2023MNRAS.522.3439C

We compile optical and mid-infrared light curves from the time-domain surveys (i.e. CRTS, PTF, ZTF, and ASAS-SN) and Wide-field Infrared Survey Explorer (WISE) archive for a selected sample of active galactic nuclei (AGNs) with Hβ reverberation mapping (RM) measurements. We measure the time lags (and thus torus sizes) of W1 (∼3.4 $\mu$ m) and W2 (∼4.6 $\mu$ m) band light curves relative to the optical one using the MICA method. Through Hβ RM, the sample has well-measured AGN properties, therefore allowing us to reliably constrain the relations between torus sizes and AGN properties. We perform linear regressions for the relations between torus sizes and 5100 Å luminosities ($R\propto L_{5100}^{\beta }$ ) in two cases: β = 0.5 and β set free. The latter case yields β ≈ 0.37 ± 0.028 for both W1 and W2 bands, shallower than the expected value of 0.5, possibly due to the dependence of torus size on accretion rate. For β = 0.5, by combining with the previous K band RM measurements, we obtain the characteristic broad-line region (BLR) and tours sizes following R_BLR:R_K :R_W1:R_W2 = 1.0:6.2:9.2:11.2. We investigate the deviations of the W1 and W2 band observed torus sizes from the corresponding best-fitting relations (with β = 0.5) and find that they both are correlated with accretion rate. As the accretion rate increases, the torus sizes tend to be shortened compared to the anticipated sizes from the best-fitting relations, similar to the behaviour found in BLRs. Such behaviours can be explained by the self-shadowing effect of slim discs. This is further supported by ratios of the W1 and W2 band torus sizes to BLR sizes, which do not show significant correlations with AGN properties.