# Strong correlation between Fe II/Mg II ratio and Eddington ratio of type 1
Active galactic nuclei

Jaejin Shin1,2 Jong-Hak Woo244affiliation: Author to whom any correspondence
should be addressed Tohru Nagao3 Minjin Kim1 Hyeonguk Bahk2 1Department of
Astronomy and Atmospheric Sciences, Kyungpook National University, Daegu
41566, Republic of Korea
2Astronomy Program, Department of Physics and Astronomy, Seoul National
University, Seoul, 08826, Republic of Korea
3Research Center for Space and Cosmic Evolution, Ehime University, Bunkyo-cho
2-5, Matsuyama, Ehime 790-8577, Japan

###### Abstract

The Fe II/Mg II line flux ratio has been used as an indicator of the Fe/Mg
abundance ratio in the broad line region (BLR) of active galactic nuclei
(AGNs). On the basis of archival rest-frame UV spectra obtained via the Hubble
Space Telescope and the Sloan Digital Sky Survey, we investigate the Fe II/Mg
II ratios of type 1 AGNs at z ¡ 2. Over wide dynamic ranges of AGN properties
(i.e., black hole mass, AGN luminosity, and Eddington ratio), we confirm that
the Fe II/Mg II ratio strongly correlates with Eddington ratio but not with
black hole mass, AGN luminosity, or redshift. Our results suggest that the
metallicity in the BLR are physically related to the accretion activity of
AGNs, but not to the global properties of galaxies (i.e., galaxy mass and
luminosity). With regard to the relation between the BLR metallicity and the
accretion rate of AGNs, we discuss that metal cooling may play an important
role in enhancing the gas inflow into the central region of host galaxies,
resulting in the high accretion rate of AGNs.

###### Subject headings:

galaxies: active — galaxies: ISM — galaxies: nuclei — quasars: emission lines
— ultraviolet: galaxies

##  1\. INTRODUCTION

In understanding galaxy evolution, the chemical properties of galaxies have
been considered as one of the key parameters since they are closely related to
the star formation history (see Maiolino & Mannucci 2019 for a review). For
normal galaxies, gas metallicity exhibits tight scaling relations with galaxy
properties (i.e., mass and luminosity) with these relations evolving as a
function of redshift up to $\sim$3.5 (e.g., Erb et al., 2006; Maiolino et al.,
2008; Mannucci et al., 2009; Yabe et al., 2012; Onodera et al., 2016), which
indicates the cosmic evolution of galaxy metallicity. At a higher redshift
(i.e., z ¿ 3.5), however, the characteristic of galaxy metallicity is poorly
understood since it is challenging to measure the gas metallicity of normal
galaxies at such redshift levels (but see e.g., Nagao et al., 2012; Shapley et
al., 2017; Tadaki et al., 2019).

Alternatively, active galactic nuclei (AGNs) can be investigated thanks to
their high luminosity. Through theoretical models (e.g., CLOUDY), several
ultraviolet (UV) line flux ratios (e.g., N V$\lambda$1240/C IV$\lambda$1549;
hereafter N V/C IV) have been proposed as indicators of the metallicity of the
broad line region (BLR) of AGNs with these line ratios have exhibiting a
correlation with AGN luminosity (e.g., Hamann & Ferland, 1992, 1993; Nagao et
al., 2006). Since AGN luminosity is determined by the combination of the mass
of supermassive black holes (SMBHs) and Eddington ratio, there were efforts to
reveal the physical origin of the BLR metallicity – AGN luminosity relation
between black hole mass and Eddington ratio.

On the one hand, it has been found that BLR metallicity correlates with black
hole mass (Warner et al., 2004; Matsuoka et al., 2011). The mass of SMBHs
shows scaling relations with the properties of their host galaxies (i.e.,
mass, luminosity and stellar velocity dispersion), implying the co-evolution
of SMBHs and their host galaxies (Magorrian et al., 1998; Ferrarese & Merritt,
2000; Gebhardt et al., 2000; Marconi & Hunt, 2003; Häring & Rix, 2004;
Kormendy & Ho, 2013; Woo et al., 2013, 2015). Therefore, based on the relation
between the global properties (i.e., mass) and the gas metallicity of
galaxies, BLR metallicity can be expected to be connected to the galaxy
metallicity. On the other hand, Shemmer et al. (2004) reported a correlation
between BLR metallicity and Eddington ratio, but not black hole mass. This
finding was confirmed by Shin et al. (2013), who investigated low redshift
AGNs over a larger dynamic range (e.g., $\sim$3 dex) of black hole mass and
Eddington ratio. Based on the findings, they discussed a physical connection
between the accretion activity of AGNs and the star formation history of the
central region of galaxies.

