J/A+A/550/A43 Equation of state for magnetized plasmas (Potekhin+, 2013)
Equation of state for magnetized Coulomb plasmas.
Potekhin A.Y., Chabrier G.
<Astron. Astrophys. 550, A43 (2013)>
=2013A&A...550A..43P 2013A&A...550A..43P
ADC_Keywords: Models ; Stars, late-type ; Magnetic fields
Keywords: dense matter - equations of state - magnetic fields - stars: neutron -
white dwarfs
Abstract:
We have developed an analytical equation of state (EOS) for magnetized
fully-ionized plasmas that cover a wide range of temperatures and
densities, from low-density classical plasmas to relativistic, quantum
plasma conditions. This EOS directly applies to calculations of
structure and evolution of strongly magnetized white dwarfs and
neutron stars. We review available analytical and numerical results
for thermodynamic functions of the nonmagnetized and magnetized
Coulomb gases, liquids, and solids. We propose a new analytical
expression for the free energy of solid Coulomb mixtures. Based on
recent numerical results, we have constructed analytical
approximations for the thermodynamic functions of harmonic Coulomb
crystals in quantizing magnetic fields. The analytical description
ensures a consistent evaluation of all astrophysically important
thermodynamic functions based on the first, second, and mixed
derivatives of the free energy. Our numerical code for calculation of
thermodynamic functions based on these approximations has been made
publicly available. Using this code, we calculate and discuss the
effects of electron screening and magnetic quantization on the
position of the melting point in a range of densities and magnetic
fields relevant to white dwarfs and outer envelopes of neutron stars.
We consider also the thermal and mechanical structure of a magnetar
envelope and argue that it can have a frozen surface which covers the
liquid ocean above the solid crust.
Description:
The FORTRAN codes implement the formulae for the EOS of fully-ionized
nonideal Coulomb plasmas. The subroutines are collected in two files:
one file contains the complete set of subroutines for nonmagnetized
plasmas, and the other is needed when a quantizing magnetic field is
present. In the latter case the two files must be linked together.
File Summary:
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FileName Lrecl Records Explanations
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ReadMe 80 . This file
eos12.f 97 2264 Set of FORTRAN subroutines for the EOS of
nonmagnetized Coulomb plasmas
eosmag12.f 75 1393 Additional FORTRAN subroutines for the EOS
of magnetized Coulomb plasmas, needed when
a quantizing magnetic field is present; to be
linked with eos12.f
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Description of file: eos12.f
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Name of Description
subroutine
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MAIN Example driving routine (normally commented-out)
MELANGE9 For arbitrary ionic mixture, renders total (ion+electron)
pressure, internal energy, entropy, heat capacity (all normalized
to the ionic ideal-gas values), logarithmic derivatives of
pressure over temperature and density.
EOSFI8 Nonideal (ion-ion + ion-electron + electron-electron)
contributions to the free and internal energies, pressure,
entropy, heat capacity, derivatives of pressure over logarithm of
temperature and over logarithm of density (all normalized to the
ionic ideal-gas values) for one ionic component in a mixture.
FITION9 Ion-ion interaction contributions to the free and internal
energies, pressure, entropy, heat capacity, derivatives of
pressure over logarithms of temperature and density.
FSCRliq8 Ion-electron (screening) contributions to the free and
internal energies, pressure, entropy, heat capacity,
derivatives of pressure over logarithms of temperature and
density in the liquid phase for one ionic component in a mixture.
FSCRsol8 Ion-electron (screening) contributions to the free and
internal energies, pressure, entropy, heat capacity,
derivatives of pressure over logarithms of temperature and
density for monoionic solid.
FHARM12 Harmonic (including static-lattice and zero-point) contributions
to the free and internal energies, pressure, entropy, heat
capacity, derivatives of pressure over logarithms of temperature
and density for solid OCP.
HLfit12 The same as FHARM12, but only for thermal contributions.
