Alignment of black hole spin with a warped accretion disc in BHXBs

A thin viscous accretion disc around a Kerr black hole, which is warped due to the Lense-
Thirring (LT) precession, was shown to cause the spin axis of the black hole to precess and align with the outer disc. Here, we calculate, analytically and numerically, the total LT torque acting on the black hole taking contribution from the entire disc, and thus compute the alignment and precession time-scales of the black hole for both persistent and transient accretors. We find that there exists a critical value of the Kerr parameter, below which, the alignment time-scale decreases with the increasing value of Kerr parameter contrary to earlier predictions and can be significantly longer an be significantly longer than the previously computed time-scale value in similar scenarios. Besides, the time-scales are generally longer for transience relative to, what was reported earlier, and our computed time-scales for persistent accretion. From our analysis of the transient case, we find that the black hole in the low mass X-ray binary (LMXB) 4U 1543–47 could be misaligned, whereas that in the LMXB XTE J1550–564 has aligned itself with the outer disc. We also find that a typical Galactic LMXB can take a significantly longer time to align than what was estimated in the past, using the average properties of such sources. This may have an important implication on the measurement of black hole spin using the continuum X-ray spectral fitting method.