Publications
of the
MPIfR
Optical & Infrared
Interferometry Group
W. Stolzmann and T. Blöcker:
Thermodynamical properties of stellar
matter:
II. Internal energy, temperature and density exponents, and specific
heats for stellar interiors
Astronomy & Astrophysics 361, 1152-1168
(2000)
Abstract.
Starting from the Helmholtz free energy we calculate analytically
first- and second-order derivatives, as internal energy and specific
heats, for the ideal system and the exchange and correlation
interactions covering a broad range of degeneracy and relativity.
The complex physics of Coulomb interactions is expressed by Pade
Approximants, which reflect the actual state of our knowledge with high
accuracy. We assume complete ionization and provide a base system of
thermodynamical functions from which any other thermodynamical
quantities can be calculated.
We chose for the base system the free energy, the pressure, the
internal energy, the isothermal compressibility (or density exponent),
the coefficient of strain (or temperature exponent), and the isochoric
specific heat. By means of the latter potentials entropy, isobaric
specific heat and adiabatic temperature gradient can be determined. We
give comparisons with quantities which are composed by numerical
second-order derivatives of the free energy and show that numerical
derivatives of the free energy as calculated, for instance, from EOS
tables, may produce discontinuities for astrophysically relevant
quantities as,
e.g., the adiabatic temperature gradient.
Adiabatic temperature gradients are shown for different chemical
compositions (hydrogen, helium, carbon). Finally the used formalism of
Pade Approximants allows immediate incorporation of recent results from
many particle statistics.
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