## 4. Thermal equilibrium quantitiesFor simplicity, we only employ the partition functions in the ground state for the dominant elements and . Considering the correction of nonideality and electron degeneracy to thermodynamic quantities, the modified Saha equation can be written as (Christensen-Dalsgaard 1977; Pols et al. 1995): and where the total correction to the electron chemical potential is is the configuration energies in unit of electron volts, i.e., For the number , , , and of neutral and ionized hydrogen and helium particles, we introduce a set of dependent variables, i.e., , , , and , being the occupation numbers of particles divided by the number of nuclei of the respective or species. With these definitions, we have the occupation number for hydrogen species where the partition functions are given according to with the normalization condition For helium species where the partition functions are with the normalization condition Under conservation constraints, the number of free electrons per unit mass is given by Since the present model considers six species , Eqs. (56) and (58)-(62) are six simultaneous equations for the six unknown with a unique unknown variable, i.e., the electron degeneracy . Here defined in Eq. (54) is also an explicit function of the electron degeneracy by means of the free electron number . © European Southern Observatory (ESO) 2000 Online publication: January 29, 2001 |