Hydromagnetic stability of a slim disc in a stationary geometry
Abstract
The magnetorotational instability originates from the elastic coupling of fluid elements in orbit around a gravitational well. Since inertial accelerations play a fundamental dynamical role in the process, one may expect substantial modifications by strong gravity in the case of accretion on to a black hole. In this paper, we develop a fully covariant, Lagrangian displacement vector field formalism with the aim of addressing these issues for a disc embedded in a stationary geometry with negligible radial flow. This construction enables a transparent connection between particle dynamics and the ensuing dispersion relation for magnetohydrodynamic wave modes. The magnetorotational instability (MRI)  in its incompressible variant  is found to operate virtually unabated down to the marginally stable orbit; the putative inner boundary of standard accretion disc theory. To obtain a qualitative feel for the dynamical evolution of the flow below r_{ms}, we assume a mildly advective accretion flow such that the angular velocity profile departs slowly from circular geodesic flow. This exercise suggests that turbulent eddies will occur at spatial scales approaching the radial distance while tracking the surfaces of null angular velocity gradients. The implied field topology, namely largescale horizontal field domains, should yield strong mass segregation at the displacement nodes of the nonlinear modes when radiation stress dominates the local disc structure (an expectation supported by quasilinear arguments and by the nonlinear behaviour of the MRI in a nonrelativistic setting). Under this circumstance, baryonpoor flux in horizontal field domains will be subject to radial buoyancy and to the Parker instability, thereby promoting the growth of poloidal field.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 December 2002
 DOI:
 10.1046/j.13658711.2002.05826.x
 arXiv:
 arXiv:astroph/0204003
 Bibcode:
 2002MNRAS.337..795A
 Keywords:

 black hole physics;
 gravitational waves;
 instabilities;
 MHD;
 Astrophysics
 EPrint:
 submitted to M.N.R.A.S. (3/29/02), 14 pages, 2 figures v2 accepted paper: clarified text and added discussion on radial flow effects. Added references