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UV/optical disk thermal reverberation in AGN: an in-depth study with an analytic prescription for the time-lag spectra

Several active galactic nuclei show correlated variations in the ultraviolet/optical range, with time delays increasing at longer wavelengths. Thermal reprocessing of the X-rays illuminating the accretion disk has been proposed as a viable explanation. In this scenario, the variable X-ray flux irradiating the accretion disk is partially reflected in X-rays, and partially absorbed, thermalized and re-emitted with some delay by the accretion disk at longer wavelengths. We investigate this scenario assuming an X-ray point-like source illuminating a standard Novikov-Thorne accretion disk, around a rotating black hole. We consider all special and general relativistic effects to determine the incident X-ray flux on the disk and in propagating light from the source to the disk and to the observer. We also compute the disk reflection flux taking into consideration the disk ionization. We investigate the dependence of the disk response function and time lags on various physical parameters, such as black hole mass and spin, X-ray corona height, luminosity, and photon index, accretion rate, inclination, and inner/outer disk radii. We found it is important to consider relativistic effects and the disk ionization in estimating the disk response. We also found a strong non-linearity between the X-ray luminosity and the disk response. We present an analytic function for the time-lags dependence on wavelength, which can be used to fit observed time-lag spectra. We also estimate the fraction of the reverberation signal with respect to the total flux and we suggest possible explanation for the lack of X-ray-ultraviolet/optical correlated variations in a few sources.