SpringerLink
Forum Springer Astron. Astrophys.
Forum Whats New Search Orders


Astron. Astrophys. 358, L33-L36 (2000)

Previous Section Next Section Title Page Table of Contents

3. The absorption coefficient

Under chemical equilibrium among different atomic and molecular species in their standard states, the number density of [FORMULA] for the molecular equilibrium reaction [FORMULA] can be written as (Sharp 1985)

[EQUATION]

where [FORMULA] and [FORMULA] are the partition functions for C and [FORMULA], m is the "multiple" reduced mass and [FORMULA] is the dissociation energy of [FORMULA] in eV, [FORMULA] and [FORMULA] are the number densities of C and [FORMULA], [FORMULA] where [FORMULA] is in Kelvin, and the other symbols have their usual meaning. Although chemical equilibrium of C and [FORMULA] should be coupled with some other molecules, dominance of [FORMULA] molecule in the atmosphere would make the above equilibrium the most probable one. Hence, we ignore, for the present, chemical equilibrium of C and [FORMULA] 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 [FORMULA], in a specified rotation level J is related to the total number of particles in all levels, [FORMULA], according to the following relation (Larson 1994):

[EQUATION]

where (2J+1) is the degeneracy factor and [FORMULA] is the Boltzmann factor. Now the integrated line absorption coefficient can be written as

[EQUATION]

where f is the oscillator strength of the transition. We calculate the Q's for [FORMULA] 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 [FORMULA] of [FORMULA] is taken to be 4.38 eV (Jorgenson 1994). We use the continuum absorption coefficient [FORMULA] provided by D. Saumon.

Previous Section Next Section Title Page Table of Contents

© European Southern Observatory (ESO) 2000

Online publication: June 8, 2000
helpdesk.link@springer.de