A generalized version of the Rankine-Hugoniot relations including ionization, dissociation and related phenomena

For purposes of computing shocks in stellars atmospheres and winds we have developed a generalized version of the Rankine-Hugoniot relations including ionization, dissociation, radiation and related phenomena such as excitation, rotation and vibration of molecules. The new equations are given in analytical form. They are valid as long as the internal energy E, the total pressure P, and the first adiabatic coefficient gamma(sub 1) can be evaluated. However, we have not treated shock structures. In the case of non-LTE we have to employ an approximation for gamma(sub 1) because in that case no definition exists. Our new version of the Rankine-Hugoniot relations can easily be used for many purposes including ab-initio modeling. In our derivation we introduce a parameter gamma(sub H), which is definded as the ratio of the enthalpy H (sometimes called heat function w) to the internal energy E (sometimes called U). Using this parameter we solve the equations for changing mu and (d(natural log P)/d(natural log rho))(sub ad) identically equal to gamma(sub 1) on both sides of the shock. Both gamma(sub H) and gamma(sub 1), and also mu are functions of pressure P and temperature T. We present: (1) the derivation, (2) examples of gamma(sub 1) (P,T) and gamma(sub H) (P,T) which include/exclude ionization and radiation, and (3) as an example the differences in post-shock parameters as function of the pre-shock temperature for the case with ionization and without radiation.