Continuum reverberation mapping of accretion disks depending on the vertical structures in active galactic nuclei

Reverberation mapping (RM) of accretion disks is a powerful tool for probing the radial structures of active galactic nuclei (AGNs). Recent RM campaigns involving a dozen AGNs have revealed that the measured sizes of the accretion disks are 2–3 times larger than those predicted by the Shakura-Sunyaev disk model. In this study, we present a self-consistent model that accounts for the vertical structures and radiation transfer of accretion disks across multiple radii, which produces photons that are not fully thermalized. Our findings demonstrate that the observed discrepancies between the predictions of the Shakura-Sunyaev model and the RM-measured radii can be explained well by the present model. The results indicate that the derived effective radii are sensitive to the dimensionless accretion rates, less influenced by the black hole masses and independent of the inclination. Combining black hole masses and accretion rates measured from RM of broad-lines and continuum respectively, inclination angles of accretion disks can be obtained by fitting the spectral energy distributions (SEDs) of AGNs avoiding high degeneracy of the three parameters. We apply the present model to the mapped AGNs and find some AGNs are explained very well but others are not well for SEDs likely due to inaccurate estimation of black hole masses with large uncertainties of virial factor f, model applicability, SED contamination and mismatches between the SED and continuum RM observation periods.