Modeling overcontact binaries I. The effect of tidal deformation

Context. In the realm of massive stars, strong binary interactions are commonplace. One extreme case is that of overcontact systems, which are expected to be part of the evolution of all stars evolving towards a merger and hypothesized as playing a role in the formation of binary black holes. However, important simplifications are made to model the evolution of overcontact binaries. The deformation from tidal forces is almost always put aside, and even rotation is frequently ignored in such models. Yet, both observations and theory have shown that overcontact stars are tidally deformed to a great extent, leaving a potentially important effect on the outer layers unaccounted for in models. Furthermore, in eclipsing binaries where radii can be determined to high precision, the question of how large the effect of tidal deformation is on the inferred properties of stellar models is still uncertain. Aims. We aim to consistently model overcontact binary stars in a one-dimensional (1D) stellar evolution code. To that end, we developed the required methodology to represent tidally distorted stars in 1D evolution codes. Methods. Using numerical methods, we computed the structure correction factors to the 1D spherical stellar structure equations of hydrostatic equilibrium and radiative energy transfer due to the binary Roche potential. We then compared them to existing results and the structure corrections of single, rotating stars. We implemented the new structure correction factors in the stellar evolution code MESA and explored several case studies. We compared the differences between our simulations: when no rotation is included, when we treat rotation using single star corrections (only accounting for centrifugal deformation), or when we use tidal deformation. Results. We find that ignoring rotation in deformed detached eclipsing binaries can produce a radius discrepancy of up to 5%. The difference between tidal and single star centrifugal distortion models is more benign at 1%, showing that single rotating star models are a suitable approximation of tidally deformed stars in a binary system. In overcontact configurations, we find a similar 5% variation in surface properties as a result of tidal distortion with respect to non-rotating models, showing that it is inappropriate to model binary stars filling their Roche lobe significantly as non-rotating.

Automated summary

This study aims to consistently model overcontact binary stars using a one-dimensional stellar evolution code. The results show that ignoring rotation in deformed detached binaries can result in a radius discrepancy of up to 5%, while the difference between tidal deformation models and single-star rotating models is relatively small at 1%.