The size of the continuum emission region and its scaling relations with active galactic nucleus luminosity and the broad-line region size

We present a continuum lag analysis for a sample of 37 relatively high-luminosity active galactic nuclei (AGNs) from the Seoul National University AGN Monitoring Project (SAMP), utilizing the light curve data in $B$ and $V$ bands from SAMP and in $g,r,i$ bands from the Zwicky Transient Facility. We find that the inter-band lags ($\tau$) increase with wavelength (i.e., $\tau \propto \lambda^{\sim 4/3}$) as prescribed by the standard disk model (SSD), suggesting consistency with the "lamp-post" reprocessing model. We report that the size of the continuum emitting region (CER) normalized at 2500 {\AA} ($R_{2500}$) is a factor of $\sim$5 (i.e, $0.69\pm0.04$ dex) larger than predicted by SSD. By combining our new measurements with the re-measurements of the literature sample, we report a correlation between $R_{2500}$ and AGN continuum luminosity as $R_{2500} \, \propto \, L_{5100}^{0.58\pm0.03}$, which suggests that the observed continuum could be composed of both the disk emission and the diffuse emission from the broad line region (BLR). The size of CER shows a tight relation with the size of H$\beta$ BLR with a sublinear slope (i.e., $R_{\text{BLR}} \, \propto \, R_{\text{2500}}^{0.87\pm0.07}$) and a scatter of 0.29 dex. This empirical relation offers a promising method for estimating single-epoch black hole masses, once established over a large dynamic range of AGN luminosity.