An introduction to the physics of the interstellar medium

I. Overview

II. Thermal processes in the ISM

III. Hydrodynamics in the ISM

IV. Gravity in the ISM

V. Magnetohydrodynamics in the ISM

An introduction to the physics of the interstellar medium

I. Overview

Patrick Hennebelle

The Milky Way

about 1011 stars mass of gas : 5% mass of stars

STARS

Hot Ionised Gas

Warm Ionised GasWarm Neutral Gas

Cold Neutral Gas

Heavy ElementsKinetic energy

Radiation Cosmic Rays

Molecular Gas

Dense Cores€

n =10−2cm−3,T =106K

€

n =102cm−3,T =102K

€

n =103cm−3,T =10K

€

n =106cm−3

T =10K

€

n >1022cm−3

Cooling, mhd

turbulence, mhd, gravity

Gravity, mhd

Gravity, mhd

Accretion discs

Large scale structures

The Interstellar CyclePlanets

What do we find in the Interstellar Medium ?

-photons

-gas

-magnetic field

-dust

-cosmic rays

As we will see, they all interact with each other, they carry comparable energies and none of them can be ignored…

Welcome in the ISM!

The Radiation

Due to the contribution of the stars, the dust, the CMB, the hot gas.It heats and ionizes the gas. It fluctuates very strongly (neighbourhood of a O or B stars).

Radiation energy is about:Urad = 10-12 erg/cm3

Energy flux as a function offrequency (Black 1987)

submillimeterCMB

Far InfraredDust

Visiblestarlight

UVOB star

H,Heabsorption

X-raysExtragalacticHIM

The Gas in the ISM

The ISM is very inhomogeneous in density and temperature.

HIM: Hot Ionised Medium ionised, 106 K, 0.01 cm-3, 108 solar masses

produced by supernovae explosions WIM: Warm Ionised Medium ionised, 8000 K, 0.5 cm-3, 109 solar masses WNM: Warm Neutral Medium atomic neutral, 8000 K, 0.5 cm-3, 1.5 109 solar masses

CNM: Cold Neutral Medium atomic neutral, 70 K, 50 cm-3, 1.5 109 solar masses

Molecular Hydrogen: neutral, 10 K, 103-106 cm-3, 109 solar masses

Com

para

ble

Pre

ssur

e H

ighe

rpr

essu

re

Abundances of heavy elements

He/H~10-1

D/H~3 10-5

C/H~3 10-4

N/H~1 10-4

O/H~7 10-4

Metals: 10-7 -10-5

Although the abundances are relatively small, the heavy elements are playing a very important role in the physics of the ISM in particular for the thermodynamics.

Galactic south pole (IRAS)Emission of the dust associated to the HI.

21 cm line, emission and absorptionKulkarni & Heiles (1987)Parkes Survey

Atomic hydrogen

Atomic hydrogen: a thermally bistable Medium

Warm Neutral Medium (0.5 cm-3, 104 K)

Cold Neutral Medium (50 cm-3, 102 K)

HI Spectra (21cm)

Absorption:

Emission: E

mis

sion

Heiles 2001

Ab

sorp

tion

€

n dl∫€

n /T dl∫

Molecular Clouds of the Galaxy

Extinction Map in Near Infrared of the

Orion Molecular Cloud

(Bontemps et al., 2MASS data)

CO Map of our Galaxy

(Dame et al. 1987)

50 pc

Padoan, Cambresy et al. 04

Ward-Thompson et al. 01

Oph molecular cloud seen at 1.3 mm with the Iram 30m telescopeSeveral dense cores can be seen

Taurus molecular cloud seen in infrared extinction(total mass about 104 Ms)

L1544 dense core (belonging to Taurus)Seen at 1.3 mm (dust emission)total mass is about 2 solar mass

Molecular clouds and Dense coresmolecular clouds (104-105 Ms) contain dense core (0.1-10 Ms)roughly 10-100 times denser

Molecular cloudsare often (not always) filamentary.

The Mechanical Energies

Non thermal line width implies that significant motions are observed in the gas.

Thermal Energy:P/k=4000 K/cm3, Utherm=10-12 erg/cm3

Kinetic Energy:sonic to supersonic velocity dispersion (up to Mach 5)=> Eturb / Etherm = 1-20

PDF of the Mach number in HI clouds (Crovisier 91)

Big powerlaws in the sky….. Turbulence ?

Density of electrons within WIM (Rickett et al. 1995)

Intensity of HI and dust emission Gibson 2007

The Larson Laws (1981) A Turbulent Cascade ?

In the molecular gas, Power laws are observed over several order of magnitude.

