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Accretion disks around supermassive black holes in active galactic nuclei produce continuum radiation at ultraviolet and optical wavelengths. Physical processes in the accretion flow lead to stochastic variability of this emission on a wide range of time scales. We measured the optical continuum variability observed in 67 active galactic nuclei and the characteristic time scale at which the variability power spectrum flattens. We found a correlation between this time scale and the black hole mass extending over the entire mass range of supermassive black holes. This time scale is consistent with the expected thermal time scale at the ultraviolet-emitting radius in standard accretion disk theory. Accreting white dwarfs lie close to this correlation, suggesting a common process for all accretion disks.

 

We studied the accretion disc structure in the doubly imaged lensed quasar SDSS J1339+1310 using r -band light curves and UV-visible to near-IR spectra from the first 11 observational seasons after its discovery. The 2009−2019 light curves displayed pronounced microlensing variations on different timescales, and this microlensing signal permitted us to constrain the half-light radius of the 1930 Å continuum-emitting region. Assuming an accretion disc with an axis inclined at 60° to the line of sight, we obtained log( r 1/2 /cm) = 15.4 −0.4 +0.93 . We also estimated the central black hole mass from spectroscopic data. The width of the C  IV , Mg  II , and H β emission lines, and the continuum luminosity at 1350, 3000, and 5100 Å, led to log( M BH / M ⊙ ) = 8.6 ± 0.4. Thus, hot gas responsible for the 1930 Å continuum emission is likely orbiting a 4.0 × 10 8   M ⊙ black hole at an r 1/2 of only a few tens of Schwarzschild radii.