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

Abstract

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 disk and are scattered into our lineof-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 stellarmass 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 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 (∼ 7 million compared with ∼ 14 − 26 million M ).

Exploring the radial disc ionization profile of the black hole X-ray binary GRS 1915+105

“…reproduced in general relativity for a very compact source located very close to the black hole (Wilkins & Fabian 2012;Dauser et al 2013;Ingram et al 2019). However, q out ≈ 0 is rather unphysical, requiring the irradiation to be ∼constant with radius despite the supply of gravitational potential energy dropping off as ∼ r −3 .…”

“…M13 use the abundances of (Equation 2). Here, T in is the peak disc temperature, i is the inclination angle (angle between the line of sight and the inner disc rotation axis), A Fe is the disc iron abundance relative to solar, f R is the reflection fraction (the system reflection fraction in the nomenclature of Ingram et al 2019) and log ξ xill sets the ionization of the distant reflection. ξ is in units of erg cm s −1 .…”

“…For a bright source such as GRS 1915+105 the inner regions of the disc, which dominate the reflection emissivity, are likely in the zone A regime. In both cases, the peak ionization parameter is a model parameter and the calculation is discretized into 10 ionization zones (set by the environment variable ION_ZONES), which Ingram et al (2019) found to be sufficient. For the absorption model, we consider both the abundances of Anders & Grevesse (1989) and those of Wilms et al (2000).…”

A dynamic black hole corona in an active galaxy through X-ray reverberation mapping

“…We jointly fit all 16 lag-frequency spectra simultaneously within XSPEC using the KYNREVERB model 22,36 . This uses a fully relativistic ray-tracing code in a vacuum to calculate photon paths from the corona to the disc and to the observer, as well as the reflected photons from the disc to the observer.…”

“…The strong and short timescale variability in IRAS 13224-3809 means we can model the time lags as they rapidly evolve, helping to break these degeneracies, whilst the number of observations allows us to create a movie for how the corona evolves.We model the Fourier lag-spectra using a transfer function which can be seen as the response of the disc to a flash of X-rays coming from the corona, encoding all the effects of geometry, relativity and light bending 24 -see Figure 1. The disc-reflection scenario 17,18,19,20,22,25 assumes the corona to be a static, point-like X-ray source located at height h on the rotation axis above the black hole, and which isotropically emits a power-law of flux with energy (flux ∝ ;< ). This illuminates a geometrically thin, optically thick and ionised accretion disc which extends down to some radius => (and which we fix to have an outer radius at 400 + ), and which the observer sees at some inclination i (where = 0° is a disc seen face-on).…”