Rockwell array which,

together with the internal optics, provides a total field of view of 92.9## " 92.9## and a

pixel scale of 0.091## per pixel.

Individual frames were obtained in a 9–point jitter pattern (with 10## E–W and 20##

N–S o!sets) and mosaics were constructed in both the (1,0) S(1) and the (2,1) S(1) tran-

sition lines of H2 using narrow-band filters centered on " = 2.122 µm and " = 2.248 µm

respectively with FWHM = 0.02 µm. Both filters are situated in the K-band where atmo-

spheric transmission is high. The integration time for each individual frame was 100 sec.

The total on-source exposure times were 15 mins and 90 mins per filter, respectively.

70


The Starlink packages CCDPACK and KAPPA were used to reduce the data. Dark

exposures were subtracted from each frame. A set of target frames was combined into

a flatfield frame using standard routines (FLATCOR and MAKEFLAT). Using the target

frames themselves provides an accurate flatfield frame because the sky background level

is high in the K-band and the separation of the frames is such that the bright object features

do not overlap. The flatfield frame is the normalised median average of all the target

frames and consists of an array of values which represents the sensitivity of each pixel,

and hence the response of the CCD detector to uniform illumination. Each image frame

was then divided by the flatfield frame to correct for the pixel-to-pixel sensitivity.

For each frame the mean count per pixel, determined from the full array, was used to

subtract o! the background sky level. This was found to set the average sky level of the

reduced images to zero. Guide star tracking was maintained throughout and the telescope

registered o!sets were used to create the final mosaics due to the lack of field stars.

The standard stars HD18881 (spectral type A0 and K-band brightness of 7.14 mag)

and HD43244 (spectral type F0V and K-band brightness of 6.52 mag) were observed, at

the same airmass as L 1634, in both filters in order to flux calibrate the images as follows:

1. Due to the atmospheric extinction experienced at the location of UKIRT a K-band

magnitude of 0.0 mag (m0) corresponds to a flux density F0 of 657 Jy (1 Jy = 10!16

W m!2 Hz!1), i.e. this is the flux density received at UKIRT from a star with a

K-band magnitude of 0.0 mag. The standard star K-band flux density F% is then

determined using

m% # m0 = #2.5 log#F%F0

$(3.1)

where m% is the K-band magnitude of the standard star.

2. F% is converted to W m!2 by multiplying by the band-width given by

%! =c ("2 # "1)"

[Hz] (3.2)

where c is the speed of light and "1 and "2 are the filter 50% cut-on and cut-o!

71


wavelengths.

3. The total number of counts s!1 detected for the standard star is determined by in-

tegrating the counts s!1 pixel!1 over a circular aperture containing the image of the

star.

4. Finally, the object image is converted to units of W m!2 pixel!1 by dividing the

object counts s!1 pixel!1 by the standard star counts s!1 pixel!1 and multiplying by

F%. To convert to flux units per arcsec2 it is necessary to divide by the pixel area (in

arcsec2).

After calibrating, the flux from the star in HH240C was compared in both filters and

found to be about equal as would be expected from a continuum source.

Seeing throughout the observations was measured as FWHM & 0.7##. The images

were smoothed by applying a 4 " 4 pixel box filter to estimate the mean.

3.2.2 Position-Velocity (P-V) Spectroscopy

Echelle spectra centered on the H2 (1,0) S(1) emission line "vac = 2.1218334 µm (Bragg

et al., 1982) were obtained between the 5th and 7th February 1999 (UT) at the UKIRT

using the cooled grating spectrometer CGS 4. The instrument was equipped with a 256 "

256 pixel InSb array; the pixel scale was 0.41## " 0.90## (0.41## in the dispersion direction).

A 2-pixel-wide slit was used, resulting in a velocity resolution of ! 15 km s!1. The

instrumental profile in the dispersion direction, measured from Gaussian fits to sky lines,

was ! 18 km s!1.

Data at seven slit positions in HH240 and five in HH241 were obtained (see below).

A position angle of 63% was used in HH240 and 100% in HH241. Object-sky-sky-object

sequences were repeated at each slit location to build up signal-to-noise, the sky position

being o!set from the east-west outflow axis. Each spectral image was bias subtracted

and flat-fielded. Sky-subtracted object frames were then co-added into reduced “groups”

(one group frame per slit position). Each reduced group spectral image was subsequently

wavelength calibrated using four well-spaced atmospheric OH sky lines (Oliva & Origlia,

72


1992) following the steps described by Davis et al. (2001). The absolute velocity cali-

bration, measured from the wavelengths of the OH lines in wavelength calibrated “raw”

spectral images2, was of the order of 4 – 5 km s!1, although the relative calibration along

each slit (from row to row in each spectral image) was much better than this, the optical

distortion along columns (sky lines) in the reduced spectral images being much smaller

than the pixel scale. This data was reduced and kindly provided by Dr. Chris Davis (Joint

Astronomy Centre, Hawaii) and Dr. Klaus Hodapp (University of Hawaii, Institute for

Astronomy).

3.3 Results

3.3.1 Imaging

Figure 3.1 displays the HH240 outflow. The sequence of principle knots is denoted

HH240 A to D with increasing distance from the IRAS source. The photometric re-

sults are presented in Table 3.1 along with the integrated H2 (2,1) S(1) / (1,0) S(1) flux

line ratios for each bow feature.

Figure 3.2 displays the bow shocks, HH 240A and HH 240C, in detail. The close-

up images highlight the spatial resolution of the shock structure. Intensity profiles are

displayed for horizontal (slit 1) and vertical (slit 2) slits, to facilitate a comparison to

models. Horizontal and vertical slits were chosen in order not to make any presumption

about the inclination of the outflow axis in the plane of the sky and because of the more

simple approach of summing up pixel values along rows and columns. The slit locations

were chosen to highlight the general trend of the flux distribution. The particularly bright

region A1 was avoided as this feature dominates the emission to a large extent and is

likely the result of the impact of a fast reverse shock (Mach disk) which is not included

in the modelling (See Section 3.8). Along HH240C the star is avoided in order not to

include the continuum flux. Note the narrow peaks as well as the extended distribution.2The raw spectral images were used to check the velocity calibration before subtraction of the sky OH

spectral lines.

73


Figure 3.1: HH240 in the H2 (1,0) S(1) 2.12 µm line. The entire outflow imaged byDavis et al. (1997) is shown above where the position of the IRAS source at R.A.(2000)= 05h 19m 48.9s, Dec(2000) = -05% 52# 05## (Nisini et al., 2002a) is marked by the cross.O!sets in the close-up image are measured from the peak value at A1 which is at positionR.A.(2000) = 05h 19m 40.5s, Dec(2000) = -05% 51# 42.3## (Davis et al., 1997). The dottedlines represent the positions of echelle spectroscopy slits. The slit numbers correspondto the position velocity diagrams in Fig. 3.5. Note that the slits here do not represent theactual slit lengths. The colour-scale (bottom image) is logarithmic with a minimum valueof 10 " 10!19 W m!2 arcsec!2 (just above the noise level) and maximum value of 200 "10!19 Wm!2 arcsec!2.

Note also that for the chosen slit locations HH 240C has a larger horizontal extent but a

smaller vertical profile.

Projected onto HH 240C is a star, evident from the fact that the feature has a sharp

point spread function where the flux through both filters is equal: characteristic of a con-

tinuum source. This feature has been utilised to align the images in both filters more

accurately as there are no other stars within the field of view.

74


Figure 3.2: Individual images of HH240A (top) and HH240C (bottom) in the H2(1,0) S(1) line along with vertical and horizontal slices to indicate the flux variationthrough the bows. The contour levels are 12, 32, 52, 72 (black), 100, 170, and 240 (white)" 10!19 W m!2 arcsec!2 for both bows. The solid line in the profiles represents the H2(1,0) S(1) transition and the dotted line represents the emission from the H2 (2,1) S(1)transition in units of 10!19 W m!2 arcsec!2. O!sets are measured from the peak value ineach contour image. The grey-scale images are logarithmic with a minimum value of 10 "10!19Wm!2 arcsec!2 (just above the noise level) and maximum values of 126 " 10!19Wm!2 arcsec!2 and 316 " 10!19 Wm!2 arcsec!2 for HH 240A and HH240C, respectively.

75


Table 3.1: Photometric results for HH 240

Circular H2 H2 ExcitationObject Aperture† (1, 0) S(1)$ (2, 1) S(1)$ Ratio‡

HH240A 30## 401 43 0.11(0.02)A1 6## 157 24 0.15(0.02)HH240B 28## 149 33 #B1 12## 51 13 #B2 16## 91 20 #HH240C 18## 285 42 0.15(0.02)HH240D 14## 139 25 0.18(0.04)

†Circular apertures were chosen which include all the di!use emission from each object. Adjacent circularregions of equal size were subtracted in order to minimise any contribution from the background.!Flux in units of 10"18Wm"2‡The excitation ratio is the integrated H2 (2,1) S(1) / (1,0) S(1) flux ratio. The HH240C flux values weredetermined after the continuum at 2.104µm was subtracted. Errors determined from the variance in thebackground are quoted in brackets.

A regular asymmetric structure is present: the northern flank of each bow is brighter

than the southern edge. This is particularly evident in HH 240C. The bright peak in

HH 240A corresponds in position to the optical HH Object, imaged by Bohigas et al.

(1993).

Despite the weaker fluxes of the components, the distribution of emission in the (2,1)

image (not presented) closely resembles that of the (1,0) image. However, there are some

significant variations which are evident in the flux ratio measurements given in Table 3.1.

The variation of this ratio across the bows is presented in Fig. 3.3 where the intensity pro-

files through slits passing through bright and extended emission locations were measured

and divided. Both bows possess high excitation peaks at the leading edge followed by

low excitation plateaus.

A significant variation in excitation is also present between bows. In particular,

HH 240A has a relatively low vibrational excitation. (2,1)/(1,0) S(1) ratios of 0.11 and

0.15 are measured (with estimated error of 18% and 7.5%) for HH240A and HH240C,

respectively (Table 3.1). This result is consistent with the line strengths tabulated by

Nisini et al. (2002a), on integration along a slit of width 1##. They found (2,1)/(1,0) S(1)

76


Figure 3.3: The H2 (2,1)/(1,0) flux ratio along HH240A and HH240C (left column). Theprofile for HH240A is along slit 3 in Fig. 3.2 and the profile for HH240C is along slit1 in Fig. 3.2. For comparison to the models the flux ratio profiles generated in similarlocations are shown for C-bow and J-bow models (middle and right column respectively).Note that the profiles for the models cover the whole x-scale whereas the observed ratiosonly cover the portion of the slit which gives measurable quantities.

ratios of 0.11 and 0.17 (also with errors of a few per cent) for HH240A and HH240C,

respectively.

3.3.2 Near-Infrared Echelle Spectroscopy

The positions of 12 slits which pass through interesting features of the shocked H2 emis-

sion are marked on Fig. 3.1 (HH 240) and Fig. 3.4 (HH 241).

The corresponding position-velocity images are displayed in Fig. 3.5. The spatial

pixel scale of the images is 0.9## and the angular extension of each image along the y-axis

is 83##. The systematic velocity of the region, derived from the N2H+ J = (1,0) hyperfine

ensemble, is +8 km s!1 (De Vries et al., 2002).

The most remarkable result is that the H2 emission from HH 240 is blue-shifted

relative to the cloud by typically -10 to -50 km s!1. Wide velocity profiles, exceeding

77


Figure 3.4: Spectroscopic slits for HH241. Each slit is 82.8## in length. The slit numberscorrespond to the position velocity diagrams in Fig. 3.5. The colour-scale is linear with aminimum of 5 " 10!19 Wm!2 arcsec!2 and maximum of 60 " 10!19 Wm!2 arcsec!2.

70 km s!1 in some locations, are found. However, some emission, in particular from the

HH 240A peak in Slit 1, is at the cloud radial velocity. For slits passing through distinct

bows (slits 1, 2, 4, 5 and 7) the emission is characterised by a wide peak close to the front

followed by emission which grows fainter and trails o! at zero velocity. Unlike the H2

bow-shaped structures along the outflow in L1448 (Davis & Smith, 1996), double peaked

velocity profiles (indications of bow shock geometry where the H2 emission derives from

the front and rear edges of the 3 dimensional bow) are absent except for slit 5 which

passes through the compact HH 240C knot. The blue-shifted peak is displaced 2## back

from the red-shifted peak indicating that the bow direction of motion is inclined to the

line of sight with the HH240C bow directed toward the observer.

The obvious di!erence between HH241 and HH240 is that the H2 emission is almost

exclusively red-shifted in all the HH241 slits. Slits 8 to 12 reveal emission which is on

average red-shifted by ! 26 km s!1. The HH241 outflow is clearly directed away from

78


Figure 3.5: Position-velocity diagrams for HH240 (1 – 7) and HH 241 (8 – 12). Labelsare according to the slits in Figs. 3.1 and 3.4. The location is measured from the westernside of the slits in pixels where 1 pixel corresponds to 0.9## (y-axis) and the velocity inkm s!1 (x-axis) is relative to the Local Standard of Rest (LSR).

the observer.

Interestingly, the velocity profiles are narrower in HH241. They possess an average

width of ! 45 km s!1. This would be expected if we are observing individual shock fronts

in HH241 rather than superimposed near and far sides of bow shocks. It would still be

unclear, however, why the material is exclusively deflected away from the observer. A

more detailed investigation and interpretation is required. In Section 3.5, the profiles will

be modeled in terms of bow-shaped shock geometries.

79


3.4 Analysis

3.4.1 Background

At first sight, all the position-velocity diagrams display features which can be qualitatively

attributed to emission resulting from bow-shocked molecular material. The bows are

moving (1) su"ciently fast so that H2 is dissociated near the apex and (2) at an angle out

of the plane of the sky so that emission from the rear side and front side of the bow shock

surface are projected onto di!erent locations. The HH240 bows are moving towards us

and inclined at an angle to the line of sight so that the rear sides of the bows (i.e. the

forward part of the bow surface but located on the rear side, away from the observer)

give rise to the leading emission when projected onto the sky. Therefore, slits through

the front of the bow generate emission which is relatively red-shifted at the front, with

a following blue-shifted peak. Moving along the slit into the bow tail, the spread in

velocities becomes narrower and the emission intensity fainter. Detailed modelling is

presented in Section 3.5.

To model the flux, excitation and velocity information, the bow model described in

Section 2.3 was employed.

To initiate the modelling, some of the parameters need to be estimated; we begin with

the density and iterate the fitting of all parameters until a fit is reached which satisfac-

torily reproduces the observed data, including the size and morphology of the bow. The

exploration proceeds one parameter at a time and is a subjective process. The observed

set of data imposes restrictions on the possible range of parameter space and confidence

is gained by beginning the iteration from di!erent parameter configurations. Appendix A

contains figures in which the parameters are consistently varied in order to highlight the

sensitivity of the bow appearance, luminosity and vibrational excitation ratio to each pa-

rameter.

A reddening factor %J!H can be determined from the two brightest [Fe II] forbidden

transition lines at 1.257µm and 1.644 µm which both originate from the same upper level

(this method is described in detail in Section 4.3). Using this method and adopting the

80


Table 3.2: Model parameters derived to fit the bow images with C-type shocks. Through-out, n = n(H) + 2n(H2) is taken as the hydrogen nucleon density.

Parameter HH 240A HH240C

Size, Lbow 1.7 " 1016 cm 1.3 " 1016 cm(1)HDensity, n 2.5 " 103 cm!3 7.0 " 103 cm!3(2)Molecular Fraction f $ 0.2 0.2(3)Alfven Speed, vA 5 kms!1 5 km s!1

Magnetic Field 135 µG 226µGIonFraction, & 1 " 10!5 5 " 10!5

(4)BowVelocity, vbow 70 km s!1 50 kms!1(5)Angle to l.o.s. 60% 60%(6) sParameter 2.35 1.9(7)Field angle, µ 30% 60%

! – The molecular fraction is given by f = n(H2)/n so when f = 0.5 the gas is fully molecular.

Rieke & Lebofsky (1985) extinction law, Nisini et al. (2002a) determine a visual extinc-

tion AV = 2.5 ± 0.8 mag towards HH240A. Adopting the standard gas-to-dust ratio given

by Eq. 2.5, and that the HH240A bow lies at a distance of ! 300## (2 " 1018 cm at the

distance of 460 parsecs) from the edge of the L1634 cloud (from DSS2 image), an aver-

age hydrogen density of ! 2.5 " 103 cm!3 is estimated. This estimate assumes that the

extinction is dominated by intervening gas lying between the object and the edge of the

cloud.

3.4.2 Modelling HH240A as a C-type Bow

After considerable exploration, the parameters which are listed in Table 3.2 were derived

for HH240A. For clarity and to highlight the modelling technique, I present here a dis-

cussion of the role of each of the parameters and the extent to which they influence the

appearance of the bow.

A bow shape given by s = 2.35 and size scale Lbow = 1.7 " 1016 cm are found to

reproduce the overall wide angle and dimensionality of the bow. In the figures Lbow is

represented by 9 pixels. This implies 1 pixel is 0.28## at the adopted distance.

1. The low H2 (1,0) S(1) luminosity of 2.6 " 10!3 L" constrains the hydrogen density

81


Table 3.3: Observed and predicted bow shock luminosities and (2,1) S(1) / (1,0) S(1)vibrational excitation ratios for HH240A and HH240C. Luminosities are in units of L".A source distance of 460 pc is assumed. K-band extinctions of 0.28 and 1.0 mag are ap-plied to HH240A and HH240C, respectively, to determine the dereddened luminosities.A di!erence in the adopted K-band extinction values of 50% leads to a variation in thedereddened (1,0) S(1) luminosities of ± ! 12% and ± ! 37% for HH240A and HH240C,respectively.

Line Observed Dereddened C # type J # typeModel Model

HH 240A

H2 (1, 0)S(1) 2.6 " 10!3 3.4 " 10!3 4.4 " 10!3 2.4 " 10!3H2 (2, 1)S(1) 2.8 " 10!4 3.6 " 10!4 5.5 " 10!4 4.0 " 10!42/1 ratio 0.11 0.11 0.12 0.17

HH 240C

H2 (1, 0)S(1) 1.9 " 10!3 4.7 " 10!3 7.7 " 10!3 4.0 " 10!3H2 (2, 1)S(1) 2.8 " 10!4 6.9 " 10!4 1.0 " 10!3 6.1 " 10!32/1 ratio 0.15 0.15 0.13 0.15

and bow velocity. A K-band extinction of 0.28 mag raises the intrinsic (1,0) S(1) lumi-

nosity to 3.4 " 10!3 L". A low density of n = 2.5 " 103 cm!3 and a velocity of 60 km s!1

result in a su"ciently low model luminosity. Increasing the density to n = 4.0" 103 cm!3

has the e!ect of doubling the luminosity. The total cooling through line emission calcu-

lated in the chosen bow model is 4.4 " 10!3 L" in the (1,0) S(1) line, 1.36 " 10!1 L" in

H2 lines (all rotational and vibrational) and 0.17L" for the total line emission. Thus, as

expected, H2 cooling dominates in low density bow shocks.

2. The molecular fraction f (= n(H2)/n where n is the total number of H nuclei =

n(H)+ 2n(H2)) is constrained to be ! 0.2 ± 0.1, in order to keep the luminosity and vi-

brational excitation ratio low. Table 3.3 contains a detailed comparison of the observed

and model characteristics. It is assumed in these initial models that the magnetic field

direction is parallel to the direction of motion of the bow.

3. Emission from closer to the bow apex is characterised by higher molecular exci-

tation since the shock strength is determined by the component of the bow speed trans-

verse to the bow surface. The flux ratio between the H2 (2,1) S(1) and H2 (1,0) S(1)

82


Figure 3.6: C-bow models for HH 240A in which the magnetic field strength is varied.The magnetic field strength (related through the Alfven speed) determines the observedstructure to a large extent. Other parameters are fixed to those in Table 3.2.

vibrational-rotational transition lines measures the vibrational excitation. According to

the detailed physics and chemistry of C-type shocks (Draine, 1980; Draine et al., 1983),

the ion-fraction and magnetic field strength determine the shock velocity at which molec-

ular hydrogen dissociates. There will thus be a dissociated cap if vbow is greater than this

critical breakdown velocity. An Alfven speed of 5 km s!1 and an ion-fraction & (= ni/nn

where ni is the number density of ions and nn is the number density of neutrals) of 1"10!5

is found to correctly reproduce the observed flux ratio and the position of dissociation, for-

ward of which no H2 emission is observed. The shock thickness, inversely proportional

to the ion fraction, is also then reproduced. In addition, it is found that a high magnetic

field is necessary to reduce the length of the H2 bow wings.

The cushioning e!ects of the magnetic field are illustrated in Fig. 3.6. A strong mag-

netic field results in a increase of the streaming velocity between the ions and the neutrals

which allows the molecules to survive a stronger shock. In this case emission is inhibited

in the oblique bow wings and can be seen from closer to the front of the bow but not

from the apex (that would require an even stronger magnetic field and smaller fraction of

ions, see Appendix A Fig. A.5). The cooling length increases with a higher magnetic field

causing the emission to be located some distance back from the shock front, drastically

83


Figure 3.7: C-bow models for HH240A. The dependence of (1,0) S(1) emission on thebow shock velocity is shown here. The bow speed controls the compactness of the bow.Adopting a source distance of 460 pc gives a pixel scale of 1 pixel = 0.28##. Other param-eters are fixed to those in Table 3.2.

altering the appearance of the bow. Lowering the magnetic field has the opposite e!ect.

4. The bow velocity is constrained by the observed flux distribution. Fig. 3.7 shows

that a bow velocity of 40 km s!1 results in a region of compact emission beginning at the

bow apex. There is no dissociated cap because the dissociation speed is not exceeded. In

contrast, a bow velocity of 80 km s!1 generates a bow with little emission from the front;

most of the emission is contained in the extended wings. Between these extremes, a bow

velocity of 60 km s!1 closely resembles the observed bow morphology.

5. The bow appearance depends on the direction of motion relative to the line of

sight, as demonstrated in Fig. 3.8. An angle of 40% results in a gaping hole behind a

strong leading edge. In contrast, when the angle is 80% no dip is present at all and the

bow becomes over extended along the direction of motion in comparison to the observed

HH240A bow.

6. The bow structure is also very sensitive to the shape parameter s. Fig. 3.9 explores

this variable and it can be seen that a bow characterised by s = 2.65 is too broad. When

s is lowered to 2.05, the shape becomes too sharp. In this manner, the value of s = 2.35

has been chosen to fit the appearance of the bow. The shape also influences the integrated

H2 (2,1) S(1) to H2 (1,0) S(1) line flux ratio. The ratio increases from 0.107 (s = 2.05),

0.124 (s = 2.35) to 0.135 (s = 2.65). These values are in the observed range of 0.11 ±

0.02 (Table 3.3).

84


Figure 3.8: C-bow models for HH 240A. Di!erences in the orientation between the bowshock motion and the line of sight drastically alter the appearance of the bow to the ob-server. Here C-type bow models are shown with orientations of 80% (right panel) and 40%(left panel) to the line of sight. It is found that for HH 240A an angle of 60± 10 degreessatisfactorily reproduces the observed image characteristics. Other parameters are fixedto those in Table 3.2.

