Updating the theoretical tidal evolution constants: Apsidal motion and the moment of inertia^⋆

¹ Instituto de Astrofísica de Andalucía, CSIC, Apartado 3004, 18080 Granada, Spain
e-mail: claret@iaa.es
² Dept. Física Tórica y del Cosmos, Universidad de Granada, Campus de Fuentenueva s/n, 10871 Granada, Spain

Received: 3 June 2019
Accepted: 1 July 2019

Abstract

Context. The theoretical apsidal motion constants are key tools to investigate the stellar interiors in close eccentric binary systems. In addition, these constants and the moment of inertia are also important to investigate the tidal evolution of close binary stars as well as of exo-planetary systems.

Aims. The aim of the paper is to present new evolutionary models, based on the MESA package, that include the internal structure constants (k₂, k₃, and k₄), the radius of gyration, and the gravitational potential energy for configurations computed from the pre-main-sequence up to the first ascent giant branch or beyond. The calculations are available for the three metallicities [Fe/H] = 0.00, −0.50, and −1.00, which take the recent investigations in less metallic environments into account. This new set of models replaces the old ones, published about 15 years ago, using the code GRANADA.

Methods. Core overshooting was taken into account using the mass-f_ov relationship, which was derived semi-empirically for models more massive than 1.2 M_⊙. The differential equations governing the apsidal motion constants, moment of inertia, and the gravitational potential energy were integrated simultaneously through a fifth-order Runge-Kutta method with a tolerance level of 10⁻⁷.

Results. The resulting models (from 0.8 up to 35.0 M_⊙) are presented in 54 tables for the three metallicities, containing the usual characteristics of an evolutionary model (age, initial masses, log T_eff, log g, and log L), the constants of internal structure (k₂, k₃, and k₄), the radius of gyration β, and the factor α that is related with the gravitational potential energy.