Title: Ab Initio Equation of State Calculations of Hydrogen-Helium Mixtures and Application to the Mass-Radius Relationship of Solar and Extrasolar Giant Planets Authors: B. Militzer, W. B. Hubbard Table: Coefficients of Free Energy Fit for the equation of state ================================================================================ Byte-by-byte Description of file: EOS_fit.txt -------------------------------------------------------------------------------- Bytes Format Units Label Explanations -------------------------------------------------------------------------------- 1- 1 A1 --- t 1=F, 2=dF/dT, 3=dF/dnn 4=d^2F/dnn/dT 3- 14 F12.10 atomic units rs Density parameter 16- 27 F12.10 atomic units T Temperature 29- 45 E17.10 atomic units F Free energy or derivative -------------------------------------------------------------------------------- This table contains the coefficient of the Helmholtz free energy fit that we constructed to reproduce the pressure, internal energy, entropy, and free energy from our ab initio simulations a hydrogen-helium mixture of a solar-type composition with 18 heliums in 220 hydrogen (helium mass fraction Y=0.245). The density parameter rs is given by 4/3*pi*rs^3=V/N_e where N_e is total number of electrons in volume V. The number density of electrons is nn=N_e/V. The fit uses atomic units: rs is given Bohr radii = 5.29177208607e-11 m T is given in Hartree/k_b = 3.15774660873e+05 K F is given in Hartree/electron = 4.35974380267e-18 J Because this is a two dimensional spline fit in density, nn, and temperature, T, we need specify the certain derivatives at boundaries of the fit domain. type=1 means column 4 specifies the free energy, F, at this rs and T point. type=2 means column 4 contains temperature derivative of the free energy, dF/dT. type=3 means column 4 contains density derivative of the free energy, dF/dnn. type=4 means column 4 contains cross derivative of the free energy, d^2F/dnn/dT. -------------------------------------------------------------------------------- 2 3.5811439043 0.0010133809 -4.8585676991e+00 1 3.5811439043 0.0010133809 -1.0843586568e-01 1 3.5811439043 0.0022187379 -1.1459213725e-01 1 3.5811439043 0.0038337239 -1.2402554301e-01 1 3.5811439043 0.0059975473 -1.3814988835e-01 1 3.5811439043 0.0088967253 -1.5900540299e-01 1 3.5811439043 0.0127811610 -1.8955085098e-01 1 3.5811439043 0.0179856846 -2.3433637209e-01 1 3.5811439043 0.0249589155 -3.0024867787e-01 1 3.5811439043 0.0343019318 -3.9860737843e-01 1 3.5811439043 0.0468200820 -5.4149629455e-01 1 3.5811439043 0.0635924050 -7.4655967194e-01 1 3.5811439043 0.0860646404 -1.0394217674e+00 1 3.5811439043 0.1161738484 -1.4621222349e+00 1 3.5811439043 0.1565153805 -2.0678129075e+00 1 3.5811439043 0.2105665936 -2.9345454724e+00 1 3.5811439043 0.2829865905 -4.1646940556e+00 1 3.5811439043 0.3800178256 -5.8942578432e+00 2 3.5811439043 0.3800178256 -1.8250284661e+01 4 3.5811439043 0.0010133809 +1.4644924544e+02 3 3.5811439043 0.0010133809 +1.7016513363e-01 3 3.5811439043 0.0022187379 +3.4571879403e-01 3 3.5811439043 0.0038337239 +5.7511066947e-01 3 3.5811439043 0.0059975473 +8.7221634555e-01 3 3.5811439043 0.0088967253 +1.2131292640e+00 3 3.5811439043 0.0127811610 +1.6623265346e+00 3 3.5811439043 0.0179856846 +2.3092232274e+00 3 3.5811439043 0.0249589155 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