J/A+A/621/A128 Equation of state of dense water (Mazevet+, 2019)
Ab initio based equation of state of dense water for planetary and
exoplanetary modeling
Mazevet S., Licari A., Chabrier G., Potekhin A.Y.
<Astron. Astrophys. 621, A128 (2019)>
=2019A&A...621A.128M 2019A&A...621A.128M (SIMBAD/NED BibCode)
ADC_Keywords: Models ; Planets ; Exoplanets
Keywords: equation of state - planets and satellites: interiors -
planets and satellites: general
Abstract:
The modeling of planetary interiors requires accurate equations of
state for the basic constituents with proven validity in the difficult
pressure-temperature regime extending up to 50000K and hundreds of
Mbars. While equations of state based on first principles simulations
are now available for the two most abundant elements, hydrogen and
helium, the situation is less satisfactory for water where no
wide-range equation of state is available despite its need for
interior modeling of planets ranging from super-Earths to planets
several times the size of Jupiter.
As a first step toward a multi-phase equation of state for dense
water, we develop a temperature-dependent equation of state for dense
water covering the liquid and plasma regimes and extending to the
super-ionic and gas regimes. This equation of state covers the
complete range of conditions encountered in planetary modeling.
We use first principles quantum molecular dynamics simulations and its
Thomas-Fermi extension to reach the highest pressures encountered in
giant planets several times the size of Jupiter. Using these results,
as well as the data available at lower pressures, we obtain a
parametrization of the Helmholtz free energy adjusted over this
extended temperature and pressure domain. The parametrization ignores
the entropy and density jumps at phase boundaries but we show that it
is sufficiently accurate to model interior properties of most planets
and exoplanets.
We produce an equation of state given in analytical form that is
readily usable in planetary modeling codes and dynamical simulations
(a fortran implementation can be found at
http://www.ioffe.ru/astro/H2O/). The EOS produced is valid for the
entire density range relevant to planetary modeling, for densities
where quantum effects for the ions can be neglected, and for
temperatures below 50000K. We use this equation of state to calculate
the mass-radius relationship of exoplanets up to 5000M⊕,
explore temperature effects in ocean and wet Earth-like planets, and
quantify the influence of the water EOS for the core on the
gravitational moments of Jupiter.
Description:
The FORTRAN code implement the fitting formula for the EOS of dense
water in the interiors of planets and exoplanets. Detailed
descriptions of all subroutines are given by comment lines in the
files. For the domain of applicability of the underlying data and
fitting formulae, see the text and Fig.5 of the paper
File Summary:
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FileName Lrecl Records Explanations
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ReadMe 80 . This file
eoswater.f 74 461 Set of FORTRAN subroutines for the water EOS
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Description of file: eoswater.f
H2OFIT : Given the mass density RHO(g/cm3) and temperature T(K),
returns the fits to the thermodynamic functions:
PnkT - pressure, normalized to (kT times number density)
FNkT - Helmholtz free energy per atom, normalized by kT
UNkT - internal energy per atom, normalized by kT
CV - specific heat per atom in units of Boltzmann constant k
CHIT - logarithmic derivative of pressure over temperature
CHIR - logarithmic derivative of pressure over density
PMbar - pressure in Mbar
USPEC - specific internal energy in ergs/gram
ELECNR : For a given electron number density and temperature (in atomic
units), returns normalized thermodynamic functions in the model
of an ideal nonrelativistic Fermi gas: chemical potential
divided by kT; Helmholtz free energy and internal energy per
electron, divided by kT; specific heat per atom in units of k;
logarithmic derivatives of electron pressure over temperature
and density
FERINT : fits (according to Antia 1993ApJS...84..101A 1993ApJS...84..101A) to nonrelativistic
Fermi integrals of the order of -1/2, 1/2, 3/2, and 5/2
FINVER : fits (according to Antia 1993ApJS...84..101A 1993ApJS...84..101A) to the inverse Fermi
integrals of the order of -1/2, 1/2, 3/2, and 5/2
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Acknowledgements:
Alexander Y. Potekhin, palex(at)astro.ioffe.ru
(End) Patricia Vannier [CDS] 21-Jan-2019