Warped discs and the directional stability of jets in active galactic nuclei

Warped accretion discs in active galactic nuclei (AGN) exert a torque on the black hole that tends to align the rotation axis with the angular momentum of the outer disc. We compute the magnitude of this torque by solving numerically for the steady-state shape of the warped disc, and verify that the analytic solution of Scheuer & Feiler provides an excellent approximation. We generalize these results for discs with strong warps and arbitrary surface density profiles, and calculate the time-scale over which the black hole becomes aligned with the angular momentum in the outer disc. For massive black holes and accretion rates of the order of the Eddington limit, the alignment time-scale is always short (≲ 10⁶ yr), so that jets accelerated from the inner disc region provide a prompt tracer of the angular momentum of gas at large radii in the disc. Longer time-scales are predicted for low-luminosity systems, depending on the degree of anisotropy in the hydrodynamic response of the disc to shear and warp, and for the final decay of modest warps at large radii in the disc that are potentially observable via very-long-baseline interferometry (VLBI). We discuss the implications of this for the inferred accretion history of those AGN with jet directions that appear to be stable over long time-scales. The large energy deposition rate at modest disc radii during rapid realignment episodes should make such objects transiently bright at optical and infrared wavelengths.