Black hole-disc coevolution in the presence of magnetic fields: refining the Thorne limit with emission from within the plunging region

Abstract

The accretion of material onto a black hole modifies the properties of that hole owing to the capture of both matter and radiation. Adding matter to the hole through an accretion disc generally acts to increase the hole's spin parameter, while the capture of radiation generally provides a retarding torque. The balance between the torques provided by adding matter and radiation leads to a maximum spin parameter that can be obtained by a black hole which grows by accretion, known as the Thorne limit. In the simplest theory of thin disc accretion this Thorne limit has the value $a_{\bullet, {\rm lim}} \simeq 0.998$. The purpose of this paper is to highlight that any modification to theories of accretion flows also modify this limiting value, and to compute precisely the modification arising from a particular extension of accretion theory: the inclusion of bright emission from within the plunging region which is sourced from the magnetohydrodynamic stresses ubiquitously observed in simulations. This extra emission further suppresses black hole spin-up and results in new, lower, limits on the final black hole spin. These limits depend on the details of the magnetic stresses acting within the plunging region, but typical values seen in simulations and observations would lower the limit to $a_{\bullet, {\rm lim}} \simeq 0.99$, a subtle but not negligible deviation.