Misalignment of the Lense-Thirring precession by an accretion torque

¹ Department of Astronomy, Astrophysics & Space Engineering, Indian Institute of Technology Indore, Simrol Indore 453552 Madhya Pradesh, India
² Center for Interdisciplinary Exploration & Research in Astrophysics (CIERA), Physics & Astronomy, Northwestern University Evanston IL 60202, USA
³ Astronomical Institute, Academy of Sciences Boční II 141 31 Prague 4, Czech Republic
⁴ Nicolaus Copernicus Astronomical Center ul. Bartycka 18 PL 00-716 Warsaw, Poland
⁵ Department of Physics and Astronomy, College of Charleston 66 George St Charleston SC 29424, USA
⁶ Center for Computational Astrophysics, Flatiron Institute 162 5th Avenue New York NY 10010, USA

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Received: 19 March 2025
Accepted: 30 November 2025

Abstract

Context. Orbiting matter misaligned with a spinning black hole undergoes Lense-Thirring precession due to the frame-dragging effect. This phenomenon is particularly relevant for type-C QPOs observed in the hard states of low-mass X-ray binaries. However, the accretion flow in these hard states is complex, consisting of a geometrically thick, hot corona surrounded by a geometrically thin, cold disk. Recent simulations demonstrate that, in such a truncated disk scenario, the precession of the inner, hot corona slows due to its interaction with the outer, cold disk.

Aims. This paper aims to provide an analytical description of the precession of an inner (hot) torus in the presence of accretion torques exerted by the outer (cold) disk.

Methods. Using the angular momentum conservation equation, we investigated the evolution of the torus angular momentum vector for various models of accretion torque.

Results. We find that, in general, an accretion torque tilts the axis of precession away from the black hole spin axis. In all models, if the accretion torque is sufficiently strong, it can halt the precession; any perturbation from this stalled state causes the torus to precess around an axis that is misaligned with the black hole spin axis.

Conclusions. The accretion torque exerted by the outer thin disk can cause precession around an axis that is neither aligned with the black hole spin axis nor perpendicular to the plane of the disk. This finding may have significant observational implications, as the jet direction, if aligned with the angular momentum axis of the torus, may no longer reliably indicate the black hole spin axis or the orientation of the outer accretion disk.