Normalizing a Relativistic Model of X-ray Reflection: The Definition of the Reflection Fraction and its Implementation in relxill

The only relativistic reflection model that implements a parameter relating the intensity incident on an accretion disk to the observed intensity is relxill. The parameter used in earlier versions of this model, referred to as the reflection strength, is unsatisfactory, and it has been superseded by a parameter that provides insight into the accretion geometry, namely the reflection fraction. The reflection fraction is defined as the ratio of the coronal intensity illuminating the disk to the coronal intensity that reaches the observer. The relxill model combines a general relativistic ray-tracing code and a photoionization code to compute the component of radiation reflected from an accretion that is illuminated by an internal source. The reflection fraction is a particularly important parameter for relativistic models with well-defined geometry, such as the lamppost model, which is a focus of this paper. Relativistic spectra are compared for three inclinations and for four values of the key parameter of the lamppost model, namely the height above the black hole of the illuminating, on-axis point source. In all cases, the strongest reflection is produced for low source heights and high spin. A low-spin black hole is shown to be incapable of producing enhanced relativistic reflection. Results for the relxill model are compared to those obtained with other models and a Monte Carlo simulation. Fitting data using the relxill model and the recently implemented parameter the reflection fraction, one can constrain the geometry of a system, under the assumption of a lamppost-like accretion geometry. The reflection fraction is independent of such system parameters as inclination and black hole spin. The reflection fraction parameter was implemented with the name refl_frac in all flavors of the relxill model, and the nonrelativistic reflection model xillver, in v0.4a (18 January 2016).