The Most Luminous H$\beta$ Reverberation Mapping of E1821+643 Indicates the Lower Boundary of the Radius-Luminosity Relation

Abstract

The radius-luminosity ($R_{\rm BLR}$-$L_{5100}$) relation is fundamental to active galactic nucleus (AGN) studies, enabling supermassive black hole (SMBH) mass estimates and AGN-based cosmology applications. However, its high-luminosity end remains poorly calibrated due to insufficient reliable reverberation mapping (RM) data. We present a four-year RM campaign of the luminous quasar E1821+643 using the Lijiang 2.4-m telescope, supplemented by archival multi-wavelength data. E1821+643 is the most luminous AGN with an \hb\ RM measurement to date. The measured time lag of $83.2_{-18.7}^{+17.5}$ days is a factor of 5.6 shorter than predicted by the canonical $R_{\rm BLR}$-$L_{5100}$ relation. By compiling the full \hb\ RM sample, we find that such deviation defines a lower envelope ($0.2R_{\rm BLR}$) of measured lags across the entire luminosity range, while the upper envelope lies near $2R_{\rm BLR}$, implying that the scatter for individual AGNs can reach 1 dex. Spectral decomposition reveals two distinct \hb\ components: a core component with a lag of $267.0_{-17.6}^{+16.6}$ days closer to the $R_{\rm BLR}$-$L_{5100}$ relation, and a redshifted tail with a much shorter lag of $-49.0_{-34.5}^{+50.5}$ days. The short-lag component not only accounts for the significantly shortened overall lag, but also leads to an opposite interpretation of the intrinsic BLR kinematics. These effects can introduce systematic uncertainties in black hole mass estimates by factors of up to tens. Our findings demonstrate that shortened lags in high-accretion-rate AGNs arise from multi-component BLR structures, posing substantial challenges to single-epoch mass estimates and impacting SMBH demographics and cosmological applications.