Zhang, XiaoHe (1989) Interactions of magnetohydrodynamic waves with gravitomagnetic fields, and their possible roles in blackhole magnetospheres. Physical Review D, 40 (12). pp. 38583883. ISSN 05562821. http://resolver.caltech.edu/CaltechAUTHORS:ZHAprd89a

PDF
See Usage Policy. 4Mb 
Use this Persistent URL to link to this item: http://resolver.caltech.edu/CaltechAUTHORS:ZHAprd89a
Abstract
The magnetospheres of rotating, magnetized black holes are thought to generate some of the jets observed in quasars and active galactic nuclei. Previous research on such magnetospheres has focused on stationary configurations. This paper is an initial, exploratory study of dynamical magnetospheres. Because a dynamical study in a rotating hole's Kerr spacetime would be exceedingly difficult, this paper introduces a class of simpler, planesymmetric or cylindrically symmetric model spacetimes in which to explore the dynamics. These model spacetimes preserve the key physical features of the Kerr geometry: they have a Kerrtype gravitomagnetic potential (shift function), a Kerrtype horizon, and a Kerrtype asymptotically flat region far from the horizon. This first exploratory study is restricted to the simplest of these spacetimes, one with the planar metric ds2=dt2+(dx+βdt)2+dy2+dz2, gravitomagnetic potential β=VF(tanh z1), and horizon lateral velocity dx/dt=2VF. In this spacetime the asymptotically flat region is at z≫1, and the horizon has been pushed off to z=∞. We treat the dynamical magnetospheres using the 3+1 formalism of generalrelativistic magnetohydrodynamics (GRMHD) developed in an earlier paper. Kerrtype models of stationary magnetospheres are built in this spacetime as exact solutions to the fully nonlinear equations of GRMHD. In these solutions the magnetic field, under the influence of the horizon's lateral motion, is driven to move laterally with velocity dx/dt=VF; and plasma particles (e+e pairs) are created at z=0, and are then driven up to relativistic velocities by magneticgravitomagnetic coupling, as they flow off to "infinity" (z=+∞) and down toward the "horizon" (z=∞). Weak perturbations of these analytic magnetospheres are studied using a linearization of the GRMHD perturbation equations. The linearized perturbation equations are Fourier analyzed in t and x[exp(iωt+ikxx)] and are solved numerically to obtain the z dependence of the perturbations. The numerical solutions describe the response of the magnetosphere to oscillatory driving forces in the plasmainjection plane, z=0. This models the response of a Kerr hole's magnetosphere to oscillatory driving forces near the plasmaproduction region—forces that might arise when lumpy magnetic fields, anchored in an accretion disk, orbit the hole, pressing inward on the magnetosphere. In our model spacetime the magnetosphere responds resonantly at frequencies (as measured at infinity) ω=kxVF, i.e., at frequencies for which the perturbations are stationary as seen in the field lines' rest frame. The analog for a Kerr magnetosphere would be resonant responses at ω=mΩF, where m is the azimuthal quantum number of the perturbation and ΩF is the fieldline angular velocity (roughly equal to half the horizon angular velocity). Such resonances, if they occur in real blackhole magnetospheres, would show up as a modulation of the jet's outflowing energy flux.
Item Type:  Article 

Additional Information:  ©1989 The American Physical Society Received 19 July 1989 The author is indebted to Kip Thorne, who suggested this problem and has given considerable help in the course of this work and in the writing of this manuscript. The author would like to thank Paul Coppi for help in some of the graphic presentations of the numerical results. He has also benefited from discussions with Charles Evans in dealing with numerical difficulties. This work was supported in part by NSF Grants Nos. AST8514911 and AST8817792. 
Record Number:  CaltechAUTHORS:ZHAprd89a 
Persistent URL:  http://resolver.caltech.edu/CaltechAUTHORS:ZHAprd89a 
Alternative URL:  http://dx.doi.org/10.1103/PhysRevD.40.3858 
Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  6479 
Collection:  CaltechAUTHORS 
Deposited By:  Archive Administrator 
Deposited On:  11 Dec 2006 
Last Modified:  26 Dec 2012 09:21 
Repository Staff Only: item control page