Interestingly, no cosmic evolution of the BLR metallicity based on N V/C IV
has been reported up to redshift$\sim$6 (e.g., Nagao et al., 2006; Juarez et
al., 2009), suggesting that the BLR metallicity was already enriched at a
universe age of 1 Gyr (z$\sim$6) and that the first star formation episode
occurred at a redshift of higher than $\sim$10\. This is inconsistent with the
trend of galaxy metallicity, which clearly exhibits cosmic evolution (e.g.,
Maiolino et al., 2008; Troncoso et al., 2014).

In understanding the chemical properties of the BLR, another flux ratio
between UV Fe II multiplet and Mg II$\lambda$2800 (hereafter Fe II/Mg II), has
been investigated as a first-order proxy of the Fe/Mg abundance ratio in the
BLR. Similar to the BLR metallicity indicator (i.e., N V/C IV), the Fe II/Mg
II ratio also shows no dependency on redshift up to z$\sim$7 (e.g., Barth et
al., 2003; Maiolino et al., 2003; De Rosa et al., 2011; Mazzucchelli et al.,
2017; Shin et al., 2019; Onoue et al., 2020; Sameshima et al., 2020; Schindler
et al., 2020), which supports the idea of an absence of cosmic evolution in
the chemical properties of the BLR. However, in contrast to the BLR
metallicity indicators, the Fe II/Mg II ratio shows different relations with
AGN properties since the Fe II/Mg II ratio correlates with Eddington ratio and
black hole mass, but not with AGN luminosity (Dong et al., 2011; Shin et al.,
2019, see also Sameshima et al. 2017).

In our previous study (Shin et al., 2019, hereafter Paper I), we discussed
potential sample selection bias that likely led to the absence of a
correlation between the Fe II/Mg II ratio and AGN luminosity. The limitation
of the previous studies (i.e., Dong et al. 2011 and Paper I) is that only
luminous and massive AGNs were investigated (i.e., log L${}_{\rm Bol}>$46, MBH
¿ $10^{8}\rm M_{\odot}$). The enrichment of galaxy metallicity is found to be
less significant in massive galaxies as a function of cosmic time, which may
mean that massive galaxies are likely chemically matured (see e.g., Maiolino
et al., 2008). Similarly, the luminous and massive AGNs can be likely
chemically matured. This, in turn, may be a reason why no dependency of the Fe
II/Mg II ratio on redshift and AGN luminosity was observed in the previous
works.

Motivated by this consideration, we investigate the Fe II/Mg II ratio of type
1 AGNs at z ¡ 2 over wide dynamic ranges of AGN properties (i.e., black hole
mass, AGN luminosity, and Eddington ratio) to better understand the relation
between the Fe II/Mg II ratio and the AGN properties. In section 2, we
describe the sample and data. The analysis is described in section 3, and our
main results and discussion are presented in sections 4 and 5. We adopt a
cosmology of $H_{\rm 0}=70$ km s-1 Mpc-1, $\Omega_{\Lambda}=0.7$ and
$\Omega_{\rm m}=0.3$.

##  2\. Sample and Data

In this work, we investigate two type 1 AGN samples: (i) low redshift type 1
AGNs (z ¡ $\sim$0.4) with available archival UV spectra and (ii) Sloan Digital
Sky Survey (SDSS) quasars at 0.46 ¡ z ¡ 2.02.

