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We explore the effect of anisotropic wind driving on the properties ofaccretion onto black holes in close binaries. We specifically focus online-driven winds, which are common in high-mass X-ray binaries. In closebinary systems, the tidal force from the companion star can modify the windstructure in two different ways. One is the reduction of wind terminal velocitydue to the weaker effective surface gravity. The other is the reduction in massflux due to gravity darkening. We incorporate these effects into the so-calledCAK theory in a simple way and investigate the wind flow around the accretor onthe orbital scale. We find that a focused accretion stream is naturally formedwhen the Roche lobe filling factor is $\gtrsim0.8$-0.9, analogous to that ofwind Roche lobe overflow, but only when the velocity reduction is taken intoaccount. The formation of a stream is necessary to bring in sufficient angularmomentum to form an accretion disc around the black hole. Gravity darkeningeffects reduce the amount of accreted angular momentum, but not enough toprevent the formation of a disc. Based on these results, we expect there to bea discrete step in the observability of high-mass X-ray binaries depending onwhether the donor Roche lobe filling factor is below or above $\sim$0.8-0.9.

Conditions for accretion disc formation and observability of wind-accreting X-ray binaries