CH+ and SH+ absorption spectroscopy with Herschel: probingthe turbulent dissipation in the diffuse ISM.

B. Godard, E. Falgarone, G. Pineau des ForêtsM. Gerin, P. Lesaffre, F. Levrier

1 Quick overview of turbulence and its unkowns

2 The TDR (turbulent dissipation regions) model

3 Derive turbulence properties from molecular observations

Quick overview of turbulence 2/13

turbulent cascadeadvection force u · ∇udissipation forces

I friction ν∇2u

I compression 13ν∇[∇ · u]

I ambipolar diff. γin(ui − un)I magnetic diff. µ∇2b

transfer rate

ε = 2× 10−25 erg cm−3 s−1

Hennebelle & Falgarone (2012)

Quick overview of turbulence 3/13

intermittency

in space & timelocal dissipation ε = ε/fv

Frish (1995)

Moisy & Jimenez (2004)

unresolved questions

dissipative scales ?dissipative structure ?physical processes involved ?local rate of dissipation ?

The TDR (turbulent dissipation regions) model 4/13

dissipative phase

magnetized vorticesa2 = 4ν/l, uθmLagrangian approachnon-equilibrium chemistryturbulent heating processes

I viscous frictionI ion-neutral friction

relaxation phase

Eulerian approachno turbulent heating

courtesy of P. Hily-Blant

The TDR (turbulent dissipation regions) model 5/13

model parameters

• density nH

• shielding AV

• CR ionization ζ

• stretching a → l

• max rot. vel. uθm → uin

• transfer rate ε → NV

• lifetime τV → NR

The TDR (turbulent dissipation regions) model 6/13

Strategy to derive turbulent properties

% vortex

% relaxation% ambient0

0 0

100

100 100

% vortex

% relaxation% ambient0

0 0

100

100 100

CH+ SH+ CO HF CH

% vortex

% relaxation% ambient0

0 0

100

100 100

% vortex

% relaxation% ambient0

0 0

100

100 100

HCO+ C2H OH H2O H/H2

nH increases with increasing symbol sizeAV = 0.4, ζ = 3× 10−17 s−1

Turbulence properties from molecular observations 7/13

Large scale turbulent energy

1e+10

1e+11

1e+12

1e+13

1e+14

1e+15

1e+16

1e+20 1e+21 1e+22

N(C

H+ ) (

cm-2

)

NH tot (cm-2)

PDR models

nH = 10 cm-3

nH = 100 cm-3

visibleHerschel

1e+10

1e+11

1e+12

1e+13

1e+14

1e+15

1e+16

1e+20 1e+21 1e+22

N(C

H+ ) (

cm-2

)

NH tot (cm-2)

PDR models

nH = 10 cm-3

nH = 100 cm-3

N(CH+)local = 3×N(CH+)disk

N(CH+)NH

∝ ε n−2.2H A−0.32

V a−0.5

nH < 200 cm−3

15< ε

10−24 erg cm−3 s−1 < 5

IJ

I

I

II

I

II

I

I

I

I

C C+

CH CH+

CH2 CH+2

CH+3

γ

e−

γH2

H2

4640

H2

H2

γ

γ

2200H

H2

1760

e−

e−

Turbulence properties from molecular observations 7/13

Large scale turbulent energy

1e+10

1e+11

1e+12

1e+13

1e+14

1e+15

1e+16

1e+20 1e+21 1e+22

N(C

H+ ) (

cm-2

)

NH tot (cm-2)

TDR models

nH = 30 cm-3

nH = 100 cm-3

visibleHerschel

1e+10

1e+11

1e+12

1e+13

1e+14

1e+15

1e+16

1e+20 1e+21 1e+22

N(C

H+ ) (

cm-2

)

NH tot (cm-2)

TDR models

nH = 30 cm-3

nH = 100 cm-3

N(CH+)local = 3×N(CH+)disk

N(CH+)NH

∝ ε n−2.2H A−0.32

V a−0.5

nH < 200 cm−3

15< ε

10−24 erg cm−3 s−1 < 5

IJ

I

I

II

I

II

I

I

I

I

C C+

CH CH+

CH2 CH+2

CH+3

γ

e−

γH2

H2

4640

H2

H2

γ

γ

2200H

H2

1760

e−

e−

Turbulence properties from molecular observations 8/13

Ion-neutral drift in dissipative regions

10-3

10-2

10-1

100

101

10-9 10-8 10-7

N(S

H+ )/N

(CH

+ )

N(CH+)/NH

TDR, uem = 2 km s-1Godard et al. (2012)

