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

TL;DR

The paper investigates the high-luminosity end of the BLR radius–luminosity relation by presenting a four-year RM campaign of the luminous quasar E1821+643, revealing a H$eta$ lag of $83.2_{-18.7}^{+17.5}$ days that is far shorter than the $R_{ m BLR}-L_{5100}$ prediction. Spectral decomposition uncovers two BLR components: a core with a lag of $267.0_{-17.6}^{+16.6}$ days and a redshifted tail with a short lag of $-49.0_{-34.5}^{+50.5}$ days, which together bias the overall lag to lie near the lower envelope of the empirical relation. Across the full RM sample, this lower envelope and an upper envelope near $2R_{ m BLR}$ imply up to ~1 dex scatter, challenging the precision of single-epoch SMBH mass estimates, especially for high-accretion-rate AGNs. The results suggest a multi-component, spatially complex BLR structure (potentially including an inner elliptical disk) that can significantly affect mass measurements and cosmological applications, motivating further high-quality RM studies to map BLR structure more comprehensively.

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.

Figures (6)

• Figure 1: Light curve and cross-correlation analysis results of emission lines. The left panels show the light curves. From top to bottom, they correspond to the photometric continuum, H$\alpha$, H$\beta_{\rm red}$, H$\beta_{\rm core}$, H$\beta$, and H$\gamma$. The gray solid lines and shaded regions represent the light curves reconstructed by JAVELIN, along with their associated uncertainties. Emission-line fluxes are measured in units of $10^{-13}~\rm erg\,s^{-1}\,cm^{-2}$, while the photometric continuum is in arbitrary flux units. The right panels display the results of the ACF and ICCFs (black lines), and CCCDs (blue step lines). The gray step curves show the posterior JAVELIN time-lag distributions. The red dashed lines mark zero time lag.
• Figure 2: Spectral fitting result for the mean spectrum. The left panel displays the observed spectrum (black line) and the best-fit model (red line), with individual components color-coded as follows: AGN continuum (blue), Fe ii template (green), broad Balmer lines (magenta), narrow lines (orange), and broad He ii and He i lines (cyan). Vertical dotted lines indicate the positions of two telluric absorption bands that were masked during the fitting. The right panel presents the residual profiles of the broad H$\alpha$, H$\beta$, and H$\gamma$ lines after subtraction of the other best-fitting spectral components.
• Figure 3: The $R_{\rm H\beta}-L_{\rm 5100}$ relation. The black line shows the best-fit relation from Bentz2013, while the shaded region marks the range between 0.2 and 2 times the radius predicted by this relation. Circles represent data points from the sample of Wang2024, and the green line denotes their best-fit result. Colored stars show our measurements for E1821+643: the red star corresponds to the result from the total H$\beta$ profile, the orange star to the redshifted component (H$\beta_{\rm red}$), and the blue star to the core component (H$\beta_{\rm core}$).
• Figure 4: Velocity-resolved time lag measurements for the broad H$\beta$ and H$\gamma$ emission lines, as well as for the core component of H$\beta$. In each top panel, the time lag as a function of velocity bin is shown. The horizontal dotted line indicates the mean time lags of the corresponding emission line, and the gray shaded region denotes the associated uncertainty range. In each bottom panel, the step line represents the residual rms spectrum, with vertical dashed lines marking the boundaries of the velocity bins used in the lag analysis. The flux is in $10^{-15}~\rm erg\,s^{-1}\,cm^{-2}\,\AA^{-1}$.
• Figure A1: Same as Figure \ref{['fig:1']}, but for the infrared data.