Theoretical modelling of the AGN iron line vs. continuum time-lags in the lamp-post geometry

Context. Theoretical modelling of time-lags between variations in the Fe Kα emission and the X-ray continuum might shed light on the physics and geometry of the X-ray emitting region in active galaxies (AGN) and X-ray binaries. We here present the results from a systematic analysis of time-lags between variations in two energy bands (5-7 vs. 2-4 keV) for seven X-ray bright and variable AGN.
Aims: We estimate time-lags as accurately as possible and fit them with theoretical models in the context of the lamp-post geometry. We also constrain the geometry of the X-ray emitting region in AGN.
Methods: We used all available archival XMM-Newton data for the sources in our sample and extracted light curves in the 5-7 and 2-4 keV energy bands. We used these light curves and applied a thoroughly tested (through extensive numerical simulations) recipe to estimate time-lags that have minimal bias, approximately follow a Gaussian distribution, and have known errors. Using traditional χ² minimisation techniques, we then fitted the observed time-lags with two different models: a phenomenological model where the time-lags have a power-law dependence on frequency, and a physical model, using the reverberation time-lags expected in the lamp-post geometry. The latter were computed assuming a point-like primary X-ray source above a black hole surrounded by a neutral and prograde accretion disc with solar iron abundance. We took all relativistic effects into account for various X-ray source heights, inclination angles, and black hole spin values.
Results: Given the available data, time-lags between the two energy bands can only be reliably measured at frequencies between ~5 × 10^-5 Hz and ~10^-3 Hz. The power-law and reverberation time-lag models can both fit the data well in terms of formal statistical characteristics. When fitting the observed time-lags to the lamp-post reverberation scenario, we can only constrain the height of the X-ray source. The data require, or are consistent with, a small (≲ 10 gravitational radii) X-ray source height.
Conclusions: In principle, the 5-7 keV band, which contains most of the Fe Kα line emission, could be an ideal band for studying reverberation effects, as it is expected to be dominated by the X-ray reflection component. We here carried out the best possible analysis with XMM-Newton data. Time-lags can be reliably estimated over a relatively narrow frequency range, and their errors are rather large. Nevertheless, our results are consistent with the hypothesis of X-ray reflection from the inner accretion disc.