Revisiting the Dust Torus Size–Luminosity Relation Based on a Uniform Reverberation-mapping Analysis

Abstract

We investigate the torus size–luminosity relation of Type 1 active galactic nuclei (AGNs) based on the reverberation-mapping analysis using the light curves of the optical continuum and the IR continuum obtained with the W1 and W2 bands of the Wide-field Infrared Survey Explorer survey. The final sample consists of 446 and 416 AGNs, respectively, for W1- and W2-band light curves, covering a large dynamic range of bolometric luminosity from 1043.4 to 1047.6 erg s−1, which show reliable lag measurements based on our quality assessment analysis. After correcting for the accretion disk contamination in the observed IR flux, we constrain the torus size (Rdust) and AGN bolometric luminosity (Lbol) relationship with the best-fit slope of 0.39 (0.33) for the W1 (W2) band, which is shallower than expected from the dust radiation equilibrium model. By combining the previous K-band lag measurements, we find that the measured torus size depends on the observed wavelength of the dust radiation, as Rdust,K: Rdust,W1: Rdust,W2 = 1.0:1.5:1.8 (Rdust ∝ λ0.80) at Lbol = 1046 erg s−1, confirming a stratified structure of the torus, where wavelength-dependent emissions originate from distinct regions of the torus. By investigating the deviation from the best-fit torus size–luminosity relation, we find a moderate correlation between the offset from the Rdust–Lbol relation and Eddington ratio. This suggests a possible influence of the Eddington ratio on the observed flattening of the Rdust–Lbol relationship.