Local dynamical instabilities in magnetized, radiation pressure-supported accretion disks

We present a general linear dispersion relation that describes the coupled behavior of magnetorotational, photon bubble, and convective instabilities in weakly magnetized, differentially rotating accretion disks. We presume t he accretion disks to be geometrically thin and supported vertically by rad iation pressure. We fully incorporate the effects of a nonzero radiative di ffusion length on the linear modes. In an equilibrium with a purely vertica l magnetic field, the vertical magnetorotational modes are completely unaff ected by compressibility, stratification, and radiative diffusion. However, in the presence of azimuthal fields, which are expected in differentially rotating flows, the growth rate of all magnetorotational modes can be reduc ed substantially below the orbital frequency. This occurs if diffusion dest roys radiation sound waves on the length scale of the instability and the m agnetic energy density of the azimuthal component exceeds the nonradiative thermal energy density. While sluggish in this case, the magnetorotational instability still persists and will still tap the free energy of the differ ential rotation. Photon bubble instabilities are generically present in rad iation pressure-dominated flows where diffusion is present. We show that th eir growth rates are limited to a maximum value that is reached at short wa velengths where the modes may be viewed as unstable slow magnetosonic waves . We also find that vertical radiation pressure destabilizes upward-propaga ting fast waves, and that waves can be unstable. Alfven These instabilities typically have smaller growth rates than the photon bubble/slow modes. We discuss how all these modes behave in various regimes of interest and specu late how they may affect the dynamics of real accretion disk flows.