The origin of the lag spectra observed in AGN: Reverberation and the propagation of X-ray source fluctuations

The X-ray emission from active galactic nuclei (AGN) is highly variable. Measurements of time lags (characterized by lag spectra) between variability in the light curves in energy bands corresponding to directly observed continuum emission from the corona around the black hole and to X-rays reflected from the accretion disc add a further dimension to studies of the structure and energetics of these systems. We seek to understand these measurements in terms of the physical parameters of the X-ray source (its location, extent, etc.) through the calculation of theoretical lag spectra for a range of source parameters in general relativistic ray-tracing simulations, combined with the knowledge of the observed variability of the X-ray emission from AGN. Due to the proximity of the emission to the central black hole, Shapiro delays are important and the effects of general relativity should be considered when interpreting the lags as the light travel time between the source and reflector. We show that it is important to consider dilution of the lag by the contribution of both the primary and the reflected spectral components to the observed energy bands rather than observing pure continuum and reflected emission, reducing the measured lag by up to 75 per cent compared to the 'intrinsic' time lag due to light travel times. We find that the observed lag spectrum of the narrow-line Seyfert 1 galaxy 1H 0707-495 implies an X-ray source extending radially outwards to around 35r(g) and at a height of around 2r(g) above the plane of the accretion disc, consistent with the constraints obtained independently by considering the emissivity profile of the accretion disc. By investigating the influence of the propagation of X-ray luminosity fluctuations through the source region, we find it is possible to reproduce the shape of the low-frequency part of the lag spectrum (where the hard 'primary' band lags behind the soft 'reflected' band) as the effect of luminosity fluctuations originating in the centre of the X-ray source, close to the black hole, and propagating outwards.