Universal Mass Spectrum dN/dM M-1.6 (Heithausen et al .98)

L (pc)L (pc)

M (

sola

r m

ass)

Vel

ocit

y d

ispe

rsio

n (k

m/s

)Mass versus size of CO clumps

Velocity dispersion versus size of CO clumps

Falgarone 2000

The structure of the gas appears to be fractal

The molecular gas presents the following power laws over 4orders of magnitude:

This suggests that there is a turbulent energy cascade,presumably from the large towards the small scales

In any case, there is a continuous energy injection in theISM. What are the possible sources ?

Falgarone et al. 91

€

σ ≈1km /sL

1pc

⎛

⎝ ⎜

⎞

⎠ ⎟

0.5

M ≈103 Ms

L

10pc

⎛

⎝ ⎜

⎞

⎠ ⎟

2.3

Sources of Energy Injection (Mac Low and Klessen 2004)

How to produce and sustain turbulence in the ISM ?

Energy Dissipation: turbulent energy is dissipated in about a crossing time:

For typical numbers, we get:

Sources of Energy must compensate this dissipation.

What are the possible sources ?

€

τ diss =L

Vrms

€

˙ ε =1

2

ρVrms2

τ diss

=1

2

ρVrms3

L

€

˙ ε = 3×10−27ergcm−3 s−1 n

1cm−3

Vrms

10 km /s

⎛

⎝ ⎜

⎞

⎠ ⎟

3100 pc

L

Supernovae Explosions:probably the most significant source ofenergy injection in the ISM

: mean mechanical energy of a supernovae remnant

: galactic supernovae rate (1/50 year-1)

: efficiency of energy injection

€

ESN

€

σ SN

€

ηSN

€

˙ ε =η SN ESNσ SN

πRsf2 Hc

€

˙ ε = 3×10−26ergcm−3s−1 η SN

0.1

ESN

1051erg

σ SN

SNu

15kpc

Rsf

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

−2

150pc

H

⎛

⎝ ⎜

⎞

⎠ ⎟−1

and also:

Galactic Differential Rotation (e.g. through the magneto-rotational instabilities)

Gravitational Instabilities (spiral arms of the galaxies)

Massive Stars (ionisation pressure, winds)

Jets and Outflows

The Magnetic FieldMagnetic field is observed through the Galaxy. Its origin is still debated, likely to be some sort of dynamo.

Magnetic Energy:magnetic intensity: 5 G => Emag / Etherm = 1-5

Magnetic Intensity as a function of density (Troland & Heiles 86)

Han et al. 06

The Dust

solid phase of the ISM : 1% of the gas phase complex chemical and physical structure (amorphous carbon, graphite, silicate…). Size a, from a=0.01 to a=1 m, dn=A a-3.5da (Mathis et al. 1977).

Play an important rôle for the thermal (heating and cooling of the gas), for the chemistry, for the absorption and diffusion of the interstellar radiation.

Emission of the dust (Desert et al. 1990)Absorption by the dust (Draine & Lee 1984)

Energy equipartition in the ISM

Urad~Utherm~Uturb~Umag~Ucosmic~10-12 erg cm-3

Physical reasons not fully understood yet but suggest that the various processes are coupled to each other and exchange energy.

Some examples will be given in the lectures.

An introduction to the physics of the interstellar medium

II. Thermal processes

Patrick Hennebelle

Thermal processes in the ISM

-Heating

-Cooling

-Cooling time

-Thermal balance and equilibrium

Heating Processes

Several heating mechanisms. Most of them are based on the ionisation of an ISM components by an energetic radiations. Then the electrons quickly (~1 year) interact with the ISM gas and thermalise.

Cosmic rays (the first proposed source of heating)Low energy protons (few MeV) ionise the gas during collisions.

The heating is related to the ionisation rate, p, induced by cosmic rays (Black 1987, Lequeux 2002).

=>relatively low value but may be important in well shielded clouds as the dense cores.€

Γcr = 3.510−28 ξ

4 10−17

⎛

⎝ ⎜

⎞

⎠ ⎟ergs-1 cm−3

Photoelectric effect on small dust grains and PaHUV radiation leads to the ionisation of interstellar grains (particularly the small one). The electrons undergo collisions in the ISM and heat it (Watson 1972, de Jong 1977, Draine 1978,

d’Hendecourt & Léger 1987, Bakes & Tielens 1994).Full calculations not straighforward.

