We investigate the effect of black hole spin on warped or misaligned accretion discs - in particular i) whether or not the inner disc edge aligns with the black hole spin and ii) whether the disc can maintain a smooth transition between an aligned in
ner disc and a misaligned outer disc, known as the Bardeen-Petterson effect. We employ high resolution 3D smoothed particle hydrodynamics simulations of $alpha$-discs subject to Lense-Thirring precession, focussing on the bending wave regime where the disc viscosity is smaller than the aspect ratio $alpha lesssim H/R$. We first address the controversy in the literature regarding possible steady-state oscillations of the tilt close to the black hole. We successfully recover such oscillations in 3D at both small and moderate inclinations ($lesssim 15^{circ}$), provided both Lense-Thirring and Einstein precession are present, sufficient resolution is employed, and provided the disc is not so thick so as to simply accrete misaligned. Second, we find that discs inclined by more than a few degrees in general steepen and break rather than maintain a smooth transition, again in contrast to previous findings, but only once the disc scale height is adequately resolved. Finally, we find that when the disc plane is misaligned to the black hole spin by a large angle, the disc tears into discrete rings which precess effectively independently and cause rapid accretion, consistent with previous findings in the diffusive regime ($alpha gtrsim H/R$). Thus misalignment between the disc and the spin axis of the black hole provides a robust mechanism for growing black holes quickly, regardless of whether the disc is thick or thin.
We use three dimensional hydrodynamical simulations to show that a highly misaligned accretion disk around one component of a binary system can exhibit global Kozai-Lidov cycles, where the inclination and eccentricity of the disk are interchanged per
iodically. This has important implications for accreting systems on all scales, for example, the formation of planets and satellites in circumstellar and circumplanetary disks, outbursts in X-ray binary systems and accretion on to supermassive black holes.
Be/X-ray binary systems exhibit both periodic (Type I) X-ray outbursts and giant (Type II) outbursts, whose origin has remained elusive. We suggest that Type II X-ray outbursts occur when a highly misaligned decretion disk around the Be star becomes
eccentric, allowing the compact object companion to capture a large amount of material at periastron. Using 3D smoothed particle hydrodynamics simulations we model the long term evolution of a representative Be/X-ray binary system. We find that periodic (Type I) X-ray outbursts occur when the neutron star is close to periastron for all disk inclinations. Type II outbursts occur for large misalignment angles and are associated with eccentricity growth that occurs on a timescale of about 10 orbital periods. Mass capture from the eccentric decretion disk results in an accretion disk around the neutron star whose estimated viscous time is long enough to explain the extended duration of Type II outbursts. Previous studies suggested that the outbursts are caused by a warped disk but our results suggest that this is not sufficient, the disk must be both highly misaligned and eccentric to initiate a Type II accretion event.
