Astronomy and Astrophysics – Astrophysics
Scientific paper
Dec 1993
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993a%26a...280..195n&link_type=abstract
Astronomy and Astrophysics (ISSN 0004-6361), vol. 280, no. 1, p. 195-200
Astronomy and Astrophysics
Astrophysics
10
Astronomical Models, Hydrodynamics, Mathematical Models, Rankine-Hugoniot Relation, Shock Wave Propagation, Shock Waves, Stellar Atmospheres, Stellar Winds, Adiabatic Conditions, Dissociation, Enthalpy, Internal Energy, Ionization, Molecular Excitation, Molecular Rotation, Vibration
Scientific paper
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 gamma1 can be evaluated. However, we have not treated shock structures. In the case of non-LTE we have to employ an approximation for gamma1 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 gammaH, 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))ad identically equal to gamma1 on both sides of the shock. Both gammaH and gamma1, and also mu are functions of pressure P and temperature T. We present: (1) the derivation, (2) examples of gamma1 (P,T) and gammaH (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.
Achmad L.
Cuntz Manfred
de Jager Cornelis
Lobel Alex
Nieuwenhuijzen Hans
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