Figure 3.9: The e!ect of altering the shape parameter s is illustrated by these simulated(1,0) S(1) images of C-type bows with s = 2.05 (left panel) and s = 2.65 (right panel).Other parameters are fixed to those in Table 3.2.

85


Figure 3.10: A magnetic field oblique to the bow axis results in image asymmetry forC-type bows. Combined with a slightly higher bow speed, it is possible to reproducethe observed structure. Note that the grey-scale levels have been adjusted here to displayless di!use structure: the flux profiles demonstrate quantitatively the relative intensities.Other parameters are fixed to those in Table 3.2.

7. Axial symmetry in the model bow structure can be broken by varying the magnetic

field direction, as shown in Fig. 3.10. Various angles µ and , were tried in order to better

match the observations. A positive angle µ tends to increase the peak emission from the

lower flank of the bow. The magnetic field provides greater cushioning along this edge

and the symmetry is broken across the bow. An angle µ = 30% and a somewhat higher bow

speed of vbow = 70 km s!1 provides an excellent fit. In the symmetric case, the vertical slit

profile of the (2,1) S(1) emission is relatively stronger on the northern bow wing. This

might be expected since the slit cuts through the bow nearer to the apex where the shock

reaches higher temperatures. It is, however, contrary to the observed emission profiles

shown in Fig. 3.2. Taking an oblique magnetic field, the excitation along the flanks is

no longer symmetric. The southern peak may then be stronger in the (2,1) S(1) line, as

indeed found and displayed in Fig. 3.10.

The theoretical rate at which a bow of speed vbow converts the driving energy into

heat, P, is proportional to the bow area facing the oncoming flow, the flux of kinetic

energy across the shock and a non-dimensional factor related to the aerodynamical drag.

86


These are combined into the form

P = 2$v3bowL2bow#/2 (3.3)

= 0.15 2! n2.5 " 103 +cm!3,

" ! vbow60+km s!1

,"3 ! Lbow1.7 " 1016 +cm,

"2 +L",

(3.4)

where 2 is of order unity, n is the density of hydrogen nucleons (and the mass density

is given by $ = 2.32"10!24 n [g cm!3], including 10% helium atoms). Therefore, the

derived numbers are consistent with expectations from the model which calculates the

total line cooling to be 0.17 L" for HH240A.

The mass outflow rate necessary to drive the bow can also be estimated. A somewhat

larger driving jet speed is used to obtain a twin-jet mass outflow rate of

Mout = 1.5 " 10!6#

nc2.5 " 103 +cm!3,

$ # v jet100+km s!1

,$ #

Lbow1.7 " 1016 +cm,

$2 +M" yr!1

,

(3.5)

This can be compared to the model-dependent infall rate derived by Beltran et al. (2002)

of Min = 2.6 # 8.0 " 10!5 M" yr!1 which implies that well under 10% of the inflowing

mass is ejected.

3.4.3 Modelling the HH240C image and power

Although part of the same outflow, HH240C has obvious di!erences to HH240A. No

dissociated cap is apparent as the (1,0) S(1) emission appears to originate from close to

the front of the bow. As a result, the model for this object employs a smaller and more

focused bow geometry propagating through the cloud material with a lower velocity (50

km s!1) than found for HH240A. Wide ranges of parameter space were again explored in

determining the model shown in Fig. 3.11 and described in Table 3.2.

HH 240C has a (1,0) S(1) luminosity comparable to HH240A despite the smaller scale

and speed. It was therefore deduced that the bow is moving into a denser region where

the hydrogen density is 7.0" 103 cm!3. Although surprising, this is actually supported by

87


Figure 3.11: A C-bow model for HH240C. The (1,0) S(1) emission image and flux pro-files for the (1,0) S(1) (full line) and (2,1) S(1) (dotted line). Adopting a source distanceof 460 pc gives a pixel scale of 1 pixel = 0.21##. Other parameters are fixed to those inTable 3.2.

the fact that a higher extinction is necessary for HH240C in order to explain the observed

relative line intensities from the H2 ro-vibrational energy levels (see Section 3.6).

In order to account for the asymmetry in the observed bow, a magnetic field was

introduced which is at an angle relative to the direction of motion of the bow. Referring

to Fig. 2.5, , was kept at zero and µ was set equal to 60%. Therefore, the transverse

components of the bow velocity range from being perpendicular to being parallel to the

field lines as we move along the bow surface: the emission from one side of the bow front

is enhanced and emission on the opposite side is depleted.

A value of s = 1.9 was found in order to give the bow a more focused appearance. This,

however, has the e!ect of reducing the excitation ratio as the wings become extended

and emission from the cooler regions of the bow contribute relatively more. In order

to counteract this e!ect, the fraction of ions present in the pre-shock gas is raised to

5.0" 10!5. This has the e!ect of increasing the excitation ratio to 0.133, smaller than the

measured value of 0.15 but within the estimated error range.

88


Figure 3.12: The best-fit J-type bow model for the (1,0) S(1) emission from HH240A(top) and HH240C (lower). The pixel scales are 1 pixel = 0.28## (top) and 0.21## (lower).The full parameter set is listed in Table 3.4. The model yields a (1,0) S(1) luminosityof 2.4" 10!3 L" and a (2,1) S(1)/(1,0) S(1) luminosity ratio of 0.17 for HH240A and4" 10!3 L" and a (2,1) S(1)/(1,0) S(1) luminosity ratio of 0.15 for HH240C.

3.4.4 Modelling with J-type shocks

Modeling the HH240A bow with a J-type bow shock in which the cap is dissociative and

the flanks non-dissociative was attempted. Speeds exceeding ! 50 km s!1 generate long

tails of strong (1,0) S(1) emission. Speeds of ! 40 km s!1 produce structure reminiscent of

that observed but only when combined with a relatively strong magnetic field. An oblique

field angle also improves the fit to the flux profiles.

In order to obtain a reasonable luminosity, a model with a higher density was chosen.

89


Table 3.4: Model parameters derived to fit the bows with J-type shocks.

Parameter HH 240A HH240C

Size, Lbow 1.7 " 1016 cm 1.3 " 1016 cmHDensity, n 5.0 " 103 cm!3 2.0 " 104 cm!3Molecular Fraction, f 0.2 0.3AlfvenSpeed, vA 5 kms!1 6 kms!1Magnetic Field 191 µG 458 µGIonFraction, &$ $ 10!4 $ 10!4BowVelocity, vbow 42 km s!1 42 km s!1Angle to l.o.s., 1 60% 60%ShapeParameter, s 2.0 2.0Field Angle, µ 45% 60%

!The ion fraction is not considered as a parameter in the J-bow code as ambipolar di!usion does not occurin a J-shock. For this regime to be valid (i.e. not a C-shock) the ion fraction needs to be larger than about10"4, see Smith & Brand (1990a).

Although it was di"cult to simultaneously produce an excitation as low as observed with

a su"ciently high luminosity, the best fit shown in Fig. 3.12 does approach observed val-

ues. The model yields a (1,0) S(1) luminosity of 2.4" 10!3 L" and a (2,1) S(1)/(1,0) S(1)

luminosity ratio of 0.17. Parameters for this model are listed in Table 3.4. In general, J-

type bows show high excitation unless geometrically long tails (low values of s) are taken.

This, however, generates long tails of (1,0) S(1) emission.

The general structure of HH240C can be modelled with a J-type bow, as shown in the

lower panel of Fig. 3.12. For HH240C a high magnetic field is again required to inhibit

the formation of a long tail. A high density is also essential to produce the luminosity

from such a small J-type bow. The density is 3 times higher than required for the C-type

bow. The model yields a (1,0) S(1) luminosity of 4.0" 10!3 L" and a (2,1) S(1)/(1,0) S(1)

luminosity ratio of 0.15. A lower velocity than for the HH240A J-type model is not

necessary, and a magnetic field at a large angle to the bow direction is favoured (see

Table 3.4).

The main conclusions are that HH240A corresponds exceedingly well to a C-type

bow shock model in both image and excitation. HH240C corresponds closer to a J-

type bow in excitation but the structure can be modelled by either shock physics. Quite

90


Figure 3.13: Position-velocity diagrams for the best-fit C-type bow models for HH 240A(top) and HH240C (bottom). The modelled line is the H2 (1,0) S(1). Slit positions areindicated and labelled to correspond to the observations. The bows and slits have beenrotated for display purposes. The flow axis is -75% and the slit axis is +63%. A Gaussianstandard deviation of 4.3 km s!1 was applied to match the instrumental accuracy. The yaxes in each image represent pixels (one pixel corresponds to 0.28## for HH240A and to0.21## for HH240C). The x axes in the position velocity diagrams (slits 1 – 6) representradial velocities in km s!1.

high and oblique magnetic fields are predicted. The magnetic field inferred from the H2

modelling is contained within processed outflowing gas rather than ambient molecular

cloud gas (see below).

3.5 Modelling the velocity distribution

3.5.1 C-type bows

Independent of the imaging, the derived bow shock models can be tested against the

position-velocity (P-V) data in the H2 (1,0) S(1) emission line. P-V diagrams were gener-

91


ated for the best-fit C-type models. The bow axis and slits were re-orientated in Fig. 3.13

for display purposes, maintaining the angle of 42% between the two directions. Model slit

numbers correspond to the observed slits shown in Fig. 3.1.

For the HH240A model (upper panels), the simulated P-V structure resembles the

observed P-V structure. Along Slit 1, a broad velocity width is seen with a strong leading

peak at low velocity although the observed weak extension ahead of the bow, at high

blue-shifted speeds, is not reproduced here.

A narrowing tail along the slits approaches zero velocity. Note that the observed tail

also approaches zero radial velocity, although the background cloud has a radial speed of

+ 8 km s!1 (De Vries et al., 2002). In other words, the bow moves within gas which is

already in motion with a radial component of - 8 km s!1. Given the derived orientation,

the pre-shock outflow speed is estimated to be ! 16 km s!1.

Simulated Slit 2 possesses a second strong peak located towards the back. Towards

the apex, the rear and near bow wings combine to produce an increasing width with a very

sharp edge at zero velocity. These features are also observed. However, the leading peak

is slightly redshifted in the simulated bow (since the projected leading edge is on the rear

side of the bow). This structure is not apparent in the observed bow which has a quite

broad-width leading edge.

For the HH240C model (lower panels), some of the structure is reproduced. For Slit

4, the simulated diagram has a strong peak followed by two tails separated in velocity by

about 15 km s!1 and a very extended tail. This has an overall similarity to the observed

structure but the full velocity width of the observed line, ! 80 km s!1, is much greater.

For Slit 5, the strong low-velocity peak and the twin velocity-separated wings are

similar to the observed features (although the blue wing possesses a distinct peak). For

Slit 6, two peaks are predicted, each with two linear extensions. The two linear extensions

are indeed observed but somewhat more overlapping in position. Full widths of ! 50 –

60 km s!1 are predicted, which do match the observations.

In general, much of the observed P-V structure is reproduced in the simulated bows.

However, it is clear that a non-uniform or clumpy medium, along with dynamical or

92


thermal instability is leading to fine structure and line broadening in the bows, see, for

example, Hester et al. (1998).

3.5.2 J-type bows

Corresponding P-V diagrams for the best-fit J-type models are presented in Fig. 3.14.

For HH240A, J-type bow models predict very narrow H2 lines. The near and far wings

of the bow are well separated in velocity space. This is as expected since the (1,0) S(1)

emission is not generated immediately behind the J-shock jump where the gas is relatively

hot. Instead, the emission arises from material which has been deflected, decelerated and

re-cooled down to under ! 4 000 K. The resulting structure does not resemble HH240A.

For HH240C, the two distinct velocity wings along Slits 4 and Slits 5 are hinted at

in the observations. Especially noteworthy is the convergence of the two wings in Slit 5

of Fig. 3.14 which has a corresponding structure in the observed Slit 5. Slit 6 possesses

two very distinct linear features. The observed slit 6 also possesses two linear features

although the displacement between them does not closely match the modelled structure.

The molecular breakdown speed, vd, is defined as the maximum speed of a planar

shock in which molecules survive in significant numbers. The full width of the lines

from bow shocks have a theoretical upper extent of twice the breakdown speed (Smith &

Brand, 1990b). To reach this maximum line width, however, the bow must be moving in

the plane of the sky as well as at a speed far in excess of the breakdown speed (otherwise,

the shocked gas is accelerated more towards the bow axis than transversely). At an angle

of 60% to the line of sight the maximum line width is approximately 2 vd sin 60% (Smith &

Brand, 1990b).

For J-type bows, the predicted line widths can be close to the maximum since the

emission from H2 (1,0) S(1) arises from the deflected and cooled gas. Given also the

strong magnetic field and the quite low density, a value of vd ! 35 km s!1 is found

(Smith, 1994). Therefore, full line widths can approach 55 km s!1 for the HH240 flow.

This value is consistent with that found for the simulated bows and also with some of the

observations but not the observed widths within HH240A.

93


Figure 3.14: Position-velocity diagrams for the best-fit J-type bow models for HH 240A(top) and HH240C (bottom). The modelled line is the (1,0) S(1) H2. Slit positions areindicated and labelled to correspond closely to the observations. Thus, the bows and slitshave been rotated for display purposes. The bow flow axis is at a position angle of -75%and the slit axis is +63%. A Gaussian standard deviation of 4.3 km s!1 was applied tomatch the instrumental accuracy. The y axes in each image represent pixels (one pixelcorresponds to 0.28## for HH 240A and to 0.21## for HH240C). The x axes in the positionvelocity diagrams (slits 1 – 6) represent radial velocities in km s!1.

To summarise these results, HH240A can be interpreted as a C-type bow, according

to structure, excitation and velocity distribution. On the other hand, HH 240C possesses

elements of both J and C-type shocks, neither of which on its own provides a full inter-

pretation. Predicted infrared luminosities from these bow models are listed in Table 3.5.

The major di!erences result from the higher density in the J-type model along with a

higher compression before emission lines from cooler gas (often with long wavelength)

are produced. Ro-vibrational H2 cooling dominates across the low-density C-type bow.

94


Table 3.5: Predicted infrared line fluxes from the C-type bow shock model for HH 240Aand the J-type bow model for HH240C, as defined in Tables 3.2 and 3.4, respectively.

Line Wavelength HH 240A HH240Cµm L" L"

H2 (0, 0)S(5) 6.9 2.1 " 10!2 4.7 " 10!3H2 (0, 0)S(1) 17.0 2.1 " 10!3 1.1 " 10!3[O I] 63 6.9 " 10!3 3.2 " 10!2COJ = 30 # 29 87 5.0 " 10!5 2.8 " 10!4COJ = 20 # 19 130 7.1 " 10!4 3.0 " 10!3COJ = 10 # 9 260 5.1 " 10!3 1.0 " 10!3[C I] 372 1.1 " 10!3 9.3 " 10!4

3.5.3 The HH 241 system of shocks

HH 241A possesses spatial structure similar to HH240A with two strong H2 bow flanks.

This bow appears on all 5 slits, Slits 8 – 12, appearing in Fig. 3.5 at pixel locations 1 – 25.

Speeds of +50 km s!1 are detected along the bow axis (Slit 10). Positive radial speeds of

20 – 30 km s!1 are found in the wings. There are clear departures in the overall velocity

from that found in HH240. Most significant is that there is very little emission from

between 0 and 20 km s!1 on both sides of the outflow; what emission there is could occur

from deflection by the flanks of the bows nearer to the plane of the sky.

HH 241B possesses a higher H2 velocity dispersion at its western edge (i.e positions

40 – 50 in Slits 9 and 10 of Fig. 3.5). This is the side facing the driving source and so

this can be interpreted as a reverse bow in the flow. The spatial structure provides some

support although the wings do not appear to be well developed.

3.6 Column density distributions

3.6.1 Extinction modelling

A fully consistent model must account for the observed emission fluxes from various

other molecular hydrogen lines. Many fluxes, originating from several vibrational levels,

95


have been measured by Nisini et al. (2002a). The H2 column densities in the upper energy

levels T j of the transitions required to produce these fluxes were calculated. The derived

columns can be directly modelled in terms of an excitation temperature. The columns

range over several orders of magnitude although individual error bars are under 20% for

many lines. This is mainly because the gas temperature is in the range 2 000 – 3 000K

whereas upper energy levels range from 6 000K to above 20 000K. Therefore, to make

the error bars visible, each column is divided by the predicted column from molecular gas

taken to be at a fixed 2 000K, a method first employed by Brand et al. (1988). The result-

ing quantities are the Column Density Ratios (CDRs) for which the strong exponential

dependence of the columns on the upper energy level has been removed. For modeling

convenience, the CDRs are expressed relative to the CDR for the upper level, V = 1, J = 3

of the (1,0) S(1) line at 6 956K.

The first factor to constrain with a CDR diagram is the extinction to the bow shocks

caused by dusty gas along the line of sight. Extinction acts di!erentially, to mainly reduce

the observed fluxes from shorter wavelengths. Ideally, lines originating from the same

upper energy level but at di!erent wavelengths would be employed for which the intrinsic

flux ratio is a well-determined physical constant. However, the only pairs of lines with

this property in the data set involve (1,0) Q-branch lines with wavelengths > 2.4 µm. The

fluxes of these lines are notoriously unreliable from ground-based observations.

The extinction is estimated by applying physical constraints, following the method de-

scribed by Smith et al. (2003a). CDR diagrams for HH240C are shown in Fig. 3.15. The

data in the panels di!er by the amount of imposed foreground extinction. For no extinc-

tion (top panel) the data points possess a wide scatter transverse to the overall trend. The

extinction is then gradually increased until the tightest correlation is found, checking for

consistency with the non-LTE conditions expected at densities near 104 cm!3. HH 240C is

thus constrained to lie behind 1± 0.2 mag of K-band extinction (middle and lower panels).

Adopting an extinction law of the form "!1.7, this is su"cient to modify the excitation de-

rived from the (2,1)/(1,0) flux ratio by a small amount, decreasing the excitation by about

10%.

96


Figure 3.15: Column Density Ratio diagrams for HH240C evaluated from line fluxespresented by Nisini et al. (2002a). The top panel presents the data assuming no extinction.The symbols represent H2 (1,0) (squares), (2,1) and (2,0) (crosses), the (3,2) and (3,1)(triangular) data points. The faint squares represent (1,0)Q branch measurements. Themiddle panel demonstrates the much better intrinsic consistency when one magnitude ofK-band extinction is applied. Superimposed is the C-type best-fit model lines with threevibrational levels, solid (first), dotted (second) and dot-dashed (third) represented. Thelower panel displays the corresponding best-fit J-type bow.

97


Figure 3.16: Column Density Ratio diagram for HH240A evaluated from line fluxespresented by Nisini et al. (2002a). Details are as described in Fig. 3.15. The model linesare taken from the best-fit C-type bow model. The meaning of the symbols is given inFig.3.15.

A similar analysis for HH 240A demonstrates that very little extinction is permitted

(see Fig. 3.16). An extinction (AK) of 0.28± 0.2 is estimated from the CDR data. This

value is consistent with the low extinction found by Nisini et al. (2002a) from the near

infrared [Fe II] line analysis. These [Fe II] lines were not detected in HH240C so it is not

possible to check for consistency. The non-detection is probably consistent with the low

speed of HH240C.

For HH 241A and HH 241B, there is also su"cient data to constrain the extinction. K-

band extinctions of 0.25±0.15 (HH 241A) and 0.3±0.1 (HH 241B) are found. Therefore,

high extinctions are excluded even though this side of the outflow is moving away from

the observer. Nisini et al. (2002a) derive a K-band extinction of 0.45±0.1 from the [Fe II]

line analysis of HH 241A, consistent with the H2 CDR range here.

3.6.2 Bow shock models

The CDR plots can be compared with the column density ratios predicted by the bow

shock models. HH240C is overplotted with the best-fit C-type model predictions in

Fig. 3.15. Note that the three lines correspond to the first three vibrational levels, with

the solid line modelling the (1,0) (square) data points, the dotted line modelling the (2,1)

(crosses) data points and the dot-dash linemodelling the (3,2) (triangular) data points. The

98


Figure 3.17: Column Density Ratio diagram for HH240A evaluated from line fluxespresented by Nisini et al. (2002a). The model lines are taken from the best-fit J-type bowmodel. The meaning of the symbols is given in Fig.3.15.

agreement is quite good although there is a general tendency to underpredict the higher

level excitation. Note also the large scatter in the Q-branch data points, represented by

faint square symbols, while the discrepant (1,0) S(3) line flux at T j = 8 000K is definitely

as a result of measurement error, lying on the far opposite edge of the K-band window.

The J-type bow model is also displayed in the lower panel of Fig. 3.15. The major

di!erence is that the vibrational levels are much closer to LTE. This is a consequence of

the higher density as well as the nature of a J-type shock. Although the J-type model

better fits the higher vibrational levels, neither model can be dismissed.

HH 240A is fitted with the best-fit C-type model in Fig. 3.16. The C-type bow model

provides an excellent fit to all three vibrational levels. This provides yet more support for

this model for HH240A. In contrast, the J-type bow model CDRs displayed in Fig. 3.17

overpredicts emission from the (3,2) lines with the predicted columns being much closer

to LTE.

3.7 CO structure

CO imaging and spectroscopy in the J= (1,0) line of the L1634 outflow have been pre-

sented by Lee et al. (2000a) (see Appendix C). They demonstrated that cold gas in motion

is associated with HH240A, where it curves around with the H2 shape.

99


Figure 3.18: CO J=(1,0) model generated image with pixel size of 1.24## from the best-fitbow model for HH 240A (left). The corresponding position velocity diagram (right) istaken from a horizontal slit.

For comparison, the predicted CO image and P-V diagram employing the C-bow

model for HH 240A (discussed above) are displayed in Fig. 3.18. The model includes

the non-LTE approximation of McKee et al. (1982) in calculating the CO emission. Note

the large image scale in Fig. 3.18 (1 pixel = 1.24## whereas the pixel scales for the HH240

A and C images are 0.28## and 0.21## respectively) employed in which a long CO tail is

exhibited. The two panels are comparable to the CO map and P-V diagrams of Lee et al.

(2000a), where the large tailed bow was found to be associated with HH 240A. More blue

emission, however, is observed to be associated with the southern wing, not predicted

here.

The main observed features on the CO P-V diagram, Fig. 8 in Lee et al. (2000a),

are also reproduced with the C-shock model. The model bow, however, does not predict

the observed strong red peak at +1 km s!1 although a red-shifted extension feature is

simulated.

Most remarkable are the radial speeds of the gas components near the HH 240A and

HH 241 bow shocks. The molecular cloud radial speed is +8 km s!1. One would expect

that the CO gas would also show the flux peak near ! +8 km s!1, as is indeed found.

However, the H2 radial speeds associated with the HH240 bows is almost exclusively <

0 km s!1 while that associated with the HH241 bows is almost exclusively > +20 km s!1.

