Broad iron-Kα emission lines as a diagnostic of black hole spin

We address the ability of broad iron emission lines from black hole accretion disks to diagnose the spin of the black hole. Using a high-resolution three-dimensional MHD simulation of a geometrically thin accretion disk in a pseudo-Newtonian potential, we show that both the mid-plane density and the vertical column density of the accretion flow drop dramatically over a narrow range of radii close to the innermost stable circular orbit (ISCO). We argue that this drop of density is accompanied by a sharp increase in the ionization parameter of the X-ray photosphere, and that the resulting imprint of the ISCO on the X-ray reflection spectrum can be used to constrain spin. Motivated by this simulation, we construct a simplified toy model of the accretion flow within the ISCO of a Kerr black hole, and use this model to estimate the systematic error on inferred black hole spin that may result from slight bleeding of the iron line emission to the region inside of the ISCO. We find that these systematic errors can be significant for slowly spinning black holes but become appreciably smaller as one considers more rapidly rotating black holes.