Mid-infrared dusty torus sizes in active galactic nuclei with Hβ reverberation mapping.

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 W 1 (∼3.4  |$\mu$| m) and W 2 (∼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 W 1 and W 2 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: RK : R W 1: R W 2 = 1.0:6.2:9.2:11.2. We investigate the deviations of the W 1 and W 2 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 W 1 and W 2 band torus sizes to BLR sizes, which do not show significant correlations with AGN properties. [ABSTRACT FROM AUTHOR]