100


According to the simulated P-V diagrams, the radial speed ahead of both HH240A and

HH240C, as given by the tail emission as well as the modelling of the leading edge,

should be the same for both the H2 and CO, contrary to what is observed.

The resolution of this problem is probably that the accelerated CO gas and the excited

H2 gas possess distinctly di!erent origins. The existence of twin outflow channels are

required which lie within the static background cloud. The mean outward speed in the two

oppositely-directed channels is ! 20 km s!1, yielding radial speeds relative to the cloud

of ± 10 km s!1. Bow shocks begin to propagate within these channels at typical speeds

of ± 80 – 90 km s!1 relative to the cloud, yielding bow speeds ± 60 – 70 km s!1 relative

to the channel. These bows produce the H2 emission. The CO, emission, however, is

predominantly produced from the ambient cloud immediately surrounding the channels,

set in motion by weak expanding shock fronts prompted by the outflow and the bow shock

HH240A, in particular.

No bow shock beyond HH240A is detectable in CO. One explanation would be that

the CO is depleted from the cloud in this region. Although a higher density is derived,

from both the H2 luminosity and the H2 column ratios, the density would appear insuf-

ficient to cause a high depletion. The explanation favoured here is that the dense gas is

distributed within sheets and clumps occupying a small fraction of the volume. Since

the CO emission traces all the gas set in motion, whereas the H2 emission traces just the

presently shocked gas, the CO emission may not be detectable. The high density and

magnetic field would be consistent with the HH240C bow now entering one such clump.

The clump has been formed by the passage of an earlier shock which has raised both the

magnetic field and the Alfven speed during the cooling and compression. Upon entering,

the bow is transforming from J-type to C-type due to a large drop in ionisation fraction.

The time scale for the transformation is estimated to be Ln/vA where Ln is the thickness

of a C-shock (Smith & Mac Low, 1997). The thickness is of order & 1015 [cm] /n where &

is the ion fraction. Taking values from Table 3.2 yields a timescale of ! 4 " 109 s which

is of the same order as the bow travel time, d/vbow ! 3 " 109 s, where d is taken as being

equivalent to the model bow size scale Lbow = 1.3 " 1016 cm. Therefore, it is very likely

101


that we would capture a shock undergoing the neutral transformation stage , see Smith &

Mac Low (1997).

This picture then implies that there is a cloud edge near HH240A beyond which there

is only fragmentary but compressed dense cloud material. This material may be the result

of the sweeping e!ect of previous bow shock fronts.

The above discussion leads to the suggestion that, while HH240A is almost certainly

a C-shock, HH 240C is a J-shock with a developing magnetic precursor. The contrasting

shock physics explains the contrasting H2 vibrational excitation.

3.8 Optical structure

Atomic emission lines have been studied in the optical and the near-infrared. Measure-

ments of [O III] lines imply high shock speeds near HH240A. In contrast, [S II] lines

suggest low speeds (Bohigas et al., 1993). The contrasting speeds could be reconciled by

introducing a very high speed bow shock in which the [S II] is produced from the highly

oblique bow wings. Bohigas et al. (1993) suggest a shock speed of 260 km s!1, based on

a specific [O III] line ratio. This is, however, inconsistent with the proper motions and the

location of the H2 emission just o!set from the apex. This then suggests that a large frac-

tion of the optical emission arises from the impact of a fast jet which drives the slow bow

shock through the outflow. The structure and location of the optical emission is actually

consistent with three components: a slender jet (seen in H(), a compact Mach disk (seen

in [O I] and [N II]) located at HH 240A, and the bow shock (seen in [S II] and H2), all

presented by Bohigas et al. (1993). The approximate locations of the [S II] and H2 are also

illustrated in Fig. 3.19. It is important to note that the bow shock code does not consider

these components, but only emission which derives from the cooling layer behind the

ambient shock where most of H2 emission is generated. The higher excitation conditions

required for the optical emission have the e!ect of dissociating the H2 molecules.

The [O III](4959Å+5007Å) / H. flux ratio in HH240A is 0.3 (The line strengths were

corrected for an extinction in the visible of AV = 1.65). This is consistent with a planar

102


Figure 3.19: An [S II] 6 729Å optical image of HH240 kindly provided by J. Bohigas,as described in Bohigas et al. (1993), roughly superimposed as a contour image over theH2 (1,0) S(1) image (colour-scale as in Fig. 3.1). Contour levels increase logarithmicallyand represent 0.3, 0.8, 1.9, 4.8, 12, 30 and 76% of the maximum value. The alignmentbetween the data sets was done manually. Nevertheless, the figure demonstrates thatatomic and molecular emission is associated with each HH knot.

shock of speed 90 – 100 km s!1 according to Table 1 of Hartigan et al. (1987). In the

near-infrared, HH 240A is detected in lines of [C I] and [S II]. In contrast, other lines

dominated by emission from the proposed Mach disk, such as the [O I] 6 300Å and [N II]

lines at 5 755Å, 6 548Å and 6 584Å, require a shock speed of 200 – 300 km s!1. This

gas cools slowly after the Mach disk shock, with a distance to cool down to 1 000K of

! 1.3 " 1016 cm for a pre-shock (jet) density of 100 cm!3 (Hartigan et al., 1987). This is

equal to the bow size. Therefore, the S II and H( emission distributions should be quite

extended, as observed. Optical spectroscopy should confirm this set up, in which a light

and fast atomic jet pushes through a dense molecular medium.

Fig. 3.19 shows that weak optical [S II] line emission also arises from locations close

to the H2 emission from HH240B, C and D (Bohigas et al., 1993) (not only HH240A is

visible in the optical). It is intriguing that optical emission is detectable from HH240C

given the K-band extinction of 1 mag, which implies a red band extinction of AR ! 7 mag

(Rieke & Lebofsky, 1985). The optical emission appears curved, consistent with an align-

ment with the H2 bow. Note, however, that the images in Fig. 3.19 have been aligned

103


according to the HH240A peaks in the absence of precise spatial information. One inter-

pretation is that the optical emission arises from a portion of the bow shock not subject

to high red extinction. This could be consistent with the model for HH 240C in which the

ambient medium is highly inhomogeneous with dense material possessing a small volume

filling factor. The predicted column of gas through the bow, however, is not su"cient to

provide the extinction. That is, the extinction should be caused primarily by foreground

L1634 cloud material.

It thus appears that the optical emission fromHH240B, C and D has still been detected

despite quite high extinction. This is consistent with the non-detection of the [Fe II]

0.947µm line in these objects (Nisini et al., 2002a), suggesting that the intrinsic emission,

even in the optical, is not strong and located at the bow shocks. These bows are probably

not jet driven but are drifting along, still pushed by the decelerating remnants of jet-swept

clumps.

3.9 Conclusions

The structure of the HH240/HH 241 outflow in L1634 has been examined. Images of the

HH240 bow shocks in (1,0) and (2,1) ro-vibrational H2 emission lines have revealed the

excitation properties. Spectroscopy has provided detailed information on the bow shock

dynamics.

In an attempt to extract the physical and dynamical parameters, the bows have been

modeled as steady-state curved shock fronts. Several parameters were varied, including

the bow physics, bow speed, bow shape, magnetic field and density.

The derived models were then compared with published data on H2 line fluxes, to

determine column densities, and CO imaging and spectroscopy. From this vast body of

data, several conclusions have been reached.

• The HH240 bow shocks propagate within an outflow medium with a radial pro-

jected speed of -10 km s!1 relative to the cloud, implying an intrinsic outflow speed

104


of 20 km s!1.

• The opposing bow shocks in HH 241 propagate within an outflow medium with

a radial projected speed of +10 km s!1 relative to the cloud, implying an intrinsic

outflow speed of 20 km s!1.

• The CO outflow is associated with the stationary cloud material i.e. no high radial

speed is detected. Therefore, the gas set in motion, accelerated by just a few km s!1

on both sides of the outflow, is molecular cloud material.

• HH240A corresponds very closely to a C-type bow. Several model parameters

can be well constrained by the combined data sets including the orientation, bow

velocity, density, ion fraction and intrinsic bow shape.

• A quite high magnetic field, as indicated by the Alfven speed, implies that the

material being shocked is the outflow itself and not undisturbed cloud material since

the cloud would not be in virial equilibrium with the implied magnetic pressure.

This is consistent with the pre-shock forward motion of the H2 gas.

• The H2 emission observed is associated with partly atomic gas. The distribution

and excitation of shock-excited atomic gas suggests that a fast atomic jet impacts

and drives along HH240A.

• HH240C has higher vibrational excitation, higher pre-shock density and higher ex-

tinction than HH240A. Yet there is no associated CO outflow component. It is

therefore suggested that the HH240C bow is now entering a denser region. While

H2 emission is abruptly generated by the shock, su"cient CO gas has not yet ac-

cumulated. Furthermore, it is best modelled as a J-type bow undergoing transition

into a C-type bow as it enters the denser region.

The moderate molecular fractions found suggest that the outflow has partly dissoci-

ated molecules in previous outburst episodes. Molecules may have partly reformed in

105


between episodes. The timescale for reformation at a density of 104 cm!3, assuming

the gas cools to 100K is ! 1.6 " 105 yr. In comparison the outflow dynamical time is

! 0.42 pc / 60 km s!1 = 7 " 103 yr. This implies that only a few per cent reformation may

occur unless reformation occurs within dense clumps. More probably, most of the molec-

ular gas in the outflow has not been previously dissociated but, instead, has passed through

bow wings which sweep through most of the outflow without destroying the molecules.

The combination of the best-fit 70 km s!1 bow with a 20 km s!1 pre-shock outflow

speed (given by the radial velocity data) yields a total speed of 90 km s!1 relative to the

source. This is in excellent agreement with the early astrometric proper motion studies

by Jones et al. (1984) of the optical emission associated with HH240A which yielded a

proper motion of 90 km s!1, but probably with large errors in magnitude and direction.

The fractional ionisation & derived for the HH240AC-type bow shock is 1"10!5. This

is well above the predicted ion fraction for cosmic-ray induced ionisation at the density

of 2.5 " 103 cm!3 of & = 2 " 10!7. We are, however, close to the densities appropriate for

di!use clouds in which external UV radiation penetrates and maintains a high fractional

ionisation of the metals. A relationship of the form & ! 10!3n!1/210!0.5AV within the range

of partially optically thick clouds exposed to the Galactic UV field is estimated. Given

the low extinction of AV = 2 – 3 found here and by Nisini et al. (2002a), su"cient UV

flux penetrates to maintain a fractional ionisation & of order 10!5. The origin of the high

ion fraction which has maintained HH240C as a J-type shock (& $ 10!4) is not clear.

A global model for the outflow is suggested by the accumulated conclusions, as fol-

lows. Twin jets have driven out and pushed aside the background cloud. The jets are

slowly precessing and have so produced a bipolar outflow which occupies two channels

with mean outflow speeds of 20 km s!1. Furthermore, the jets are episodic, and so form

and drive each bow shock for a limited time span after which the bow drifts until the as-

sociated momentum is drained. The question for theorists now is whether such an MHD

model scenario can reproduce the observed spatial and velocity characteristics.

The conclusions can be tested through (1) infrared predictions and (2) numerical sim-

ulations. Predicted infrared and far-infrared line luminosities are listed in Table 3.5. Many

106


of the associated fluxes should be detectable from space-borne telescopes (JWST, SOFIA,

SIRTF) in the coming years.

Numerical simulations in three dimensions are necessary to simulate precessing jets.

Spectroscopic predictions have been presented from such hydrodynamic simulations for

atomic flows (Masciadri et al., 2002) and molecular flows (Smith et al., 1997b; Volker

et al., 1999). Based on the Smith et al. (1997b) simulations, a jet-driven bow shock model

for HH 240/241 was advanced by Lee et al. (2000a). A new programme of molecular

simulations is in progress within which strong support for the suggested global model is

found (see Rosen & Smith (2003); Smith & Rosen (2005) and Section 1.3.4).

107

Chapter 4

The HH211 Protostellar Outflow

108

Chapter 4. The HH211 Protostellar Outflow

Figure 4.1: HH211 imaged at 2.122 µm by MAGIC at the 3.5 m telescope on CalarAlto. O!sets are measured from the position of the driving source HH211-mm at positionR.A.(2000) = 03h 43m 56.7s, Dec(2000) = +32% 00# 50.3## which is marked by the cross.The colour-scale is logarithmic with a minimum value of 1.6 " 10!10Wm!2 arcsec!2 (justabove the noise level) and maximum value of 500 " 10!10 Wm!2 arcsec!2.

4.1 Introduction

HH211 is a bipolar molecular outflow which was discovered by McCaughrean et al.

(1994). The outflow imaged at 2.122 µm is shown in Fig. 4.1. It lies near the young

stellar cluster IC 348 IR in the Perseus dark cloud complex at an estimated distance of

315 pc (Herbig, 1998). The outflow is bilaterally symmetric and highly collimated with

an aspect ratio of ! 15:1. The total extent of the outflow is 106## which is 0.16 pc at the

adopted distance. A H2 (1,0) S(1) wide-field survey of the IC 348 cluster was carried out

by Eislo!el et al. (2003) covering a 6.8# " 6.8# region; no HH 211 outflow remnants were

detected beyond the outer knots. This makes it one of the smaller outflows, which sug-

109


gests that it may also be one of the youngest since the average length within an unbiased

sample of Class 0/I jets was found to be 0.6 – 0.8 pc (Stanke, 2003).

The conclusion that HH 211 is a jet driven outflow with a timescale of order 1000

years was derived from interferometric CO observations (Gueth & Guilloteau, 1999),

which confirms it as one of the youngest infrared outflows to be discovered. Although

the outflow lobes are visible in both blue-shifted and red-shifted CO emission, a small

inclination angle to the plane of the sky is suggested by (i) the lack of strong di!erential

extinction in the H2 brightness distribution, (ii) the high degree of separation of the blue

and red CO lobes and (iii) the relatively small radial components of the SiO and H2 flow

speeds (Chandler & Richer, 2001; Salas et al., 2003).

The central engine driving the outflow is HH211-mm, a low-mass protostar with a

bolometric luminosity of 3.6 L" and bolometric temperature of 33K. It is surrounded by

a ! 0.8 M" dust condensation (Froebrich, 2005)1. Since 4.6 per cent of the bolometric

luminosity is attributed to the submillimeter luminosity Lsmm, HH 211-mm is classified as

a Class 0 type protostar.

A compact and collimated SiO jet extends in both flow directions out to a projected

distance of 20## from the central source (Chandler & Richer, 1997, 2001). This is also

another indication of the Class O nature of the source (Gibb et al., 2004b). The clumpy na-

ture of the observed SiO emission suggests a shock origin resulting from a time-dependent

jet velocity. Nisini et al. (2002b) observed HH 211 in SiO lines originating from high ro-

tational energy levels and deduced a high jet density of nH2 ! 2 – 5 " 106 cm!3 and gas

temperature - 250K. However, no SiO emission is detected beyond 20## where the H2(1,0) S(1) emission is found suggesting that the conditions, such as shock velocity and

pre-shock density, vary considerably along the flow direction.

Imaging of [Fe II] emission in the H-band at 1.644 µm has recently played a major

role in our understanding of shocked outflows (see Reipurth et al. (2000) for a summary).

Where [Fe II] emission is observed it traces the fast (> 50 km s!1) and dissociative shocks.

Combined with K-band imaging of H2 rotational-vibrational lines, which trace less ex-1See also http://www.dias.ie/protostars/

110


treme shock conditions, important information about outflow excitation may be gathered,

see e.g. Khanzadyan et al. (2004).

Previous studies employing bow-shock models have focused on larger, more evolved

systems (Eislo!el et al., 2000; Smith et al., 2003b). HH 211 provides us with the unique

opportunity of studying what has been deemed as an exceptionally young outflow cover-

ing a small spatial extent. New high resolution images of H2 and [Fe II] lines and K-band

spectroscopy of the outflow are presented in Section 4.3. The visible impact regions are

anlysed in the near-infrared. Section 4.4 presents steady-state C-type bow-shock models

which are used to interpret the remarkable set of bows propagating through a changing

environment along the western outflow. The issues which have arisen from this set of

data are discussed in Section 4.5 before concluding and pooling the findings together in

conjunction with previous studies to suggest a global outflow mechanism for HH 211 in

Section 4.6.

4.2 Observations and data reduction

4.2.1 KSPEC observations

Near-infrared spectra covering the 1 – 2.5 µm region in medium resolution were obtained

in the period 26 – 29 August 1996 with the K-band spectrograph (KSPEC) at the Uni-

versity of Hawaii 2.2–m telescope. This cross dispersed Echelle spectrograph is equipped

with a HAWAII 1 024" 1 024 detector array and optimised for 2.2 µm. Observations were

performed at two bright H2 emission locations. The 0.96## width slits ran in an east-west

direction passing through knots f and d in the west and through knots i and j in the east

(positions are indicated in Fig. 4.2). Data reduction, including flatfielding, sky-subtraction

and extraction of the spectra, was performed using the routines of ESO–MIDAS (Euro-

pean Southern Observatory – Munich Image Data Analysis System). An absolute cali-

bration of the fluxes was not possible due to non-photometric weather conditions (light

cirrus clouds). Wavelength calibration was performed using OH-night-sky emission lines

and the tables of Rousselot et al. (2000). The results are presented in Table 4.1. Note

111


that fainter emission lines are detected in knots i and j due to the stronger emission here

compared to knot d (see Table 4.2). These data (in reduced form) were kindly provided

by Dirk Froebrich (Dublin Institute of Advanced Studies).

Table 4.1: KSPEC relative fluxes. For both slit positions, the measured fluxes lie abovethe continuum and are presented relative to the H2 (1,0) S(1) line flux. Three observationswere carried out at each slit location. The relative fluxes have been averaged and thespread in values is quoted in brackets as an error estimate.

Line "(µm) east west

(1,0) S(9) 1.687 0.02 (0.01) –(1,0) S(7) 1.748 0.12 (0.01) –(1,0) S(6) 1.788 0.07 (0.01) –(1,0) S(5) 1.835 0.62 (0.04) –(1,0) S(4) 1.891 0.20 (0.01) –(1,0) S(2) 2.033 0.36 (0.01) 0.30 (0.05)(3,2) S(5) 2.065 0.03 (0.01) –(2,1) S(3) 2.073 0.10 (0.01) 0.18 (0.07)(1,0) S(1) 2.121 1.00 (0.05) 1.00 (0.05)(3,2) S(4) 2.127 0.02 (0.01) –(2,1) S(2) 2.154 0.05 (0.01) –(3,2) S(3) 2.201 0.03 (0.01) –(1,0) S(0) 2.223 0.25 (0.01) 0.31 (0.02)(2,1) S(1) 2.247 0.13 (0.01) 0.17 (0.06)(2,1) S(0) 2.355 0.03 (0.01) –(3,2) S(1) 2.386 0.03 (0.01) –(1,0) Q(1) 2.406 0.96 (0.05) 1.25 (0.17)(1,0) Q(2) 2.413 0.38 (0.05) 0.54 (0.11)(1,0) Q(3) 2.423 0.95 (0.05) 1.13 (0.05)(1,0) Q(4) 2.437 0.33 (0.04) 0.41 (0.15)(1,0) Q(6) 2.475 0.19 (0.06) –(1,0) Q(7) 2.499 0.43 (0.03) –

4.2.2 MAGIC observations

The NIR images were taken in November 1995 at the 3.5–m telescope on Calar Alto

using the MPI fur Astronomie General-Purpose Infrared Camera (MAGIC) (Herbst et al.,

1993) in its high resolution mode (0.32## per pixel). Images were obtained using narrow

band filters centered on the H2 (1,0) S(1) emission line at 2.122 µm, the (2,1) S(1) line

at 2.248 µm, the (3,2) S(3) line at 2.201 µm and on the nearby continuum at 2.140 µm.

112


The per pixel integration time was 1740 seconds. Seeing throughout the observations

was ! 0.9## except for the 2.14 µm image where it is ! 1.8##. The narrow-band image

containing the (1,0) S(1) line (Fig. 4.1) has been previously published in Eislo!el et al.

(2003). These data (as reduced data arrays in FITS format) were kindly provided by

Dirk Froebrich (Dublin Institute of Advanced Studies) and Jochen Eislo!el (Thuringer

Landessternwarte Tautenberg).

The data could not be accurately flux calibrated due to non-photometric conditions.

The total integrated H2 (1,0) S(1) flux from the entire outflow has been previously mea-

sured to be 1.0" 10!15 W m!2 by McCaughrean et al. (1994) which agrees with the flux

calibration found for the (1,0) S(1) image presented here. A calibration factor for each of

the narrow band images was determined according to the (1,0) S(1) image by assuming

that the average integrated flux from several bright unsaturated field-of-view stars should

be similar in each filter. This should be the case because each filter FWHM is equal to

0.02 µm and the spectral energy distribution (SED) is likely to be relatively flat on aver-

age between 2.122 µm and 2.248 µm. Although the accuracy of this method is uncertain,

confidence is gained due to the fact that the features containing large amounts of contin-

uum emission (such as knot-g, see Table 4.2) show similar levels of flux at 2.248 µm,

2.201 µm and 2.14 µm (continuum image) where the H2 line emission contribution, from

higher vibrational levels, should be weak.

4.2.3 UFTI observations

Further NIR observations of HH211 were carried out on December 12th 2000 (UT) at

the U.K. Infrared Telescope UKIRT using the near-infrared Fast Track Imager UFTI,

see Roche et al. (2003). The camera is equipped with a Rockwell Hawaii 1024" 1024

HgCdTe array which has a plate scale of 0.091## per pixel and provides a total field of view

of 92.9## " 92.9##. The observations were carried out by Chris Davis (Joint Astronomy

Centre, Hawaii) and kindly provided (in raw format).

Images in the [Fe II] 4D7/2 – 4F9/2 transition were obtained using a narrow-band filter

centered on " = 1.644 µm with %" (FWHM) = 0.016 µm. The outflow was also imaged

113


using the broad-band K[98] filter centered on " = 2.20 µm with %" (FWHM) = 0.34 µm.

Seeing throughout the observations was ! 0.8##. Images in each filter were obtained fol-

lowing a nine-point jitter pattern to cover the entire outflow.

Standard reduction techniques were employed (using the Starlink packages CCD-

PACK and KAPPA) including bad-pixel masking, sky subtraction and flat-field creation

(from the jittered source frames themselves). The image o!sets were registered according

to the positions of common stars in overlapping regions and then mosaicked. The observa-

tions were conducted under photometric conditions, so the faint standard FS 11 (spectral

type A3 and H-band magnitude 11.267 mag – Hawarden et al. (2001)) was also observed

and used to flux calibrate the [Fe II] image. The final images were binned to a pixel size

of 0.36## to increase the signal to noise ratio without compromising the resolution.

4.3 Results

Fig. 4.2 displays the HH 211 outflow in the K-band between 2.03 µm and 2.37 µm which

contains all the K-band line emission as well as a large proportion of continuum emission.

The principal knots have been labeled as in McCaughrean et al. (1994). The features

lying at the end of each outflow are stars, almost perfectly aligned with the outflow axis

by coincidence.

