Equation of state SAHA-S meets stellar evolution code CESAM2k

¹ Sternberg Astronomical Institute, Lomonosov Moscow State University, 119234 Moscow, Russia
e-mail: vab@sai.msu.ru
² Department of Physics and Astronomy, University of Southern California, Los Angeles, CA 90089, USA
³ Université de La Côte d’Azur, OCA, Laboratoire Lagrange CNRS, BP 4229, 06304 Nice Cedex, France
⁴ Institute of Problems of Chemical Physics RAS, 142432 Chernogolovka, Russia
⁵ Tomsk State University, 634050 Tomsk, Russia
⁶ Joint Institute for High Temperatures RAS, 125412 Moscow, Russia
⁷ Moscow Institute of Physics and Technology, 141701 Dolgoprudnyi, Russia
⁸ Troitsk Institute for Innovation and Fusion Research, 142190 Troitsk, Russia

Received: 26 May 2017
Accepted: 1 August 2017

Abstract

Context. 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.

Aims. 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.

Methods. 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.

Results. 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.

Conclusions. 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.