X-ray variability of an illuminated irregular accretion disk around a black hole

Models for active galactic nuclei and X-ray binaries where "cold" rotating matter is illuminated by a nonthermal source above it have been widely studied, and they successfully explain the main spectral features of black hole candidates, including reflection humps above 10 keV and the iron line at 6.4 keV. Making the reasonable assumptions that the innermost part of an accretion disk around a black hole is unstable and clumpy and that it is illuminated by X-ray sources originating above it, we compute the X-ray variability induced by both a clump of matter moving relativistically around the black hole and the nonthermal source moving above the disk. One interesting new result we find is that even for a face-on geometry, rotation-induced variability can still be observed as long as the nonthermal source is not exactly at the symmetry axis; this is true even if the accretion disk is smooth. We also show that the reflected X-ray component, peaked around 10 or several tens of keV, can vary more than other spectral components, such as the thermal emission from the disk and the external power-law flux, and that it carries richer information on the nonthermal sources. This is because the reflected component experiences a double path through the gravitational field of the central mass, i.e., from the source to the disk and then from the disk to the observer. Thus our study is most relevant to X-ray variability of black hole candidates where relativistic effects are strong. These results may provide a partial explanation of why some Seyfert 1 galaxies exhibit rapid X-ray variability with timescales comparable to the fastest orbital periods, and why soft X-rays and UV emission generally show slower variability than do the hard X-rays.