Parameterizing the AGN Radius–Luminosity Relation from the Eigenvector 1 Viewpoint

Abstract

The study of the broad-line region (BLR) using reverberation mapping has allowed us to establish an empirical relation between the size of this line-emitting region and the continuum luminosity that drives the line emission (i.e., the RHβ − L5100 relation). To realize its full potential, the intrinsic scatter in the RHβ − L5100 relation needs to be understood better. The mass accretion rate (or equivalently the Eddington ratio) plays a key role in addressing this problem. On the other hand, the Eigenvector 1 schema has helped to reveal an almost clear connection between the Eddington ratio and the strength of the optical Fe II emission that originates from the BLR. This article aims to reveal the connection between theoretical entities, such as the ionization parameter (U) and cloud mean density (nH) of the BLR, with physical observables obtained directly from the spectra, such as optical Fe II strength (RFeII) that has shown immense potential to trace the accretion rate. We utilize the photoionization code CLOUDY and perform a suite of models to reveal the physical conditions in the low-ionization, dust-free, line-emitting BLR. The key here is the focus on the recovery of the equivalent widths (EWs) for the two low-ionization emission lines—Hβ and the optical Fe II—in addition to the ratio of their EWs, i.e., RFeII. We compare the spectral energy distributions, I Zw 1 and NGC 5548, of prototypical Population A and Population B sources, respectively, in this study. The results from the photoionization modeling are then combined with the existing reverberation-mapped sources with observed RFeII estimates taken from the literature, thus allowing us to assess our analytical formulation to tie together the aforementioned quantities. The recovery of the correct physical conditions in the BLR then suggests that—the BLR “sees” only a very small fraction (∼1–10%) of the original ionizing continuum.

Standardizing reverberation-measured C IV time-lag quasars, and using them with standardized Mg II quasars to constrain cosmological parameters

“…The constraints on the intercept parameter of the C 𝑅 − 𝐿 relation, 𝛽 , range from a low of 0.970 +0.136 −0.108 (flat XCDM) to a high of 1.076 +0.087 −0.074 (non-flat 𝜙CDM), with a difference of 0.68𝜎. A summary value of the measured C 𝑅 − 𝐿 relation slope, 𝛾 0.45 ± 0.04, indicates that it is about 1𝜎 lower than and consistent with the prediction of simple photoionization theory (𝛾 = 0.5, Karas et al 2021;Panda 2022), on the other hand a summary value of the measured Mg 𝑅 − 𝐿 relation slope, 𝛾 0.3 ± 0.05 (also see Khadka et al 2021aKhadka et al , 2022a, indicates that it is about 4𝜎 lower than 𝛾 = 0.5. 6 Khadka et al (2021a6 Khadka et al ( , 2022a had earlier shown that the symmetric errors Mg cosmological constraints are mutually consistent with those from 𝐻 (𝑧) + BAO data.…”

“…However, we find a 2.3𝜎 difference in the measured slopes of the C and Mg 𝑅 − 𝐿 relations, in the flat ΛCDM model asymmetric error bars results of Table 3, or from the summary values of the measured C and Mg 𝑅 − 𝐿 relation slopes, 𝛾 0.45 ± 0.04 and 𝛾 0.3 ± 0.05. And while the C slope is only about 1𝜎 lower than the 𝛾 = 0.5 slope predicted by simple photoionization theory (Bentz et al 2013;Karas et al 2021;Panda 2022) or a dust-based model of the BLR (Czerny & Hryniewicz 2011), the Mg slope is about 4𝜎 lower than 𝛾 = 0.5, which is more statistically significant.…”

Consistency study of high- and low-accreting Mg ii quasars: No significant effect of the Fe ii to Mg ii flux ratio on the radius-luminosity relation dispersion

“…(vi) The smaller slope of the Mg -based 𝑅 − 𝐿 relation in comparison with both the H𝛽-based 𝑅 − 𝐿 correlation slope (Martínez-Aldama et al 2019;Khadka et al 2021a) and the slope predicted by simple photoionization theory (𝛾 ion =0.5; Karas et al 2021;Panda 2022) is either caused by the source selection effect (cumulation of SDSS-RM sources at intermediate luminosities) or by the different photoionization mechanism and/or distribution of Mg -emitting gas (e.g. lack of the intrinsic "breathing" effect for Mg -emitting material; Guo et al 2020;Wang et al 2020).…”

“…This is unlike H𝛽 sources where high-accretors exhibit a larger scatter with respect to low-R Fe sources. (Martínez-Aldama et al 2019;Du & Wang 2019;Khadka et al 2021a;Panda 2022), (ii) The sample of 66 Mg quasars used here is about a factor of 2 smaller than the H𝛽 sample of 118 sources. The majority of the Mg sources, 57, are from the SDSS-reverberation-mapping (SDSS-RM) program (Homayouni et al 2020) and cover a rather narrow range in monochromatic luminosity and rest-frame timedelay.…”

The Relation between the Optical Fe ii Emission and the Dimensionless Accretion Rate for Active Galactic Nuclei

“…In Figure 2, we show the distributions of FWHM Hβ , σ Hβ , and the broad Hβ shape D Hβ,mean ≡ FWHM Hβ /σ Hβ from the mean spectrum for the RM subsample (red lines). It was found that D Hβ,mean has a relation with L Bol /L Edd or M  (e.g., Du et al 2016a;Yu et al 2020a;Panda 2022). We also show the distribution of FWHM Hβ and σ Hβ from the single-epoch spectrum for the SDSS subsample (blue lines).…”