For the low redshift AGNs, we first selected 84,040 type 1 AGNs at z ¡ 0.75
from the Million Quasars (MILLIQUAS) catalog (Version 6.3, June 2019, Flesch
2015), with an object classification of either A (25,989) or Q (58,051). Among
them, we found 77 objects with available archival Hubble Space Telescope (HST)
spectroscopic data (i.e., COS, STIS, and FOS), which was searched within a
radius of 3″, covering the wavelength range of 2600-3050Å in the rest frame.
In previous works of Fe II/Mg II ratio, Fe II flux has been generally fitted
and integrated over the wavelength range of 2200-3090Å (e.g., Maiolino et al.
2003; Sameshima et al. 2017; Paper I). However, the requirement of the wide
wavelength range limits sample size. In Paper I, we demonstrated that a
narrower wavelength range of 2600–3050Å is acceptable for the flux estimation
of Fe II, albeit a non-negligible uncertainty could emerge. This wavelength
range of 2600-3050 was thus adopted to expand the sample size.

We retrieved the single epoch spectra of the 77 objects that showed the best
data quality (i.e., signal-to-noise ratio, SNR, at 3000Å continuum). We then
finalized the sample of 29 type 1 AGNs using the following five criteria, (i)
amplitude-to-noise ratio of Mg II, ANRMgII ¿ 5, (ii) ANR of Fe II, ANRFeII ¿
3, (iii) SNR at 3000Å continuum, SNR3000 ¿3, (iv) no narrow or broad
absorption lines (NAL or BAL) objects, and (v) no type 2 AGNs. The first,
second, and third criteria were adopted to obtain reliable measurements of Mg
II and Fe II fluxes and AGN luminosity. For the second criteria, we defined
the ANRFeII as the ratio of the peak flux density of the best-fit iron model
to the noise at 3000Å. There is one issue for measuring the ANRFeII that Fe II
is blended with Mg II, the power-law continuum, and Balmer pseudo continuum.
This means that deblending Fe II is required through multi-component fitting
to measure the ANRFeII. Moreover, due to the blending with Mg II, the choice
of Mg II line profile in the multi-component fitting can affect the value of
the ANRFeII. In this work, we adopted the ANRFeII from the fitting with double
Gaussian profile for Mg II. We refer to Section 3 for more details. We
excluded three AGNs with prominent absorption features (NAL: NGC 4151 and NGC
3227, BAL: UGC 8058) since the absorption features can severely affect the
line flux estimations of both Mg II and Fe II. Lastly, we found three type 2
AGNs (Mrk 348, Mrk 3, and NGC 1068), which are misclassified as type 1 AGNs in
the MILLIQUAS catalog. Since type 2 AGNs do not present broad emission lines
(i.e., Mg II and Fe II), which is our main area of interest, they were
excluded. The information on the final sample is presented in Table 1. We note
that 11 of the 29 type 1 AGNs ($\sim$38%) cover the full wavelength range of
Fe II, 2200-3090Å.

In addition, we included a number of SDSS quasars from the SDSS DR7 quasars
catalog (Shen et al., 2011). We selected 5,441 quasars in the redshift range
of 0.46 ¡ z ¡ 2.02, whose spectrum covers the rest-frame wavelength range of
2600-3050Å, and the SNR at 3000Å continuum is larger than 20. Among them, we
excluded 1,380 objects with strong absorption lines (i.e., BAL and NAL) and/or
weak emission lines (i.e., ANR${}_{\rm Mg~{}{\sevenrm II}}$ ¡ 5 and
ANR${}_{\rm Fe~{}{\sevenrm II}}$ ¡ 3), leaving a final sample of 4,061
quasars. Note that this sample includes the 3,164 quasars in a narrower
redshift range (i.e., 0.75 ¡ z ¡ 1.96), which were investigated in Paper I,
and the majority (895) of the newly included 897 quasars are at low redshift
(i.e., 0.46¡z¡0.75).

