Spectral Properties of Accretion Disks around Galactic and Extragalactic Black Holes: Erratum

Abstract

We derive a self-consistent set of equations that describe the propagation of nonlinear shear Alfvén waves in the solar wind. The equations include the interaction between the waves and wind plasmas and has an exact energy conservation law. Using a truncated Fourier series, we further reduce the system to a simplified nonlinear model with multiple waves. We solve the model numerically in a radially expanding box with a finite angular size. We find that for linear waves in a time-varying plasma background, the for the WKB are violated in practically the entire radial domain (even at high frequencies), although the scaling of wave amplitudes (δB) with radial distance and the equipartition between the magnetic and kinetic energy are similar to the WKB results. For nonlinear waves, equipartition still holds, but nonlinear wave reflection enhances the backward propagating waves (in the rest frame of the wind), which leads to a faster drop in δB than the linear waves. As a result, there is a "soft" saturation in which δB approaches the background magnetic field gradually at large distance. The simplified nonlinear model produces reasonably high wind speed (between 600 and 700 km s<SUP>-1</SUP>).