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

## TL;DR

This paper presents updated stellar evolutionary models incorporating internal structure constants, radius of gyration, and gravitational potential energy, covering a wide mass range and metallicities, to improve understanding of tidal evolution and stellar interiors.

## Contribution

The paper introduces new evolutionary models with detailed internal structure constants and related parameters, replacing older models and covering a broader mass and metallicity range.

## Key findings

- Models include k2, k3, k4 constants, radius of gyration, and gravitational potential energy.
- Calculations cover stars from 0.8 to 35 solar masses and three metallicities.
- Models are provided in 54 tables with comprehensive stellar characteristics.

## Abstract

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. The aim of the paper is to present new evolutionary models, based on the MESA package, that include the internal structure constants (k$_2$, k$_3$, and k$_4$), the radius of gyration, and the gravitational potential energy for configurations computed from the pre-main-sequence (PMS) 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. 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$_{\odot}$. 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$^{-7}$. The resulting models (from 0.8 up to 35.0 M$_{\odot}$) are presented in 54 tables for the three metallicities, containing the usual characteristics of an evolutionary model (age, initial masses, log T$_{\rm eff}$, log g, and log L), the constants of internal structure (k$_2$, k$_3$, and k$_4$), the radius of gyration $\beta,$ and the factor $\alpha$ that is related with the gravitational potential energy.