Probing the Dust Torus Radius–Luminosity Relation: A WISE View

Abstract We present measurements of the dusty torus sizes of 51 active galactic nuclei (AGNs) with a redshift of z < 0.8. Our analysis utilizes about 16 yr of optical photometric data of 146 AGNs from various time-domain surveys, including ASAS-SN, CRTS, and ZTF, along with 14 yr of infrared data in the W1 (∼3.4 μ m) and W2 (∼4.6 μ m) bands obtained from the Wide-Field Infrared Survey Explorer. The estimated dust torus size ranges from 1000 to 3000 days, using both the cross-correlation analysis and light-curve modeling through “MICA.” The measured lag has been corrected by (1 + z ) −0.37 , to account for cosmological time dilation and the torus temperature-gradient scaling. We conduct a linear regression analysis for both the W1 and W2 bands to examine the radius–luminosity ( R – L BOL ) relationship under two conditions: one where the slope is fixed at 0.5 and one where it is allowed to vary. For the fixed slope of 0.5, we find the ratio of R BLR : R W1 : R W2 to be 1: 9: 12, indicating that the torus lies outside the BLR and that its size increases with wavelength. Furthermore, we determine the relationship between torus size and L BOL , yielding best-fit slopes of 0.413 ± 0.047 for the W1 band and 0.397 ± 0.058 for the W2 band. Both slopes are shallower than predicted by the dust radiation equilibrium model. Furthermore, our findings indicate that the torus size systematically decreases as the Eddington ratio increases, a trend that can be explained by the self-shadowing effects of slim disks.