MoBiDICT: New 3D static models of close synchronised binaries in hydrostatic equilibrium

Context. In close binary systems, tidal interactions and rotational effects can strongly influence stellar evolution as a result of mass transfer and common envelope phases. These aspects can only be treated following improvements of theoretical models to take into account the breaking of spherical symmetry occurring in close binaries. Current models of binary stars rely on either the so-called Roche model or the perturbative approach, both of which result in several assumptions concerning the gravitational, tidal, and centrifugal potentials.Aims. Our aim is to develop a precise 3D model of stellar deformations and to study the robustness of the Roche and perturbative models in different deformation regimes.Methods. We developed a new non-perturbative method to compute the precise structural deformation of a binary system in three dimensions that is valid even in the most distorted cases. We then compared our new method to the Roche and perturbative models for different orbital separations and binary components.Results. We found that in the most distorted cases, both the Roche and perturbative models significantly underestimate the deformation of binaries. The effective gravity and the overall structural deformations are also noticeably different in the most distorted cases, leading to modifications of the usual gravity darkening generally obtained through the Roche model when interpreting the observations. Moreover, we found that the dipolar term of the gravitational potential, usually neglected by the perturbative theory, has the same order of magnitude as the leading tidal term in the most distorted cases.Conclusions. We developed a new method that is capable of precisely computing the deformations of a binary system composed of any type of stars, even compact objects. For all the stars we studied, the differences in deformation with respect to the Roche or perturbative models are significant in the most distorted cases, which impacts both the interpretation of observations and the theoretical structural depiction of these distorted bodies. In the weaker deformation regimes, the Roche model is a viable option for studying the surface properties of binaries, while the perturbative model is strongly favoured when evaluating structural deformations.

Automated summary

This study developed a precise 3D model to calculate the deformations of binary star systems and examined the reliability of the Roche and perturbative models in different deformation regimes. It was found that both the Roche and perturbative models significantly underestimate the deformations of binaries in the most distorted cases. Additionally, the dipolar term of the gravitational potential, usually neglected by the perturbative theory, has the same order of magnitude as the leading tidal term in the most distorted cases.