2.5 6 uθm 6 3.5 km s−1

reproduces the correlationSH abundance reproduced(SOFIA-GREAT, Neufeld et al. 2012)

II

II

I

I

I

I

C+

CH+

CH+2

S+

SH+

SH+2

S

SH

H2

4640

H2

H2

9860

H2

8500

γ

γe−

e−

N(SH+)

N(CH+)∝ exp(−5220/Teff)

Teff = Tr +13µku2

in

independent of a and ε

Turbulence properties from molecular observations 8/13

Ion-neutral drift in dissipative regions

10-3

10-2

10-1

100

101

10-9 10-8 10-7

N(S

H+ )/N

(CH

+ )

N(CH+)/NH

TDR, uem = 3 km s-1Godard et al. (2012)

2.5 6 uθm 6 3.5 km s−1

reproduces the correlationSH abundance reproduced(SOFIA-GREAT, Neufeld et al. 2012)

II

II

I

I

I

I

C+

CH+

CH+2

S+

SH+

SH+2

S

SH

H2

4640

H2

H2

9860

H2

8500

γ

γe−

e−

N(SH+)

N(CH+)∝ exp(−5220/Teff)

Teff = Tr +13µku2

in

independent of a and ε

Turbulence properties from molecular observations 8/13

Ion-neutral drift in dissipative regions

10-3

10-2

10-1

100

101

10-9 10-8 10-7

N(S

H+ )/N

(CH

+ )

N(CH+)/NH

TDR, uem = 5 km s-1Godard et al. (2012)

2.5 6 uθm 6 3.5 km s−1

reproduces the correlationSH abundance reproduced(SOFIA-GREAT, Neufeld et al. 2012)

II

II

I

I

I

I

C+

CH+

CH+2

S+

SH+

SH+2

S

SH

H2

4640

H2

H2

9860

H2

8500

γ

γe−

e−

N(SH+)

N(CH+)∝ exp(−5220/Teff)

Teff = Tr +13µku2

in

independent of a and ε

Turbulence properties from molecular observations 8/13

Ion-neutral drift in dissipative regions

10-3

10-2

10-1

100

101

10-9 10-8 10-7

N(S

H+ )/N

(CH

+ )

N(CH+)/NH

TDR, uem = 3 km s-1Godard et al. (2012)

2.5 6 uθm 6 3.5 km s−1

reproduces the correlationSH abundance reproduced(SOFIA-GREAT, Neufeld et al. 2012)

II

II

I

I

I

I

C+

CH+

CH+2

S+

SH+

SH+2

S

SH

H2

4640

H2

H2

9860

H2

8500

γ

γe−

e−

N(SH+)

N(CH+)∝ exp(−5220/Teff)

Teff = Tr +13µku2

in

independent of a and ε

Turbulence properties from molecular observations 9/13

Turbulent dissipation timescale

106

107

108

109

1010

1011

1012

102 103 104 105

vorte

x co

lum

n de

nsity

(cm

-2)

time (yr)

CH

CH+

OHH2O

HCO+

CO

106

107

108

109

1010

1011

1012

102 103 104 105

vorte

x co

lum

n de

nsity

(cm

-2)

time (yr)

CH

CH+

OHH2O

HCO+

CO

• CO formation in TDR : CH+ 99K CH+3 → HCO+ → CO

• τR(CO) ∼ 100× τR(CH+) ∼ 100τR(HCO+)

• N(CO) ∝ τR/τV → 102 6 τV 6 103 yr

Turbulence properties from molecular observations 9/13

Turbulent dissipation timescale

106

107

108

109

1010

1011

1012

102 103 104 105

vorte

x co

lum

n de

nsity

(cm

-2)

time (yr)

CH

CH+

OHH2O

HCO+

CO

106

107

108

109

1010

1011

1012

102 103 104 105

vorte

x co

lum

n de

nsity

(cm

-2)

time (yr)

CH

CH+

OHH2O

HCO+

CO

1013

1014

1015

1016

1017

1011 1012 1013

N(C

O) (

cm-2

)

N(HCO+) (cm-2)

TDR, o = 104 yrLiszt Lucas (1998)

• CO formation in TDR : CH+ 99K CH+3 → HCO+ → CO

• τR(CO) ∼ 100× τR(CH+) ∼ 100τR(HCO+)

• N(CO) ∝ τR/τV → 102 6 τV 6 103 yr

Turbulence properties from molecular observations 9/13

Turbulent dissipation timescale

106

107

108

109

1010

1011

1012

102 103 104 105

vorte

x co

lum

n de

nsity

(cm

-2)

time (yr)

