The Story of Star Birth

Shantanu Basu

University of Western Ontario

CAP Lecture, UWO, April 2, 2003

Understanding our Origins

The Galaxy

Molecular Clouds

Disorderly

Complex

Nonlinear

Giant Molecular Cloud in Orion

Infrared view

From IRAS satellite

Molecular Clouds

Order?

Solomon et al. (1987)

From CO (J=1-0) maps.

2

1/ 2

2

2 0

3 32 0

2 5

if constant.

T

MM G

R

R R

Theory: equilibrium =>

1/ 2S

approx. true empirically = 1-dimensional velocity dispersion.

Effect of Magnetic Fields

Mathewson & Ford (1970)

Polarized starlight yields information about plane-of-sky component of interstellar magnetic field.

1950’s – Chandrasekhar, Fermi use polarization data to estimate interstellar B strength ~ few G (1 G = 10-4 T). Similar estimate from cosmic ray data by Schluter, Biermann, Alfven, and Fermi.

Magnetic Fields and PolarimetryŠ

Background Star emits Unpolarized Continuum

Result: Observed -vector is parallel to plane-of-the-sky component of .

EB

B

ee

Most Likely Orientation

Least Likely Orientation

Polarization of Background Starlight by Magnetically Aligned Grains

E

B

(Partial) Polarization Observed

Courtesy A

. Goodm

an

Taurus Dark Cloud Complex ( 1 - 10 pc scales)

Magnetic Field Strength Data

From measurements of the Zeeman effect.

Data from Crutcher (1999)

12/12

GB

Let mN Empirically, see

B In particular,

Best fit => 1.6.

Note: =1 =>gravitational potential energy = magnetic energy.

Dimensionless mass-to-flux ratio

Key Questions of the Early Stages of Star Formation

• How does matter arrange itself within interstellar clouds? Clarify the role of B and turbulence.

• Are clouds in approximate equilibrium between magnetic and turbulent support vs. gravity? Can we explain the observed correlations between , R, B, n?

• What is the dissipation time scale of MHD turbulence? If much less than cloud lifetime, why is it commonly observed? Are driving sources adequate?

• How do star-forming cores get established within clouds? Inefficiency of star formation.

Why Magnetic Fields?

Q. Why no large scale electric field?

A. Overall charge neutrality in plasma means that E is shorted out rapidly by moving electric charges.

In contrast, the required currents for large scale B can be set up by tiny drifts between electrons and ions.

Finally, once large scale B is set up, it cannot be shorted out by (nonexistent) magnetic monopoles, nor can the very low resistivity dissipate the currents in a relevant time scale.

Maxwell’s equations: 6

3

3 10 G on pc scales

10 cm/s.i ee

B

jv v

n e

Flux Freezing

In a highly conducting plasma cloud, contraction generates currents that make the magnetic field inside grow stronger, so that magnetic flux is conserved. The magnetic field lines are effectively “frozen” into the matter.

Self-inductance

Magnetic Pressure and Tension

2

1

4

1.

8 4

L

jf B B B

c

BB B

B

sn

B of bar magnet

B near solar surface

2 2

ˆ ˆIf .8 4L

c

B BB Bs f n

n R

Magnetic pressure gradient Magnetic tension due to finite radius of curvature Rc.

Magnetohydrodynamic Waves

2

4 c

B

RMagnetic tension

Alfven waves propagate like a wave on a tensioned string.

Propagation speed restoring term

inertial term

Alfven speed20 .

4A

Bv

Other wave modes include longitudinal motions as well.

Empirical evidence for MHD Waves/Turbulence

Basu (2000)

1

1

/ 2 , where

where4

,

.A

Ac

B

v

mn

Bv

1Best fit 0.45.c

i.e., Alfvenic motions in molecular clouds?

Outflows

MHDWaves

Thermal Motions

MHDTurbulence

InwardMotions

SNeH II Regions

Scenario for a Molecular Cloud B

A New Computational Model of MHD Turbulence

• Numerical solution of equations of ideal magnetohydrodynamics, .i.e., fluid equations + Maxwell’s equations in low frequency limit

• Start with one-dimensional self-gravitating equilibrium state 2 / 2

0 0, 0 sech for .

