Waves and Instabilities in Accretion Disks : MHD Spectroscopic Analysis

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 mag-netohydrodynamic perturbations, the full magnetohydrodynamic spectra for a realistic accretion disk model demonstrates 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 non-axisymmetric instabilities. The ability to characterize all waves arising in accretion disks holds great promise for magnetohydrodynamic spectroscopic analysis. 1. Hydromagnetic stability for stationary equilibria Magnetohydrodynamic (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 analyse the entire MHD spectrum of gravitationally and thermally stratified, rotating , magnetized equilibrium configurations, we use the formalism of Frieman and Rotenberg (1960). The equation of motion for the Lagrangian displacement ξ of a fluid element is ρ ∂ 2 ξ ∂t 2 + 2ρv· ∇ ∂ξ ∂t + ∇Π−B · ∇Q−Q · ∇B+ ∇ · (ρξ)g−∇ · [ρξ(v · ∇)v − ρvv · ∇ξ] = 0, (1)