The effect of an optically thin region on stability of an accretion disk around a supermassive black hole

We analyse conditions of the innermost portion of an accretion disk and establish a set of equations for this region. A stable innermost region may exist, which can probably explain the observed UV and X-ray spectra, avoiding the unstable emission. We then discuss the detailed radial structure of a disk around a black hole for typical AGN parameters and obtain different kinds of- relationships for different regions of a disk. On the basis of this, we discuss the stability. A new type of cycle is present, which we call a double S shaped cycle. In this cycle, the extent of accretion rate variability is much larger than that in dwarf nova cycles. This probably solves the problem of violent variability of AGN. In the meantime, the very high accretion rate at the hottest state in limit cycles in the unstable region may provide continuous injection of matter to the jet and power the relativistic motion of the jet.