Revisiting the dust torus size-luminosity relation based on a uniform reverberation mapping analysis

We investigate the torus size – luminosity relation of Type 1 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 (WISE) 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 10^43.4 to 10^47.6 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 (R_dust) and AGN bolometric luminosity (L_bol) 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 R_dust,K:R_dust,W1:R_dust,W2 = 1.0:1.5:1.8 (R_dust ∝ λ^0.80) at L_bol = 10^46 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 R_dust–L_bol relation and Eddington ratio. This suggests a possible influence of the Eddington ratio on the observed flattening of the R_dust–L_bol relationship.