Alignment and precession of a black hole misaligned with its accretion disc: application to low-mass X-ray binaries

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 timescales 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.

A review of quasi-periodic oscillations from black hole X-ray binaries: Observation and theory

“…equations 21-23 in [169]). Solving equations 10 and 11 then indicates that β(R) tends to the initial tilt angle β = β 0 for large R and to β = 0 at small R, with the two regimes connected by a smooth warp (also see [38,18]). This result was first derived by Bardeen and Petterson [19], and therefore such a setup is often called the Bardeen-Patterson configuration.…”

“…Accretion onto the hole will then drive the system towards alignment over time. King and Nixon [111] show that this is a slow process, with the BH needing to accrete ∼ 10% of its initial mass before the misalignment angle is significantly altered (also see [137,18]), indicating that modest misalignments could be common amongst the BH XRB population. Even more mass would need to be accreted if the Bardeen-Petterson transition radius is smaller than analytic predictions, as recent GRMHD simulations imply [123].…”

Effects of precession versus instabilities on the jets of GRS 1758–258

“…Therefore, for jet precession driven by BZ, or by BP together with the Bardeen-Petterson effect, a tilted, spinning black hole is needed. Although BZ is probably not behind the precession in our system because of the small angular momentum of the disc compared to that of the black hole (which seems to be the common case, making the precession of black hole spin axes difficult to observe at human timescales; see Nixon & King 2013;Banerjee et al 2019), observational evidence exists to support the idea that the black hole spin axis could be misaligned with the orbital and accretion disc angular momentum in X-ray binaries (see e.g. Hjellming & Rupen 1995;Maccarone 2002;Caproni et al 2006).…”

“…Hjellming & Rupen 1995;Maccarone 2002;Caproni et al 2006). This different spinning axis in accretion disc and black holes may be related to the violent birth of the system together with a corresponding long alignment timescale which has been estimated to be on the order of 10 6 years (Maccarone 2002), or even higher (Banerjee et al 2019); being, thus, greater than, or at least similar to, the system lifetime. On the other hand, jet precession may be due to a disc tilted by an external torque from the companion and a BP launching mechanisms, no matter the black hole spin.…”

The Spin and Orientation of the Black Hole in XTE J1908$+$094

“…Note that the inclination of the inner disk does not necessarily match that of the outer regions of the accretion disk and of the binary system, as a result of the Bardeen-Petterson effect (see, e.g., Bardeen & Petterson 1975;Nealon et al 2015;Liska et al 2020). Still, the orientation of the black hole spin and the inner accretion disk can precess due to the Lense-Thirring effect and align itself with the outer accretion disk (see, e.g., Banerjee et al 2019).…”