Local Dynamical Instabilities in Magnetized, Radiation Pressure–supported Accretion Disks

We present a general linear dispersion relation which describes the coupledbehavior of magnetorotational, photon bubble, and convective instabilities inweakly magnetized, differentially rotating accretion disks. We presume theaccretion disks to be geometrically thin and supported vertically by radiationpressure. We fully incorporate the effects of a nonzero radiative diffusionlength on the linear modes. In an equilibrium with purely vertical magneticfield, the vertical magnetorotational modes are completely unaffected bycompressibility, stratification, and radiative diffusion. However, in thepresence of azimuthal fields, which are expected in differentially rotatingflows, the growth rate of all magnetorotational modes can be reducedsubstantially below the orbital frequency. This occurs if diffusion destroysradiation sound waves on the length scale of the instability, and the magneticenergy density of the azimuthal component exceeds the non-radiative thermalenergy density. While sluggish in this case, the magnetorotational instabilitystill persists and will still tap the free energy of the differential rotation.Photon bubble instabilities are generically present in radiation pressuredominated flows where diffusion is present. We show that their growth rates arelimited to a maximum value which is reached at short wavelengths where themodes may be viewed as unstable slow magnetosonic waves. We also find thatvertical radiation pressure destabilizes upward propagating fast waves, andthat Alfv\'en waves can be unstable. These instabilities typically have smallergrowth rates than the photon bubble/slow modes. We discuss how all these modesbehave in various regimes of interest, and speculate how they may affect thedynamics of real accretion disk flows.Comment: 30 pages, 5 figures, Submitted to the Astrophysical Journa