ANHARM8 Anharmonic contributions to the free and internal energies,
pressure, entropy, heat capacity, derivatives of pressure
over logarithms of temperature and density for solid OCP.
CORMIX Correction to the linear mixing rule for the Coulomb liquid
ELECT11 For an ideal electron gas of arbitrary degeneracy and relativity
at given temperature and electron chemical potential, renders
number density (in atomic units), free energy, pressure, internal
energy, entropy, heat capacity (normalized to the electron
ideal-gas values), logarithmic derivatives of pressure over
temperature and density. This subroutine is actually split into
ELECT11a, which realizes general fitting expressions via the
Fermi-Dirac integrals, and ELECT11b, which employs the Sommerfeld
expansions in the case of a very strong electron degeneracy.
SOMMERF Provides the Sommerfeld expansion up to order T2 for the
relativistic Fermi-Dirac integrals of orders 1/2, 3/2, 5/2,
together with the corresponding approximations for their first,
second, and some third derivatives.
EXCOR7 Electron-electron (exchange-correlation) contributions to the free
and internal energies, pressure, entropy, heat capacity,
derivatives of pressure over logarithm of temperature and over
logarithm of density (all normalized to the classical electron
ideal-gas values).
FERINV7 Inverse non-relativistic Fermi integrals of orders -1/2, 1/2, 3/2,
5/2, and their first and second derivatives.
BLIN9 Relativistic Fermi-Dirac integrals of orders 1/2, 3/2, and 5/2,
together with their first, second, and some third derivatives.
CHEMFIT7 Electron chemical potential at given density and temperature, and
its first derivatives over density and temperature and the second
derivative over temperature.
Detailed description of file: eos12.f
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Name of Description
subroutine
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MAIN Example driving routine (normally commented-out)
EOSMAG EOS of a homogeneous magnetized electron-ion plasma
Input: ion charge and mass numbers (Z, A), mass density rho in
CGS, temperature T and magnetic field strength B in atomic units
Output: electron number density ne; ion Coulomb coupling constant
Gamma; electron chemical potential in units of kBT; ion plasma
temperature Tp divided by T; indicator of the phase state
(liquid or solid); pressure P divided by nikBT, where ni=ne/Z is
the ion number density; internal energy per ion per kBT;
entropy S; specific heat CV; logarithmic derivatives of P over T
and rho.
CHEMAG8 EOS of magnetized electron ideal gas (input are density,
temperature, and magnetic field strength).
ELECTMAG EOS of magnetized electron ideal gas (input are density,
temperature, and the chemical potential of the ideal electron gas)
MAGNION EOS of nonrelativistic nondegenerate magnetized ion gas.
SPINION Contributions to the EOS of nonrelativistic nondegenerate ion gas
due to the spin degeneracy and magnetic moments.
EOSFIM12 Non-ideal parts of thermodynamic functions.
EXCORM Exchange-correlation contribution for the electron gas in a
magnetic field.
FHARMAG Harmonic (including static-lattice and zero-point) contributions
to the free and internal energies, pressure, entropy, heat
capacity, derivatives of pressure over logarithms of temperature
and density for solid OCP, and the energy difference for two
characteristic orientations of the Coulomb crystal in a
quantizing magnetic field.
HLMAG Thermal phonon contributions to the internal energy, heat
capacity, entropy, pressure, logarithmic pressure derivatives,
and several auxiliary quantities.
QDMAG Quantum-diffraction correction to the EOS of the magnetized
liquid EIP.
darcth Function that realized the inverse hyperbolic tangent
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Detailed descriptions of all subroutines are given by comment lines in the
corresponding codes.
The second file (eosmag12.f - magnetic EOS), unlike the first one (eos12.f -
nonmagnetic EOS), is designed for an EIP containing only one kind of the ions,
but not a mixture.
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Acknowledgements:
Alexander Potekhin, palex(at)astro.ioffe.ru
(End) Patricia Vannier [CDS] 24-Dec-2012