Scaling Relations of the Dusty Torus with Luminosity and the Broad-line Region

We measure and compare the size of the dusty torus with active galactic nucleus (AGN) luminosity and the size of the broad-line region (BLR), using a sample of 182 AGNs with the best H β lag measurements. After correcting for accretion-disk contamination, torus sizes are determined from the time lags of the Wide-field Infrared Survey Explorer W1 and W2 band light curves relative to the optical band variability based on the interpolated cross-correlation function analysis and the Multiple and Inhomogeneous Component Analysis. We find that the torus size from the W1-band (W2-band) tightly correlates with the 5100 Å continuum luminosity with an intrinsic scatter of 0.15–0.16 dex and the best-fit slope of 0.35 ± 0.03 (0.33 ± 0.03), which is clearly shallower than the expected 0.5 slope from the sublimation radius–luminosity relation. We find a moderate negative trend that higher Eddington AGNs tend to have smaller torus sizes than expected from the best-fit, suggesting the Eddington ratio plays a role in flattening the torus size–luminosity relation. By comparing the torus size with the H β reverberation time lag for a subsample of 67 AGNs, we find that the torus size is a factor of ∼10 and ∼14 larger than the BLR size, respectively for W1 and W2 bands. The torus size based on the W1 (W2) band correlates with the BLR size with the best-fit slope of 1.28 ± 0.16 (1.10 ± 0.15), which is comparable but slightly steeper than a linear correlation.