THE RADIAL-AZIMUTHAL INSTABILITY OF ACCRETION DISKS .1. RADIATION PRESSURE DOMINATION

By analyzing the fourth-order dispersion relation, the influence of coupled radial and azimuthal perturbations on the stability of a radiation-pressure-dominated accretion disk is investigated. If the azimuthal perturbations are considered, we find that the stability properties of disk are different from that in purely radial perturbation case. For a standard alpha disk model, the thermal instability is the dominant instability, and it is enhanced in the presence of azimuthal perturbations, while the viscous mode and the acoustic modes tend to become stable with the increase of azimuthal perturbation wavenumber. The increase of viscosity will enhance the instabilities of thermal and viscous modes, as well as that of acoustic modes. The acoustic instability exists only in the case without azimuthal perturbations or with very low azimuthal wavenumber. For a slim disk model, the situation is quite similar except that the thermal and viscous modes are never unstable in the absence of azimuthal perturbations, where the acoustic instability is dominant.