Amplification of Slow Magnetosonic Waves by Shear Flow: Heating and Friction Mechanisms of Accretion Disks

Abstract

Propagation of three dimensional magnetosonic waves is considered for a homogeneous shear flow of an incompressible fluid. The analytical solutions for all magnetohydrodynamic variables are presented by confluent Heun functions. The problem is reduced to finding a solution of an effective Schrodinger equation. The amplification of slow magnetosonic waves is analyzed in great details. A simple formula for the amplification coefficient is derived. The velocity shear primarily affects the incompressible limit of slow magnetosonic waves. The amplification is very strong for slow magnetosonic waves in the long-wavelength limit. It is demonstrated that the amplification of those waves leads to amplification of turbulence. The phenomenology of Shakura-Sunyaev for the friction in accretion disks is derived in the framework of the Koknogorov turbulence. The presented findings may be the key to explaining the anomalous plasma heating responsible for the luminosity of quasars. It is suggested that wave amplification is the keystone of the self-sustained turbulence in accretion disks.

Nonlinear Terms of MHD Equations for Homogeneous Magnetized Shear Flow

“…This saturation simulates strong turbulence for small wave-vectors, but definitely for large wave-vectors |K y | ≫ 1 at τ → ∞ we have a wave type turbulence with a given frequency. We have to mention that the linearized case of pure shear is exactly integrable in terms of the Heun functions [1,5]. Investigating numerically this case with ω C = 0 and B z = 0 in his Ph.D. thesis [6] T. Hristov discovered in 1990 the amplification of slow magnetosonic waves (SMWs) by shear flows.…”