A research team from the Yunnan Observatories of the Chinese Academy of Sciences, in collaboration with partners, has refined constraints on the broad-line region (BLR) radius–luminosity (R–L) relation at high luminosities. Their findings, recently published in The Astrophysical Journal, reveal that a multi-component BLR structure can introduce biases into single-epoch black hole mass estimates.

In active galactic nuclei (AGNs), the BLR consists of fast-moving, photoionized gas bound to the central supermassive black hole, producing broad emission lines with widths ranging from 10³ to 10⁴ km/s. Reverberation mapping (RM) measures the time delay between continuum and line variability, offering a direct method to estimate the characteristic size of the BLR. Decades of RM campaigns have established the BLR R–L relation, which serves as the foundation for single-epoch black hole mass estimators and various AGN-based research applications.

However, the R–L relation remains poorly constrained at the high-luminosity end, as RM monitoring of luminous AGNs is observationally costly. Furthermore, high-accretion-rate AGNs often exhibit lags shorter than those predicted by the R–L relation, and the roles of intrinsic scatter and BLR structural complexity have yet to be fully quantified.

To address these challenges, the team conducted a four-year RM monitoring campaign of E1821+643 using the 2.4-meter telescope at the Lijiang Astronomical Observatory. As the most luminous AGN with an Hβ RM measurement to date, E1821+643 is a key target for anchoring the R–L relation and investigating the aforementioned effects.

The results indicate that the Hβ lag in E1821+643 is only 83.2 days—less than one-fifth of the value predicted by the R–L relation. Spectral fitting shows that, in addition to a normal broad-line component, the Hβ profile includes a significantly redshifted component.

The researchers found that the lag of the normal Hβ component is closer to the value predicted by the R–L relation, while the redshifted component has an extremely short lag and originates from a region with a characteristic scale comparable to that of the accretion-disk continuum-emitting region. Consequently, the overall Hβ lag is substantially "pulled down" by this redshifted component. Moreover, this redshifted component may interfere with the interpretation of intrinsic BLR kinematics, further increasing the uncertainty in black hole mass measurements.

Notably, the study also reveals that across the full luminosity range, the shortest lags measured from RM observations tend to cluster around 0.2 times (or approximately one-fifth) the R–L prediction, suggesting a potential lower boundary of the R–L relation. Further analysis indicates that the upper boundary of the R–L relation may exceed predicted values by a factor of two, implying that the effective scatter could be as large as an order of magnitude in extreme cases.

When combined with the potential impact of a multi-component BLR on kinematic inferences, single-epoch black hole mass estimates that assume a single, homogeneous BLR may suffer systematic biases of up to several tens of times—far exceeding commonly accepted uncertainty levels.

These findings enhance the understanding of BLR structure and the R–L relation, providing critical observational evidence for more accurate measurements of supermassive black hole masses and the development of more realistic physical models of AGNs.