Impact of tides on non-coplanar orbits of progenitors of high-mass X-ray binaries

Context. An important stage in the evolution of massive binaries is the formation of a compact object in the system. It is believed that in some cases a momentum kick is imparted to the newly born object, changing the orbital parameters of the binary, such as eccentricity and orbital period, and even acquiring an asynchronous orbit between its components. In this situation, tides play a central role in the evolution of these binaries.Aims. In this work we aim to study how the orbital parameters of a massive binary change after the formation of a compact object when the stellar spin of the non-degenerate companion is not aligned with the orbital angular momentum.Methods. We used MESA, which we modified to be able to evolve binaries with different values of the inclination between the orbital planes before and just after the formation of the compact object. These modifications to the equations solved by the MESA code are extended to the case of non-solid body rotation.Results. We find that the impact of having different initial inclinations is mostly present in the evolution towards an equilibrium state that is independent of the inclination. If the binary separation is small enough such that the interaction happens when the star is burning hydrogen in its core, this state is reached before the beginning of a mass-transfer phase, while for a wider binary not all conditions characterizing the equilibrium are met. We also explore the effect of having different initial rotation rates in the stars and how the Spruit-Tayler dynamo mechanism affects the angular momentum transport for a non-coplanar binary.Conclusions. These findings show that including the inclination in the equations of tidal evolution to a binary after a kick is imparted onto a newly born compact object changes the evolution of some parameters, such as the eccentricity and the spin period of the star, depending on how large this inclination is. Moreover, these results can be used to match the properties of observed X-ray binaries to estimate the strength of the momentum kick.