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 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 ($R_{dust} \, \propto \, \lambda^{0.80}$) 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.