Accretion disk models and their X-ray reflection signatures. I. Local spectra

X-ray illumination of accretion disks is an invaluable diagnostic of the structure of these disks because of the associated iron K$\alpha$ emission. Here we point out that the resulting reflected spectra depend very sensitively on the geometry of the X-ray source, and that this fact can be efficiently used to test these models observationally. In particular, we discuss three different accretion disk geometries: the ``lamppost model'', accretion disks with magnetic flares, and the model with a full corona overlying a cold thin disk. We show that in the case of the lamppost model, unless the X-ray luminosity of the central source is larger than that of the cold disk by a factor of 10 or more, a significant fraction of iron in the ionized skin of the disk is in the hydrogen and helium-like ions. Because these ions have large fluorescence yields, the resulting reflected spectra look strongly ionized, with Equivalent Width (EW) of the line {\em increasing} with X-ray luminosity $L_x$ up to the maximum of $\sim 500$ eV. This situation contrasts to the magnetic flare model, where the large X-ray flux near flares completely ionizes the skin of the disk and thus the resulting spectra appear to be that from a neutral material. The line EW in this model {\em anti-correlates} with X-ray luminosity, and becomes arbitrarily small when $L_x$ is a good fraction of the Eddington luminosity. Finally, in the full corona case, due to the additional pressure and weight of the corona, the gas pressure (and its density) below the corona is always large enough to make the gas very cool and effectively neutral. No highly ionized skin forms in such a model. If the corona is Thomson thin, then EW of the line does not depend on the accretion disk or corona luminosities for the full corona model.