The H2 (2,1) S(1) image is displayed in Fig. 4.3. The continuum at 2.14 µm has been

subtracted in order to indicate locations of pure (2,1) S(1) emission (grey-scale). Contours

of the non continuum subtracted image are also displayed in order to indicate the extent

of the continuum emission at 2.248 µm. The line emission is produced from an excitation

level which is 12 550K above the ground state whereas the (1,0) S(1) arises from 6 953K.

Therefore, it is expected to highlight the hotter parts of molecular shocks. The western

outflow shows particularly interesting structures which can be described as a series of

bow shocks propagating along the outflow away from the source. Bows de and bc display

a common asymmetric structure: the lower bow wing is approximately 1.5 times brighter

than the upper wing. This asymmetry is interpreted here as due to a misalignment of the

114


Figure 4.2: Broad-band K image of HH211 which covers wavelengths between 2.03 µmand 2.37 µm. Features are labeled according to the nomenclature of McCaughreanet al. (1994). The exciting source HH211-mm at position R.A.(2000) = 03h 43m 56.7s,Dec(2000) = +32% 00# 50.3## (Avila et al., 2001) is indicated by the cross. KSPEC spec-troscopic slit positions are indicated by the dotted lines. The colour-scale is logarithmicwith a minimum value of 0.5 " 10!19 W m!2 arcsec!2 and maximum value of 400 "10!19Wm!2 arcsec!2. The contour levels increase logarithmically and are at 1.4, 2.5, 0.7,5.0, 20.0, 39.8, 79.4, 125.9 and 251.2 " 10!19 W m!2 arcsec!2. Note that the star in thesouth-west of this image (and following images) has been masked for display purposes.

magnetic field with the flow through which the bow shock configurations with C-type

flanks are propagating (in Section 4.4).

Emission detected at 1.644µm is displayed in Fig. 4.4. Most of the emission detected

here is attributed to the high level of continuum flux, as is seen in the K-band (Fig. 4.2).

Steeply rising above this continuum level are several concentrated [Fe II] emission con-

densations, labeled 1 – 3, one of which forms part of a well defined bow-shock, bow-de.

The existence of a band of continuum emission which extends along the western outflow

is confirmed. It becomes visible 5## from the driving source and maintains a relatively

constant flux out to 17## from the source. Eislo!el et al. (2003) suggest that this con-

tinuum is scattered radiation from HH211-mm which opens the possibility of indirectly

obtaining a spectrum of the outflow source. The band of continuum is prominent in the

115


Figure 4.3: HH211 at 2.248 µm. The grey-scale is the continuum subtracted image show-ing only the (2,1) S(1) line emission. Overlaid are contours representing the non contin-uum subtracted image. Thus the contours nearer the source trace predominantly scatteredlight while the contours further out mostly trace compact, line-emission features. Thecontour levels, which are scaled logarithmically, are at 0.22, 0.44, 0.87, 1.74, 3.47 "10!18 W m!2 arcsec!2. The colour-scale is logarithmic with a minimum value of 0.16 "10!18 Wm!2 arcsec!2 and maximum value of 50.12 " 10!18 Wm!2 arcsec!2.

K-band as well as at 1.644 µm.

The photometric results for knots a – j are listed in Table 4.2. Knots d,e and b,c are

interpreted as bow-shock components and are labeled as bow-de and bow-bc. The im-

plications of these fluxes is briefly discussed. The eastern outflow is ! 1.5 times brighter

than the western outflow. However, the cause of this di!erence is not necessarily due to an

unequal jet power output as Giannini et al. (2001) detected similar levels of OI 63 µm in

both lobes (1.02 L" in the eastern flow and 0.94L" in western flow). This line is relatively

una!ected by extinction and represents the main cooling channel in the post-shocked gas.

The di!erence in flux measurements using 8## apertures placed at various locations on the

sky background were used to estimate the 10 errors in determining the flux for the knots

in each image. Most of the emission in the (3,2) S(3) image is actually continuum emis-

sion except possibly for bow-de. Interestingly, the fluxes at 1.644 µm are also comparable

to the continuum fluxes. This implies that the extinction corrected continuum fluxes are

116


Figure 4.4: HH211 at 1.644 µm. The grey-scale and contours both trace the [Fe II] lineplus continuum emission. Consequently, most of the distributed flux can be attributed tocontinuum emission, although some concentrated condensations of [Fe II] line emissionare observed. These are labelled 1 – 3. The logarithmically scaled contours show theflux at 0.63, 1.0, 1.58, 2.51, 3.98, 6.31 " 10!19 W m!2 arcsec!2. The colour-scale islogarithmic with a minimum value of 0.30 " 10!19 W m!2 arcsec!2 and maximum valueof 39.81 " 10!19 Wm!2 arcsec!2.

2 – 5 times brighter at 1.644 µm than at 2.14 µm taking into consideration the higher

extinction (AH & 1.6 AK), the range of extinctions explored (see below and Section 4.5),

and that the 1.644 µm filter width is 25% narrower than the 2.14 µm filter. The (2,1) S(1)

/ (1,0) S(1) ratios are calculated with the continuum subtracted. The error propagation

results in very large errors at locations where the continuum forms a large fraction of the

H2 emission.

From the KSPEC data, several pieces of information can be extracted. The di!erential

extinction between two transition lines (in magnitudes) can be determined using

% = 2.5 log#F1"1g2Z2F2"2g1Z1

$(4.1)

where "1 and "2 are the transition wavelengths, F1 and F2 are the relative fluxes, g1 and g2

are the upper level degeneracies, and Z1 and Z2 are the spontaneous electric quadrupole

117

Chapter

4.TheHH211

ProtostellarOutflow

Table 4.2: Photometric results for HH211. The flux in units of 10!18Wm!2 is measured over the indicated circular apertures. Note that themeasurements were made from images which are not continuum subtracted because of the low S/N of the continuum image. To infer the lineemission fluxes the continuum values$ need to be subtracted. The (2,1) S(1)/(1,0) S(1) (labeled 2/1) ratios have been determined after subtractingthe 2.14 µm continuum emission. In the case of knot g the (2,1) S(1) flux is equal to the continuum flux so no ratio was derived.

Knot aperture (1,0) S(1)† (2,1) S(1)† (3,2) S(3)† 2.14 µm Cont.†$ Broad-band K‡ [FeII] 1.644µm† 2/1 ratio

HH 211-west 57## 413 61 34 42 1285 28 0.05 (0.04)HH 211-east 42## 575 98 63 55 2197 41 0.08 (0.03)bow-a 5.3## 7.2 0.6 no det. no det. 9 no det. 0.08 (0.04)bow-bc 7.7## 32.0 2.3 no det. no det. 65 no det. 0.07 (0.02)bow-de 10.1## 155.5 18.1 7.3 3.1 335 11.8 0.09 (0.02)

b 4.9## 19.3 1.5 no det. no det. 41 no det. 0.08 (0.02)c 4.9## 11.2 0.9 no det. no det. 21 no det. 0.08 (0.03)d 6.0## 89.6 10.2 4.0 1.9 192 6.1 0.09 (0.03)e 6.0## 57.5 7.9 3.3 1.3 131 4.8 0.12 (0.03)f 10.1## 157.2 19.3 9.1 8.9 395 9.0 0.07 (0.04)g 10.1## 41.9 20.6 20.6 19.6 380 14.3 –h 10.1## 60.3 9.8 5.1 4.7 190 4.6 0.09 (0.08)ij 17.9## 458.3 54.3 27.9 24.6 1364 25.0 0.07 (0.03)

† As an indication of the error, the background 1! flux variations over an 8 ## aperture (placed at various background locations) are: 2.8 for H2 (1,0) S(1); 0.2 for H2 (2,1) S(1);0.7 for H2 (3,2) S(3); 1.1 for the 2.14 µm continuum; and 3.4 for the [Fe II] at 1.644 µm, also in units of 10"18Wm"2.‡ As a standard star was not observed in the K[98] fi lter the broad-band fluxes are rough estimates. The flux calibration factor which was used was derived from the (1,0) S(1)calibration and a comparison of the broad-band and narrow-band fi lters.

118


Table 4.3: AK values (in magnitudes) which have been determined from the KSPEC rel-ative fluxes in Table 4.1. The flux errors have been propagated and yield a realistic AKerror estimate.

Q(2)/S(0) Q(3)/S(1) Q(4)/S(2)

AK east 2.7 ± 1.5 1.5 ± 0.5 1.8 ± 0.5AK west 3.9 ± 2.3 2.4 ± 0.5 3.2 ± 2.0

transition probabilities taken from Wolniewicz et al. (1998).

When both lines originate from the same upper level and an extinction law of the form

"!1.7 (Davis et al., 2003) is adopted, the absolute extinction is given by

AK =%

7%2.2 µm"2

&1.7 #%2.2 µm"1

&1.78 (4.2)

Three pairs of H2 v = (1,0) lines from the KSPEC data were used in order to determine

AK: Q(2)/S(0), Q(3)/S(1) and Q(4)/S(2). The results are presented in Table 4.3.

Immediately evident is that the extinction is higher in the western knots although the

extinction determination in the west is rather tentative due to the observing conditions. A

higher extinction than in the east is plausible since the western lobe is redshifted and the

embedded cloud (observed in H13CO+ by Gueth & Guilloteau (1999), see Appendix C)

extends predominantly in this direction. In order to determine the average value of AK

each line pair was assigned with the relative line strength as a statistical weight. The

statistically-weighted average AK values for the eastern and western components are 1.8

and 2.9 magnitudes respectively. These values are used to deredden the luminosities in

Section 4.4. The main source of this extinction is the probably the intervening gas lying

between the object and the cloud edge along the line of sight. Variations in the extinction

values for each object could be due to the density structure of the cloud. Dense clumps of

material along the outflow or infront of the objects could raise the extinction considerably.

The values estimated here which are used to correct the observed luminosities include

extinction which is due to all the gas lying both within the extended object itself and in

the foreground.

119


Figure 4.5: Column density ratio diagrams for HH211, produced from vertical slits run-ning through locations of peak emission. The extinction has been adjusted to minimise thedi!erences in (1,0) S-branch and Q-branch lines originating from the same upper energylevel. H2 (1,0) transitions are represented by squares, (2,1) transitions by crosses, and(3,2), (3,1) and (3,0) transitions by triangles. The faint squares represent (1,0) Q branchmeasurements.

In order to interpret the data, the ColumnDensity Ratio (CDR) method was employed.

The column of gas, N j, in the upper energy level kBT j necessary to produce each line

was determined. These values were then divided by the columns predicted from a gas

at 2 000K in local thermodynamic equilibrium with an ortho to para ratio of 3. After

normalising to the (1,0) S(1) line, the CDRs are plotted against T j, as displayed in Fig. 4.5.

It can be immediately seen that the CDRs are not constant but a function of the excitation

temperature, and thus not consistent with emission from a uniform temperature region or

from a single planar shock. Furthermore, no significant deviations from a single curve

are identified (apart from that derived from the (1,0) S(5) which is not confirmed by the

(1,0) Q(7) from the same T j). Hence, the ortho to para ratio is consistent with the value

120


of three, usually associated with H2 shocks.

The extinction determined in the east location also constrains the H-band lines. A

significantly lower extinction would raise the CDRs for these (1,0) H2 lines above those

of the (2,1) K-band lines. This would have implied non-LTE low density conditions.

As it stands, the fact that a single curve is predicted suggests a density su"ciently high

to ensure LTE. Given a high fraction of hydrogen atoms, the lower vibrational levels of

hydrogen molecules reach LTE at densities above ! 104 cm!3.

4.4 Analysis

4.4.1 Modelling the bow shocks

The structure of the western outflow, shown in detail in Fig. 4.6, raises an ideal interpre-

tation scenario. The excited H2 can be found in several distinct knots along an outflow

axis. McCaughrean et al. (1994) suggested that this well organised appearance might

prove particularly amenable to modelling. A series of bow-shocks is propagating along

the outflow. They gradually exhaust their momentum and slow down as they plough

through either ambient gas or the material in the wakes of upstream bow shocks. They

encounter less dense gas towards the edge of the cloud. The submillimeter observations

of Chandler & Richer (2000) show that the HH 211-mm envelope density decreases with

distance from the source. The azimuthally averaged density structure is well fitted by a

single power-law, $ , r!1.5, out to 0.1 pc (the projected distance of the outer knots of

the outflow from the source). However, the density profile is extended in a direction per-

pendicular to the outflow and the outer western knots are located outside this dense core

region.

The bow-shock models used to investigate the HH240 bow shocks are employed here

and serve as a valuable tool for interpreting the observed structures. I wish to determine if

a systematic change of one or more parameters results in a close match with the observed

bow structures and thus to analyse the outflow’s changing environment. I have applied

the bow-shock model to the three leading structures: de, bc and a.

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Figure 4.6: The HH211 western outflow is shown here in H2 (1,0) S(1), H2 (2,1) S(1) and[Fe II] emission lines. The images are not continuum subtracted as the bow shocks in thisregion are relatively free from continuum radiation. Grey-scale bars represent flux levelsper arcsec!2 in units of 10!18 Wm!2. O!sets are measure from the star in the north westof each image.

122


Jump-type (J-type) bow shocks can account for many of the features associated with

high excitation emission regions. They cause rapid heating and dissociate H2 molecules

for shock speeds greater than 24 km s!1 (Kwan, 1977). However, Continuous-type (C-

type) bow shocks have proved extremely successful in explaining most of the observed

structures. The measured low fraction of ions in molecular clouds is consistent with

their application. The magnetic field cushioning has results in less energy going into

molecule dissociation; they can explain the high infrared fluxes which are observed in

bow shocks. However, their observed velocities often exceed the H2 dissociation speed of

! 40 – 50 km s!1 (Smith et al., 1991) giving rise to a double-zone bow shock composed

of (1) a curved J-type dissociative cap (responsible for atomic emission) and (2) C-type

wings (where H2 emission is radiated).

The systematic method of exploration of parameter space and the level of confidence

involved in finding the best-fit model are discussed in detail Section 3.4 and Appendix A.

To summarise the selection technique, the bow luminosities provide the best constraints

on the density and bow speed. The location of the emission in the flanks or apex also

constrains the bow speed. In addition, the ion fraction constrains the transverse bow

thickness as well as the bow speed. The magnetic field strength strongly influences the

extent of the wing emission and the atomic fraction a!ects the line ratios.

The observed H2 (1,0) S(1) luminosity for each bow provides the strongest constraint.

For a given bow size, Lbow, the line emission is directly proportional to the mass density

(= 2.32 " 10!24 n [g]) and (vbow)3. The observed bow luminosities have been corrected for

extinction using the average K-band extinction of AK = 2.9 mag (Section 4.3). It is worth

noting that this value of AK seems unusually high, especially when compared to the value

of AV ! 10 mag (AK ! 1.2 mag) estimated by McCaughrean et al. (1994). They estimated

AV by comparing the broadband K’, J and H flux ratios with the predicted ratios from the

shock models of Smith (1995a). However, the ratios derived were not continuum sub-

tracted as the extent of continuum emission in the outflow was unknown. For this reason,

their AK value may be underestimated. To be consistent with the current set of measure-

ments I have used the value of AK = 2.9 mag to deredden the knot luminosities. Adopting

123


Table 4.4: Observed and predicted bow shock luminosities and (2,1) S(1) / (1,0) S(1) fluxratios. Luminosities are expressed in units of L" and a distance of 315 pc is adopted.Luminosities have been extinction corrected using K-band and H-band extinctions of 2.9and 4.5 magnitudes – using AH = 1.56 " AK from Rieke & Lebofsky (1985) – although theerrors in these values are relatively large, see table 4.3. Note that the [Fe II] luminositieshave been predicted using a J-type shock model.

Line Observed$ Extinction C-typeCorrected Model

bow-de

H2 (1,0) S(1) 4.6 " 10!4 6.5 " 10!3 6.8 " 10!3H2 (2,1) S(1) 4.3 " 10!5 6.1 " 10!4 7.3 " 10!4H2 (3,2) S(3) 9.8 " 10!6 1.4 " 10!4 1.6 " 10!4

[FeII] 4D7/2 – 4F9/2 3.6 " 10!5 2.2 " 10!3 2.3 " 10!32/1 ratio 0.09 (0.02) 0.09 (0.02) 0.11

bow-bc

H2 (1,0) S(1) 9.7 " 10!5 1.4 " 10!3 1.4 " 10!3H2 (2,1) S(1) 6.85 " 10!6 9.7 " 10!5 1.5 " 10!4H2 (3,2) S(3) no det.$ – 2.7 " 10!5

[FeII] 4D7/2 – 4F9/2 no det.$ – 1.2 " 10!42/1 ratio 0.07 (0.02) 0.07 (0.02) 0.12

bow-a

H2 (1,0) S(1) 2.2 " 10!5 3.1 " 10!4 3.2 " 10!4H2 (2,1) S(1) 1.7 " 10!6 2.4 " 10!5 2.5 " 10!5H2 (3,2) S(3) no det.$ – 2.6 " 10!6

[FeII] 4D7/2 – 4F9/2 no det.$ – 1.2 " 10!62/1 ratio 0.08 (0.04) 0.08 (0.02) 0.08

!The 3! detection limits for the observed knots over an 8## circular aperture are: 2.6 " 10"5 for (1,0) S(1);1.8 " 10"6 for (2,1) S(1); 6.4 " 10"6 for (3,2) S(3); and 3.1 " 10"5 for the [Fe II] image.

AK values of 2.0 and 1.2 mag would decrease the extinction corrected luminosities by

56% and 79% respectively. Table 4.4 lists the observed extinction corrected luminosities

for each knot along with the predicted model luminosities.

The parameters selected in order to model each bow are given in Table 4.5 (see Fig. 2.3

for a schematic of the geometry). A constant Alfven speed is maintained so that the

magnetic field varies with density%B = vA

64#$&. From the H2 radial velocity structure

described in Salas et al. (2003) and assuming that the H2 knots have an average velocity

projected onto the plane of the sky of ! 50 km s!1 (such a velocity is consistent with the

124


Table 4.5: Model parameters derived to fit the bow images with C-type shocks.

Parameter bow-de bow-bc bow-a

Size, Lbow (cm) 1.0 " 1016 1.0 " 1016 1.0 " 1016H Density, n (cm!3) 8.0 " 103 4.0 " 103 3.0 " 103Molecular Fraction 0.2 0.2 0.2Alfven Speed, vA (km s!1) 4 4 4Magnetic Field (µG) 193 137 118Ion Fraction, & 1.0 " 10!5 3.0 " 10!5 5.5 " 10!5Bow Velocity, vbow (km s!1) 55 40 29Angle to l.o.s. 100% 100% 100%s Parameter 2.10 1.90 1.75Field angle, µ 60% 60% 60%

modelling results) an inclination angle to the plane of the sky is estimated to be between

5% and 10%, directed away from the observer. The bows have been modelled propagating

at this angle, i.e. inclined at 1 = 100% (see Fig. 2.5) to the line-of-sight as the western

outflow is redshifted.

The field angle µ, (the angle between the bow direction of motion and the magnetic

field) was varied in order to produce the asymmetric bow wings. The best results were

found for µ ! 60% ± 15%.

Fig. 4.7 displays the simulated bow image to compare to bow-de in (1,0) S(1) and

(2,1) S(1) ro-vibrational transition lines of H2, as well as the [Fe II] 4D7/2 – 4F9/2 transition

line. The bow speed is 55 km s!1 and the pre-shock density is 8 " 103 cm!3. The bow

size, Lbow, has been chosen in order to match the distance between the upper and lower

wings, in this case ! 5##(= 2.4 " 1016 cm).

The [Fe II] emission is generated by a J-type dissociative bow and is restricted to a

compact but elongated zone towards the bow apex where the highest temperatures are

reached. However, the observed [Fe II] emission is restricted to a single compact con-

densation, unlike the model distribution. According to this model the bow luminosity in

the (1,0) S(1) line is 6.8 " 10!3 L" , in all the H2 rotational and vibrational lines it is

1.4 "10!1 L" and the total luminosity, in emission lines from both atomic and molecular

species (including H2), is 2.4 "10!1 L"Bow-bc is observed in both the (1,0) S(1) and (2,1) S(1) lines. Fig. 4.8 displays the

125


Figure 4.7: A C-type bow shock model for bow-de shown in H2 (1,0) S(1) and (2,1) S(1)excitation lines. Adopting a source distance of 315 pc gives a pixel scale along the x and yaxes of 1 pixel = 0.18##. The bow direction of motion is inclined to the plane of the sky byan angle of 10%, away from the observer, i.e. 100% to the angle of sight. The bow is movingat 55 km s!1 relative to the ambient medium of H density n = 8 " 103 cm!3. All flux levelsare indicated normalised to the maximum H2 (1,0) S(1) line flux. Hot dissociative shocksare necessary to induce emission from [Fe@II]. Here a J-shock model is explored (sameparameters) to simulate the flux distribution at 1.644 µm.

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Figure 4.8: C-type bow shock model for bow-bc which reproduces the observed H2(1,0) S(1) and (2,1) S(1) flux distribution. Adopting a source distance of 315 pc givesa pixel scale of 1 pixel = 0.18##. Here a lower bow speed of 40 km s!1 is taken togetherwith a pre-shock H density of 4 " 103 cm!3 to match the observed luminosity. Otherparameters are given in table 4.5. The grey scale flux indications are normalised to themaximum (1,0) S(1) level for bow-de in Fig. 4.7.

model generated images which closely resemble the observations. The distance between

the upper and lower wings is ! 3## (= 1.4 " 1016 cm). This knot is modeled with a

reduced bow speed of 40 km s!1 which is propagating into a lower density medium of

n = 4.0 " 103 cm!3. No [Fe II] emission is observed, consistent with the fact that its

predicted luminosity lies below the detection threshold. According to this model the bow

luminosity in the (1,0) S(1) line is 1.4 " 10!3 L" , in all the H2 rotational and vibrational

lines it is 3.6 "10!2 L" and the total luminosity, in emission lines from both atomic and

molecular species (including H2), is 5.4 "10!2 L".

Bow-a appears in the (1,0) S(1) line of H2 as a compact knot of emission with a

(2,1) S(1) / (1,0) S(1) ratio of 0.08 ± 0.02. A bow speed of 29 km s!1 results in (1,0) S(1)

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Figure 4.9: Faint (1,0) S(1) emission is detected at bow-a. A bow propagating at 29km s!1 generates the correct (1,0) S(1) luminosity with luminosities from the other linesbelow the level of detectability, see table 4.4. Adopting a source distance of 315 pc givesa pixel scale of 1 pixel = 0.18##. The grey scale flux indications are normalised to themaximum (1,0) S(1) level for bow-de in Fig. 4.7.

emission which is restricted to the bow apex (Fig. 4.9). The calculated line luminosity is

3.2" 10!4 L" in the (1,0) S(1) line, 8.8" 10!3 L" in all H2 lines and 1.3" 10!2 L" in all

atomic and molecular lines (including H2).

