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Hydromagnetic stability of a slim disc in a stationary geometry

Araya-Góchez, Rafael Angel (2002) Hydromagnetic stability of a slim disc in a stationary geometry. Monthly Notices of the Royal Astronomical Society, 337 (3). pp. 795-807. ISSN 0035-8711. https://resolver.caltech.edu/CaltechAUTHORS:20170409-083426461

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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 large-scale horizontal field domains, should yield strong mass segregation at the displacement nodes of the non-linear modes when radiation stress dominates the local disc structure (an expectation supported by quasi-linear arguments and by the non-linear behaviour of the MRI in a non-relativistic setting). Under this circumstance, baryon-poor flux in horizontal field domains will be subject to radial buoyancy and to the Parker instability, thereby promoting the growth of poloidal field.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1046/j.1365-8711.2002.05826.xDOIArticle
https://arxiv.org/abs/astro-ph/0204003arXivDiscussion Paper
Alternate Title:Hydromagnetic Stability of a Slim Disk in a Stationary Geometry
Additional Information:© 2002 RAS. Accepted 2002 July 1. Received 2002 June 18; in original form 2002 March 29. It is a great pleasure to acknowledge stimulating and instructive discussions with Lee Lindblom, Roger Blandford, Ethan Vishniac, Thierry Foglizzo and Sterl Phinney. I am also very grateful to an anonymous referee for useful comments that helped to improve the manuscript. I am greatly indebted to the Theoretical Astrophysics and Relativity Group at Caltech for their hospitality.
Group:TAPIR
Subject Keywords:black hole physics – gravitational waves – instabilities – MHD
Issue or Number:3
Record Number:CaltechAUTHORS:20170409-083426461
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170409-083426461
Official Citation:Rafael Angel Araya-Góchez; Hydromagnetic stability of a slim disc in a stationary geometry, Monthly Notices of the Royal Astronomical Society, Volume 337, Issue 3, 11 December 2002, Pages 795–807, https://doi.org/10.1046/j.1365-8711.2002.05826.x
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:76458
Collection:CaltechAUTHORS
Deposited By: 1Science Import
Deposited On:04 Apr 2018 18:07
Last Modified:03 Oct 2019 17:01

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