# Alignment and precession of a black hole misaligned with its accretion disc: Application to Low Mass X-ray Binaries

## TL;DR

This paper investigates the alignment and precession of a black hole's spin axis caused by a warped accretion disc, providing new calculations for alignment timescales and implications for observed low mass X-ray binaries.

## Contribution

It introduces a detailed calculation of the Lense-Thirring torque on black holes considering the inner disc, revealing longer alignment timescales for transient accretors and implications for spin measurements.

## Key findings

- Alignment timescales increase with decreasing Kerr parameter below a critical value.
- Transient accretors have longer alignment timescales than persistent ones.
- Some LMXBs may have misaligned black holes, affecting spin measurement methods.

## Abstract

A thin viscous accretion disc around a Kerr black hole, which is warped due to the Lense-Thirring (LT) effect, was shown to cause the spin axis of the black hole to precess and align with the outer disc. We calculate the total LT torque acting on the black hole, and compute the alignment and precession time-scales for both persistent and transient accretors. In our analysis, we consider the contribution of the inner disc, as it can stay misaligned with the black hole spin for a reasonable range of parameter values. We find that the alignment time-scale increases with a decrease in the Kerr parameter below a critical Kerr parameter value, contrary to earlier predictions. Besides, the time-scales are generally longer for transience than the time-scales calculated 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. The age of the LMXB H 1743-322 is estimated assuming a misaligned disc. We also find that the black hole in a typical Galactic LMXB can take a significantly longer time to align than what was estimated in the past. This may have an important implication on the measurement of black hole spin using the continuum X-ray spectral fitting method.