Reverberation Measurements of the Inner Radius of the Dust Torus in Nearby Seyfert 1 Galaxies

The most intense monitoring observations yet made in the optical (UBV) and near-infrared (JHK) wave bands were carried out for nearby Seyfert1 galaxies of NGC 5548, NGC 4051, NGC 3227, and NGC 7469. Over three years of observations with MAGNUM telescope since early 2001, clear time-delayed response of the K-band flux variations to the V-band flux variations was detected for all of these galaxies. Their H-K color temperature was estimated to be 1500-1800 K from the observed flux variation gradients, which supports a view that the bulk of the K flux should originate in the thermal radiation of hot dust that surrounds the central engine. Cross-correlation analysis was performed to quantify the lag time corresponding to the light-travel distance of the hot dust region from the central engine. The measured lag time is 47-53 days for NGC 5548, 11-18 days for NGC 4051, about 20 days for NGC 3227, and 65-87 days for NGC 7469. We found that the lag time is tightly correlated with the optical luminosity as expected from dust reverberation ($\Delta t \propto L^{0.5}$), while only weakly with the central virial mass, which suggests that an inner radius of the dust torus around the active nucleus has a one-to-one correspondence to central luminosity. In the lag time versus central luminosity diagram, the K-band lag times place an upper boundary on the similar lag times of broad-emission lines in the literature. This not only supports the unified scheme of AGNs, but also implies a physical transition from the BLR out to the dust torus that encircles the BLR. Furthermore, our V-band flux variations of NGC 5548 on timescales of up to 10 days are found to correlate with X-ray variations and delay behind them by one or two days, indicating the thermal reprocessing of X-ray emission by the central accretion flow.