Lag-Luminosity Relationship for Interband Lags between Variations in B, V, R, and I Bands in Active Galactic Nuclei

We determine interband lags between variations in the B band and variations in the V, R, and I bands for 14 active galactic nuclei observed at the Crimean Astrophysical Observatory. The computed lags range from tenths of a day to several days, and it is positive (that is, V, R, and I bands lag behind the B band) in most cases, except for a few cases for the V filter. In some cases, the lag is greater than zero, with more than 3 σ confidence. The lag is systematically less for the V filter than for the red filters, and the lag determined from the cross-correlation function (CCF) centroid is systematically greater than the lag determined from the CCF peak. We find that the lag scales with luminosity as Lb, where b ≈ 0.4-0.5. We attribute this lag to the light time travel effect, so it reflects the geometrical size of the region that emits optical continuum. We consider a model in which optical emission is mainly reprocessed emission that arises in the accretion disk heated by an X-ray source above the disk.