----------------------------------------------------------------------- This directory contains equation of state(EOS) data files and corresponding interpolation codes. The equation of state tables are an extension and update of the EOS and EOSplus tables. The temperature-density range of the EOS and EOSplus tables accommodates temperature-density values characteristic of stars having masses greater than about 0.8 solar. The EOS_2001 tables cover temperature_density values encountered in stars having masses greater than about 0.1 solar. A number of changes have been made to the OPAL EOS code since the 1996 tables were calculated; primarily electrons are now treated relativistically and the activity expansion method has been improved for repulsive interactions. In addition to H2 and H2_plus molecules, and the H_, negative ion, He2+, HeH+ are now also included. ----------------------------------------------------------------------- NOTE: Updates to the fortran codes: IEOSxtrin.f and IEOSxtrin_H_He.f were made on 6 Mar 2002. These updates include bug fixes. If you use these codes, please download the latest versions. ----------------------------------------------------------------------- The format of the tables is different than that used in the opacity directory. For the EOS, data is tabulated at constant T6 and density(rho), rather than constant T6 and R (T6=temperature in units of 10**6 K, R=rho/T6**3), rho is density in g/cc). Herein, X is the hydogen mass fraction, and Z is the mass fraction of all elements heavier than helium. The helium mass fraction,Y, is thus, Y=1-X-Z. The EOS data is tabulated at Z=0.0,0.02,and 0.04; X=0.0,0.2,0.4,0.6 and 0.8. A pure hydrogen table (X=1, Z=0) is also available. The number of Z and X values is less than for the opacity tables, due to that fact that the EOS does not vary as greatly with changes in these variables. The temperature is tabulated in the range 0.002 to 100.0 and the density in the range 10**(-14) to 10**7 grams/cc. (Note: much of the region around rho=10**(-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 IEOS*z%x.gz files are the EOS data in compressed format for Z=* and X=%;i.e., IEOS02z4x.gz corresponds to Z=0.02 and X=0.4. The Z_interp_IEOS.f code interpolates the IEOS*z%x files for a fixed value of Z, creating a file 'EOSdata.gz'. The EOSdata.gz file is used by IEOS_xtrin.f to interpolate in X, T6, and rho at the fixed value of Z used to construct the EOSdata.gz file. The accuracy of the interpolation has been checked by comparison with a large sample of test calculations. Better than four place accuracy is generally achieved with both first and second order properties. At very low density (rho < 1.e-8), in regions of rapid change, the first order properties are occasionally off by as much as a few % and the second order properties can be off by 10 percent. Direct differentiation of the interpolated first order properties is most likely less accurate and is not recommended. [[ Since the Z dependent effects are quite modest for population I & II mixtures, the Z=0 EOS is adequate for many purposes. In this case the Z_interp_IEOS.f is not required to create the EOSdata.gz file. Instead the EOSdata_H-He.gz file can be used in conjunction with the Z_interp_IEOS_H-He.f interpolation code. The EOS-data_H-He file covers the full range of X and Y;i.e., the 5 IEOS0z%x files plus the IEOS0zxx file (for pure H). In order to calculate derivatives of the EOS, a very fine temperature-density grid was used. The tabulated data is a condensation of this information. The computer time required to calculate for the actual stellar mixture 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 never contribute substantially The fractional elemental number components of Z for the reduced mixture are (Grevesse, N. 1991, A&A 242,488): XC= 0.2471362 XN= 0.0620778 XO= 0.528368 XNe=0.1624178 The corresponding number fractions, including hrdrogen and heliun, are listed at the front of each of the IEOS*z%x files. More recent estimates of steller element abundances change these values slightly, but have very small affect on the EOS. ----------------------------------------------------------------------- Recent references to this equation of state work: Rogers, FJ., CONTRIBUTIONS TO PLASMA PHYSICS, 2001, V41(N2-3):179-182. Rogers, FJ., PHYSICS OF PLASMAS, JAN, 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 --------------------------------------------------------------------