Non-Blackbody Disks Can Help Explain Inferred AGN Accretion Disk Sizes

If the atmospheric density $\rho_{atm}$ in the accretion disk of an active galactic nucleus (AGN) is sufficiently low, scattering in the atmosphere can produce a non-blackbody emergent spectrum. For a given bolometric luminosity, at ultraviolet and optical wavelengths such disks have lower fluxes and apparently larger sizes as compared to disks that emit as blackbodies. We show that models in which $\rho_{\rm atm}$ is a sufficiently low fixed fraction of the interior density $\rho$ can match the AGN STORM observations of NGC 5548 but produce disk spectral energy distributions that peak at shorter wavelengths than observed in luminous AGN in general. Thus, scattering atmospheres can contribute to the explanation for large inferred AGN accretion disk sizes but are unlikely to be the only contributor. In the appendix section, we present unified equations for the interior $\rho$ and $T$ in gas pressure-dominated regions of a thin accretion disk.