The conclusion reached is that the observed structures are recreated in the model by

solely altering the density, bow speed and ion fraction while all other parameters remain

fixed. The extent of the bow is influenced principally by the bow speed as it determines

the location of the H2 emission. A slower bow is characterised by emission concentrated

closer to the bow front. For this reason a constant Lbow was maintained for all the mod-

els. The bow speed systematically decreases as an otherwise similar bow ploughs into a

material of decreasing density. An increase in the ion fraction is expected in less dense

regions where cosmic rays and UV photons can more easily penetrate the gas.

The driving power of a bow is converted into heat at a theoretical rate given by Eq. 3.3.

For the case of HH211 the derived power is given by

P = 0.13 2! n8.0 " 103 cm!3

" ! vbow55 km s!1

"3 ! Lbow1.0 " 1016 cm

"2L" (4.3)

where 2 is a non-dimensional factor related to the aerodynamical drag and is of order

128


Figure 4.10: A map showing the ratio of the 2.248 µm and 2.122 µm images. The twoimages have not been continuum-subtracted (due to the very low S/N of the continuumimage), so the map only reveals the H2 (2,1) S(1) / (1,0) S(1) line ratio towards the endsof the outflow, where the continuum is weak; the darker regions near the center of theimage are where the emission is dominated by the continuum. Logarithmically increasingcontour levels are at 0.08, 0.11, 0.16, 0.22, 0.32, 0.45 (black) and 0.63, 0.89 (white).

unity. The derived numbers are thus consistent with expectations.

4.4.2 The outflow continuum emission and excitation

The fluxes in the narrow-band images containing the (1,0) S(1) flux and the (2,1) S(1)

flux were divided to produce the (2,1) S(1) / (1,0) S(1) ratio image displayed in Fig. 4.10.

In order to produce this map both images were first smoothed with a Gaussian FWHM

= 0.6## and values lying below the noise level were excluded from the division. Note

that the images were not continuum subtracted, due to the poor quality of the continuum

image at 2.14 µm, so Fig. 4.10 reveals two distinct outflow regions: (1) areas where the

continuum emission is relatively strong possess a ratio above 0.3 and approach 1.0 where

only continuum emission is present and (2) parts of the outflow not e!ected by continuum

emission where the H2 excitation (! 0.1) is revealed.

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The outflow regions dominated by continuum emission are located along the edges

of the SiO jet imaged by Chandler & Richer (2001). This supports the idea that the

continuum arises through light from the protostar which is scattered by dust grains. The

light escapes along a jet excavated cavity but not along the high density jet itself. It is cut

o! at 17## (8.0 " 1016 cm) along the western outflow where it possibly encounters a high

density 1 M" filament (Gueth & Guilloteau, 1999). It is also possible that the filament lies

in front of the flow. This projection e!ect would explain the higher extinction measured

in the western outflow, contrary to the submillimeter dust emission maps of Chandler &

Richer (2000) which do not reveal a strong asymmetrical density distribution between

the eastern and western outflows. Continuum light encounters less hindrance along the

eastern outflow where it terminates alongside shock-excited H2 emission at knots i and

j, 45## (2.1 " 1017 cm) from its protostellar origin. Here continuum emission is seen at

2.14 µm (Eislo!el et al., 2003) but not in the ratio image as the H2 emission is relatively

strong in this region. The origin and implications of the continuum emission will be

discussed in Section 4.5.

The vibrational excitation ratio (as measured from the observed H2 (1,0) S(1)/(2,1) S(1)

flux ratio) along the western outflow, ! 0.1, is typical of outflows seen in collisionally ex-

cited emission (Black & Dalgarno, 1976; Shull & Beckwith, 1982). There is an increase

in the excitation ratio towards the leading edge of bow-de where higher shock velocities

and temperatures are reached and the H2 line emission reaches its maximum value. Simi-

lar conditions are found for the HH 240 bow shocks and they are well explained through

the bow shock interpretation. However, a strong deviation from this picture is found in

the [Fe II] image: The localised [Fe II] emission is coincident with a region of higher

ratio, (labelled [Fe II] — 3) and, puzzlingly, not at the expected H2 dissociated bow apex

as seen in the model generated image, Fig. 4.7.

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4.5 Discussion

Which mechanisms give rise to the series of near-infrared bow shocks? The analysis

suggests a combination of two processes:

(1) The bow shocks are generated by a series of similar outflow accretion/ejection

events. Using the model velocities, the time lapses between the bows (and therefore

between outflow events) are ! 425 and ! 290 years. These numbers are consistent with

the detection of three bows given the dynamical age of ! 1 000 years. Fluctuations in jet

activity probably manifest themselves as bow shocks at the jet cloud impact region, which

is Knot-f, where the high speed CO jet terminates (see Appendix C) and H2 shock heating

is initialised. At Knot-f two H2 (1,0) S(1) velocity components have been observed by

Salas et al. (2003). This reverse/transmitted shock pair seems to indicate the critical zone

of jet impact where H2 bow shocks are born. After formation, the bows propagate away

from the protostar towards the cloud edge and through a changing environment; they

become less luminous as the density decreases and they lose their momentum. Bow-a

represents the final stages in the detectable life of one of these bow shocks. In support of

this process, it is noted that the molecular jet demonstrates an apparent acceleration along

its length of value ! 5" 10!3 km s!1 AU!1 (Chandler & Richer, 2001). Given ballistic

motions, this implies that the entire jet now observed was ejected within a relatively short

period of time just 100 – 150 years ago.

(2) The bow shocks become illuminated within regions where the outflow impacts on

denser clumps of gas. This idea is supported by the implied high (although uncertain)

K-band extinctions of 2.9 and 1.8 magnitudes for knots de and i which could be due to

intrinsic gas as well as clumpy dense foreground gas associated with the bows. The esti-

mated values do not represent the entire outflow and cannot be used to infer the extinction

corrected luminosity for the whole outflow. Additionally, strong continuum emission is

detected in the eastern outflow at knots i and j where the extinction is high (AK ! 1.8).

If this is indeed scattered light from the protostar then it has channeled through to where

the enhanced density has resulted in scattering. The passage of a C-shock will increase

the post-shock density with a compression ratio of)2 times the magnetic Mach number

131


(shock speed divided by the Alfven speed) (Spitzer, 1978). Therefore, the continuum

emission is likely to be seen alongside the shock-excited H2 emission as is the case for

HH 211.

McCaughrean et al. (1994) suggested an average AK of 1.2 magnitudes which is lower

than the values derived in Section 4.3 but is consistent to within the error limits. Adopting

this as the average extinction over the entire outflow it is found that the total H2 (1,0) S(1)

luminosity of the outflow is 0.009 L". According to the predictions of the bow shock

models, ! 4% of the total H2 line emission (2.7% of total line cooling) is emitted in the

(1,0) S(1) which gives an intrinsic H2 luminosity for HH 211 of ! 0.23 L" and a total lu-

minosity Lrad, resulting from all line emission, of ! 0.34 L" . If all the mechanical energy

is converted into radiation then Lmech is equivalent to Lrad and Lmech / Lbol = Lrad / Lbol (the

ratio of the outflow total luminosity in all emission lines to the bolometric luminosity of

the driving source) is ! 10%.

Provided that the velocity of the swept-up gas, which coincides with the CO outflow,

roughly equals the shock velocity (i.e. a radiative shock), Davis & Eislo!el (1996) have

shown that Lrad should be roughly equal to the kinetic luminosity Lkin of the outflow-

ing material as measured through the CO luminosity. These criteria are indeed met for

HH 211 as Lkin ! 0.24 L" and the CO and H2 are coincident suggesting that the shock

is essentially radiative (Gueth & Guilloteau, 1999; Giannini et al., 2001). Note that the

average extinction is restricted to about 1 magnitude in the K-band in order to meet these

criteria.

The driving source HH211–mm has a bolometric temperature of 33K which implies a

youthful outflow system. However, the HH 211 outflow itself does not reveal any charac-

teristic signs of its assumed youthfulness besides the small spatial extent which implies a

dynamical timescale of order 1000 years. This outflow age is limited by the density struc-

ture of the environment, as older bow shocks may simply have disappeared into sparse

material. For this reason the outflow extent itself cannot be used to infer the full duration

of outflow activity.

The high density jet (2 – 5 " 106 cm!3) observable in SiO J = (5,4) emission implies a

132


pre-shock density of about 2 " 105 cm!3 (Gibb et al., 2004b) and thus a maximum jet-to-

ambient density ratio of ! 20. The CO J = (2,1) maximum radial velocity is ! 40 km s!1

(Gueth & Guilloteau, 1999) implying a jet velocity of 230 – S460 km s!1 given an in-

clination angle to the plane of the sky of between 5% and 10%. Hydrodynamic numerical

simulations show that a low density envelope generally develops around jets of density

! 105 cm!3 and a jet-to-ambient density ratio of 10 (Suttner et al., 1997; Volker et al.,

1999; Rosen & Smith, 2004b). Could (pulsed) C-type jets which are heavier, denser and

more ballistic than those simulated excavate even more pronounced low density cocoons

through which continuum emission might escape along the outflow? To date, such high

density and high velocity jets involving C-type physics have not been simulated. The new

challenge for theorists is to simulate such MHD jets.

HH 211 is of particular interest due to its unusually strong continuum emission. The

original radiation may have escaped from the source along a cavity of low optical depth

which must have been excavated by powerful jet events. This radiation is then scattered

by dust when it encounters dense walls or clumps where the NIR optical depth along the

direction facing the source is of order unity. Some of the scattered radiation then exits

along the line-of-sight. This interpretation thus requires the original radiation to penetrate

a distance of order 1017 cm with a mean density of less than 105 cm!3 before encounter-

ing walls of thickness of order 1016 cm and density 106 cm!3. A moderate fraction of

the scattered radiation then escapes without encountering further dense features along the

line-of-sight. The high density and clumpiness of the jet as revealed through SiO obser-

vations (Chandler & Richer, 2001; Nisini et al., 2002b) are important factors to consider

in this interpretation.

The [Fe II] emission at 1.644 µm originates from an upper energy level of 11 300

K (compare to 6 953 K for H2 (1,0) S(1)) therefore it is expected to highlight the hotter,

high excitation regions of an outflow. As shown in Section 4.4, the [Fe II] emission from a

typical bow shock should be located towards the front of the bow, where H2 is dissociated.

Clearly, this is not the case for HH211 bow–de. The most likely explanation is that the

front of the bow shock is traversing a low density region. Material has been swept out

133


by outflow activity and the bow shocks become luminous only where they interact with

the wall of this hollowed out cavity. In this way it is possible to see [Fe II] emission

coincident with bright H2 emission in the ‘shoulders’ of bow–de. Such an explanation

is also supported by the distinct possibility that continuum emission from the source is

escaping along an outflow excavated cavity. Beyond bow–de, the H2 emission is weaker

and [Fe II] emission is not generated at observable levels.

4.6 Conclusions

The HH211 protostellar outflow has been studied in the near-infrared regime through

high resolution imaging and spectroscopy. Images in the (1,0) S(1) and (2,1) S(1) ro-

vibrational transitions of H2 have been analysed in order to study the excitation through-

out the outflow. A narrow-band image at 1.644 µm ([Fe II] + continuum) was presented

where the outflow is clearly detected and several confined condensations of [Fe II] emis-

sion are identified. In addition, K-band spectroscopic flux measurements are presented

for two separate prominent locations from which the extinction and excitation conditions

have been investigated. The series of bow-shocks in the western outflow have been suc-

cessfully modeled as curved 3–dimensional shock fronts with steady state C–type physics.

The findings have lead to several conclusions about the nature of the outflow:

• C-type bow shocks propagate along the western flow. Model fitting has constrained

several parameters including the density, bow velocity, ion fraction, intrinsic bow

shape and magnetic field strength and direction.

• The bow shocks appear to be passing through dense clumps where their luminosity

is accentuated. High values of extinction are measured in these regions which may

be due to the dense clumps associated with each bow.

• Bows de, bc and a are plausibly modeled as a series of initially identical bow shocks

propagating through a medium of decreasing density. The bows slow down and

134


disappear as they approach the cloud edge.

• A misalignment of the magnetic field and outflow directions can account for the

observed bow shock asymmetries.

• Themost likely source of the continuum emission along the outflow is light from the

protostar which evades dense core obscuration by escaping through a low density

cavity excavated by the jet. The continuum light is scattered when it encounters the

denser material aligning the jet tunnel and the dense clumps throughout the outflow.

• The excitation along the outflow is typical of outflows in general. The ortho to para

ratio of 3 for molecular hydrogen indicates collisional heating (as opposed to UV

fluorescence, see Section 2.1.2) as the source of the near-infrared line emission.

• The [Fe II] emission is predicted and detected in isolated condensations. These

condensations are coincident with strong H2 emission. However, the location of

the [Fe II] emission is puzzling; it is not found in the expected bow apex region as

predicted. This may also be due to the low density tunnel through which the bow

apex is propagating.

These findings together with the large volume of previously published material is sug-

gesting a global outflow model, as follows. Episodic fluctuations in accretion/ejection

(of order a few hundred years) give rise to a variable jet velocity. The resulting shocks

manifest themselves as C-type bow shocks at the principal jet/ambient medium impact

region where they are detected outside the dense core where the extinction is lower. The

bows propagate towards the cloud edge through a changing environment. The model sug-

gests that the mean density decreases with distance from the core but that the bow shocks

brighten where they encounter dense clumps. It is feasible that these clumps consist of

gas swept up by the passage of previous bows driven by the alternating outflow power.

It is clear that in-depth studies of a wide range of protostellar outflows will yield

valuable insight into how the cloud environment sculpts the outflow and how much the

135


environment itself has been influenced by the star forming process.

136

Chapter 5

Integral Field Spectroscopy of HH212

137

Chapter 5. Integral Field Spectroscopy of HH212

5.1 Introduction

Concealed within the dusty gas of the Orion Cloud is IRAS 05413–0104, a protostellar

condensation which is powering a spectacular outflow called HH212. Containing two

prominent inner knots, which appeared point-like in the initial low resolution IR obser-

vations, the outflow was originally though to be a young binary system (Reipurth, 1989;

Zinnecker et al., 1992). Further investigating and deeper observations revealed otherwise

(Zinnecker et al., 1996, 1998). The two bright points are the first in a series of knots and

bow shocks which delineate the outflow which was first discovered in the NIR at 2.12 µm.

The entire H2 outflow is shown in Fig. 5.1. The outflow displays a remarkable degree of

symmetry and collimation. The IRAS source and its outflow lie in the L1630 molecular

cloudlet about 90# north-east of the Horsehead nebula at a distance of !460 pc.

IRAS 05413–0104 was detected at 25, 60, and 100 µm but is still too cold and embed-

ded to be detected at 12 µm (Beichman et al., 1986b). It is a low-mass (0.4 M") protostar

with a bolometric luminosity of about 14 L " and is associated with a 1.3 mm continuum

source which is due to dust emission from the surrounding gas (Zinnecker et al., 1992).

The central position of the IRAS source is R.A.(2000) = 05h 43m 51.4s, Dec(2000) = -01%

02# 52##. The ratio of submillimetre to bolometric luminosity, Lsmm/Lbol, of about 0.02, as

well as a temperature of !30K classify it as a Class 0 object. The extent and nature of the

encompassing envelope has been studied in maser emission by Wiseman et al. (2001) us-

ing the VLA to obtain ammonia (J,K) = (1,1) and (2,2) (at rest frequencies of 23.694495

and 23.722733 GHz) inversion transition maps. The detected envelope mass is 0.2 M"

which is distributed in a structure which is flattened along the outflow direction with an

axis ratio of about 2:1. The major axis has an FWHM extent of 29## which corresponds

to 0.06 pc at the adopted distance. The cold envelope is heated to 14K in a centrally

condensed area surrounding the jet source.

The outflow itself covers an extent of ! 240##, or 0.54 pc. The total H2 (1,0) S(1)

luminosity (not corrected for extinction) is 6.9 " 10!3 L" (Stanke, 2000). The morphology

of the outflow is striking and has attracted a considerable amount of attention in recent

years. The extremely symmetric features make HH212 an ideal subject for investigation

138


Figure 5.1: The entire HH212 outflow at 2.122 µm (1,0) S(1) line of H2. The imagewas obtained at the Calar Alto 3.5–m telescope. The position of the driving source IRAS05413–0104 at R.A.(2000) = 05h 43m 51.4s, Dec(2000) = -01% 02# 52## is marked by thecross. Published in Zinnecker et al. (1998).

139


as they represent a ticker-tape record of the accretion/ejection history of the source. The

important observed features are summarised and discussed here:

1. On both sides of the bipolar H2 outflow extend a series of inner knots which are reg-

ularly spaced with inter-knot distances of about 4## or !2 000 AU. Emission is also

seen in the inter-knot spaces; the knots appear to be connected by a thin stream of

emission (McCaughrean et al., 2002). Both series of knots terminate in small bow

shocks at a distance of about 18 000 AU from the central position. The bow shocks

are composed of two separate components. Whereas the knot brightness decreases

with distance from the source, the bow shocks break the trend and appear relatively

bright again. This may be due to a reduction in the extinction as the outflow breaks

free of its maternal envelope. Although the proper motion velocities of the outflow

features are pending, a typical jet speed of ! 120 km s!1 is a reasonable estimate

from examination of two aligned and overlaid H2 (1,0) S(1) images of the outflow

covering a timebase of 7 years. The first epoch image was observed with the Calar

Alto 3.5–m telescope in November 1994 Beichman et al. (1986b) (Fig. 5.1) and the

second epoch image was observed with the VLT in January 2002 (McCaughrean

et al., 2002) (the blinked images were kindly provided by Thomas Stanke, IFA,

Hawaii).

2. The outflow is inclined at a very small angle to the plane of the sky of about 2%.

This is evident from the small di!erence in radial velocities between the two inner

knots of ! 9 km s!1 (Zinnecker et al., 1998) and assuming a jet speed of !120

km s!1. The inner H2 emission is equally bright on each side, suggesting that the

inner outflow has equal intrinsic brightness and extinction on both sides and that the

density structure is quite smooth and symmetrical about the source. The emission

from the larger outer bows is not equally bright which would imply that the external

medium is no longer evenly distributed at this distance from the source. Indeed, the

giant southern bow SB4 has no northern counterpart.

3. The outer bows SB 3 and NB 3 are unlike the typical bow shocks which have

140


been examined in this thesis. They are wide and open and show line emission

in the extended wings but the emission from the bow apices does not disappear.

Appearing near bow NB3 is a cluster of background galaxies suggesting that there

must be very little ambient material in this area. How can there be any shock excited

material in this region of space? Perhaps the outflow itself has expelled some of its

entrained material outside of the cloud. The SB4 bow shock, on the other hand,

seems to form as the outflow collides with another dense cloud core; we may be

witnessing the e!ects of feedback in a star formation group.

4. A pair of di!use nebulae which is divided by a dark lane are seen at the base of the

jet which resemble the edge-on disk system seen in HH30, see Fig. 1.6. However,

the HH212 nebulae are almost exclusively detected in the 2.12 µm line (McCaugh-

rean et al., 2002) implying that the source of illumination is not the protostar itself.

One likely explanation is that the bright inner knots provide the line emission which

is reflected from the outer surface of the flattened rotating cloud core surrounding

the protostar.

5. Deep optical images have failed to detect emission from H( and [S II] (Zinnecker

et al., 1996). HH212, therefore, is likely to be an almost purely molecular hydrogen

jet, similar to HH211. In addition, it is one of the few jet sources not showing 3.6

cm radio continuum emission from ionised gas.

6. The source position is coincident with a 1.3 cm water maser (Wouterloot et al.,

1989).

7. The source shows variability of a factor !3 on a timescale of a few years (Galvan-

Madrid et al., 2004) as observed in multi epoch 3.5 cm VLA observations.

8. SiO J = (2,1) and J = (5,4) observations reveal emission close to the central source

(Chapman et al., 2002; Gibb et al., 2004a) as well as along the southern jet (at a

position 20## from the source) (Gibb et al., 2004a). They calculate the H2 density in

the SiO emitting region to be of order 105 cm!3, with the silicon abundance to be a

141


few 10!9 (relative to H2), and a temperature range of 50 – 150K (source position)

and 50 – 100K (along jet). The SiO relative abundance is lower than that observed

for cool dusty gas which is of order a few 10!6 (Savage & Sembach, 1996). The

relatively low abundance measured by Gibb et al. (2004a) may be due to the SiO

arising in clumps which are small compared to the beam size of 22##. The SiO

abundance may also be lowered by conversion to SiO2 in shocked gas (Gibb et al.,

2004a). The detection of strong SiO emission in the jet is indicative of the Class 0

nature of the outflow, as discussed in Gibb et al. (2004a).

9. HH212 was mapped in the CO J = (1,0) emission line by Lee et al. (2000b). A close

relationship is found between the morphologies of the H2 and CO outflows. The

CO emission is found close to the H2 bow shocks, suggesting that the CO emission

traces material which is being entrained by jet driven bow shocks. Furthermore,

the broadest range in CO radial velocities (as revealed in P-V diagrams) is found

to be coincident with the tips of the bow shocks as was also seen for HH240/241

(Lee et al., 2000b). Such P-V spur structures are also reproduced in the bow shock

models, see Fig. 3.18.

10. The southern and northern jet directions are determined from the inner knots out

as far as the double bow shocks SB 1/SB 2 and NB1/NB2. The jet and counter jet

deviate by ! 2% from 180% which may suggest that the driving source is moving rela-

tive to the cloud core (of order a few km s!1) or that the cloud core is moving relative

to the external cloud medium (ram pressure). Another, more likely, explanation is

that the jet direction could be influenced by the orbital motion of the jet source in

a young binary system (Fendt & Zinnecker, 1998, 2000). The apices of the giant

outer bows appear to be displaced from the jet directions by small amounts and in

opposite directions. A weak S-shaped curve as well as the regular knot intervals are

suggestive of binary activity where the accretion/ejection events are connected with

the orbital motion.

11. The outermost southern bows SB 3 and SB 4 exhibit a twisted 3D helical morphol-

142


ogy and appear to be connected. This appearance of the H2 shock features might

serve as evidence of directional variability and rotation of the jet during early ejec-

tion events.

12. Continuing with the theme of rotation, the NH3 core which was observed by Wise-

man et al. (2001) shows a smooth velocity gradient of about 4 – 5 km s!1 pc!1

across the flattened disk-like core, suggestive of rotation in a clockwise direction

when looking at the displayed features from the north towards the south.

13. Echelle spectroscopy on the inner knots and bows has opened the door to under-

standing the outflow in greater depth (Davis et al., 2000). The authors describe

an apparent acceleration of the H2 features with distance from the source. The

northern jet shows increasingly red-shifted radial velocities whereas the southern

jet shows increasing blue-shifted velocities. However, it must be entertained that

such a shift in radial velocities could also be caused by a small S-shaped bending of

the jet of order a few degrees every 10 000AU; such a bending is compatible with

the non-collinearity of the jet seen in the plane of the sky.

Spectra were obtained from three di!erent slit positions along the jet and show

transverse velocity gradients across some of the knots in a direction perpendicular

to the jet axis. Although the trend was not observed in all knots the evidence for jet

rotation can be treated as suggestive as the measured velocities depend crucially on

the slit positioning. The implied jet rotation direction was also in the same sense

as detected for the NH3 core, i.e. clockwise when looking at the displayed features

from the north towards the south.

