The Magnetic Rayleigh-Taylor Instability in Astrophysical Disks

TL;DR

This paper investigates the magnetic Rayleigh-Taylor instability at the inner edge of astrophysical disks around black holes, deriving stability criteria in general relativistic magnetohydrodynamics and exploring implications for black hole jet power.

Contribution

It derives the instability criteria in general relativistic MHD and analyzes the effects of black hole spin on disk stability and magnetic flux accumulation.

Findings

Static disks are unstable around Schwarzschild black holes.

Rotation stabilizes disks around Kerr black holes.

Magnetic flux accumulation is proportional to black hole spin.

Abstract

This is our first study of the magnetic Rayleigh-Taylor instability at the inner edge of an astrophysical disk around a central back hole. We derive the equations governing small-amplitude oscillations in general relativistic ideal magnetodydrodynamics and obtain a criterion for the onset of the instability. We suggest that static disk configurations where magnetic field is held by the disk material are unstable around a Schwarzschild black hole. On the other hand, we find that such configurations are stabilized by the spacetime rotation around a Kerr black hole. We obtain a crude estimate of the maximum amount of poloidal magnetic flux that can be accumulated around the center, and suggest that it is proportional to the black hole spin. Finally, we discuss the astrophysical implications of our result for the theoretical and observational estimations of the black hole jet power.