Modeling accretion disk emission with generalized temperature profile and its effect on AGN spectral energy distribution

The broadband spectral energy distribution (SED) of Active Galactic Nuclei (AGN) is investigated for a well-selected sample composed of $23$ Seyfert 1 galaxies observed simultaneously in the optical/UV and X-ray bands with the Neil Gehrels {\it Swift} Observatory. The optical to UV continuum spectra are modeled, for the first time, with emission from an accretion disk with a generalized radial temperature profile, in order to account for the intrinsic spectra which are found to be generally redder than the model prediction of the standard Shakura-Sunyaev disk (SSD) ($F_\nu\propto\nu^{+1/3}$). The power-law indices of the radial temperature profile ($T_{\rm eff}(R)\propto R^{-p}$, $R$ is the radius of the accretion disk) are inferred to be $p=0.5$ -- $0.75$ (a median of $0.63$), deviating from the canonical $p=0.75$ for the SSD model as widely adopted in previous studies. A marginal correlation of a flatter radial temperature profile (a smaller $p$ value) with increasing the Eddington ratio is suggested. Such a model produces generally a lower peak of accretion disk emission and thus a smaller bolometric luminosity in some of the AGN, particularly those with high Eddington ratios, than that based on the SSD model by a factor of several. The broadband SED, the bolometric correction factors and their dependence on some of the AGN parameters are re-visited. We suggest that such non-standard SSD disks may operate in AGN and are at least partly responsible for the reddened optical/UV spectra as observed. One possible explanation for these flattened temperature profiles is the mass loss process in form of disk winds/outflows.