CH

CH+

OHH2O

HCO+

CO

106

107

108

109

1010

1011

1012

102 103 104 105

vorte

x co

lum

n de

nsity

(cm

-2)

time (yr)

CH

CH+

OHH2O

HCO+

CO

1013

1014

1015

1016

1017

1011 1012 1013

N(C

O) (

cm-2

)

N(HCO+) (cm-2)

TDR, o = 102 yrLiszt Lucas (1998)

• CO formation in TDR : CH+ 99K CH+3 → HCO+ → CO

• τR(CO) ∼ 100× τR(CH+) ∼ 100τR(HCO+)

• N(CO) ∝ τR/τV → 102 6 τV 6 103 yr

Turbulence properties from molecular observations 10/13

Stretching of turbulent dissipation regions

10-25

10-24

10-23

10-22

101 102 103 104 105 106

C+ c

oolin

g ra

te (e

rg c

m-3

s-1

)

time (yr)

AV = 0.1AV = 0.2AV = 0.4AV = 1.0

02468

10121416

0.0 0.5 1.0 1.5 2.0 2.5

I C+ (

10-6

erg

cm

-2 s

-1 s

r-1)

NH (mag)

PDR

Ingalls et al. (2002)

0 100 200 300 400 500

IFIR (10-6 erg cm-2 s-1 sr-1)

• under-emission during the dissipative burst ∼ 100 yr• over-emission during the relaxation period ∼ 104 yr

• 10−12 6 a 6 10−10 s−1 → 100 6 l 6 1000 AU

Turbulence properties from molecular observations 10/13

Stretching of turbulent dissipation regions

10-25

10-24

10-23

10-22

101 102 103 104 105 106

C+ c

oolin

g ra

te (e

rg c

m-3

s-1

)

time (yr)

AV = 0.1AV = 0.2AV = 0.4AV = 1.0

02468

10121416

0.0 0.5 1.0 1.5 2.0 2.5

I C+ (

10-6

erg

cm

-2 s

-1 s

r-1)

NH (mag)

TDR, a = 10-11 s-1

TDR, a = 10-10 s-1

Ingalls et al. (2002)

0 100 200 300 400 500

IFIR (10-6 erg cm-2 s-1 sr-1)

• under-emission during the dissipative burst ∼ 100 yr• over-emission during the relaxation period ∼ 104 yr• 10−12 6 a 6 10−10 s−1 → 100 6 l 6 1000 AU

Turbulence properties from molecular observations 11/13

Additional TDR predictions

Levrier et al. (2012)

1012

1013

1014

1015

1016

1020 1021 1022

N(C

O) (

cm-2

)

NH (cm-2) (assuming fH2 = 0.5)

TDR, AV = 0.02TDR, AV = 0.10TDR, AV = 0.20TDR, AV = 0.40TDR, AV = 0.60

Scheffer et al. (2008)

realistic fragmentation + PDR TDR

• N(CO)obs/N(CO)PDR > 10

• explains the bending ofN(CO) at N(H2) ∼ 2× 1020

• if complete fragment. no bending• if no fragment. strong bending

and N(CO) too small at small NH

Turbulence properties from molecular observations 12/13

Additional TDR predictions

1012

1013

1014

1015

1011 1012 1013

N(O

H) (

cm-2

)

N(HCO+) (cm-2)

PDR TDR

Lucas and Liszt (1996)

1012

1013

1014

1011 1012 1013

N(H

2O) (

cm-2

)

N(HCO+) (cm-2)

PDR TDR

Olofsson et al. (2010)

1012

1013

1014

1011 1012 1013

N(C

2H) (

cm-2

)

N(HCO+) (cm-2)

PDR

TDRLucas and Liszt (2000)

1013

1015

1017

1019

1021

0 1000 2000 3000

N(H

2)/g

j (cm

-2)

Energy (K)

PDR

TDR

Gry et al. (2002), Lacour et al. (2004)

Conclusions 13/13

Summary

properties of turbulent dissipationI CH+ / H → dissipation rate nH, ε

I SH+ / CH+ → ion-neutral decoupling nH, uθm = uinI C+(160µm) / FIR → stretching a→ l

I CO / HCO+ → timescale τV

agreement with other molecular tracersI CO / H2 → fragmented mediumI column densities of OH, H2O, C2H, CH, SH, and H?2I ... and their correlations

Future contributions

open issues

explain H2S abundances

interpret velocity profiles

ALMA perspectives

mapping the dissipative scales

turbulence in extragalactic media