X-ray illuminated accretion discs and quasar microlensing disc sizes

We study the half-light radius versus black hole mass as well as the luminosity versus black hole mass relations in active galactic nuclei (AGN) when the disc is illuminated by the X-ray corona. We used KYNSED, a recently developed spectral model for studying broadband spectral energy distribution in AGN. We considered non-illuminated Novikov-Thorne discs and X-ray illuminated discs based on a Novikov-Thorne temperature radial profile. We also considered the case where the temperature profile is modified by a colour-correction factor. We assumed that the X-ray luminosity is equal to the accretion power that is dissipated to the disc below a transition radius. The half-light radius of X-ray illuminated radii can be up to some three to four times greater than the radius of a standard disc, even for a non-spinning black hole, due to the fact that the absorbed X-rays act as a secondary source of energy, increasing the disc temperature. Non-illuminated discs are consistent with observations, but only at the 2.5sigma level. On the other hand, X-ray illuminated discs can explain both the half-light radius-black hole mass as well as the luminosity-black hole mass relation in AGN, for a wide range of physical parameters. In addition, we show that the observed X-ray luminosity of the gravitationally lensed quasars is fully consistent with the X-ray luminosity that is necessary for heating the disc. X-ray disc illumination was proposed many years ago to explain various features that are commonly observed in the X-ray spectra of AGN. Recently, we showed that X-ray illumination of accretion disc can also explain the observed UV/optical time-lags in AGN, while in this work, we show that the same model can also account for the quasar micro-lensing disc size problem. These results support the hypothesis of the disc X-ray illumination in AGN.