A physical model of the broad-band continuum of AGN and its implications for the UV/X relation and optical variability

We develop a new spectral model for the broad-band spectral energy distribution (SED) of active galactic nuclei (AGN). This includes an outer standard disc, an inner warm Comptonizing region to produce the soft X-ray excess and a hot corona. We tie these together energetically by assuming Novikov-Thorne emissivity, and use this to define a size scale for the hard X-ray corona as equal to the radius where the remaining accretion energy down to the black hole can power the observed X-ray emission. We test this on three AGN with well-defined SEDs as well as on larger samples to show that the average hard X-ray luminosity is always approximately a few per cent of the Eddington luminosity across a large range of Eddington ratio. As a consequence, the radial size scale required for gravity to power the X-ray corona has to decrease with increasing Eddington fraction. For the first time, we hardwire this into the spectral models, and set the hard X-ray spectral index self-consistently from the ratio of the hard X-ray luminosity to intercepted seed photon luminosity from the disc. This matches the observed correlation of steeper spectral index with increasing Eddington ratio, as well as reproducing the observed tight UV/X relation of quasars. We also include the reprocessed emission produced by the hot inner flow illuminating the warm Comptonization and standard disc regions and show that this predicts a decreasing amount of optical variability with increasing Eddington ratio as observed, though additional processes may also be required to explain the observed optical variability.