Table 1Log of archival HST UV spectroscopic data

Object | Redshift | Instrument | Grating | Obs. Date
---|---|---|---|---
(1) | (2) | (3) | (4) | (5)
KUG 0003+199 | $0.026$ | FOS | G270H | 1994 Dec 16
FIRST J0012-1022 | $0.228$ | STIS | G430L | 2011 May 14
PGC 87392 | $0.029$ | FOS | G270H | 1996 Jul 30
ESO 113-45 | $0.046$ | FOS | G270H | 1993 Jan 22
HE 0132-4313 | $0.237$ | FOS | G270H, G400H | 1996 Sep 21
3C 48.0 | $0.367$ | STIS | G430L | 2011 Mar 3
SDSS J015530.02-085704.0 | $0.165$ | STIS | G430L | 2011 Feb 2
AKN 120 | $0.033$ | FOS | G270H | 1995 Jul 29
PG 0844+349 | $0.064$ | FOS | G270H | 1992 Jan 10
KUG 0921+525 | $0.035$ | STIS | G230L | 2017 Dec 25
SDSS J094603.94+013923.6 | $0.220$ | STIS | G430L | 2011 Mar 24
NGC 3516 | $0.009$ | FOS | G270H | 1996 Feb 21
MCG 10-16-111 | $0.028$ | STIS | G230L | 2013 Jul 12
MCG 9-19-073 | $0.021$ | STIS | G230L | 2013 Apr 29
CGCG 13-24 | $0.020$ | STIS | G230L | 2013 Jun 7
MARK 50 | $0.024$ | STIS | G230L | 2012 Feb 12
3C 273 | $0.158$ | STIS | G430L | 1999 Jan 31
RXS J12517+2404 | $0.188$ | STIS | G430L | 2011 Apr 26
3C 277.1 | $0.320$ | FOS | G400H | 1991 Nov 2
NGC 5548 | $0.017$ | FOS | G270H | 1992 Jul 5
UGC 10120 | $0.031$ | STIS | G230L | 2017 Aug 29
SBS 1701+610 | $0.165$ | STIS | G430L | 1999 May 2
SDSS J171448.50+332738.3 | $0.181$ | STIS | G430L | 2010 Oct 15
CGCG 229-15 | $0.027$ | STIS | G230L | 2013 Jul 23
NGC 6814 | $0.006$ | STIS | G230L | 2013 May 7
MARK 509 | $0.035$ | STIS | G230L | 2017 Oct 22
B2 2201+31A | $0.298$ | FOS | G270H, G400H | 1991 Sep 6
MR 2251-178 | $0.064$ | FOS | G270H | 1996 Aug 2
NGC 7469 | $0.017$ | FOS | G270H | 1996 Jun 18

Note. — Col. (1): Target name from the MILLIQUAS catalog (Flesch, 2015).

##  3\. Analysis

To measure the Fe II/Mg II ratios of the type 1 AGNs, we performed multi-
component fitting analysis using the components of Mg II, Fe II, the power-law
continuum and Balmer pseudo continuum, as performed in Paper I. For the
fitting of Fe II, we adopted the iron template provided by Tsuzuki et al.
(2006). Note that we did not use the iron template of Vestergaard & Wilkes
(2001) because of the lack of iron information around Mg II (2770-2820Å),
which may lead over- or under- estimation of Mg II and Fe II fluxes,
respectively (Dietrich et al. 2003; Woo et al. 2018; Paper I; Schindler et al.
2020). In addition to the analysis method described in Paper I, we considered
two more issues, 1) the line profile of Mg II, and 2) the contribution of host
galaxy in UV spectra, which will be described as follows.

###  3.1. Line profile of Mg II

In previous works, Mg II has been analyzed with various line profiles because
of the complex line profile of Mg II. Among them, double Gaussian and Gauss-
Hermite series have been widely adopted to reproduce the observed Mg II line
profile showing a wing component (e.g., Marziani et al., 2013; Kovačević-
Dojčinović & Popović, 2015; Woo et al., 2018; Bahk et al., 2019; Le & Woo,
2019; Popović et al., 2019; Le et al., 2020). On the other hand, for AGNs with
high accretion rate, it has been reported that a Lorentzian profile gives
better fitting result than the double Gaussian and Gaussian profiles (Marziani
et al., 2013).

In Paper I, we adopted a single Gaussian profile for Mg II fitting due to the
low data quality of high redshift quasars (i.e., at z$\sim$3) in the work. As
a comparison, we performed another fitting with a 6th order Gauss-Hermite
profile for Mg II and found that the measured Fe II/Mg II ratios from fitting
with the single Gaussian and Gauss-Hermite profiles are consistent within
$\sim$7%. However, we did not test fitting with other line profiles (i.e.,
double Gaussian and Lorentzian).

