Internal circulation in tidally locked massive binary stars: Consequences for double black hole formation

Context. Steady-state currents, so-called Eddington-Sweet circulation, result in the mixing of chemical elements in rotating stars, and in extreme cases lead to a homogeneous composition. Such circulation currents are also predicted in tidally deformed binary stars, which are thought to be progenitors of double black-hole merger events.Aims. This work aims to quantitatively characterise the steady-state circulation currents in components of a tidally locked binary system and to explore the effects of such currents on numerical models.Methods. Previous results describing the circulation velocity in a single rotating star and a tidally and rotationally distorted binary star are used to deduce a new prescription for the internal circulation in tidally locked binaries. We explore the effect of this prescription numerically with a detailed stellar evolution code for binary systems with initial orbital periods between 0.5 and 2.0 days, primary masses between 25 and 100 M-circle dot and initial mass-ratios q(i)=0.5, 0.7, 0.9, 1.0 at metallicity Z=Z(circle dot)/50.Results. When comparing circulation velocities in the radial direction for the cases of a single rotating star and a binary star, it is found that the average circulation velocity in the binary star may be described as an enhancement to the circulation velocity in a single rotating star. This velocity enhancement is a simple function depending on the masses of the binary components and amounts to a factor of approximately two when the components have equal masses. After applying this enhancement to stellar models, it is found that the formation of double helium stars through efficient mixing occurs for systems with higher initial orbital periods, lower primary masses and lower mass ratios, compared to the standard circulation scenario. Taking into account appropriate distributions for primary mass, initial period and mass ratio, models with enhanced mixing predict 2.4 times more double helium stars being produced in the parameter space than models without.Conclusions. We conclude that the effects of companion-induced circulation have strong implications for the formation of close binary black holes through the chemically homogeneous evolution channel. Not only do the predicted detection rates increase but double black-hole systems with mass ratios as low as 0.8 may be formed when companion-induced circulation is taken into account.