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

TL;DR

This paper investigates how broad iron K-alpha emission lines from accretion disks can be used to measure black hole spin, highlighting the importance of density drops near the ISCO and potential systematic errors.

Contribution

It demonstrates that density and ionization changes near the ISCO affect iron line profiles and introduces a toy-model to estimate systematic errors in spin measurements.

Findings

Density drops sharply near the ISCO influence the reflection spectrum.

Systematic errors in spin estimation are larger for slowly spinning black holes.

Rapidly spinning black holes have smaller systematic errors in spin inference.

Abstract

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 3-dimensional MHD simulation of a geometrically-thin accretion disk in a Pseudo-Newtonian potential, we show that both the midplane 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.