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

## TL;DR

This paper introduces the reltrans model, a fast and flexible tool for analyzing X-ray reverberation in accreting black holes, enabling improved geometric and mass constraints by fitting energy-dependent timing and spectral data.

## Contribution

The paper presents reltrans, a publicly available relativistic transfer function model that accounts for all general relativistic effects and telescope response, improving black hole parameter estimation.

## Key findings

- Reltrans enables simultaneous fitting of energy-dependent cross-spectrum and time-averaged spectrum.
- Previous analyses underestimated source heights and lag magnitudes due to neglecting certain effects.
- Application to Mrk 335 yields a smaller black hole mass than optical reverberation estimates.

## Abstract

We present the publicly available model \textsc{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 disk 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 disk 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 under-estimated, and the magnitude of lags attributed to thermal reverberation in X-ray binaries may have been over-estimated. We fit \textsc{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 ($\sim 7$ million compared with $\sim14-26$ million $M_\odot$).