Mass and spin coevolution during the alignment of a black hole in a warped accretion disc

In this paper, we explore the gravitomagnetic interaction of a black hole (BH) with a misaligned accretion disc to study BH spin precession and alignment jointly with BH mass MBH and spin parameter a evolution, under the assumption that the disc is continually fed, in its outer region, by matter with angular momentum fixed on a given direction Ĵdisc,out. We develop an iterative scheme based on the adiabatic approximation to study the BH-disc coevolution: in this approach, the accretion disc transits through a sequence of quasi-steady warped states (Bardeen-Petterson effect) and interacts with the BH until the spin JBH aligns with Ĵdisc,out. For a BH aligning with a co-rotating disc, the fractional increase in mass is typically less than a few percent, while the spin modulus can increase up to a few tens of percent. The alignment timescale tal ∝ a5/7Ṁ−32/35 is of ∼ 10 − 10 yr for a maximally rotating BH accreting at the Eddington rate. BH-disc alignment from an initially counter-rotating disc tends to be more efficient compared to the specular co-rotating case due to the asymmetry seeded in the Kerr metric: counter-rotating matter carries a larger and opposite angular momentum when crossing the innermost stable orbit, so that the spin modulus decreases faster and so the relative inclination angle.