Modelling the broad Fe Kα reverberation in the AGN NGC 4151

The recent detection of X-ray reverberation lags, especially in the Fe Kα line region, around active galactic nuclei (AGN) has opened up the possibility of studying the time-resolved response (reflection) of hard X-rays from the accretion disc around supermassive black holes. Here, we use general relativistic transfer functions for reflection of X-rays from a point source located at some height above the black hole to study the time lags expected as a function of frequency and energy in the Fe Kα line region. We explore the models and the dependence of the lags on key parameters such as the height of the X-ray source, accretion disc inclination, black hole spin and black hole mass. We then compare these models with the observed frequency- and energy-dependence of the Fe Kα line lag in NGC 4151. Assuming the optical reverberation mapping mass of 4.6 × 107 M⊙, we get a best fit to the lag profile across the Fe Kα line in the frequency range (1-2) × 10− 5 Hz for an X-ray source located at a height h=7+2.9−2.6RG with a maximally spinning black hole and an inclination i < 30°.