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

TL;DR

This paper analyzes how shear flows amplify slow magnetosonic waves in accretion disks, leading to turbulence and plasma heating, which may explain quasar luminosity.

Contribution

It provides analytical solutions for wave amplification in shear flows and links wave amplification to turbulence and heating in accretion disks.

Findings

Strong wave amplification in long-wavelength limit.

Amplification leads to turbulence enhancement.

Potential explanation for quasar plasma heating.

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 Schroedinger 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 Kolmogorov 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.