ˆ( , 0) .

z H

z

z t z H e z H

B z t B z

• Cloud is bounded by a hot external medium

•Add nonlinear driving force near z = 0 =>

Kudoh & Basu (2003)

.1.0for 2sin),( 000 HzztatzF a

(Spitzer 1942)

self-gravity

perturbation

Molecular cloud

Magnetic field line

Schematic picture of our simulation

A sinusoidal perturbation is input into the molecular cloud.

Magnetic field line

Low-density andhot medium

Simulationbox

z

Molecular cloud

Hot medium

Kudoh & Basu (2003)

Basic MHD equations in 1.5 dimensions

2

0

1

8

1

4

0

0

4

z

yz zz z

y y yz z

z

yy z z y

z

vt z

Bv v Pv g

t z z z

v v Bv B

t z z

T Tv

t zB

v B v Bt z

gG

zkT

Pm

mass continuity

z-momentum

y-momentum

isothermality

magnetic induction

self-gravity (Poisson’s eqn.)

ideal gas law

A Model for Turbulent Molecular Clouds

Kudoh & Basu (2002)

Highlights: Cloud expands due to turbulent pressure, achieves “steady state” between t = 10 and t = 40; later contracts when forcing discontinued at t = 40. Outer cloud undergoes largest amplitude oscillations.

Resolution: 50 points per length H0 .

in this model.1,,30 00

20 HcHca ss

Parameters:

A Model for Turbulent Molecular Clouds

A snapshot.

Averaged.

A Model for Turbulent Molecular Clouds

Time average within the standard cloud.

Rms speeds increase toward cloud boundary.

21,

2 yv2

,8

yB

21

,2 zv nkT

Transverse standing wave => boundary is a node for By, antinode for vy.

Results for an ensemble of clouds with different turbulent driving strengths:

.50,40,30,20,10 02

0 Hca s

Solid circles => half-mass position

Open circles => edge of cloud

1/ 2Z

0.5 Av

Correlations of Global Properties

What Have We Learned?

• Clouds can be in a time-averaged balance between turbulent support and gravity.

•Inner cloud obeys equipartition of transverse wave energy,

• Transverse modes dominate,

• Outer low density part of cloud undergoes large longitudinal oscillations, and exhibits transverse (Alfvenic) standing wave modes.

• Correlations and naturally satisfied.

• Further progress includes two- and three-dimensional simulations – need to scale to multi-processor systems, e.g., SHARCNET.

221.

8 2y

y

Bv

2 2.y zv v

0.5 Av 1/ 2Z

What Happens Next?

Motte et al. (1998)

HH47 jet seen by HST

Young stellar object and disk - HST

Local collapse of cores intensifies rotation and magnetic field strength.

Rotation => disks

Rotation + magnetic field => jets.

Outflow Model

Tomisaka (2002)

Critical interplay of rotation and magnetic field

Red = Magnetic field lines

Solid black = isodensity contours

Arrows = velocity vectors

Molecular or Dark Clouds

"Cores" and Outflows

Stages of Star Formation

Jets and Disks

Extrasolar System

1 p

c

Expansion Wave

Static outer core

Free-fall onto point mass

Region of infall moves outward at sound speed cs. Instantaneous radius of expansion wave is r = cst.

Based on model of Shu (1977)

Mass infall rate 3

.scdM

dt G

Q. But when does it end? How is the mass of a star determined?

sr c t

Key Questions of the Late Stages of Star Formation

• What sets the size scale of a collapsing region? Inefficiency of star formation.

• Do cores undergo fragmentation during collapse?

• Does most collapsing material land on a disk first? If so, how does accretion from disk onto star proceed?

• Jet/outflow formation and its interaction with disk dynamics.

• After a central point mass (the star!) forms, an expansion wave moves outward – when does it stop? This sets the maximum possible mass of a star.

Clues to the Mass Scale

• New two-dimensional MHD simulation (Basu & Ciolek 2003) – calculate nonlinear evolution of cloud column density integrated along mean field direction; no turbulent driving; periodic domain; initially critical mass-to-flux ratio =1)

Column density image Gravitational field vectors

Final Thoughts

• Fundamental question: how does matter arrange itself within interstellar molecular clouds?

• The role of magnetic fields and MHD turbulence is critical

• MHD simulations of turbulent support and core formation provide insight into the early stages of star formation

• Various groups have developed models for individual stages of the star formation process

• Progress can be made with high dynamic range simulations that tie together many different stages

• An ultimate question: how are stellar masses determined?