Seems to be enough to explain the temperature of the diffuse gas (WNM, CNM)

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Γcr =10−24εχnH ergs-1 cm−3

Other heating processes:

-ionisation of atoms and molecules (like C) by UV

-X-rays (ionisation of ions and atoms, efficient at low column density)

-chemistry (formation of H2 onto grains)

-exchange between gas and grains (probably important deep inside the dense cores, FIR heats the dust)

-mechanical heating (discussed in next lectures)

Cooling ProcessesLet us consider an atom with 2 energy levels l and u which is excited from l to u by collisions and desexcited by spontaneous radiative emission or collisions (radiatively induced excitation of desexcitation can be neglected) with some impactor of density ni.

Stationary state:

If the gas density is smaller than some critical density:

€

n1C12 = n2C21 + n2A21,where C12 = ni vσ 12

but n = n1 + n2 ⇒ n2 = nC12

C12 + C21 + A21

g1C12 = g2C21 exp(−E21 /kT)

⇒ n2 = n1

1+ 1+ A21 /C21( )g1

g2

exp(E21 /kT)

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A21 /C21 >>1 ⇔ ni << nc ⇒ n2 = n C21 / A21( )g2

g1

exp(−E21 /kT) ∝ n2 exp(−E21 /kT)

⇒ Ii,1→2 =1

4πn2E21A21 =

1

4πE21 vσ 12 nni exp(−E21 /kT)ergs−1 cm−3 sterad−1

The most important lines for the cooling are the fine structure lines which result of the L-S coupling. Those lines are “forbidden”.

Lequeux 2002

Energy of the transitions are:

-158 m (or 92 K) for CII

-63 m (or 230 K) and 145 m for O

-370 m and 610 m for C

€

nH2Λe,CII =1.2310−27 nH

2dC2 exp(−92K /T)

T

100K

⎛

⎝ ⎜

⎞

⎠ ⎟−1/ 2

ergs−1 cm−3

nH2ΛH ,CII = 7.910−27 nH

2dC exp(−92K /T)T

100K

⎛

⎝ ⎜

⎞

⎠ ⎟−1/ 2

ergs−1 cm−3

Expression of the cooling by CII due to collisions with electrons and H:

Other cooling mechanisms

-atomic cooling in other type of transitions Ly of atomic hydrogen. Level n=2.

-electron recombination onto positively charged grains as it removes an energy 3/2kT from the gas phase.Reverse of the photo-electric effects. Can be important at high temperature or if the grains charge is significant.

-molecular cooling (e.g. Goldsmith & Langer 1978)for example at low temperatures: CO molecule rotation linesAt high temperature H2 lines can be very efficient

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Λe,H = 7.310−19 exp(−118400K /T) ergs−1 cm3

The various heating and cooling contributions of the atomic phase

Wolfire et al. 1995

Cooling Processes: summary

-due to collisional excitation followed by a radiative deexcitation (photon energy is lost)

H (Lyman alpha) for T> few 1000K, •and C+, O for T < few 1000 K

-mainly proportional to the square of density

-strong dependence on the temperature(depending on whether the dominant lines are

saturated)

Cooling function of the ISM

Dalgarno & Mac Cray 72

Cooling Times

€

dε

dt= −Λ(T)n, ε =

kbT

(γ −1)M p

= CvT ⇒

τ cool ≈CvT

Λ(T)n

τ cool,him ≈ 2 ×1015 T

106K

10−2cm−3

ns

τ cool,wnm ≈ 2 ×1013 T

104 K

1cm−3

ns

τ cool,cnm ≈ 2 ×1011 T

102K

102cm−3

ns

Cooling time for HIM: 100 Myr is very long (it is metastable)

Cooling time for WNM: 1 Myr is comparable to its dynamical time

Cooling time for CNM: 0.01 Myr is shorter than its dynamical time

Thermal balance and Thermal Instability

Temperature is determined by the equilibriumbetween cooling and heating

Heating is proportional to the densityand depends smoothly on the temperature

Cooling is proportional to the square of thedensity and depends stiffly on the temperature

If Λ(T) does not vary much with T, the gas is thermally unstable

Cooling function of the ISM

Dalgarno & Mac Cray 72

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dε

dt= Γρ − Λ(T)ρ 2

HIM(metastable)

WNM

CNM

heating

Thermal equilibrium curve (Field et al. 69, Wolfire et al. 95)

CNM

WNM

Unstable

Field 65: performs linear stability analysis of the radiatively cooling fluid equations. Obtains the isobaric criteria for instability:

€

∂P

∂ρ

⎞

⎠ ⎟L= 0

≤ 0

Wolfire et al. 95

Influence of stronger radiation flux on the thermal equilibrium

Wolfire et al. (1995)