Acoustic $\alpha$-disk

Abstract

It is shown that the turbulent flow of acoustic waves propagating outward from the inner edge of the disk causes the accretion of the matter onto the center. The exponential amplification of waves takes place in the resonance region, $\omega = (n\pm 1)\Omega$. Here $\omega$ is the frequency of the acoustic wave, $n$ is its azimuthal wave number, $\Omega (r)$ is the angular frequency of rotation of the disk. The effect is similar to the inverse Landau damping in a collisionless plasma. Energy comes from the energy of rotation of the disk. That leads to decrease of the disk angular momentum and to accretion of the matter. The value of the accretion rate $dM/dt$ is ${\dot{M}} = \pi rc_{s} \Sigma _{0} (c_{s} / v_{\phi 0})^{2} W$. Here $c_{s}$ is the speed of sound of the disk gas, $v_{\phi 0}$ is the Keplerian rotation velocity, $\Sigma _{0}$ is the surface density of the disk, $W$ is total power of the acoustic turbulence, $W \simeq \int _{0}^{\infty }d \omega \sum_{n\geq 0} | \frac{\Sigma'}{\Sigma _{0}} |^{2} (\omega , n)$, $|\Sigma'|^{2} (\omega , n)$ is the spectral power of turbulence. The presented picture of accretion is consistent with the observed variations of X-ray and optical radiation from objects whose activity is associated with accretion of gas onto them.