Transcript Distribution and Properties of the ISM
Heating and Cooling
10 March 2003 Astronomy G9001 - Spring 2003 Prof. Mordecai-Mark Mac Low
Wolfire et al. 1995, Spitzer PPISM
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
Cosmic Rays
• H ionization produces primary electrons with
CR
CR E e
• Field, Goldsmith, Habing took ζ CR – short path-lengths of low energy CRs = 4 10 -16 • Observations now suggest ζ CR = 2 10 -17 – ionization-sensitive molecules (HD, OH, H 3 + ) s -1 s -1
n
CR
28 -3 erg cm s -1
CR
17
n
E ej
1
h
1
Photoionization Heating
ei n n e i
E ej
1 2
m e
j w
3
j
1 2
A r
1 2 2
kT m e
3 2 recapture const.
2 4
he
2 3 3 2 2 3
m c e h
kT
X-ray Ionization Heating
• Transfers energy from 10 6 T << 10 4 K gas to gas with 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.
n
XR
4
n
species,i
J
h
exp
N a
i E h
i
heat from each absorption primary e of X-rays
Grain Photoelectric Heating
• Small grains (PAHs,
a <
15Å) can be efficiently photoionized by FUV (Bakes & Thielens 1994).
– 10% of flux absorption
n
– 50% of photoelectron production 24 -3 erg cm s -1 0 1/2 going to heat, which depends on G T /n , 0 e and G is FUV intensity normalized to 0 -3 -2 -1 Habing (1968) value (1.6 10 erg cm s )
grains neutral
Efficiency of Grain Heating
grains charged
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 < 10 3 ): excitation of molecular rotational and vibrational lines and atomic fine structure lines
Diffuse ISM Cooling Curve
~ T -0.7
Bremsstrahl.
~ T 1/2
Hollenbach & Tielens 1999, Neufeld et al 1995
Opaque ISM Mechanisms
• Heating – interiors • cosmic rays • grain heating by visible & IR – edges (PDRs) • grain & PAH UV photoelectric • H 2 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
Cooling in Opaque gas
• Emission from an optically thick line reaches the blackbody value: radio brightness temperature
T
T
1
e b
• velocity gradients allow escape of radiation through line wings • many molecular and atomic lines can contribute in some regimes, but CO, H 2 , H 2 O, and O most important • detailed models of chemistry required to determine full cooling function
• Homonuclear species like H 2 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
T dS dt
d n dt
3 2
kT
kT dn dt n n
cooling time
d dt
3 2
kT
3
k
T
T E
2
t c
so
t c
n
T E n
heating cooling 10 22 3 erg cm s -1 4 for 10 K
T
6 10 K 6 10 K 0.7
Thermal Instability
Balbus 1986 First law for gas being heated and cooled
dS
(
n
T n
)
dt
perturb a parcel, changing
S
S
+
S
,
d dt
S
dS dt
n
T n
If the change in net hea ting has opposite sign to change in entropy, the system will tend to return to the initial value stability
Otherwise, instability occurs when
n
T n
A
0 If gas in thermal equilibrium with
n n
, then Field (1965) instability criterion holds
T
n n
A
0 or, if independent of temper ature
T
A
0 If t cool 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
speed
v f 2 = c s 2 + v A 2
or the fast magnetosonic max
v
,
x c s
2
v A
2
Lorentz Forces
1 4
B
1 4
B
B
1 8
B
2 • 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