The Accuracy, Consistency, and Speed of Five Equations of State for Stellar Hydrodynamics

Abstract

We compare the thermodynamic properties and execution speed of five independent equations of state. A wide range of temperatures, densities, and compositions are considered—conditions appropriate for modeling the collapse of a cloud of hydrogen gas (or an exploding supernova) to the outer layers of a neutron star. The pressures and specific thermal energies calculated by each equation-of-state routine are reasonably accurate (typically 0.1% error or less) and agree remarkably well with each other, despite the different approaches and approximations used in each routine. The derivatives of the pressure and specific thermal energies with respect to the temperature and density generally show less accuracy (typically 1% error or less) and more disagreement with one another. Thermodynamic consistency, as measured by deviations from the appropriate Maxwell relations, shows that the Timmes equation of state and the Nadyozhin equation of state achieve thermodynamic consistency to a high degree of precision. The execution speed of the five equation-of-state routines—evaluated across several different machine architectures, compiler options, and modes of operation—differ dramatically. The Arnett equation of state is the fastest of the five routines, with the Nadyozhin equation of state close behind.