A Modal Analysis of the Irradiation Instability

The irradiation instability is a disk instability caused by the radiation pressure cast by a central source onto an optically thick disk. The criterion for this instability depends on a sharp transition from an optically thin inner disk to an optically thick outer disk. The quickly diminishing radiation pressure in this transition region creates a radially compressing effect, which is in many ways similar to the effects of self-gravity. In this modal analysis, we demonstrate that a disk marginally stable to irradiation can develop global modes, with growth rates being of order the dynamical timescale of the disk. The non-linear evolution of the our model shows the formation of vortices near the transition region and spiral structures propagating into the optically thick region. Consequently the scale-height of our disk's inner edge becomes time-variable and can likely be observed as a variation in its infrared flux.