Estimating AGN Black Hole Masses via Continuum Reverberation Mapping in the Era of LSST

Spectroscopic reverberation mapping (RM) is a direct approach widely used to estimate the mass of black holes (BHs) in active galactic nuclei (AGNs). However, it is very time consuming and difficult to apply to a large AGN sample. The empirical relation between the broad-line region size and luminosity (H$\beta$ $R_{\rm BLR}\unicode{x2013}L$) provides a practical alternative yet is subject to large scatter and systematic bias. Based on the relation between the continuum emitting region size and luminosity ($R_{\rm CER}\unicode{x2013}L$) reported by Netzer (2022), we present a new BH mass estimator via continuum RM (CRM) by comparing $R_{\rm CER}$ and $R_{\rm BLR}$, assuming that the continuum lags are dominated by the diffuse continuum emission. Using a sample of 21 AGNs, we find a tight $R_{\rm BLR}\unicode{x2013}R_{\rm CER}$ relation (scatter$\sim$0.28 dex) and that $R_{\rm BLR}$ is larger than $R_{\rm CER}$ at 5100 \r{A} by an average factor of 8.1. This tight relation enables the BH mass estimation based on the CRM combined with the velocity information. Applying the relation to rest objects in our CRM sample, we demonstrate that the predicted $R_{\rm BLR,CRM}$ follows the existing H$\beta$ $R_{\rm BLR}\unicode{x2013}L$ relation well and the estimated CRM BH masses are consistent with the RM/single-epoch BH masses using H$\beta$. This method will provide significant applications for BH mass estimation thanks to the short continuum lags and the easily accessible high-cadence, large-area photometric data, especially in the era of Legacy Survey of Space and Time.