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

We explore the effect of anisotropic wind driving on the properties of accretion onto black holes (BHs) in close binaries. We specifically focus on line-driven winds, which are common in high-mass X-ray binaries (HMXBs). In close binary systems, the tidal force from the companion star can modify the wind structure in two different ways. One is the reduction of wind terminal velocity due to the weaker effective surface gravity. The other is the reduction in mass flux due to gravity darkening (GD). We incorporate these effects into the so-called CAK theory in a simple way and investigate the wind flow around the accretor on the orbital scale. We find that a focused accretion stream is naturally formed when the Roche lobe filling factor is greater than or similar to 0.8-0.9, analogous to that of wind Roche lobe overflow, but only when the velocity reduction is taken into account. The formation of a stream is necessary to bring in sufficient angular momentum to form an accretion disc around the BH. GD effects reduce the amount of accreted angular momentum, but not enough to prevent the formation of a disc. Based on these results, we expect there to be a discrete step in the observability of HMXBs depending on whether the donor Roche lobe filling factor is below or above similar to 0.8-0.9.