On the determination of the spin and disc truncation of accreting black holes using X-ray reflection

We discuss the application of simple relativistically blurred X-ray reflection models to the determination of the spin and the inner radius of the disc in accreting black holes. Observationally, the nature of the corona is uncertain a priori, but a robust determination of the inner disc radius can be made when the disc emissivity index is tightly constrained. When the inner disc is well illuminated, the black hole spin can also be determined. Using reflection modelling derived from ray tracing, we show that robust determination of disc truncation requires that the location of the coronal source is quasi-static and at a height and radius less than the truncation radius of the disc. Robust spin measurements require that at least part of the corona lies less than about 10 gravitational radii above the black hole in order that the innermost regions, including the innermost stable circular orbit, are well illuminated. The width of the blurring kernel (e.g., the iron line) has a strong dependence on coronal height. These limitations may be particularly applicable at low Eddington fractions (e.g. the low/hard state and low-luminosity AGN) where the height of the corona may be relatively large, or outflowing, and tied to jet production.