Relativistic X-ray reverberation modelling of the combined time-averaged and lag-energy spectra in AGN

Abstract

General relativistic ray tracing simulations of the time-averaged spectrum and energydependent time delays in AGN are presented. We model the lamp-post geometry in which the accreting gas is illuminated by an X-ray source located on the rotation axis of the black hole. The spectroscopic features imprinted in the reflection component are modelled using reflionx. The associated time delays after the direct continuum, known as reverberation lags, are computed including the full effects of dilution and ionization gradients on the disc. We perform, for the first time, simultaneous fitting of the time-averaged and lag-energy spectra in three AGN: Mrk 335, IRAS 13224-3809 and Ark 564 observed with XMM-Newton. The best fitting source height and central mass of each AGN partly agree with those previously reported. We find that including the ionization gradient in the model naturally explains lag-energy observations in which the 3 keV and 7-10 keV bands precede other bands. To obtain the clear 3 keV and 7-10 keV dips in the lag-energy profile, the model requires either a source height > 5r g , or a disc that is highly ionized at small radii and is colder further out. We also show that fitting the lag or the mean spectra alone can lead to different results and interpretations. This is therefore important to combine the spectral and timing data in order to find the plausible but self-consistent fits which is achievable with our model.

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

“…Our proof-of-principle fit to the lag-energy spectrum of Mrk 335 in a single frequency range (Section 5) favours a black hole mass of ∼ 7 million M to the optical reverberation values in the literature of ∼ 14 million M (Peterson et al 2004) and ∼ 26 million M (Grier et al 2012), and the previous X-ray reverberation value of ∼ 13.5 million M (Chainakun et al 2016), although the higher masses are only disfavoured with 1.5 σ confidence. The confidence range on the mass is very large for such a fit to a single frequency range, partly because the size of the reverberation lag is degenerate with the reflection fraction.…”

“…We note that the X-ray reverberation analysis of Emmanoulopoulos et al (2014) returned a black hole mass estimate of M = 19.8 +11.8 −10.5 × 10 6 M for Mrk 335, which is again larger than our value. Their fit procedure was very different to ours and that of Chainakun et al (2016). They fit for time lags between two broad energy bands as a function of frequency, and employed simplified assumptions regarding the energy dependence of reflected X-rays.…”

A Hard Look at Thermal Reverberation and Optical/Ultraviolet Lags in NGC 5548

“…The best-fit results indicate a source height larger than 20 or 40 r g (3-σ limit for a * = 1 or 0, respectively). This is significantly larger than 4−5 r g which is the height estimate from the modeling of the X-ray time-lags in a few bright Seyferts, assuming the same geometry (i.e., Emmanoulopoulos et al 2014;Epitropakis et al 2016;Chainakun et al 2016;Caballero-García et al 2018). Nevertheless, our results are in agreement with Brenneman et al (2012) who inferred a height of the X-ray source in NGC 5548 ∼ 100 r g .…”

X-ray time lags in AGN: inverse-Compton scattering and spherical corona model

“…Combining these frameworks mean more parameters to add in and hence can lead to many degeneracies of the model. Fitting multi-timescale lags (Mastroserio et al 2018) or simultaneously fitting the mean and lag spectra (Chainakun et al 2016) would not only help break the model degeneracy but also put more constraints on a specific framework.…”