To better understand whether the Mg II line profiles can affect the
measurements the Fe II/Mg II ratio, we adopted various line profiles for Mg
II, 1) single Gaussian, 2) double Gaussian, 3) 6th order Gauss-Hermite series,
and 4) Lorentzian profiles in the multi-component fitting analysis.

###  3.2. Host galaxy continuum

In AGN spectra, there could be non-negligible contamination from their host
galaxy. With the detection of several stellar absorption lines (i.e., Mgb,
Fe5270, & Fe5335), the host galaxy contamination in optical window has been
identified and removed for the reliable investigation of AGN properties (e.g.,
Park et al., 2012, 2015; Bon et al., 2020). Shen et al. (2011) statistically
found that low luminous AGNs ($\rm logL_{\rm 5100\AA}$ ¡ 45 or $\rm logL_{\rm
Bol}$ ¡ 46) are more likely contaminated by the host galaxy continuum (e.g.,
$\sim$20% for AGNs with $\rm logL_{\rm 5100\AA}$ $\sim$ 44.5 or $\rm logL_{\rm
Bol}$ $\sim$ 45.5). Moreover, Bon et al. (2020) reported that host galaxy
continuum could affect the shape of Fe II in the optical window. Similarly,
the host galaxy contamination can be expected at UV, especially due to young
stellar population (e.g., Leitherer et al., 2011), which could affect the
measurement of Fe II flux and AGN luminosity in the UV window.

However, it seems challenging to investigate the host galaxy contamination in
this work due to the following reason. In the wavelength of 2600–3050Å, strong
absorption lines are Fe II $\lambda$2600, Mg II, and Mg I $\lambda$2852, while
we have no AGNs exhibiting prominent absorption features at those lines in our
sample of low redshift AGNs and SDSS quasars. During our sample selection
process, we detected such AGNs (e.g., NGC 4151 an NGC 3227, see Section 2).
However, we discarded them based on the assumption that they are NAL AGNs. We
note that 15 targets out of our 29 low redshift AGNs exhibit prominent
absorption line features, which are not related to Fe II $\lambda$2600, Mg II,
and Mg I $\lambda$2852\. By considering the redshift of the 15 targets, all of
their absorption lines are likely Milky way absorption lines (Savage et al.,
2000), which are produced by gas in the disk and halo of the Milky Way.
Therefore, the absorption lines are not related to the host galaxy continuum.
Since we can not properly investigate the host galaxy contamination without
stellar absorption lines, we decided not to consider the host galaxy
contamination in this work. We note that AGNs with the nondetection of Mg II
absorption line suggest that their host galaxy contamination maybe not
significant in their UV spectra. To investigate the host galaxy contamination
in UV, one can use high-quality spectra covering wide wavelength range (i.e.,
UV to optical) and showing prominent absorption lines (Mgb, Fe5270, and
Fe5335) in future.

###  3.3. Fitting procedure and measurement

With the four line profiles for Mg II, we performed the multicomponent fitting
analysis. We note that we accepted the fitting with the double Gaussian
profile only if the ANR of each Gaussian component is all larger than three.
Otherwise, we adopted the fitting with the single Gaussian line profile.

During the fitting process, we did not give any kinematic constraints between
Mg II and Fe II to avoid any possible bias. This is different from Paper I,
which gave constraints that Mg II and Fe II have the same velocity shift and
similar velocity dispersion ($\Delta\sigma$ ¡ 10%). However, we note that the
kinematic constraint does not significantly affect the measurements of Mg II
and Fe II fluxes and the Fe II/Mg II ratio as discussed in Paper I (see their
Figure 8).

