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Standardizing reverberation-mapped H$β$ active galactic nuclei using time-averaged radius$-$luminosity relations with 5100\,Å\,, broad H$β$, and narrow \OIII\ luminosities

Shulei Cao, Amit Kumar Mandal, Michal Zajaček, Bharat Ratra

Abstract

Active galactic nuclei (AGN) have been studied as alternate probes in cosmology due to their large and stable luminosities and broad redshift range. Previously it was shown that higher-redshift AGN that were reverberation-mapped (RM) using broad Mg\,\textsc{ii} and C\,\textsc{iv} lines are standardizable and yield weak cosmological constraints that are consistent with those from better-established probes. In contrast, lower-redshift AGN that were reverberation-mapped using the broad H$β$ line exhibited tensions with the standard cosmological model, in particular they preferred currently decelerating cosmological expansion. Here we study the standardizability of a homogeneous RM H$β$ sample of $\sim 100$ AGN (over redshifts $0.00308 \leq z \leq 0.8429$), whose H$β$ time delays and three luminosity tracers (at 5100\,Å\,, broad H$β$, and narrow [O\,\textsc{iii}]) are averaged over several epochs. We find that this averaged sample is standardizable using three $R-L$ relations. While for luminosities corresponding to 5100\,Å\, and the broad H$β$ line the cosmological constraints prefer currently decelerating cosmological expansion, the cosmological parameters for the narrow [O\,\textsc{iii}] luminosity are more consistent with those from better-established probes and they are in agreement with currently accelerating cosmological expansion. This demonstrates for the first time that narrow-line region [O\,\textsc{iii}] can be utilized for AGN standardization and cosmological constraints. Selecting proper photoionizing flux proxies for the broad-line region is thus crucial in studies of RM AGN standardizability.

Standardizing reverberation-mapped H$β$ active galactic nuclei using time-averaged radius$-$luminosity relations with 5100\,Å\,, broad H$β$, and narrow \OIII\ luminosities

Abstract

Active galactic nuclei (AGN) have been studied as alternate probes in cosmology due to their large and stable luminosities and broad redshift range. Previously it was shown that higher-redshift AGN that were reverberation-mapped (RM) using broad Mg\,\textsc{ii} and C\,\textsc{iv} lines are standardizable and yield weak cosmological constraints that are consistent with those from better-established probes. In contrast, lower-redshift AGN that were reverberation-mapped using the broad H line exhibited tensions with the standard cosmological model, in particular they preferred currently decelerating cosmological expansion. Here we study the standardizability of a homogeneous RM H sample of AGN (over redshifts ), whose H time delays and three luminosity tracers (at 5100\,Å\,, broad H, and narrow [O\,\textsc{iii}]) are averaged over several epochs. We find that this averaged sample is standardizable using three relations. While for luminosities corresponding to 5100\,Å\, and the broad H line the cosmological constraints prefer currently decelerating cosmological expansion, the cosmological parameters for the narrow [O\,\textsc{iii}] luminosity are more consistent with those from better-established probes and they are in agreement with currently accelerating cosmological expansion. This demonstrates for the first time that narrow-line region [O\,\textsc{iii}] can be utilized for AGN standardization and cosmological constraints. Selecting proper photoionizing flux proxies for the broad-line region is thus crucial in studies of RM AGN standardizability.

Paper Structure

This paper contains 9 sections, 12 equations, 7 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Cosmological models
  3. Sample and Data
  4. AGN Sample and Data
  5. $H(z)$ and BAO sample and data
  6. Data Analysis Methodology
  7. Results
  8. Discussion
  9. Conclusion

Figures (7)

  • Figure 1: Comparison of the properties of the selected Average Scheme sample of H$\beta$ RM AGN, characterized by AGN monochromatic luminosity $L_{5100}$ (red), broad H$\beta$ luminosity $L_{\text{H}\beta}$ (blue), and optical narrow [O iii] luminosity $L_{\mathrm{{[O\,\textsc{iii}]}}}$ (green), with the earlier samples of both H$\alpha$ and H$\beta$ RM AGN from Cao+25a cao_2025a (black) and the H$\beta$-only sample from Cao+25b cao25 (cyan). The top panel presents AGN luminosity as a function of redshift, while the bottom panel shows the corresponding redshift distributions in histogram form, constructed using a uniform bin size for all samples. Dot-dashed vertical lines of different colors mark the median redshift of each sample. Note that the H$\beta$ and [O iii] samples analyzed in this work originate from the same AGN dataset; therefore, the median redshift values indicated by the blue and green dot-dashed lines overlap. Additionally, the AGN sample with $L_{5100}$ analyzed in this work and that of Cao+25b cao25 span the same redshift range. The luminosities are calculated from the observed fluxes assuming a flat $\Lambda$CDM cosmology with $H_0 = 72 \, {\rm km \, s^{-1} \, Mpc^{-1}}$ and $\Omega_{m0} = 0.3$.
  • Figure 2: One-dimensional likelihoods and 1$\sigma$, 2$\sigma$, and 3$\sigma$ two-dimensional likelihood confidence contours from $\tau_{\mathrm{H}\beta}\text{-}L_{5100}$ (gray), $H(z)$ + BAO (blue), and $H(z)$ + BAO + $\tau_{\mathrm{H}\beta}\text{-}L_{5100}$ (dashed red) data for six different models, with $\Lambda$CDM, XCDM, and $\phi$CDM in the top, middle, and bottom rows, and flat (nonflat) models in the left (right) column. The black dashed zero-acceleration lines, computed for the third cosmological parameter set to the $H(z)$ + BAO data best-fitting values listed in Table \ref{['tab:BFP']} in (d), (f), divide the parameter space into regions associated with currently accelerating (below or below left) and currently decelerating (above or above right) cosmological expansion. The crimson dash-dot lines represent flat hypersurfaces, with closed spatial hypersurfaces either below or to the left. The magenta lines represent $w_{\rm X}=-1$, i.e. flat or nonflat $\Lambda$CDM models. The $\alpha = 0$ axes correspond to flat and nonflat $\Lambda$CDM models in (e), (f), respectively. (a) Flat $\Lambda$CDM. (b) Nonflat $\Lambda$CDM. (c) Flat XCDM. (d) Nonflat XCDM. (e) Flat $\phi$CDM. (f) Nonflat $\phi$CDM.
  • Figure 3: Same as Fig. \ref{['fig1']}, but for cosmological parameters only. (a) Flat $\Lambda$CDM. (b) Nonflat $\Lambda$CDM. (c) Flat XCDM. (d) Nonflat XCDM. (e) Flat $\phi$CDM. (f) Nonflat $\phi$CDM.
  • Figure 4: Same as Fig. \ref{['fig1']}, but for $\tau_{\mathrm{H}\beta}\text{-}L_{\mathrm{H}\beta}$ (gray), $H(z)$ + BAO (blue), and $H(z)$ + BAO + $\tau_{\mathrm{H}\beta}\text{-}L_{\mathrm{H}\beta}$ (dashed red) data. (a) Flat $\Lambda$CDM. (b) Nonflat $\Lambda$CDM. (c) Flat XCDM. (d) Nonflat XCDM. (e) Flat $\phi$CDM. (f) Nonflat $\phi$CDM.
  • Figure 5: Same as Fig. \ref{['fig3']}, but for cosmological parameters only. (a) Flat $\Lambda$CDM. (b) Nonflat $\Lambda$CDM. (c) Flat XCDM. (d) Nonflat XCDM. (e) Flat $\phi$CDM. (f) Nonflat $\phi$CDM.
  • ...and 2 more figures