An approach to the effects of stellar rotation on the theoretical apsidal motion constants. Calculations from 0.40 M_sol to 25.0 M_sol

Abstract

The most reliable sources for determining absolute stellar parameters are the double-lined eclipsing binary systems. Some of these systems also show apsidal motion, characterized by the variable log k$_2$. This point grants us the possibility of investigating the stellar interior, specifically the degree of stellar mass concentration. The first studies carried out about four decades ago on this topic showed appreciable discrepancies not only with respect to the comparison between the observed absolute dimensions and their theoretical counterparts, but mainly concerning the degree of mass concentration through the analysis of their apsidal motions. Fortunately, this scenario has been gradually improving with the advances in the quality of observational techniques and advances in the input physics of the evolutionary stellar models (e.g. opacities, thermonuclear reactions, equations of state, numerical techniques). These new developments in the input physics has improved the comparison between observations and the values predicted by theory, including the apsidal motion rates. This progress has lead us to investigate second-order effects such as rotation and dynamic tides. In this paper we deal with the effects of rotation on the degree of mass concentration. The stellar models were calculated using the MESA package. The mass range studied here was 0.40 to 25.0 M$_ odot $ for a generic chemical composition characterized by X = 0.70 and Z = 0.02. The present models were computed without taking into account core overshooting in order to highlight the effects of rotation. Each model was followed from the pre-main sequence until the central hydrogen content is of the order of or less than 0.03, covering the range of masses and evolutionary status of the double-lined eclipsing binaries showing apsidal motion. Regarding the calculation of the internal structure coefficients bf we integrated the Radau equation using the fifth-order Runge-Kutta method and a tolerance level of 10$^ $. As an auxiliary tool, homology transformations have been used to explain, qualitatively, how the equation of state, thermonuclear reactions, and convection impact the degree of mass concentration of the models. In our past studies on the effects of rotation on log k$_2$ an average correction was used for all models together. For this a small range of masses (2.0, 7.0, 15.0 M$_ odot $) has been used. In the present paper the corrections due to the effects of rotation in log k$_2$ are presented for each mass individually and for three evolutionary phases. This point is particularly important bf given that these corrections show a clear dependence on the mass and on the evolutionary status. Such corrections can be easily introduced into the theoretical calculation of apsidal motion rates through a linear equation. A typical correction due to the rotation effects is of the order of -0.03 in log k$_2$.