A hard look at thermal reverberation and optical/UV lags in NGC 5548

The UV/optical variations in many AGN are very well correlated, showing delays which increase with increasing wavelength. It is thought that this is due to thermal reprocessing of the X-ray emission by the accretion disk. In this scenario, the variable X-ray flux from the corona illuminates the accretion disk where it is partially reflected, and partially absorbed and thermalized in the disk producing a UV/optical reverberation signal. This will lead to a time lag increasing with wavelength. However, although the shape of the observed time-lags as a function of wavelength is consistent with the model predictions, their amplitude suggested a disk which is significantly hotter than expected. In this work, we estimate the response functions and the corresponding time lags assuming a standard Novikov-Thorne accretion disk illuminated by a point-like X-ray source. We take into account all relativistic effects in the light propagation from the X-ray source to the disk then to the observer. We also compute the disk reflection, accounting for its ionization profile. Our results show that thermal reverberation effects are stronger in sources with large X-ray source height and low accretion rate. We also found that the time lags increase with height and accretion rate. We apply our model to NGC 5548 and we show that the observed lags in this source can be explained by the model, for a source height of $\sim 60 ~\rm r_g$ and an accretion rate of a few percent of the Eddington limit for a maximally-spinning black hole.