A public relativistic transfer function model for X-ray reverberation mapping of accreting black holes

We present the publicly available model RELTRANS that calculates the light-crossing delays and energy shifts experienced by X-ray photons originally emitted close to the black hole when they reflect from the accretion disc and are scattered into our line of sight, accounting for all general relativistic effects. Our model is fast and flexible enough to be simultaneously fit to the observed energy-dependent cross-spectrum for a large range of Fourier frequencies, as well as to the time-averaged spectrum. This not only enables better geometric constraints than only modelling the relativistically broadened reflection features in the time-averaged spectrum, but additionally enables constraints on the mass of supermassive black holes in active galactic nuclei and stellar-mass black holes in X-ray binaries. We include a self-consistently calculated radial profile of the disc ionization parameter and properly account for the effect that the telescope response has on the predicted time lags. We find that a number of previous spectral analyses have measured artificially low source heights due to not accounting for the former effect and that timing analyses have been affected by the latter. In particular, the magnitude of the soft lags in active galactic nuclei may have been underestimated, and the magnitude of lags attributed to thermal reverberation in X-ray binaries may have been overestimated. We fit RELTRANS to the lag-energy spectrum of the Seyfert galaxy Mrk 335, resulting in a best-fitting black hole mass that is smaller than previous optical reverberation measurements (similar to 7 million compared with similar to 14-26 million M-circle dot).