Black holes in stellar-mass binary systems expiating original spin?

We investigate systematically whether accreting black hole systems are likely to reach global alignment of the black hole spin and its accretion disc with the binary plane. In low-mass X-ray binaries (LMXBs), there is only a modest tendency to reach such global alignment, and it is difficult to achieve fully: except for special initial conditions, we expect misalignment of the spin and orbital planes by ∼1 rad for most of the LMXB lifetime. The same is expected in high-mass X-ray binaries. A fairly close approach to global alignment is likely in most stellar-mass ultraluminous X-ray binary systems (ULXs) where the companion star fills its Roche lobe and transfers mass on a thermal or nuclear time-scale to a black hole of lower mass. These systems are unlikely to show orbital eclipses, as their emission cones are close to the hole's spin axis. This offers a potential observational test, as models for ULXs invoking intermediate-mass black holes do predict eclipses for ensembles of ≳ 10 systems. Recent observational work shows that eclipses are either absent or extremely rare in ULXs, supporting the picture that most ULXs are stellar-mass binaries with companion stars more massive than the accretor.