In order to further explore the nature of this intriguing outflow the prominent knots

and bows were observed with an instrument capable of obtaining NIR images at various

wavelengths simultaneously (UIST at UKIRT). It is then possible to measure the relative

positions of the emission peaks for various transition lines of H2 and [Fe II] (at 1.644 µm)

as well as determine the line emission fluxes. These observations and the data reduction

techniques used are described in the Section 5.2 and the results presented in Section 5.3.

143


In Section 5.4 the possible implications of the results are discussed.

5.2 Observations and Data Reduction

The UKIRT 1.5 µm Imager Spectrometer UIST was commissioned in October 2002. It

is designed to switch quickly between imaging and spectroscopy modes and is equipped

with a 1 024 " 1 024 InSb array. In spectroscopy mode the internal optics provide 0.12##

per pixel. In addition to conventional imaging and long-slit spectroscopy, UIST is capable

of spectroscopy over a two dimensional field of view using the Integral Field Unit (IFU).

The IFU provides spectroscopy of a 3.3## " 6.0## (rotatable) sky area with a plate scale

of 0.24## " 0.12##. The incident image is divided into 18 adjacent slices (14 of which are

usable) which are each 0.24## " 6.0## by an image slicing mirror. Each slice is then fed

through the UIST optical system as if it were a single long-slit, and projected onto the

CCD array, see Fig. 5.2. The resulting CCD image then contains the spectral information

for each element of the array and can be reformatted to construct 3.3## " 6.0## images of the

observed object, one image for every resolution element of the grism. The data reduction

process yields a 3-D data cube, which comprises a stack of 2-D images spanning the

full wavelength range available from the grism. The advantage of such a method is that

images are simultaneously obtained for each wavelength element (up to 1 024) and can be

accurately compared without having to rely on background stars or telescope coordinates

for positional reference.

The inner knots (NK 1 and SK 1) and bow shocks (NB1/NB2 and SB 1/SB2) of

HH212 were observed with the IFU in service mode. The observations were carried

out by Dr. Chris Davis (Joint Astronomy Centre, Hawaii) and the data were made avail-

able for downloading in raw format. The inner knots were observed on November 19th

and 20th of 2002 and the inner bow shocks were observed on November 22nd and Decem-

ber 6th of 2003 using the HK grism which gives a wavelength range of 1.4 – 2.5 µm and

wavelength increment of 1.07 " 10!3µm. Seeing throughout both sets of observations was

! 0.5##. The exposure time per frame was 120 seconds and for each knot and bow shock,

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Figure 5.2: Schematic of the IFU. A sky region is sampled by 18 slitlets which are each0.24## " 6.0##. The slitlets (excluding the first 4 which are not presently used) cover anarea of 3.3## " 6.0##. A staggered slit then projects each spectral image onto the array tocreate the raw images which are then reduced and used to construct the 3–D data cubewhich contains the spatial and spectral information. Image from UKIRT IFU webpage1.

10 object frames and 10 sky frames were observed; therefore the total on-source exposure

time was 1 200 seconds for each object. Other frames taken included flats, arcs and dark

exposures. The flat exposures were used to measure the pixel to pixel response across the

array as well as to locate the spectrum for each slice. The arc exposures were of an argon

lamp and were used to wavelength calibrate each spectrum. Dark exposures were used to

measure the dark current and 0 second exposure frames were used to determine the read-

out noise of the array. Guide-star tracking was maintained throughout the observations of

each object and the individual frames were registered according to the telescope pointing

co-ordinates.

The star HD38529 (spectral type G4V, K-band magnitude of 4.408 and black-body

temperature of 5 740K) was used to as a flux calibration standard for the inner knots and

HIP 29487 (spectral type A2V, K-band magnitude of 6.604 and black-body temperature

of 8 810K) was used flux calibrate the bows. Data reduction and flux calibration was

145


performed using software specifically written for IFU data reduction as well as standard

STARLINK routines, especially the package FIGARO which is specifically written for

spectroscopy. The data reduction process leading from raw frames to a flux calibrated 3–

D data cube are quite tedious and are not discussed in any more detail here; the necessary

steps are described in detail and regularly updated by Chris Davis and can be found at the

UKIRT IFU webpage1. From the reduced 3–D data cube it is possible to extract spectra

and images at any wavelength within the observed range.

5.3 Results

5.3.1 Inner knots: NK1 and SK1

Spectra were extracted from the data cubes containing the NK1 and SK 1 information.

The extraction was restricted to an area within the field of view which contains most

of the line emission. The spectra cover a wavelength range from 1.5 – 2.5 µm and are

presented in Figs. 5.4 and 5.5. The H2 emission lines detected are labeled as well as the

[Fe II] line at 1.644 µm.

The continuum value is close to zero across the entire spectrum and the telluric ab-

sorption lines have more or less disappeared indicating that division by the standard star

spectrum was properly carried out. Contamination by atmospheric features is high be-

tween !1.8 and !2.0 µm and after !2.4 µm and the spectra are likely to contain inac-

curacies in these regions. For each wavelength element the corresponding image can be

examined. For each transition line (or spectral feature) the emission is seen to occupy

several wavelength-specific images (2–3 images for the weaker lines and up to 10 images

for the stronger lines). The individual images we co-added to produce each final image

containing emission from a specific transition line. The extracted line emission images

for NK1 and SK 1 are shown in Figs. 5.6 and 5.7 and show a typical knot-like structure.

Extending to the north of NK1 and to the south of SK 1 a thin stream of emission can

be seen. This inter-knot emission can also be seen in deep VLT H2 (1,0) S(1) images1http://www.jach.hawaii.edu/UKIRT/instruments/uist/ifu

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Table 5.1: Photometric results for NK 1. The upper energy level of the transition is givenin the third column. The x and y peak position o!sets are relative to the (1,0) S(1) peakposition.

line " T total flux $ max. flux † x offset y offset(µm) (K) (10!18Wm!2) (10!18Wm!2 (arcsec) (arcsec)

arcsec!2)

Fe[II] 1.644 11 300 18.8 10.9 0.01 0.04(1, 0)S(7) 1.747 12 817 16.1 10.5 0.19 0.18(1, 0)S(6) 1.788 11 522 15.8 7.4 0.07 0.00(1, 0)S(5) 1.835 10 341 40.5 32.2 0.04 0.04(1, 0)S(4) 1.891 9 286 29.3 17.4 0.01 #0.01(1, 0)S(3) 1.957 8 365 137.0 65.2 0.13 0.02(1, 0)S(2) 2.033 7 584 40.7 19.2 0.06 #0.01(2, 1)S(3) 2.073 13 890 12.9 8.1 0.15 0.03(1, 0)S(1) 2.121 6 956 122.7 48.7 0.00 0.00(2, 1)S(2) 2.154 13 150 5.2 3.9 0.13 0.05(1, 0)S(0) 2.223 6 471 30.7 15.2 #0.04 #0.03(2, 1)S(1) 2.247 12 550 12.5 7.3 0.04 0.07(1, 0)Q(1) 2.406 6 149 112.3 47.4 #0.10 #0.05(1, 0)Q(2) 2.413 6 471 30.9 16.3 #0.08 0.01(1, 0)Q(3) 2.423 6 956 109.6 45.4 #0.01 0.00(1, 0)Q(4) 2.437 7 584 31.8 17.2 #0.08 0.10(1, 0)Q(5) 2.454 8 365 43.0 20.8 0.06 #0.03

0 – The 10 flux measurement uncertainty is 2.6 " 10!18Wm!2 and 5.2 " 10!18Wm!2beyond 2.4 µm. This (standard deviation) value was derived from a large sample of fluxmeasurements within apertures placed on sky regions and at various wavelengths.† – The 10 noise level is 1.0 " 10!18 Wm!2 arcsec!2.

using ISAAC (McCaughrean et al., 2002). The origin of this emission is mysterious. No

continuum emission is detected in either knot.

The peak flux positions were determined by first binning each image to a new pixel

scale of 2 " 4 pixels (= 0.48## " 0.48##) in order to match the seeing throughout the obser-

vations of ! 0.5##. Each array of binned data points was then fitted with a two dimensional

Gaussian to determine the centroid using a STARLINK object detection routine. The de-

tection threshold was set in order to include only the higher value pixels (in general >0.5

of the maximum value) which indicate the peak position. The positional error in deter-

mining the locations of the peaks is slightly less than the pixel size as a large number of

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Table 5.2: Photometric results for SK 1. The upper energy level of the transition is givenin the third column. The x and y peak position o!sets are relative to the (1,0) S(1) peakposition.


arcsec!2)

Fe[II] 1.644 11 300 10.1 18.0 0.06 #0.22(1, 0)S(9) 1.687 15 722 3.1 5.6 0.12 #0.12(1, 0)S(8) 1.714 14 221 2.9 7.6 0.30 #0.32(1, 0)S(7) 1.747 12 817 23.4 23.4 0.09 #0.15(1, 0)S(6) 1.788 11 522 13.2 14.3 0.15 #0.07(1, 0)S(5) 1.835 10 341 38.7 39.1 0.07 #0.01(1, 0)S(4) 1.891 9 286 33.7 21.0 0.02 #0.03(1, 0)S(3) 1.957 8 365 145.9 101.2 0.01 #0.01(1, 0)S(2) 2.033 7 584 43.0 32.1 0.10 #0.01(2, 1)S(3) 2.073 13 890 22.2 21.8 0.02 #0.09(1, 0)S(1) 2.121 6 956 150.2 109.9 0.00 0.00(2, 1)S(2) 2.154 13 150 6.4 8.2 0.04 #0.06(3, 2)S(3) 2.201 19 086 5.2 6.5 0.08 #0.20(1, 0)S(0) 2.223 6 471 30.3 22.9 0.01 0.00(2, 1)S(1) 2.247 12 550 23.3 19.8 0.01 #0.03(2, 1)S(0) 2.355 12 095 4.2 6.3 0.13 #0.15(1, 0)Q(1) 2.406 6 149 134.8 87.7 0.00 0.01(1, 0)Q(2) 2.413 6 471 42.4 30.6 0.04 0.05(1, 0)Q(3) 2.423 6 956 137.9 96.2 0.00 0.01(1, 0)Q(4) 2.437 7 584 42.5 34.1 0.05 0.04(1, 0)Q(5) 2.454 8 365 85.3 64.9 0.04 0.04(1, 0)Q(6) 2.475 9 286 29.1 23.7 0.01 #0.01

0 – The 10 flux measurement uncertainty is 3.3 " 10!18Wm!2 and 6.6 " 10!18Wm!2beyond 2.4 µm.† – The 10 noise level is 1.0 " 10!18 Wm!2 arcsec!2.

pixels are sampled in each case (typically about 15 – 25). As an indication of the accu-

racy achievable by this method, the di!raction limit for UKIRT (in the K-band) of 0.1##

is indicated in Figs. 5.18 – 5.21 where the centroid positions for each line emission im-

age relative to the (1,0) S(1) centroid are plotted against the upper level energy equivalent

temperature for each transition.

The centroid positions, in arcseconds, are given as o!sets relative to the peak of the

H2 (1,0) S(1) line in Tables 5.1 and 5.2 alongside the integrated and maximum fluxes

148


Figure 5.3: The centroids for each line emission image were determined by first binningthe data into 2 " 4 pixel squares to match the seeing of !0.5## (the original x pixel scale is0.24## whereas the original y pixel scale is 0.12##). The centroids of the di!use emissionwere then located by fitting a two dimensional Gaussian to the array. The image shown inthe binned NK1 (1,0) S(1) image.

measured for each transition line. In order to estimate the error in the flux measurements

the same sky region was used to measure the aperture integrated flux across a broad range

of wavelengths. The standard deviation of these values was then used as the average 10

error. Beyond 2.4 µm, where the the Q-branch lines are found, the contamination from

atmospheric lines increases and the error estimates should be doubled.

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Figure 5.4: Spectrum of the NK1 knot between 1.5 and 2.5 µm. The negative features in this spectrum and in the following spectra are due topixel defects.

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Figure 5.5: Spectrum of the SK 1 knot between 1.5 and 2.5 µm.

151


Figure 5.6: Extracted line emission images for NK1. The cross in each image (and insubsequent figures) marks the location of the (1,0) S(1) centroid which was determinedby applying a 2-D Gaussian to images which were binned to match the seeing of 0.5##. Theimages displayed here are not binned or smoothed. Intensities have been scaled linearly,beginning at zero, and the contour levels are di!erent for each image in order to highlightthe structures. The maximum intensities for each image are listed in table 5.1. Note thatthe detector was rotated by 24% in order to be aligned with the outflow axis.

152


Figure 5.7: Extracted line emission images for SK 1. The colour-scales are linear andbegin at zero and the contour levels are di!erent for each image to highlight the structure.The maximum intensities for each image are listed in table 5.2. The cross marks theposition of the (1,0) S(1) centroid.

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Table 5.3: Photometric results for NB1. The upper energy level of the transition is givenin the third column. The x and y peak position o!sets are relative to the (1,0) S(1) peakposition.


arcsec!2)

NB1(1, 0)S(7) 1.747 12 817 12.9 5.7 · · · · · ·(1, 0)S(5) 1.835 10 341 58.2 15.8 · · · · · ·(1, 0)S(4) 1.891 9 286 18.9 8.3 · · · · · ·(1, 0)S(3) 1.957 8 365 118.1 31.1 #0.04 0.09(1, 0)S(2) 2.033 7 584 33.3 7.9 #0.04 0.09(1, 0)S(1) 2.121 6 956 88.2 23.4 0.00 0.00(1, 0)S(0) 2.223 6 471 13.7 6.0 0.01 0.02(2, 1)S(1) 2.247 12 550 4.4 2.5 · · · · · ·(1, 0)Q(1) 2.406 6 149 51.9 20.9 0.06 #0.10(1, 0)Q(3) 2.423 6 956 57.2 22.0 0.10 0.01(1, 0)Q(4) 2.437 7 584 7.3 5.7 · · · · · ·(1, 0)Q(5) 2.454 8 365 13.3 10.3 · · · · · ·

0 – The 10 flux measurement uncertainty is 3.1 "10!18Wm!2. However, beyond 2.4µmthis value increases to 6.2 "10!18Wm!2.† – The 10 noise level is 1.6 " 10!18 Wm!2 arcsec!2.

5.3.2 Inner Bows: NB 1/NB2 and SB 1/SB 2

The photometric results for the inner bows are presented in Tables 5.3, 5.4 and 5.5. NB 1

and NB2 appear as two distinguishable features and their flux measurements are given

separately. The distinction between SB 1 and SB 2 is not clear and their flux measure-

ments are presented together. Where possible, the peak positions have been determined.

The fluxes are considerably weaker than for the inner knots, and distributed over a larger

area, which makes the peak positions di"cult to determine. Spectra of the bows are pre-

sented in Figs. 5.8 and 5.9. A slight bulge is seen across the spectrum as well as several

atmospheric absorption lines which appear as emission lines. This is due to a slightly

imperfect standard star observation (due to non-photometric weather conditions) and sub-

sequent erroneous flux calibration. In order to minimise this e!ect in the photometric

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Table 5.4: Photometric results for NB2. The upper energy level of the transition is givenin the third column. The x and y peak position o!sets are relative to the (1,0) S(1) peakposition.


arcsec!2)

NB2

(1, 0)S(7) 1.747 12 817 6.7 3.6 · · · · · ·(1, 0)S(5) 1.835 10 341 40.9 13.8 · · · · · ·(1, 0)S(4) 1.891 9 286 10.8 5.2 · · · · · ·(1, 0)S(3) 1.957 8 365 71.6 24.1 #0.07 0.06(1, 0)S(2) 2.033 7 584 19.7 7.1 #0.10 0.05(1, 0)S(1) 2.121 6 956 56.6 17.7 0.00 0.00(1, 0)S(0) 2.223 6 471 8.8 3.5 · · · · · ·(2, 1)S(1) 2.247 12 550 2.4 2.2 #0.16 0.18(1, 0)Q(1) 2.406 6 149 30.1 15.5 0.01 0.05(1, 0)Q(3) 2.423 6 956 31.7 16.8 0.01 0.00(1, 0)Q(4) 2.437 7 584 4 5.1 0.02 0.14(1, 0)Q(5) 2.454 8 365 3.1 · · · · · · · · ·

0 – The 10 flux measurement uncertainty is 3.1 "10!18Wm!2. However, beyond 2.4µmthis value increases to 6.2 "10!18Wm!2.† – The 10 noise level is 1.6 " 10!18 Wm!2 arcsec!2.

results, fluxes were measured from images adjacent in wavelength space containing no

line emission and subtracted from the emission flux measurements. In this way only the

emission from the line itself is included. Such measures were taken for NK1 and SK 1

also because subtraction of adjacent sky apertures proved di"cult due to the small field

of view which is occupied almost exclusively by the observed objects. Because of the

weaker fluxes, the higher excitation line emission images were di"cult or impossible to

extract. The (1,0) S(1) S/N ratios (determined for the peak flux measurements) for NB1

and SB 1 are !23 and !14, respectively. The images are presented in Figs. 5.10 and 5.11.

The bow structure of NB1 and NB2 is unresolved whereas SB 1/SB2 reveal wing emis-

sion typical of bow shocks. No [Fe II] emission is detected for either bow. The [Fe II]

flux level expected from a typical bow shock is much less than the level of (1,0) S(1) flux

and is not detected in the bows above the 10 noise level. As with the inner knots, no

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Table 5.5: Photometric results for SB 1/SB 2. The upper energy level of the transition isgiven in the third column. The x and y peak position o!sets are relative to the (1,0) S(1)peak position.

line " T total flux $ peak flux † x offset y offset(µm) (K) (10!18Wm!2) (10!18Wm!2 (arcsec) (arcsec)

arcsec!2)

(1, 0)S(7) 1.747 12817 13.4 2.9 · · · · · ·(1, 0)S(3) 1.957 8365 103.8 17.5 #0.21 #0.06(1, 0)S(2) 2.033 7584 28.1 4.9 #0.04 0.02(2, 1)S(3) 2.073 13890 10.1 2.8 · · · · · ·(1, 0)S(1) 2.121 6956 91.7 13.7 0.00 0.00(1, 0)S(0) 2.223 6471 13 3.0 · · · · · ·(2, 1)S(1) 2.247 12550 5.6 2.0 · · · · · ·(1, 0)Q(1) 2.406 6149 58.4 14.1 #0.05 0.00(1, 0)Q(3) 2.423 6956 56.6 9.7 0.01 0.07(1, 0)Q(4) 2.437 7584 13.4 5.3 0.09 0.04(1, 0)Q(5) 2.454 8365 29.9 11.2 · · · · · ·(1, 0)Q(6) 2.475 9286 9.3 3.0 · · · · · ·

0 – The 10 flux measurement uncertainty is 2.8 "10!18Wm!2 and 5.6 "10!18Wm!2beyond 2.4 µm.† – The 10 noise level is 1.0 " 10!18 Wm!2 arcsec!2.

continuum emission is detected.

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Figure 5.8: Spectrum of the NB1 bow between 1.4 and 2.5 µm.

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Figure 5.9: Spectrum of the SB 1 bow between 1.4 and 2.5 µm.

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Figure 5.10: Extracted line emission images of NB1 and NB2.

Figure 5.11: Extracted line emission images of SB 1/SB2.

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5.4 Analysis, Discussion and Speculation

The measured fluxes for the inner knots and bows of HH212 correspond well to colli-

sional excitation in shock heated gas. The highest excitation is found in the innermost

knots, 2 000AU from the source. The (2,1)/(1,0) S(1) excitation ratios, measured using

integrated fluxes, for NK 1 and SK 1 are 0.10 ± 0.02 and 0.16 ± 0.02 (which correspond

to excitation temperatures of 2 167 ± 170K and 2 586 ± 170K respectively).

Lower excitation conditions are found at a distance of 18 000AU from the source

where the inner bow shocks take form. The excitation ratios measured for NB1 and NB2

are 0.05 ± 0.04 (Tex = 1 698 ± 326K and Tex = 1 613 ± 504K, respectively). For SB 1 a

ratio of 0.06 ± 0.03 (Tex = 1 807 ± 277K) is found. These findings are not in complete

agreement with the excitation temperatures derived from deep K-band spectroscopy at the

NTT by Tedds et al. (2002). They found high excitation temperatures for the inner knots

and bow shocks (Tex & 2 300K). However, when only the peak flux is considered in each

case, equally high excitation temperatures are found (although the accompanying errors

are relatively large) for the inner knots and bows, implying that the IFU data may have

captured the lower excitation extended emission from the bows.

The extinction for each knot and bow was determined using the (1,0) Q(3) / (1,0) S(1)

ratio as described in 4.3. AK values of 1.2 ± 0.2 mag and 1.4 ± 0.2 mag were found

for NK1 and SK 1. A much lower extinction was found for NB1 and SB 1 (AK = < 0.7

mag, also consistent with zero extinction), supporting the idea that they have broken free

of the dense protostellar envelope and are now propagating through a medium of reduced

density. The symmetry found in the extinction values suggests that the density structure is

quite smooth and symmetrical about the driving source and that the outflow is not a!ected

by a complex density structure.

Column Density Ratios

The CDR method was used to analyse the results. The integrated fluxes were used to

calculate the columns of gas, N j which were then divided by the columns predicted for a

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Figure 5.12: Column density ratio diagrams for NK1. The left panel represents dataassuming no extinction whereas in the right panel the extinction has been adjusted tominimise the di!erence between the (1,0) S-branch and Q-branch lines originating fromthe same upper energy level. H2 v = (1,0) transitions are represented by squares and (2,1)transitions by crosses. The faint squares represent the (1,0) Q-branch measurements.

Figure 5.13: Column density ratio diagrams for SK 1. The left panel represents dataassuming no extinction whereas in the right panel the data points have been adjustedassuming a K-band extinction of 1.35 magnitudes. The symbol meanings are describedin Fig. 5.12. The (3,2) S(3) transition is represented by the triangle.

slab of gas at 2 000K in LTE with an ortho to para ratio of 3. Figs. 5.12 and 5.13 show

the relative columns plotted against the upper level energy equivalent temperature T j of

each level. The e!ect of added K and H-band extinction is illustrated. The CDRs show a

temperature dependence, implying that the excited gas is not of constant temperature. A

curved surface of varying temperature is consistent with the results, i.e. a bow shock.

CDR diagrams for NB1, NB2 and SB 1/SB 2 are shown in Figs. 5.14 and 5.15. The

weaker emission leads to a lack of higher excitation points and makes it impossible to

identify a temperature dependence. The position of the Q-branch (faint squares) lines

161


Figure 5.14: Column density ratio diagrams for NB1 and NB2. The symbol meaningsare described in Fig. 5.12. These data points imply no extinction however the relativelyweak Q-branch fluxes are highly a!ected by atmospheric absorption beyond 2.4 µm.

Figure 5.15: Column density ratio diagram for SB 1.

relative to the (1,0) S-Branch lines (squares) is used to constrain the extinction. An AK

extinction of ! 0.0 produces the best results confirming that the gas is of very low density.

