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 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.

Keywords

• Reverberation mapping
• Black holes
• Active galactic nuclei
• Quasars