COOLING PROCESSES IN THE ISM

1
COOLING PROCESSES IN THE ISM
In general three cooling processes
important (1) Recombination (opposite of
photoionization) (2) Collisional de-excitation
(heating via collisional excitation) (3)
Radiative cooling All three can involve all
atoms and molecules in the ISM. In the WNM, WIM
and hot Intercloud medium (high T ) cooling
involves atoms, ions and electrons, in the CNM
and, of course, in molecular phase (low T)
molecules are more important. Other cooling
processes (next lecture) are (4) Cooling by
dust (thermal emission) (5) Cooling via
collisions between dust and gas (molecules),
important at T lt 100 K
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Consider a partially ionized, hydrogen cloud
(hydrogen most abundant element) that can cool
via hydrogen recombination. In recombination ion
captures electron and emits a photon of energy hn
equal to the kinetic energy of electron.
Recombinations to energy states higher than
ground state cool the gas more efficiently
because less energetic emitted photon has lower
absorption probability by surrounding atoms. In
steady state photoionization raterecombination
rate If no other cooling processes occur the
equilibrium between the two rates will set the
temperature of the cloud. If two rates equal
then the heating by photoionization Hion
is Hion nenpa(T) lthn hnIgt , hnI being 13,6
ev for ground level of hydrogen and the mean
energy is the result of weighting over the
ambient photon flux and the (frequency dependent)
ionization cross section. The cooling rate via
recombination can be written as

Crec nenpa(T)kBT lt1/2 m
v2gt/kBT where the mean is weighted by
the Maxwell Boltzmann

distributions for velocity of electrons
Recombination coefficient
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Setting HionCrec implies kBTgas (hn hnI)
hnI. But hnI 10 ev in typical ISM conditions
(smaller than hnI of ground state because some
hydrogen atoms will be in excited states).--? so
Tgas 105 K gtgt TISM (for WNM, WIM, CNM and
molecular phase) Why is TWNM lower ( 104
K)? Because (1) atoms can cool by emission of
photons during spontaneous transition to state
of lower energy (called radiative or line
cooling) and (2) heavier elements such as carbon
and oxygen, contribute a lot to such line cooling
despite being much less abundant than hydrogen.
Will show how... RADIATIVE and COLLISIONAL
COOLING Consider partially ionized phase of ISM
(e.g. WIM) - there are free electrons
which collide with atoms (hydrogen or other
elements) -? atom goes to higher energy state by
asborbing kinetic energy from electron. It will
then decay via collisional de-excitation, or
spontaneous radiative decay. atom e- --? atom
e- --? atom e- g Collisional
de-excitation depends on collision rate, which
depends on ambient density. In typical iSM
conditions densities are low enough that
radiative emission dominates over collisions
(opposite situation in the atmosphere of the
Earth).
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v vs where vs gas sound speed
Collision rate tcoll-1 nscollv (kBT/mH)1/2
nscoll 9 x10-12 nT1/2s-1
Spontaneous emission rate for electric dipole of
hydrogen (first excited state to ground state is
A21 108 s-1 (Einsteins coefficient), much
smaller rates for transitions such as forbidden
lines (these however are commonly observed in the
ISM because thanks to very low densities excited
metastable states are not rapidly collisionally
de-excited like in Earths atmosphere) Clearly
tcoll-1 ltlt A21 for typical ISM densities and
temperatures (all phases).
In steady state collisional excitation
ratecollisional de-excitation rate radiative
cooling rate Consider two energy levels E1
(ground state) and E2 (excited state) with gap
E12 ½ me(v12 v22) (v velocity of the
electron colliding with atom) Then in steady
state one has nen1R12nen2R21 n2A21 (1)
(collision rates R21 and R12 measured per unit
volume)
5
Recall that the energy levels of distinguishable
particles (any gas except a gas of bosons or
fermions) obey the Maxwell-Boltzmann
statistics. For the principle of detailed balance
(recall from statistical/quantum
mechanics) n1R12n2R21 where
n1g1e-bE1/KT n2g2e-bE2/KT Therefore
R12 R21 g2/g1e-bE12 Solving the steady state
equation (1) for n2/n1 and recalling the above
expressions for n1 and n2 one obtains n2/n1
g2/g1 e-bE12(1 A21/neR21)-1 (2) If ne gtgt
nc, nc critical (particle) density A21/R21,
then (2) yields the result expected in
thermodynamical equilibrium. If ne ltlt nc (low
density limit) then the excited state n2 is
depleted compared to the thermodynamical
equilibrium by and the depletion depends on the
spontaneous radiative emission rate A21 The
conditions in the ISM are typically of the second
type and this is another way to see that
radiative emission is important in determining
TISM
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The cooling rate from spontaneous decay
(radiative cooling rate) will be given by C
n2A21E21 The cooling rates in the two different
regimes will be (a) Cline (ne gtgt nc)
n2A21hn21 n1(g2/g1)A21hn21e-bE12 (b) Cline (ne
ltltnc) n2A21hn21 n1neR12hn12 (from the fact
that (1) in this limit yields n2/n1 neR12/A21
see full derivation of (1) on text ), which is
independent of A21. Example of importance of
regime (b) - line cooling efficient at low
densities Gas in which cooling is provided by
OIII line (forbidden line at 5007 A, E12 2.5
ev) and hydrogen recombination. One can show
that OIII line cooling wins over recombination
cooling even though abundance of heavy ions (O,
C, N, Ne) is low in ISM (nion/nH 10-4) for gas
at T 104 K, where Cline nionnelts21vgt E12
exp(-bE12) (3) For regime (b) to apply ne ltlt
nc at T 104 K but this is always satisfied
because nc 2 x 107 cm-3 (similar high densities
can be inferred for other lines)
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(ii)Radiative cooling is the
reason why Tism lt 105 K
Many ions in the ISM get excited to metastable
states and have forbidden transitions with
energy gaps of only a few ev. Assume line cooling
of a ion (transition energy E12) and that Cline
is in the low density regime. Assume then
that Heating rate by ionization radiative
cooling rate via line emission and that steady
state holds Recombination rateionization
rate. Then, if E0 13.6 ev (ionization
potential of hydrogen ground state) aionE12ltsvgt
e -E12/kBT a(T) E0, which solving for T yields
T 104 K. From (3) plus the fact that in (3)
the cross section is effectively the cross
section of the electron in collisional excitation
(s prop. p(h/2p1/mev)2, where v vs) one
obtains the dependence of the cooling rate on
T Cline prop. to T-1/2 exp(-E12/kbT) From
which it appears that cooling is maximum when T
neither too large or too small, kBT E12 (both
at high and low T Cline tends to zero)
de Broglie wavelength of electron