Peak Flux Positions

The advantage of the IFU is that multi-wavelength information is gathered simultane-

ously. Any positional variation in the excitation conditions can be detected provided that

the separation is resolvable and that the higher excitation line emission is not too faint.

The data was examined for any spatial shift in the conditions traced by line emission.

Figs. 5.16 and 5.17 display the NK1 and SK 1 (1,0) S(1) images overlaid with [Fe II]

contours. Whereas the shift in the peak position is clearly detected between the (1,0) S(1)

162


Figure 5.16: Left: H2 (1,0) S(1) image of NK1 overlaid with [FeII] contours. Middle andright: H2 (2,1)/(1,0) S(1) ratio image of NK1 overlaid with H2 (1,0) S(1) contours at 17.4,27.8, 34.7 and 41.7 " 10!18 W m!2 arcsec!2 and [FeII] contours at 3.5, 4.9, 6.3 and 7.6 "10!18 Wm!2 arcsec!2.

Figure 5.17: H2 (1,0) S(1) image of SK 1 overlaid with [FeII] contours (left). H2(2,1)/(1,0) S(1) ratio image of NK1 overlaid with H2 (1,0) S(1) contours at 27.8, 62.5and 90.3 " 10!18 W m!2 arcsec!2 (middle) and [Fe II] contours at 5.9, 10.4 and 13.9 "10!18 Wm!2 arcsec!2 (right).

163


and [Fe II], these images show that the rest of the emission is also shifted; the bulk of the

[Fe II] emission lies ahead of the (1,0) S(1) emission (in the flow direction) as expected

for a forward moving bow shock. Also shown are maps of the (1,0)/(2,1) S(1) ratio with

overplotted contours of the (1,0) S(1) and [Fe II] emission. For NK1 no variation in the

excitation map can be detected but the SK 1 ratio map shows a clear increase in the exci-

tation towards the south with the [Fe II] shifted in the same direction. SK1 corresponds

well to a bow shock.

The peak position o!sets have been plotted against the upper level temperatures of

each transition. The results for NK1 and SK 1 are displayed in Figs. 5.18 and 5.19 where

a trend can be noted. For NK1 along the outflow axis (in the y-direction) the higher

excitation centroids tend to be located north of the (1,0) S(1) peak position (correlation

factor = 0.58), however a trend is also seen perpendicular to the flow axis (in the x-

direction) (correlation factor = 0.82). The higher excitation lines show a tendency to

be shifted in the western direction. This unexpected result indicates that the excitation

increases slightly from east to west (left to right in all the figures presented here). For

SK 1 the higher excitation lines are shifted in a y-direction towards the south, away from

the central source (correlation factor = -0.73). Interestingly, in the x-direction all the

higher excitation centroids are located to the west of the (1,0) S(1) peak position as is also

found for NK1.

A spatial variation of the excitation conditions is resolved but which underlying struc-

ture is detected? Either the shock’s cooling layer is resolved or the geometric bow shock

anatomy where the curved shock surface is the source of the variation. An expected cool-

ing length for a C-type shock is ! 1016 cm for typically expected conditions (see Smith &

Brand (1990a)). For the H2 NIR lines the e!ective cooling length is ! 1015 cm which is

!0.15## for HH 212. Although the FWHM seeing is 0.5##, such a length scale is just about

resolvable for the measured centroid o!sets suggesting that the shock front itself and bow

shock geometry are both tentative possibilities at this stage.

Possible reasons for the location of higher excitation emission to the west in both knots

are: (1) The source is moving in this direction relative to the surrounding cloud and the

164


Figure 5.18: The x (left) and y (right) peak flux positions relative to the (1,0) S(1) line areplotted here against the upper level energy of each transition for NK1. Crosses representthe v = (1,0) transitions, squares the v = (2,1), and the triangle represents the [FeII] 4D7/2– 4F9/2 transition at 1.644 µm. The approximate errors of 0.1## are indicated by the dottedred lines. The correlation factors for the distribution of points along the x and y directionsare 0.82 and 0.58 respectively.

Figure 5.19: The x (left) and y (right) peak flux positions relative to the (1,0) S(1) line areplotted here against the upper level energy of each transition for SK1. The symbols areas in Fig. 5.18 and the diamond represents the (3,2) S(3) position. The correlation factorsfor the distribution of points along the x and y directions are 0.57 and -0.73 respectively.

ram pressure results in a slightly higher excitation on one side of each knot. In this case

the misalignment of the jet and counter jet would not be caused by this relative movement

because the jets are misaligned in the opposite sense, i.e. with the jets inclined towards

the approaching cloud material. (2) The jet, possibly with a small angle of precession, is

burrowing a tunnel through the high density circumstellar gas. Higher excitation would

be expected where the jet abrades the tunnel edges; this could be happening preferentially

165


Figure 5.20: The x (left) and y (right) peak flux positions relative to the (1,0) S(1) line areplotted here against the upper level energy of each transition for NB1.

Figure 5.21: The x (left) and y (right) peak flux positions relative to the (1,0) S(1) line areplotted here against the upper level energy of each transition for SB 1.

on one side because of jet precession or relative drift. (3) Another possibility invokes the

alignment of the magnetic field. If the knots are unresolved bow shocks which are subject

to an oblique field, the bow asymmetry would result in preferential excitation toward

one side of the bow. In this case the magnetic field lines would have to be orientated in

di!erent directions for each bow, roughly perpendicular.

The o!sets measured for the bows are shown in Figs. 5.20 and 5.21. No trend can

be seen as the detected emission is too weak to locate the higher excitation line emis-

sion peaks. More sensitive observations are required to complete such an analysis. The

H2 (1,0) S(1) emission from the bows is weaker than the inner knots by a factor ! 2 so

that observations which are at least twice as sensitive will be required in order to detect

166


the higher excitation lines. The higher excitation lines from H2 in the K-band such as the

V = 4$ 3 lines (from > 23 000 K) are about 50 times weaker than the (1,0) S(1) line for

a J-type shock (several 1 000 times weaker for a C-type shock). For SK 1 the (3,2) S(3)

line is detected which is ! 30 times fainter than the (1,0) S(1) line. IFU observations

which are several times more sensitive will detect the higher excitation lines from both

the inner bows and the knots. Such observations should be possible in the near future with

the Large Binocular Telescope (see Section: Conclusions and Future Prospects).

Double Bow Shocks

The appearance of double bow shocks NB1/NB2 and SB 1/SB 2 is extremely puzzling.

Close examination of the jet knots in the high resolution image presented in McCaughrean

et al. (2002) also reveals that some of the knots can also be resolved into two components.

Close pulses in jet velocity can give rise to such double bows (a simulated outflow re-

sembling HH212 is presented in Fig. 1.10). The gravitational forces resulting from a

binary or multiple system may control the accretion/ejection phases and bring about the

necessary jet velocity variations.

Double shocks may also be due to the presence of both the forward ambient shock

front and the reverse Mach disk. At high density the cooling length is reduced and the

separation between both shock components is reduced. The clear separation seen in NB1

and SB 1 would then be due to the lower density medium in these regions. Such an idea

also provides a possible explanation for the inter-knot emission as illustrated in Fig. 5.22.

Whereas the forward shock results in the entrainment of ambient material which is pro-

jected outward, a curved reverse shock has the e!ect of entraining and refocusing the jet

material into a more collimated flow. This is because at high densities the forward and

reverse shocks come into close contact and the reverse shock is forced to adopt a curved

shape to match the forward bow. This higher momentum material would be less hindered

by the cloud resistance, break through the bow structure and give rise to the inter-knot

emission where the shearing of flow velocities occurs.

167


Jet

Ambient Medium

Forward Shock

Reverse Shock

Figure 5.22: An explanation for the inter-knot emission is provided by the the combinede!ect of a forward shock and a curved reverse shock. Whereas the ambient materialis entrained and propelled outward by the forward shock, the jet shock entrains the jetmaterial into a more collimated and focused flow which, under certain conditions such ashigh density, can breach ahead of the forward bow to shock excite gas in the inter-knotregion.

5.5 Summary of Findings

The advantages of integral field spectroscopy have been demonstrated in this work. Imag-

ing simultaneously over a wide range in wavelength space can be successfully used to

trace the excitation conditions in HH objects. The IFU and similar instruments on even

larger telescopes will no doubt play a vital role in the ongoing investigation into stellar

birth. Besides demonstrating the potential of this instrument, the main findings of this

study are as follows:

• The inner knots and bows of HH212 are seen in emission from gas which is colli-

sionally excited. The vibrational excitation temperatures are ! 2 400K for the knots

and ! 1 700K for the bows.

• The K-band extinction found for the knots is 1.3 ± 0.2 mag which corresponds to

AV = ! 12 mag, according to Rieke & Lebofsky (1985), and a H column density of

! 2.2 " 1022 cm!2. No optical emission has been detected from these bright knots.

A much lower extinction is measured for the bows of < 0.7 mag suggesting that

they have escaped from the higher density gas surrounding the outflow origin.

• 1.644 µm [Fe II] emission is detected alongside the H2 emission of the knots. The

bulk [Fe II] emission is marginally displaced in the y-direction relative to the (1,0)

168


S(1) emission for both knots and shows that higher excitation is located on the side

opposite to the driving source, typical of a forward moving bow shock. No [Fe II]

was detected in the bows.

• The peak flux positions for each line emission image were determined. The po-

sitions show a weak dependency (the measured o!sets are close to the resolution

limit) on the upper level temperatures for the knots. For SK 1 and NK1 the peak

positions show a dependency on the upper level temperature in the y-direction; the

higher excitation centroids tend to be o!set from the (1,0) S(1) centroid in a direc-

tion of increasing distance from the outflow source. The (2,1)/(1,0) S(1) excitation

ratio for SK 1 is also higher at the southern end of the knot. It is unsure which

underlying structure is resolved through the displacement of the peak positions. Ei-

ther the shock cooling layer itself is being detected or the variation in excitation

conditions due to the curved structure of a bow shock.

• A trend is also found for both knots in a direction perpendicular to the outflow axis;

in both cases the trend is in the same direction, from east to west, with the higher

excitation centroids preferentially located towards the western side of each knot.

Which mechanism could bring about this trend? Three possibilities are entertained

involving (1) the relative drift of the inner cloud material, (2) jet abrasion at the

edges of the outflow tunnel, and (3) bow shock asymmetries due to the orientation

of the magnetic field lines.

169

Chapter 6

Discussion

170

Chapter 6. Discussion

The Evolution of Protostars

Resolving the evolution of protostars beyond the categorisation into Class 0, I, II, and III

is proving to be a formidable task for astrophysicists. Newly forming stars are hidden

from view by the cloud material out of which they grow. The observable quantities have

been rigorously examined in the search for clues.

The extensively used indicators, Lsmm/Lbol and Tbol, are dependent on the accretion

rate at the time of measurement. However, aggressive and quiescent phases in the ac-

cretion rate can result in a classification which does not reflect the overall stage in the

evolution. Theoretical evolutionary models such as those presented by Smith (2000) (see

Appendix D) have met with reasonable success. The model assumes an abrupt evolution

followed by a smooth power law decrease in the accretion rate. The predicted relation-

ship between the H2 (1,0) S(1) luminosity and Lbol matches the observed measurements

reasonably well (Stanke, 2000); the outflows from Class 0 sources are found to have a

tendency towards higher LH2 than their Class I counterparts at similar Lbol.

Froebrich (2005) compiled a comprehensive list of all known Class 0 protostars along

with their broad-band 1 µm to 3.5 mm observations. The data were used to determine

the SED and infer Tbol, Lbol, Lsmm/Lbol and Menv. The evolutionary model of Smith (1998,

2000); Alves & McCaughrean (2002) was then applied to infer the final stellar masses.

Although the errors involved are relatively large, the large sample which involved 50

sources increases the level of confidence. The range of final masses was compared to the

IMF and shows good agreement for stars > 0.5 M". 25% of the objects sampled were

found to have a much lower luminosity, considering their Lbol and Lenv. Quiescent accre-

tion phases are suggested to be responsible in this case. Alternatively, these sources could

follow a di!erent evolutionary track which is more gradual. Because the outflows repre-

sent the accretion rate over a period of several 103 yr they could potentially provide better

insight into the evolutionary steps occuring on larger timescales than the instantaneous

Lsmm/Lbol measurement. For each individual outflow all the various methods of infering

age should be considered.

The three outflows investigated in this thesis are listed in Table 6.1 along with some

171


Table 6.1: Observed properties of the three protostellar outflow systems investigated. Theextents are corrected for the angle to the plane of the sky and the H2 (1,0) S(1) luminositieswere dereddened using the average AK values. dK is the distance from the driving sourceto where the outflow appears in the K-band. The representation a(b) represents a " 10b.

Outflow Extent L(1,0) S (1) LS iO J=(5,4)$ Lbol Lsmm/Lbol Tbol Menv

† dK tdyn ‡(pc) (L") (L") (L") (K) (M") (AU) (yr)

HH240 0.97 25(#3) < 5.9(#10) 17 1.4(#2) 77 0.36 36.6(3) 4700HH211 0.16 9(#3) 6.8(#9) 3.6 4.6(#2) 33 0.80 1.9(3) 800HH212 0.54 12(#3) 1.7(#9) 14 2.0(#2) < 56 0.28 3.3(3) 2600

! – The SiO J = (5,4) luminosities were derived by Gibb et al. (2004b).† – Values taken from Froebrich (2005).‡ – The dynamic age, tdyn, assumes a velocity of 100 km s"1.

of their reliably measured quantities which may be used to evaluate evolutionary status.

The true outflow extents were determined by considering the angle of the outflow relative

to the plane of the sky. The H2 (1,0) S(1) luminosities are corrected for extinction using

the AK values derived from the spectroscopic results. Based on the age criteria, HH 211

is classified as the youngest protostar in the sample. The outflow possesses the highest

SiO J = (5,4) luminosity which implies a high jet speed and that the gas resisting the jet

is of high density (5–10 " 106 cm!3) (Gibb et al., 2004b). The fact that the outflow extent

is relatively small is also suggestive of youth, although the size and dynamic timescale

are highly subject to the environmental structure. Whereas HH212 also attains a Class 0

status, HH240 has been classified as a Class 0/I object (according to its Tbol and Lsmm/Lbol

measurements) and it is interesting to note that it also possesses the largest outflow, the

lowest SiO J = (5,4) luminosity, and the smallest LH2/Lbol ratio.

The total outflow luminosity can be approximated using Lrad = 37(L(1,0) S (1)) = outflow

power P (see Section 4.5). Ignoring the radiative e"ciency (which may be close to unity

for HH240, HH 211 and HH212), the mass accretion rate can be estimated from Macc =

2P/)v2jet where ) ! 0.1 is ratio of the mass accretion rate to the mass outflow rate. An

approximate timescale for the Class 0 stage t0 can be estimated by assuming that the

accretion rate remains steady throughout and that the entire envelope mass is accreted

172


Table 6.2: The present accretion rates and Class 0 timescales.

Outflow Macc tO(M" yr!1) (yr)

HH240 4.5 " 10!6 3.6 " 104HH211 1.6 " 10!6 2.2 " 105HH212 2.2 " 10!6 5.8 " 104

OtherOutflowsL 1157 1.1 " 10!6 2.1 " 105CepE 5.9 " 10!5 1.8 " 104L 1448C 1.0 " 10!6 4.8 " 105HH25 1.2 " 10!6 4.5 " 104

(with 10% ejected), i.e. not dissipated. tO is the time taken for the protostellar mass to

equal half the envelope mass at the present accretion rate:

tO &Menv

2 Macc(6.1)

The present accretion rates and Class 0 timescales thus estimated for HH240, HH 211

and HH212 are presented in Table 6.2. Also presented in the table are values estimated

from other sources which were selected from Table 6 of Froebrich et al. (2003) and clas-

sified as definite Class 0 objects in Froebrich (2005). The extinction for these objects is

unknown so AK = 1 mag is adopted except for Cep E where AK = 2 mag was used (Smith

et al., 2003a). The uncertainties are extremely large in these estimates. If the conversion

of mechanical power to radiation is less e"cient than unity then the accretion rate is un-

derestimated as is tO . The assumption of a constant accretion rate and ) also introduce

large uncertainties. Another large source of error is the estimate of the envelope mass;

Froebrich (2005) estimate an error factor of order three. The time spent for individual

sources in the Class 0 phase of birth would also vary from source to source depending on

the local conditions such as the amount of mass available for accretion.

The Class 0 to Class I lifetime ratio has been estimated to be about 1:10 (see e.g.

Andre & Montmerle (1994)) with the Class I phase established from IR surveys to last

173


!1 – 2 " 105 yr (Greene et al., 1994; Kenyon & Hartmann, 1995). However, Visser et al.

(2002) detected roughly equal populations of Class 0 and Class I objects in a survey of

optically dark clouds using the bolometer array SCUBA on the James Clerk Maxwell

Telescope at " = 850 µm. Their survey suggests that the Class 0 and I lifetimes are about

equal, also lasting of the order 105 yr. The Class 0 timescales estimated here are subject to

large uncertainties but are located between the Class 0 ages of Andre &Montmerle (1994)

and Visser et al. (2002). Such a method could be employed in the near future when high

sensitivity data becomes available to make predictions and test the evolutionary phases.

This study into the nature of shocked emission along three prominent outflows shows

that the environment through which outflows propagate cannot be ignored. The H2 lumi-

nosity measured is dependent on the density, the extinction, the type of shock (C-shock

or J-shock), the magnetic field strength and direction, the fraction of ions present, the

molecular fraction, as well as the orientation of the outflow. All these parameters not

only vary from outflow to outflow but also between di!erent locations along the flow and

they determine the amount of emission detected as well as the observed outflow extents.

Outflows also disrupt and modify the gas into which they flow. The environments into

which jets propagate are not perfectly smooth and uniform. The extent to which the en-

vironmental structures govern the chemistry and dynamics of outflows is beginning to be

understood. A quantitative approach to deciphering the underlying interplay of physical

principles and the intrinsic outflow characteristics will involve further in-depth studies of

the outflow environments as well as the close protostellar vicinities in combination with

statistical studies of star forming regions.

174

Conclusions and Future Prospects

Conclusions

In the vicinity of star birth, molecular cloud material is disturbed and excited by high

velocity jets which are launched in the process of mass accretion onto protostars. In this

thesis I have presented an analysis of the conditions experienced as outflowing material

interacts with its surroundings. Supersonic flows shock excite the gas resulting in de-

tectable emission. The aim of this study was to explore the interaction of protostellar

jets with their environment, to reach conclusions about the dynamic outflows and their

relationship with the protostars which drive them. In order to carry out the investiga-

tion, images and spectra of three di!erent youthful protostellar outflows were obtained,

analysed and interpreted in terms of their morphology and excitation conditions. Bow

shock models were employed to elucidate the structures which form so readily in such an

environment. I firstly present the main conclusions for each outflow.

HH240/241

Narrow-band near-infrared images and position-velocity spectroscopy were obtained.

• The HH240 and HH241 bow shocks are propagating in a medium which is already

set in motion with an intrinsic outflow speed of !20 km s!1 away from the driving

source.

• The large HH240A bow corresponds closely to a C-type bow shock. The parame-

ters constrained through the model comparison include the orientation, bow veloc-

175


ity, gas density, ion fraction, intrinsic bow geometry and magnetic field. The high

magnetic field necessary to fit the data implies that the material being shocked is

the individual outflow itself as the cloud would not be in virial equilibrium with the

implied magnetic pressure.

• HH240A is interpreted in terms of the detected optical emission. The shock speed

of 260 km s!1, based on [O III] ratios, suggests the impact of a fast jet which drives

the large bow through the outflow. A slender jet seen in H( and a compact Mach

disk seen in [O I] and [N I] are suggested to explain the data.

• The smaller HH240C bow, which is more distant from the source, has higher pre-

shock density, higher vibrational excitation and higher extinction than HH240C.

Yet there is no associated CO emission suggesting that the bow is entering a denser

region. While H2 emission is abruptly generated by the shock, su"cient CO has not

yet been entrained by the smaller more bullet-like bow. The bow does not corre-

spond completely to C-type shock and it is interpreted as a J-type shock undergoing

transition to C-type as it enters the denser medium.

• The high fraction of atoms suggests that previous outflow episodes have partly dis-

sociated molecules.

• The fraction of ions (& = ni/nn, i.e, the number of ions relative to the number of

neutrals) predicted by the bow shock modelling for HH240A is ! 1 " 10!5. The

predicted level for cosmic ray induced ionisation at the density of 2.5 " 103 cm!3

is & & 2 " 10!7. At such densities exposure to external UV radiation raises the

ion fraction and a relationship of the form & ! 10!3n!1/210!0.5AV is estimated for

partially optically thick clouds exposed to the Galactic UV field.

• The CO outflow is associated with stationary cloud material. Therefore, the gas set

in motion, accelerated by just a few km s!1 on both sides of the outflow, is molecular

cloud material.

176


A global model for the outflow is suggested. Bipolar jets have driven out and accelerated

the cloud material to !20 km s!1. Occupying the two channels are the outflow features

which are formed through episodic ejection events and a slowly precessing jet (which is

suggested by numerical simulations of the outflow, see Section 1.3.4. The bow shocks are

initially driven by the episodes and then drift until their momentum is exhausted.

HH211

Narrow-band near-infrared images and K-band spectroscopy were obtained.

• vibrational excitation ratios and an ortho to para ratio of three corresponding to

shock heating are found along the outflow.

• C-type bow shocks propagate along the western outflow. The model fitting has

constrained several parameters including the density, bow velocity, ion fraction,

intrinsic bow geometry and the magnetic field strength and direction.

• The bows become luminous within dense clumps where high extinction values are

measured.

• The series of western bows is successfully modeled as a series of initially identical

bows propagating within a medium of decreasing density. The bows become less

detectable as they approach the cloud edge where they finally disappear.

• The bow shock asymmetries can be explained by the magnetic field direction lying

oblique to the jet flow direction.

• A band of continuum emission is confirmed to extend along the outflow direction.

The most likely source of this continuum is scattered light from the driving proto-

star itself. The radiation escapes along the outflow through a low density cocoon

excavated by jet activity. The continuum is scattered by dust along the cavity edges

and dense clumps along the outflow.

• Emission from [Fe II] is detected in isolated condensations along the outflow which

are coincident with strong H2 emission. For the inner western bow shock (bow-de)

177


the location of [Fe II] is extremely puzzling. Its coincidence with the strong H2

emission and not the bow apex as predicted raises questions about the underlying

bow geometry assumed. It is suggested that the gas density near the bow apex is

significantly reduced to inhibit [Fe II] emission. The jet may have ruptured and

broken through the bow shock.

A global model is evoked in which episodic outburst of jet activity give rise to the prop-

agating bow shocks. Moving through an inhomogeneous environment, the bows become

luminous where they encounter dense material, thus highlighting the clumpy nature of the

surrounding material. It is unclear what the source of inhomogeneity is. Either the clouds

intrinsically possess such structural variation or the impacting outflows sweep the gas into

such structures.

HH212

Integral field spectroscopy was carried out to simultaneously obtain narrow band images

at 1 024 di!erent wavelength locations between 1.5 and 2.5 µm.

