heating and cooling 10 march 2003 astronomy g9001 - spring 2003 prof. mordecai-mark mac low
TRANSCRIPT
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