Signatures of X-ray reverberation in the power spectra of AGN

Abstract: We compute fully relativistic disc response functions in the case of the "lamp-post" geometry using the full observed reflection spectrum for various X-ray source heights, disc inclination, and spin values of the central black hole. Since the observed PSD is equal to the product of the intrinsic power spectrum with the "transfer function" (i.e. the Fourier transform of the disc response function), we are able to predict the observed PSDs in the case of X-ray illumination of the inner disc. The observed PSD should show a prominent dip at high frequencies and an oscillatory behaviour, with a decreasing amplitude, at higher frequencies. The reverberation "echo" features should be more prominent in energy bands where the reflection component is more pronounced. The frequency of the dip is independent of energy, and it is mainly determined by the black hole mass and the X-ray source height. The amplitude of the dip increases with increasing black hole spin and inclination angle, as long as the height of the "lamp" is smaller than ~10 gravitational radii. The detection of the X-ray reverberation signals in the PSDs can provide further evidence for X-ray illumination of the inner disc in AGN. Our results are largely independent of the assumed geometry of the disc-corona system, as long as it does not change with time, and the disc response function is characterized by a sharp rise, a "plateau", and a decline at longer times. Irrespective of the geometry, the frequency of the main dip should decrease with increasing "mean time" of the response function, and the amplitude of the dip should increase with increasing reflection fraction.