Publications
of the
MPIfR
Optical & Infrared
Interferometry Group
W. Stolzmann, T. Blöcker, and D.
Schönberner:
An Equation-of-State Formalism for the
Interior of Very Low Mass
stars and Brown Dwarfs
Abstract (poster) for the
Euroconference on
Very Low-Mass Stars and Brown Dwarfs in Stellar Clusters and
Associations,
May 11th - 15th, 1998, Los Cancajos, La Palma, Spain.
Abstract.
For astrophysical applications, e.g. stellar structure and evolution or
astroseismological investigations, it is necessary
to determine a set of thermodynamical functions over a wide range of
densities
and temperatures. The accuracy of the formalism of the equation of
state is
restricted frequently by the well-known noise problems of second-order
quantities apparent in purely numerical approaches.
Starting from the Helmholtz free energy we calculate first- and
second derivatives as the pressure p (for the equation of state),
the internal energy u, the isothermal compressibility 1/k
(for the density exponent chi_rho), the strain coefficient
(for the temperature exponent chi_T) and the
isochoric specific heat c_v (for the isobaric specific heat c_p)
by explicit and simple expressions.
We present for these quantities and further relevant parameters for
astrophysical applications, as, e.g., the adiabatic
gradient, a semirelativistically analytical description being valid for
T < 2x10^9 K and any density.
Nonideal effects due to the correlations between electrons and
z-charged ions
are included by Pade approximants
which cover a wide range of electron degeneracy and Coulomb coupling.
Numerical studies and comparisons are given for fully ionized plasmas
consisting of light (H, He) and heavy (C, O) elements, respectively.