Thermodynamical properties of stellar matter: II. Internal energy,...
Thomas Bloecker
temperature and density exponents and specific heats for stellar interiors
Author(s): W. Stolzmann (1,2) and T. Bloecker (3) ((1) Institut fuer Theoretische
Physik und Astrophysik, Universitaet Kiel, Germany - (2) Astrophysikalisches
Institut Potsdam, Germany - (3) Max-Planck-Institut fuer Radioastronomie,
Bonn, Germany)
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.
Paper: astro-ph/0008399
Dated: Fri, 25 Aug 2000 08:48:49 GMT (332kb)
Comments: 17 pages including 20 PostScript figures; also available from
http://www.mpifr-bonn.mpg.de/div/speckle/publications.html; Astronomy &
Astrophysics, in press
URL: http://arXiv.org/abs/astro-ph/0008399