Waves and Instabilities in Accretion Disks: Magnetohydrodynamic Spectroscopic Analysis

Abstract

A complete analytical and numerical treatment of all magnetohydrodynamic waves and instabilities for radially stratified, magnetized accretion disks is presented. The instabilities are a possible source of anomalous transport. While recovering results on known hydrodynamic and both weak-and strong-field magnetohydrodynamic perturbations, the full magnetohydrodynamic spectra for a realistic accretion disk model demonstrate a much richer variety of instabilities accessible to the plasma than previously realized. We show that both weakly and strongly magnetized accretion disks are prone to strong nonaxisymmetric instabilities. The ability to characterize all waves arising in accretion disks holds great promise for magnetohydrodynamic spectroscopic analysis. Subject headings: accretion, accretion disks -instabilities -MHD -waves 1. HYDROMAGNETIC STABILITY FOR STATIONARY EQUILIBRIAMagnetohydrodynamic (MHD) spectroscopy (Goedbloed et al. 1994) entails the ability to calculate all MHD perturbations accessible to a particular magnetized plasma configuration (the forward spectral problem) and holds the promise to use the MHD spectrum to diagnose the internal plasma state (the backward spectral problem). In this Letter we predict all MHD waves and instabilities for magnetized accretion disks.To analyze the entire MHD spectrum of gravitationally and thermally stratified, rotating magnetized equilibrium configurations, we use the formalism of Frieman & Rotenberg (1960). The equation of motion for the Lagrangian displacement of a fluid y element is2 Ѩt Ѩt where measures the Eulerian perturbation of total pressure, is the Eulerian P p Ϫy · ١p Ϫ g p١ · y ϩ B · Q Q p ١ ؋ (y ؋ B) perturbation of the magnetic field B, and g is the gravitational acceleration. Equation (1) describes all waves supported by a timeinvariant equilibrium with density r, pressure p, flow field , gravity g, and magnetic field B; g is the ratio of specific heats. We v specify our analysis to one-dimensional axisymmetric stationary equilibria satisfying 2 2 2 2

Linear wave propagation in relativistic magnetohydrodynamics

“…23,24 Finally, knowledge of the wave properties in uniform media is indispensible to appreciate the significant modifications encountered when diagnosing waves and instabilities in nonuniform, relativistic MHD equilibrium configurations. This would lead to MHD spectroscopy 25 for accretion disks about compact objects, or for relativistic jets.…”

Flow shear stabilization of rotating plasmas due to the Coriolis effect

“…In Ref. [26] and later again in [27] an error was made in the WKB analysis as explained in [28]. In Ref.…”

“…The pressure p and density ρ should be averaged over a magnetic surface, or read ρ 0 and p 0 as defined in Eqs. (26) and (27) below. The safety factor q is the number of toroidal turns per poloidal turn of a magnetic field line.…”

Surface-wave instabilities in a plasma rotating with step-like frequency profile

“…[9,10] (see also Refs. [11][12][13][14]) and for arbitrary heat conductivity in Refs. 15 and 16. The main benchmarks of our technique are the pair of the canonical first-order differential equations for perturbations called the Hameiri-Bondeson-Iakono-Bhattacharjee (HBIB) type equations, first derived in [12,13].…”