Constraints on the Evolution of Black Hole Spin due to Magnetohydrodynamic Accretion

TL;DR

This paper analytically investigates how magnetohydrodynamic accretion influences black hole spin evolution, revealing restrictions on magnetic field inclination and showing that MHD inflows prevent reaching maximal spin.

Contribution

It introduces a trans-fast magnetosonic solution using the magnetic field line bending angle and analyzes its implications for black hole spin evolution under MHD accretion.

Findings

Magnetic field inclination at the horizon relates to energy and angular momentum transfer.

Black hole spin evolution has two asymptotic states, preventing maximal rotation.

MHD inflows inhibit black holes from reaching maximal spin.

Abstract

Stationary and axisymmetric ideal magnetohydrodynamic (MHD) accretion onto a black hole is studied analytically. The accreting plasma ejected from a plasma source with low velocity must be super-fast magnetosonic before passing through the event horizon. We work out and apply a trans-fast magnetosonic solution without the detailed analysis of the regularity conditions at the magnetosonic point, by introducing the bending angle $\beta$ of magnetic field line, which is the ratio of the toroidal and poloidal components of the magnetic field. To accrete onto a black hole, the trans-magnetosonic solution has some restrictions on $\beta$, which are related to the field-aligned parameters of the MHD flows. One of the restrictions gives the boundary condition at the event horizon for the inclination of a magnetic field line. We find that this inclination is related to the energy and angular momentum transport to the black hole. Then, we discuss the spin-up/down process of a rotating black hole by cold MHD inflows in a secular evolution timescale. There are two asymptotic states for the spin evolution. One is that the angular velocity of the black hole approaches to that of the magnetic field line, and the other is that the spin-up effect by the positive angular momentum influx and the spin-down effect by the energy influx (as the mass-energy influx) are canceled. We also show that the MHD inflows prevents the evolution to the maximally rotating black hole.