X-ray reflection from inhomogeneous accretion disks. I. Toy models and photon bubbles

Numerical simulations of the interiors of radiation-dominated accretion disks show that significant density inhomogeneities can be generated in the gas. Here, we present the first results of our study on X-ray reflection spectra from such heterogeneous density structures. We consider two cases: first, we produce a number of toy models in which a sharp increase or decrease in density, of variable width, is placed at different depths in a uniform slab. Comparing the resulting reflection spectra to those from an unaltered slab shows that the inhomogeneity can affect the emission features, in particular the Fe Kalpha and O VIII Lyalpha lines. The magnitude of any differences depends on both the parameters of the density change and the ionizing power of the illuminating radiation, but the inhomogeneity is required to be within similar to2 Thomson depths of the surface to cause an effect. However, only relatively small variations in density (by factors of a few) are necessary for significant changes in the reflection features to be possible. Our second test was to compute reflection spectra from the density structure predicted by a simulation of the nonlinear outcome of the photon-bubble instability. The resulting spectra also exhibited differences from the constant-density models, caused primarily by a strong 6.7 keV iron line. Nevertheless, constant-density models can provide a good fit to simulated spectra, albeit with a low reflection fraction, between 2 and 10 keV. Below 2 keV, differences in the predicted soft X-ray line emission result in very poor fits with a constant-density ionized-disk model. The results indicate that density inhomogeneities may further complicate the relationship between the Fe Kalpha equivalent width and the X-ray continuum. Further calculations are needed to verify that density variations of sufficient magnitude will occur within a few Thomson depths of the disk photosphere.