• The inner knots and bows are seen in collisionally excited emission in the wake of

shocks. The vibrational excitation temperatures are ! 2 400K and ! 1 700K for the

knots and bows, respectively. The lower excitation temperatures for the bows make

them less luminous than the knots.

• The K-band extinction is 1.3 ± 0.2 mag for the knots and < 0.7 mag for the bows

suggesting that they have broken free of the dense inner gas which is powering and

obscuring the jets.

• [Fe II] emission is detected in the knots. The [Fe II] is displaced relative to the H2(1,0) S(1) emission in a forward direction as is expected in a bow shock configura-

tion.

• The peak flux positions for each line transition were determined for the inner knots.

A good trend is found between the peak positions and the upper level excitation

178


temperatures of each transition. The southern knot shows increasing excitation in

the outflow direction as would be expected in a forward propagating shock. Both the

southern and northern knots show similar increasing excitation in the same sense,

perpendicular to the outflow direction. Various explanations are entertained includ-

ing relative drift between the outflow source and the ambient medium, jet abrasion

along the edges of the low density jet channel, and asymmetries cause the magnetic

field direction.

• An explanation for the observed double bow and knot features and inter-knot emis-

sion is provided. In high density gas the jet is refocused by the Mach disk and

breaks through the forward shock to excite the gas along a thin stream in the inter-

knot regions.

The environments characterising outflows vary significantly from object to object.

The volume and extent of shock excitable gas surrounding the outflow region plays a

crucial role in determining the outflow appearance. It determines to what size the outflow

may grow to and supplies the obscuring gas which absorbs the outflow radiation. On

a smaller scale, the individual outflow is subject to significant inhomogeneities which

determine the excitation conditions as well as the extinction at each location.

In order to investigate the general characteristics of outflows it is necessary to study

them in detail. Only when the intrinsic luminosities are known can they be confidently

compared with theoretical evolutionary schemes. A timescale for Class 0 objects is pro-

posed which relates the envelope mass to the present accretion rate as determined from

the intrinsic H2 luminosity. The lifetime of the Class 0 stage is uncertain. Predictions

from statistical studies range from !104 yr (10 times shorter than the Class I lifetime) to

the more recent !105 yr (equal to the Class I lifetime). The Class 0 timescales determined

for the outflows investigated here range between both lifetimes. It is worth pointing out

that di!erent mass objects are likely to evolve on di!erent timescales. To improve age

predictions it will be necessary to determine what fraction of the envelope mass is dis-

179


persed rather than accreted, how the accretion rate and accretion/ejection e"ciency vary

over time. Improved telescope sensitivity (both terrestrial and space-borne) alongside

the inevitable increase in computer capabilities are likely to yield fascinating results and

breach the gap between speculation and accepted fact.

Future Prospects

The main goal of this thesis was to intensively analyse and compare the environments of

a small number of protostellar outflows. The obvious extension to this work will be to

increase the number of outflows studied. Characterising the environments and correcting

for extinction e!ects for a larger number of outflows may yield valuable insight into the

intrinsic outflow phenomenon and better constrain the protostellar evolutionary sequence.

In addition to increasing the sample size, the move forward will be complemented by the

advent of new instruments in several ways:

• Infrared observations from space will provide high resolution and sensitive mea-

surements across a broad range of wavelengths. In particular, the James Webb

Space Telescope (scheduled for launch in August 2011) will contain near- and mid-

mid-infrared detectors capable of 0.0317##/pixel sampling between 2 µm and 4 µm

and subarcsecond pixel scales between 5 µm and 28 µm. The high resolution NIR

observations ought to reveal the width of the shock fronts, further constrain the

physics and chemistry involved and measure proper motions accurately. In addi-

tion, air-borne and space-borne mid- to far-infrared detectors (SOFIA, SIRTF) will

make it possible to detect protostars and outflows in the longer wavelength lines

predicted by the bow shock modelling (Table 3.5). Indeed, protostars emit most

of their radiation at these longer wavelengths which are obscured by the earth’s

atmosphere.

• From the ground, adaptive optics can provide higher resolution observations of the

events surrounding star birth. In particular, the VLT is allowing for serious strides

forward and can be used to constrain the excitation conditions of bow shocks by

180


performing sensitive observations at di!erent NIR wavelengths. The sample of

possible outflows is restricted, however, due to the lack of bright stars (necessary

for adaptive optics) in the cloudy regions near to protostellar sources. Weak lines

(from higher vibrational H2 levels) in the NIR and R-band should be observed in

order to determine the extent of UV excitation. Higher resolution position-velocity

data from various lines will provide valuable information about the flow dynamics

and entrainment processes involved in outflow propagation. This data can be di-

rectly compared with C-type and J-type bow shock models. The Large Binocular

Telescope (LBT), scheduled for commissioning in spring of 2006, will be com-

prised of two 8.4 meter telescopes and house a NIR imager and spectrograph (LU-

CIFER) which is also planned to be capable of integral field spectroscopy (IFU)

with extremely high resolution. This instrument will allow for the gathering of

multi-wavelength information from outflows and greatly enhance our knowledge of

the excitation conditions involved. High resolution observations will also allow for

the observations of more distant regions and open the door to a greater insight of

(the poorly understood) high mass star formation.

• The relationship between CO outflows and H2 jets will be studied to better constrain

the entrainment mechanisms. In particular the Atacama Large Millimeter Array

(ALMA) will allow for high resolution millimeter observations of CO emission,

including the high-J lines predicted for bow shocks. ALMA will also allow us

to determine the multiplicity of many of the sources involved, an important factor

when considering the outflow morphologies.

• One of the crucial factors involved in interpreting the outflows is the extinction.

The estimates of the K-band extinction AK used in this study were derived from

the (1,0) Q-branch emission lines of H2. However, the large errors associated with

these measurements when made from the Earth’s surface lead to uncertainties in the

derived values of AK . A follow-up to the analyses presented in this thesis should

include more accurate extinction estimates. Observations of the (1,0) Q-branch

181


lines from space will provide accurate measurements of AK . The ratio of [Fe II]

forbidden transitions at 1.257 µm and 1.644 µm (both originating in the same upper

level) can be used to determine the reddening factor %J!H . High resolution imaging

using narrow-band filters centered on these wavelengths or spectroscopy (using the

VLT and LBT) will provide accurate estimates and test the extinction estimates

derived from the H2 (1,0) Q-branch lines.

Alongside the new wealth of observational capabilities, the work presented in this

thesis can also be enhanced through improvements and modifications to the modelling

methods. The inevitable advances in computer power will make it possible to include

more details about the physics and chemistry in the code. In addition, there are several

modifications which should be considered:

• The bow shocks could be interpreted using a fully time-dependent fluid code instead

of the current steady state code which assumes the geometry. Such a code would

allow for the formation of instabilities, the generation of vorticity, as well as the

forward and reverse shock (Mach disk) structures. Instead of considering either the

J-type of C-type physics, the code could be modified to include both possibilities,

i.e. a switch between C and J-type for each shock element which depends on the

conditions experienced. The inclusion of a non-uniform ambient medium could be

included in order to simulate the apparent clumpiness of the observed outflows and

bow shocks which are undergoing a transition between J and C-type physics.

• The chemistry involved should be updated including the rate coe"cients and cool-

ing mechanisms. For example, the code currently only considers collisions with one

type of reduced mass (including both H and He) atom whereas greater accuracy will

be achieved by considering collisions with H and He atoms separately.

• The assumption of a constant ion fraction could be misleading. The ion fraction

would be enhanced by UV contamination (from the bow apex) or collisions. This

possibility should be accounted for in a time-dependent model.

182


• The model assumes individual planar elements for each individual shock compris-

ing the bow surface. However, pressure changes due to shearing at the bow surface

could significantly alter the appearance. This e!ect ought to be considered.

• And finally, as more of the parameters involved become constrained through better

observations, the ability to model observed bow shocks will be greatly improved.

This provides a unique way of probing the magnetic field conditions (both strength

and direction). Because of the di"culties in obtaining information about the out-

flow magnetic field directly, this exploration will prove to be extremely valuable.

183

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193

Appendix A

Model Parameter Dependence

194

Appendix A. Model Parameter Dependence

The following set of figures illustrates the extent to which the C-type model image, H2

(1,0) S(1) luminosity and (2,1) S(1) / (1,0) S(1) ratio change as the various parameters

are adjusted by relatively small amounts. The chosen bow shock has a bow velocity of

70 km s!1 and pre-shock density of 2.5 " 103 cm!3. The figures show how the individual

parameters can be systematically explored and indicate the level of confidence involved in

finding the best fit. In searching for the ideal model, several combinations are explored,

beginning from di!erent configurations. Often parameter exploration was carried out

independently by Michael Smith to search for alternative regions in parameter space.

However, we both settled on the same model to within a small margin of di!erence. The

constraining observational data limits the possibilities. Although only the C-type model

dependence is shown here, the J-type model shows a similar parameter dependence. The

J-type parameters were explored independently of the C-type model in each case.

Dependence on molecular fraction

Figure A.1: The Dependency of bow appearance on the molecular fraction f (=n(H2)/n(H) + 2n(H2)). From left to right f varies from 0.1 to 0.5

195


Dependence on magnetic field direction

Figure A.2: The Dependency of bow appearance on the magnetic field orientation µ. Themagnetic field direction relative to the bow direction of motion varies from 0% to 135% insteps of 15%. The (1,0) S(1) luminosity and vibrational excitation ratio are given for eachbow.

196


Dependence on velocity and angle to the line of sight

Figure A.3: The Dependency of bow appearance on bow velocity and the angle to the lineof sight. From left to right the bow velocity varies from 50 km s!1 to 90 km s!1 in stepsof 10 km s!1. From top to bottom the angle to the line of sight varies from 40% to 80% insteps of 10%. The magnetic field direction is parallel to the bow direction of motion foreach bow.

197


Dependence on density and velocity

Figure A.4: The Dependency of bow appearance on density and bow velocity. From leftto right the bow velocity varies from 50 km s!1 to 90 km s!1 in steps of 10 km s!1. Fromtop to bottom the density varies from 4.5 " 103 cm!3 to 0.5 " 103 cm!3 in steps of 1.0 "103 cm!3.

198


Dependence on magnetic field strength and ion fraction

Figure A.5: The Dependency of bow appearance on magnetic field strength and ion frac-tion. From left to right the Alfven speed (vA = B

964#$) varies from 1 km s!1 to 9 km s!1

in steps of 2 km s!1. From top to bottom the ion fraction varies from 1.0 " 10!4 to 1.0 "10!6.

199


Dependence on shape parameter s and velocity

Figure A.6: The Dependency of bow appearance on the shape parameter s and bow ve-locity. From left to right the bow velocity varies from 50 km s!1 to 90 km s!1 in steps of10 km s!1. From top to bottom the shape parameter s varies from 2.75 to 1.95 in steps of0.2.

200

Appendix B

Equations

201

Appendix B. Equations

B.1 Gravitational Instability

In order for a gas cloud to collapse under its own gravity an instability must form. Such

an instability may arise through turbulent compression or a break-down in the balance

between heating and cooling. The cooling leads to an increase in density and as a result,

the gas cools even faster. A perturbation can the grow in an accelerating process. The

critical mass which a volume of gas must attain in order to collapse under the force of its

own gravity is called the Jeans Mass. It can be derived by considering a small perturbation

(with prime marks) to the unperturbed gas variables (with ‘0’ subscript), see Pavlovski

(2003) and following Smith (2004),

p = p0 + p# pressure (B.1)

v = v0 + v# velocity (B.2)

+ = +0 + +# gravitational potential (B.3)

$ = $0 + $# density (B.4)

The gas hydrodynamic equations governing the gas flow are:

-$

-t+)' . $v* = 0 (B.5)

-v-t+)v .'*v = #1

$'p # '+ (B.6)

%+ = 4#G$ (B.7)

where G is the gravitational constant. In what is known as the Jeans swindle, the unper-

turbed flow variables are assumed to satisfy the equations for hydrostatic equilibrium,

p0 = #$'+0 (B.8)

%+ = 4#G$ (B.9)

202


By substituting B.1—B.4 into B.5—B.7 and using B.8—B.9, we find,

-$#

-t+ ')$0v#

*= 0 (B.10)

$0-v#-t= #c2s'$# # $0'+# (B.11)

%+# = 4#G$# (B.12)

where cs =6p0/$0 is the adiabatic sound speed. We search for solutions involving

small oscillations. Considering the first order e!ects, the variables are taken to vary as

exp+i)k.x # 3t*, where 3 is the frequency and k = 2#/" is the wave number where " is

the wavelength. Eqs. B.10—B.12 then give

#3$# + $0)k.v#* = 0 (B.13)

#$03v# = #c2sk$# # $0k+# (B.14)

#k2+# = 4#G$# (B.15)

Combining Eqs. B.13—B.15 we arrive at the dispersion equation,

32 = c2s#2#"

$2# 4#G$ (B.16)

This equation represents the propagation of acoustic waves which are modified by self-

gravity. The two terms on the right represent restoring forces which tend to re-expand the

compressed regions. And when,

" > "J =

##c2sG$

$1/2(B.17)

the system become unstable (3 becomes negative) and gravity will overcome the acoustic

restoring force resulting in collapse. For a spherical disturbance the corresponding critical

mass, called the Jeans Mass, is given by,

MJ =4#3

#"J2

$3$ =#

6

##

G

$3/2c3s $!1/2 (B.18)

203


In terms of the hydrogen number density n and using the equation of state for an ideal gas

(p = nkBT ) the Jeans mass becomes

MJ = 1.18M"#

T10 [K]

$3/2# n105 [cm!3]

$!1/2(B.19)

B.2 Rankine–Hugoniot Jump Conditions

Fluid dynamical motion is governed by the conservation of mass, momentum, and energy.

The equation of state relating the pressure to the temperature and density must also apply.

Here we restrict the description to flows without the influence of magnetic fields. The

conservation of mass is written in terms of the continuity equation:

-$

-t+ '.)$v* = 0 (B.20)

where $ is the density and v is the velocity vector. This equation implies that the rate of

change in the local density is determined by the di!erence in the flow rate into and out of

a given volume, along the direction of motion. In one dimension we get,

d$dt+ddx)$v*= 0 (B.21)

For a steady-state shock the timescale for variations are large compared to the time it takes

to flow across the shock front and the time derivatives can be dropped when relating the

pre-shock (0) and immediate post-shock (1) variables. Integrating Eq. B.21 we are left

with,

$0v0 = $1v1 (B.22)

Euler’s Force Equation describes the conservation of momentum,

$

#-v-t+)v.'*v

$= F # 'P (B.23)

204


where F is the Force vector and P is the pressure. For one dimensional flows this equation

reduces to

$dvdt+ $v

dvdx= #dP

dx(B.24)

and for a steady-state shock we drop the time dependency and integrate to get

P0 + $0v20 = P1 + $1v21 (B.25)

Eqs.B.22 and B.22 are called the Rankine–Hugoniot jump conditions for mass and mo-

mentum.

In order to derive the jump condition for energy across the shock front we can simply

consider the flow of particles across the front. The kinetic and internal energy before and

after the shock are considered. In unit time the energy, E0, of the gas entering unit area of

the shock is

E0 = $0v0#v202+ e0$

(B.26)

and immediately following the shock,

E1 = $1v1#v212+ e1$

(B.27)

where e0 and e1 are the internal energy per unit mass (= P/(' # 1)$) and ' is the usual

specific heats ratio CP/CV . The work done on the parcel of gas per unit time (energy) as it

passes through the shock is given by the pressure times the velocity. Including this energy

and equating Eq. B.26 and B.27 we find that

P0v0 + $0v0#v202+ e0$= P1v1 + $1v1

#v212+ e1$

(B.28)

Manipulation of Eq. B.28 using Eq. B.22 leads to the jump condition for the conservation

of energy,v202+'0'0 # 1

p0$0=v212+'1'1 # 1

p1$1

(B.29)

Eqs. B.22, B.25 and B.29 are the essential equations which relate the upstream flow vari-

205


ables to the immediate post-shock parameters.

206

Appendix C

CO Outflows and Protostellar Cores

207

Appendix C. CO Outflows and Protostellar Cores

HH241 / HH240 in CO J = (1,0)

Figure C.1: From Lee et al. (2000b). CO J = (1,0) emission map of the HH240/241region obtained with the BIMA 10–antenna interferometry array from Lee et al. (2000b)overlaid on the gray-scale H2 image of Davis et al. (1997). The triangle marks the positionof the driving source. The beam size is 12.11## " 8.53##. (a) The integrated CO emissionbetween 13.13 and 1.70 km s!1. (b) The red emission integrated between 13.13 and 9.32km s!1 and blue emission integrated between 7.03 and 1.70 km s!1. (c) and (d) Both showchannel maps at di!erent velocities.In panel (a) the contours begin at 16 Jy beam#1 kms!1 with a step size of 8 Jy beam#1 km s!1. In (b) the contours begin at 10 Jy beam#1km s!1 with a step size of 5 Jy beam#1 km s!1. For (c) and (d) contours begin at 4.5 Jybeam#1 km s!1 with a step size of 1.8 Jy beam#1 km s!1.

208


SFO16 in HCO+ and CO

Figure C.2: Integrated intensity maps of SFO 16 (in which the HH241 / HH240 outflowis located) in various transitions and isotopomers of HCO+ and CO. O!sets are measuredfrom the IRAS source. The CO J = (1,0) map has a lowest contour of 4.3 km s!1 andincrements of 1.4 km s!1. The CO J = (2,1) map has a lowest contour of 6.0 km s!1 andincrements of 2.5 km s!1. The C18O J = (1,0) map has a lowest contour of 0.6 km s!1 andincrements of 0.2 km s!1. The HCO+ J = (1,0) map has a lowest contour of 0.4 km s!1and increments of 0.3 km s!1. The HCO+ J = (3,2) map has a lowest contour of 0.9 km s!1and increments of 0.3 km s!1. The dotted rectangle in the HCO+ J = (1,0) map indicatesthe region over which the HCO+ centroid is shown in Fig. C.3. The dashed contour in theHCO+ J = (3,2) indicates the half-power contour of the N2H+ J = (1,0) emission. FromDe Vries et al. (2002).

209


SFO16 radial velocity structure

Figure C.3: SFO 16 centroid velocity integrated over the line core of HCO+ J = (1,0).The line-of-sight velocity has been subtracted out, and the contours and gray scale areindicated on the wedge to the right of the figure. From De Vries et al. (2002).

210


HH211 in CO J = (2,1)

Figure C.4: From Gueth & Guilloteau (1999). The bipolar molecular flow (top) andmolecular jet (bottom) of the Class 0 source HH211. Upper panel: CO J = (2,1) emissionintegrated between LSR velocities of 2.2 and 18.2 km s!1 with contours at 1.6 Jy beam#1km s!1. Lower panel: CO J = (2,1) emission integrated for velocities outside 2.2 and 18.2km s!1 with the first contour at 1 Jy beam#1 km s!1 and contour step of 1.5 Jy beam#1km s!1. The thick contours represent the 230 GHz continuum emission from the core.The systemic velocity is 9.2 km s!1.

211


HH211 in H13CO+ J = (1,0) + CO J = (2,1)

Figure C.5: From Gueth & Guilloteau (1999). H13CO+ J = (1,0) integrated emission(contour step is 50 mJy beam#1 km s!1); beam size 3.5## " 7.2##) overlaid with the lowvelocity CO J = (2,1) emission contours (as in upper panel of Fig. C.6).

212


HH212 in CO J = (1,0)

Figure C.6: From Lee et al. (2000b). CO J = (1,0) emission map of the HH212 regionobtained with the BIMA 10–antenna interferometry array from Lee et al. (2000b) overlaidon the gray-scale H2 image of Davis et al. (1997). The triangle marks the position of thedriving source. The beam size is 9.4## " 7.2##. (a) The integrated CO emission between-4.2 and 5.5 km s!1. (b) The red emission integrated between 1.96 and 5.51 km s!1. (c)The blue emission integrated between -4.5 and 1.7 km s!1. (d) and (e) Channel maps atred shifted velocities. (f) Emission at -3.7 km s!1 averaged over a 3 km s!1 to improvethe S/N ratio. In panel (a) the contours begin at 2 Jy beam#1 km s!1 with a step size of sJy beam#1 km s!1. The contours in (b) and (c) start at 1.5 Jy beam#1 km s!1 with a stepsize of 1.5 Jy beam#1 km s!1. The contours in (d) and (e) start at 2.5 Jy beam#1 km s!1with a step size of 1 Jy beam#1 km s!1. For (f) the contours start at 0.6 Jy beam#1 kms!1 with a step size of 0.3 Jy beam#1 km s!1.

213

Appendix D

Evolution Model

214

Appendix D. Evolution Model

Figure D.1: The theoretical model of protostellar evolution from Smith (2000). The timeevolution of the various quantities are plotted. The dotted vertical line represents the tran-sition from Class 0 to Class I when the model protostellar mass equals the mass containedwithin the circumstellar envelope.

The theoretical evolution of a protostar according to the evolutionary scheme proposed

by Smith (2000) is shown in Fig. D.1. The model is based on the assumption of a power

law accretion rate of the form

Macc(t) = M0

#e(

$$# tt0

$!$exp##t0t

$(D.1)

A sharp increase in the accretion rate to M0 is followed by a power law fall o!. A constant-

accretion corresponds to ( ! 0 and t0 small. Gradual accretion corresponds to ( ! 0.5

and abrupt accretion to ( ! 2 # 3.

The fraction of mass ejected in the jets is assumed to take the form

) = *

#Macc(t)M0

$&(D.2)

215


where 2 = 1 assumed to date. Hence, the mass left over which accretes onto the protostar

is given by

M%(t) =: t

0

)1 # )* Macc (D.3)

The jet speed v j is fixed to be proportional to the protostellar escape speed

v j = &#GM%R%

$1/2(D.4)

For * $ 1 and &(t) = 1, the jet power approaches the total accretion luminosity. The

models presented in Fig. D.1 adopt a maximum jet e"ciency of * = 0.4 and a jet speed

factor of & = 2.12.

The jet density, assumed to be smooth and cylindrically symmetrical, is given by

$ j =)Macc

2#r2jv j(D.5)

which gives the hydrogen nuclei density of

n j = 4.3 " 103) Macc

10!6M" [yr!1]

#102 [km s!1]

v j

$ #1016 [cm]

r j

$2[cm!3] (D.6)

The size of the protostellar outflow is determined by a ram pressure argument resulting

from the interaction with an uniform external density next. The outflow expansion speed

is given by

vext =v j

1 +)next/n j

*1/2 (D.7)

which yields the linear half-size D = d/2

D(t) =: t

0vext dt (D.8)

Of interest in this study is the relationship between the outflow luminosity (Lmech) and the

216


accretion rate which are related through

2Lmech (t) =vextD

.: t

0) Macc v2j dt

/(D.9)

The mechanical luminosity is equal to the full accumulated jet energy for a high density

external medium. But for a lower density medium the e"ciency of the momentum transfer

is roughly next/n jet.

217

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The Impact of Protostellar Jets on their Environment

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