Modeling overcontact binaries I: The effect of tidal deformation

Abstract

Context. In the realm of massive stars, strong binary interaction is commonplace. One extreme case are overcontact systems, which is expected to be part of the evolution of all stars evolving towards a merger, and is hypothesized to play 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 observation and theory show that overcontact stars are heavily tidally deformed, 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, it is still uncertain how large the effect of tidal deformation is on the inferred properties of stellar models. Aims. We aim to consistently model overcontact binary stars in a one dimensional (1D) stellar evolution code. To that end, we develop the required methodology to represent tidally distorted stars in 1D evolution codes. Methods. Using numerical methods, we compute the structure correction factors to the 1D spherical stellar structure equations of hydrostatic equilibrium and radiative energy transfer due to the binary Roche potential, and compare them to existing results and the structure corrections of single, rotating stars. We implement the new structure correction factors into the stellar evolution code MESA and explore several case studies. We compare the differences between our simulations when no rotation is included, when we treat rotation using single star corrections (i.e. 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 that fill their Roche lobe significantly, as non-rotating.