Equation of state SAHA-S meets stellar evolution code CESAM2k

TL;DR

This paper develops an interpolation module for the SAHA-S equation of state tailored for the CESAM2k stellar evolution code, enabling accurate and efficient integration of thermodynamic data in stellar modeling.

Contribution

It introduces a cubic spline interpolation approach to adapt the SAHA-S equation of state for use in CESAM2k, addressing variable discrepancies and providing a practical implementation method.

Findings

Successfully integrated SAHA-S EOS into CESAM2k

Achieved smooth and accurate thermodynamic derivatives

Validated with a solar model comparison

Abstract

We present an example of an interpolation code of the SAHA-S equation of state that has been adapted for use in the stellar evolution code CESAM2k. The aim is to provide the necessary data and numerical procedures for its implementation in a stellar code. A technical problem is the discrepancy between the sets of thermodynamic quantities provided by the SAHA-S equation of state and those necessary in the CESAM2k computations. Moreover, the independent variables in a practical equation of state (like SAHA-S) are temperature and density, whereas for modelling calculations the variables temperature and pressure are preferable. Specifically for the CESAM2k code, some additional quantities and their derivatives must be provided. To provide the bridge between the equation of state and stellar modelling, we prepare auxiliary tables of the quantities that are demanded in CESAM2k. Then we use cubic spline interpolation to provide both smoothness and a good approximation of the necessary derivatives. Using the B-form of spline representation provides us with an efficient algorithm for three-dimensional interpolation. The table of B-spline coefficients provided can be directly used during stellar model calculations together with the module of cubic spline interpolation. This implementation of the SAHA-S equation of state in the CESAM2k stellar structure and evolution code has been tested on a solar model evolved to the present. A comparison with other equations of state is briefly discussed. The choice of a regular net of mesh points for specific primary quantities in the SAHA-S equation of state, together with accurate and consistently smooth tabulated values, provides an effective algorithm of interpolation in modelling calculations. The proposed module of interpolation procedures can be easily adopted in other evolution codes.