Stellar Equations of State

1. Stellar Equations of State We have developed an electron-positron equation of state based on table interpolation of the Helmholtz free energy (Timmes \& Swesty 2000). The interpolation scheme guarantees perfect thermodynamic consistency, independent of the interpolating function. The choice of a biquintic Hermite polynomial as the interpolating function results in accurately reproducing the underlying Helmholtz free energy data in the table, and yields derivatives of the pressure, specific entropy and specific internal energy which are smooth and continuous. The execution speed - evaluated across several different machine architectures, compiler options, and mode of operation - suggest that the Helmholtz equation of state routine is faster than any of the five equation of state routines surveyed by Timmes \& Arnett (1999). When an optimal balance of accuracy, thermodynamic consistency, and speed is desirable, then the tabular Helmholtz equation of state is an excellent choice, particularly for multidimensional models of stellar phenomena. Accuracy EOS Maximum Thermodynamic Relative Routine Method % Error Consistency Timing Rank ------- ---------- ----------- --------------------- ---------- ------ Timmes analytic 0.0 perfect 106.0 5 Iben analytic 1.0 fair 28.0 6 Weaver analytic 1.0 fair 5.6 4 Nadyozhin analytic 0.8 very good 2.3 2 Arnett table 1.0 poor 1.3 3 Helmholtz table 0.001 perfect 1.0 1 An Accelerated Strategic Computing Initiative (ASCI) Academic Strategic Alliances Program (ASAP) Center at The University of Chicago