EOS_2005 Equation of State tables >>NOTES<< Revised tables were introduced on Feb. 22, 2006. These tables correct an error in earlier tables. There is small discountinuity in P/T and E/T at density=177 g/cc. This is due to switching of calculational methods (see below). The Z=0 tables extend to lower temperatue at high density than the Z=0.02 and Z=0.04 tables. This data is at or near the limits of the theory and its use is only recommended for exploratory calculations. >>END<< _______________________________________________________________________ This directory contains equation of state data files for pure H, pure He, H-He mixtures and H-He mixtures having a small admixture of C-N- O-Ne that update files available earlier on this site. Rudimentary routines for interpolating the data are also provided. The new equation of state tables have improved thermodynamic consistency and use a slightly modified method for treating the region of pressure ionization. The EOS_2005 tables cover temperature-density values encountered in stars having masses greater than about 0.1-0.15 solar. ----------------------------------------------------------------------- The activity expansion method is in principle thermodynamically consistent. However, after the EOS_2001 tables were calculated it was realized that the calculational method used was not strictly consistent and also gave inaccurate estimates for the adiabatic gradient at high density. The main source of thermodynamic inconsistency was traced to an approximation introduced to help stabilize the iterative solution of the activity equations. This approximation has not been used in the current calculations. As a result, with a few exceptions, the new tables are thermodynamically consistent to better than 0.01% when dE/dRho is calculated by two different methods (E is energy and Rho is density). We have also made a number of small changes in the physics, which mostly affect the pressure-ionization region. It has proven to be difficult to apply the activity expansion method to high-density degenerate matter. Consequently, in the current work, we have used the activity expansion method only up to densities of 177 gm/cc, where stellar matter is nearly completely ionized. At higher density we have used multi-component hypernetted chain calculations for screened, fully ionized plasmas, i.e., a generalization of the well-known one-component plasma model (OCP). The basic data files are: EOS5_00z0x EOS5_00z2x EOS5_00z4x EOS5_00z6x EOS5_00z8x EOS5_00z10x EOS5_02z0x EOS5_02z2x EOS5_02z4x EOS5_02z6x EOS5_02z8x EOS5_04z0x EOS5_04z2x EOS5_04z4x EOS5_04z6x EOS5_04z8x Where, **z indicates the value of Z, the heavy element mass fraction and *x indicates X, the H mass fraction. For pure H-He mixtures Z is by definition zero. For example EOS5_04z2x, is the data file for Z=0.04 and X=0.2. The following rudimentary interpolation routines are also provided: ZFS_interp_EOS5.f EOS5_xtrin.f EOS5_xtrin_H_He.f. The routine ZFS_interp_EOS5.f interpolates the entire data set for a given value of Z, creating the file EOS5_data. This file can then be interpolated in X, T6 (temperature in units of 10e+6K), and Rho by the routine EOS5_xtrin.f. The routine EOS5_xtrin_H_He.f interpolates the file EOS5_data_H_He (Z=0.0 data file available from the web site). Alternatively, it is possible to interpolate the Z=0.0 data using the routine EOS5_xtrin.f, but in that case interpolation is limited to the same parameter range as spanned by the Z=0.02 and Z=0.04 tables. Quadratic interpolation in X, T6, and Rho is performed and the results returned via the array eos(i). These results have been smoothed by mixing overlapping quadratics. The returned quantities are : eos(1) is the pressure in Mbar (10E+12dyne/cm^2) eos(2) is energy in 10E+12 ergs/gm. Reference zero at zero T6 eos(3) is the entropy in units of energy/T6 eos(4) is dE/dRho at constant T6 eos(5) is the specific heat, dE/dT6 at constant V. eos(6) is dlogP/dlogRho at constant T6. Cox and Guil1 eq 9.82 eos(7) is dlogP/dlogT6 at constant Rho. Cox and Guil1 eq 9.81 eos(8) is gamma1. Eqs. 9.88 Cox and Guili. eos(9) is gamma2/(gamma2-1). Eqs. 9.88 Cox and Guili. where, T6=temperature in millions of degrees Kelvin Rho=density(g/cm^3) See subroutine esac in EOS5_xtrin_H-He.f for more details. The temperature is tabulated in the range 0.002 to 100.0 and the density in the range 10E-14 to 10E+7 grams/cc. (Note: much of the region around Rho=10E-14 is radiation dominated and is included mainly for convenience of tabulation.) The lower temperature limit of the tables gradually increases for densities >0.00237 gm/cc. The EOS5_**z*x files also include the mean molecular weight, the electron number-density and the derivative of the energy with respect to Rho (dE/dRho), none of which were included in the EOS_2001 tables. For the lowest few temperatures, in order to obtain solutions to the activity equations, it was necessary to introduce an artificial electron abundance (chosen to be 0.0001 by number fraction). These temperature points can be identified by noting were the electron density suddenly increases with decreasing temperature. This affects the pressure and energy by about 0.01%, but has little affect on the derivatives. The quantity gamma3-1 is no longer tabulated. It can be obtained from the other tabulated values if needed. The computer time required to calculate the actual stellar mixture for elements up to Ni would be substantial, so a truncated mixture was used. In the truncated mixture the mass contribution of all elements above neon where added in with the neon. Contrary to the situation with opacity, these high Z elements do not contribute substantially The fractional elemental number components of Z for the reduced mixture are the same as used in previous work: (Grevesse, N. 1991, A&A 242,488): XC= 0.2471362 XN= 0.0620778 XO= 0.528368 XNe=0.1624178 The corresponding number fractions, including hydrogen and helium, are listed at the front of each of the EOS5**z*x files. More recent estimates of steller element abundances change these values slightly, but should have a small affect on the EOS. In the current context, this is accommodated by choosing a different value of Z. ----------------------------------------------------------------------- A report on this work is being prepared for publication. Some references to earlier work are: Rogers FJ, Nayfonov A, ApJ 2002, 576,1064 Rogers, F.J., Contrib. to Plasma Physics, 2001, V41 (N2-3): 179-182 Rogers, F.J., Physics of Plasmas, 2000, V7 (N1): 51-58. Rogers, F.J., Swenson, F.J. and Iglesias, C. A. 1996,ApJ, 456, 902 Rogers, F.J. 1994, in "The Equation of State in Astrophysics", IAU Colloquium 147, eds.. G. Chabrier and E. Schatzman (Cambridge University Press), p16 --------------------------------------------------------------------