*Astron. Astrophys. 358, L33-L36 (2000)*
## 3. The absorption coefficient
Under chemical equilibrium among different atomic and molecular
species in their standard states, the number density of
for the molecular equilibrium
reaction can be written as (Sharp
1985)
where and
are the partition functions for
*C* and , *m* is the
"multiple" reduced mass and is the
dissociation energy of in eV,
and
are the number densities of *C*
and ,
where
is in Kelvin, and the other symbols
have their usual meaning. Although chemical equilibrium of *C*
and should be coupled with some
other molecules, dominance of
molecule in the atmosphere would make the above equilibrium the most
probable one. Hence, we ignore, for the present, chemical equilibrium
of *C* and with other
molecules. For the purpose of calculating the number densities of the
molecules in various energy levels, we assume that the lower
atmosphere of the object is in local thermodynamic equilibrium (LTE).
Then the number of particles , in a
specified rotation level *J* is related to the total number of
particles in all levels, , according
to the following relation (Larson 1994):
where (2J+1) is the degeneracy factor and
is the Boltzmann factor. Now the
integrated line absorption coefficient can be written as
where *f* is the oscillator strength of the transition. We
calculate the Q's for and *C*
using polynomial expressions given by Sauval & Tatum(1984). For a
small value of *J*, the Boltzmann factor reduces to 1. The
dissociation energy of
is taken to be 4.38 eV (Jorgenson
1994). We use the continuum absorption coefficient
provided by D. Saumon.
© European Southern Observatory (ESO) 2000
Online publication: June 8, 2000
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