Heating and Cooling

10 March 2003

Astronomy G9001 - Spring 2003

Prof. Mordecai-Mark Mac Low

Transparent ISM Mechanisms

• Heating– cosmic rays– photoionization

• UV

• soft X-rays

– grain photoelectric heating

– shock heating

• Cooling– molecular rotation,

vibration – atomic fine structure,

metastable– resonance lines– bremsstrahlung– recombination– dust emission

Wolfire et al. 1995, Spitzer PPISM

Cosmic Rays

• H ionization produces primary electrons with <E> ~ 35 eV. Counting secondaries, <Ee>=3.4 eV.

• Field, Goldsmith, Habing took ζCR = 4 10-16 s-1

• Observations now suggest ζCR = 2 10-17 s-1

– ionization-sensitive molecules (HD, OH, H3+)

– short path-lengths of low energy CRs

CR CR eE

28 -3 -117

1.1 10 erg cm s2 10

CRCRn n

Photoionization Heating

31

2ei e i ej e jj

n n E m w

3 2

1 2

2 2r

e

A kT

m

4 2

3 2 2 3

recapture const.

2

3 e

he

m c

h

kT

1

1

1 /

/ej

h s U d

E

s U d

X-ray Ionization Heating• Transfers energy from 106 K gas to gas with

T << 104 K, with a small contribution from extragalactic sources

• To calculate local contribution, must take absorption into account

• Can maintain high electron densities even if heating rate is low.

species,i

4 exp ,iXR a h i

Jn n N E E x d

h

heat from eachprimary e-

absorptionof X-rays

Grain Photoelectric Heating• Small grains (PAHs, a < 15Å) can be

efficiently photoionized by FUV (Bakes & Thielens 1994).– 10% of flux absorption– 50% of photoelectron production

24 -3 -10

1/20 e

0

-3 -2 -1

1 10 erg cm s

where is fraction of absorbed energy

going to heat, which depends on G T /n ,

and G is FUV intensity normalized to

Habing (1968) value (1.6 10 erg cm s )

n n G

Efficiency of Grain Heating

grainsneutral

grainscharged

Shock Heating

• Extremely inhomogeneous

• Produces high-pressure regions that interact with surroundings

• Traditionally, included in equilibrium thermodynamical descriptions anyway

Cooling

• Radiative cooling requires available energy levels for collisional excitation

• Cold gas (10 < T < 103): excitation of molecular rotational and vibrational lines and atomic fine structure lines

Gae

tz &

Sal

pete

r 19

83

Bremsstrahl.~ T1/2

~ T-0.7

Diffuse ISM Cooling Curve

Opaque ISM Mechanisms

• Heating– interiors

• cosmic rays

• grain heating by visible & IR

– edges (PDRs)• grain & PAH UV

photoelectric

• H2 pumping by FUV

• Cooling– gas

• molecular rotation, vibration

• atomic fine structure, metastable

• radiative transfer determines escape of energy from gas

– grains• grain emission in FIR

• gas-grain coupling

Hollenbach & Tielens 1999, Neufeld et al 1995

Cooling in Opaque gas• Emission from an optically thick line reaches

the blackbody value:

• velocity gradients allow escape of radiation through line wings

• many molecular and atomic lines can contribute in some regimes, but CO, H2, H2O, and O most important

• detailed models of chemistry required to determine full cooling function

radio brightness temperature 1bT T e

Neu

feld

, Lep

p, &

Mel

nick

199

5

• Homonuclear species like H2 do not have low-lying energy levels

• Rarer polar species contribute most to cooling in 10 K gas

• Fine structure lines most important at surfaces of PDRs

Isothermal Equation of State

• For densities 10-19 < ρ < 10-13 cm-3, cooling is very efficient down to about 10 K

• Gas remains isothermal in this regime, ultimately due to cooling of dust grains by IR emission.

• Compressibility is high: P ~ ρ• When even dust becomes optically thick,

gas becomes adiabatic, subject to compressional heating, such as during protostellar collapse.

Energy Equation

23

2

dS d dnT n kT kT n n

dt dt dt

heating cooling

2

cooling time

3 3

2 2

so

E

c

Ec

T TdkT k

dt t

nk T Tt

n n

0.7

22 3 -16

4 6

10 erg cm s10 K

for 10 K 10 K

T

T

Thermal Instability

2

2

First law for gas being heated and cooled

( )/

perturb a parcel, changing + ,

but holding some variable fixed (e.g. , ...)

If the change in net hea

n ndS dQ T dt

T

S S S

A P

d dS n nS

dt dt T

ting has opposite sign

to change in entropy, the system will tend to return

to the initial value stability

Balbus 1986

2

2

2

Otherwise, instability occurs when

0

If gas in thermal equilibrium with ,

then Field (1965) instability criterion holds

0

or, if independent of temper

A

A

n n

S T

n n

n nT

ature

0AT

If tcool increases as T increases, then system is unstable

(Isobaric) Thermal Instability• Perturb temperature of points along the thermal

equilibrium curve

• Stable if they return to equilibrium

• Unstable if they depart from equilibrium

Two-Phase Models

Wolfire et al 1995 log ρ (cm-3)

Three-Phase Model• Attempt to extend FGH two-phase model to

include presence of hot gas (McKee & Ostriker 1977)

• Hot gas not technically stable (no continuous heating, only intermittent), but has long cooling timescale (determined by evaporation off of clouds in MO77

• Pressure fixed by action of local SNR• Temperature of cold phases fixed by points

of stability on phase diagram as in two-phase model

Turbulent Flow

• Equilibrium models only appropriate for quasi-static situations

• If compressions and rarefactions occur on the cooling timescale, then gas will lie far from equilibrium

• Conversely, rapid cooling or heating can generate turbulent flows (Kritsuk & Norman)

MHD Courant Condition

• Similarly, the time step must include the fastest signal speed in the problem: either the flow velocity v or the fast magnetosonic speed vf

2 = cs2 + vA

2

2 2max , s A

xt

v c v

Lorentz Forces

• Update pressure term during source step

• Tension term drives Alfvén waves– Must be updated at same time as induction

equation to ensure correct propagation speeds– operator splitting of two terms

21 1 1

4 4 8B

B B B B

Added Routines

Ston

e &

Nor

man

199

2b