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 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