From the best-fit model, we measured the flux and velocity dispersion of Mg
II, whereas for the flux of Fe II, we integrated the best iron model over the
wavelength range, 2600–3050Å. In Figure 1, we present the comparisons of the
Mg II flux, Fe II flux, and Fe II/Mg II ratio, which were measured from the
fitting with the four Mg II line profiles. From the comparisons, we found
three trends. First, the measurements from the fitting with the double
Gaussian and 6th order Gauss-Hermite line profiles are consistent. Second, the
fitting with double Gaussian line profile gives larger Mg II fluxes but
smaller Fe II fluxes and Fe II/Mg II ratios than those from the single
Gaussian fitting. This would be because the wing component of Mg II can not be
fitted with the single Gaussian profile. Third, the double Gaussian fitting
provides smaller Mg II flux and larger Fe II flux and Fe II/Mg II ratio than
the Lorentzian fitting, suggesting that the Lorentzian profile tends to more
fit the wing component of MgII line than the double Gaussian. While their are
non-negligible scatters and offsets described above, the measurements from the
fitting with various Mg II line profiles, generally show strong linear
relationships between each other.

Figure 1.—  Comparison of Fe II flux (left), Mg II flux (center), and the Fe
II/Mg II ratio (right) measured from fitting with various line profiles for Mg
II. X-axis shows the measurement from double Gaussian line profiles and Y-axis
shows the measurements from other profiles (top: single Gaussian, middle: 6th
order Gauss-Hermite, and bottom: Lorentzian). Blue and gray represent the
sample of low redshift AGNs and SDSS quasars, respectively. The offset and
scatter given in each panel are the average and the standard deviation of the
difference between the two measurements in each panel.

We also estimated the AGN properties (i.e., black hole mass, AGN luminosity,
and Eddington ratio) using the velocity dispersion of Mg II and the
monochromatic luminosity at 3000Å continuum. We calculated black hole mass
using the equation given in Le et al. (2020, see also ) with the coefficients
of their scheme 2. Note that the Mg II-based black hole mass measurement has
an uncertainty of 0.4-0.7 dex due to various issues (i.e., the virial factor
and AGN variability, see e.g., Le et al., 2020, and references therein). The
bolometric luminosity was converted from the 3000Å monochromatic luminosity
with a bolometric correction factor of 5.15 (Shen et al., 2008). Lastly, we
calculated the Eddington ratio by dividing the bolometric luminosity by the
Eddington luminosity, which is determined by black hole mass. We also
estimated the uncertainties of the line fluxes and AGN properties using Monte-
Carlo simulations with 1000 mock spectra created from randomizing flux within
1$\sigma$ error. We list the properties of emission lines and AGN with their
uncertainties in Table 2.

We also checked whether the choice of the Mg II line profile affects the
estimation of AGN properties. First of all, we found that AGN luminosities
from fitting with the four different line profiles are consistent within
$\sim$0.01 dex. Secondly, we obtained consistent black hole mass from the
fitting with the line profiles of single Gaussian, double Gaussian, and 6th
order Gauss-Hermite series within $\sim$ 0.1 dex, while they are significantly
lower ($\sim$20 times) than that from the Lorentzian fitting. Due to the
consistent AGN luminosities, the difference in black hole mass is mainly from
the different velocity dispersion of Mg II, meaning that the Mg II line width
measured from fitting with the Lorentz function is higher than that from
fitting with other profiles. However, when we consider the full width half
maximum of Mg II, we have consistent black hole mass measurements from the
fitting with all of the four line profiles. This issue may be due to the
different ratios between the FWHM and velocity dispersion of the line
profiles. For example, the ratio is $\sim$2.35 for single Gaussian but $\sim$1
for Lorentzian. The black hole mass estimation method using the velocity
dispersion and FWHM of Mg II measured from fitting with the line profiles of
double Gaussian and Gauss-Hermite is well calibrated based on the information
of H$\beta$ (e.g., Le et al., 2020). Therefore, our test indicate that the
velocity dispersion of Mg II from the Lorentzian fitting is not applicable for
black hole mass estimation.

As described earlier, double Gaussian and Gauss-Hermite series have been
widely adopted to estimate black hole mass. Based on our test, we found that
any of them can be adopted because adopting both of them provide consistent
measurements. However, by visual inspection, we checked Gauss-Hermite series
give unsatisfactory fitting results for a number of AGN, which fitted noise.
Therefore, we finally decided to adopt the fitting results based on the double
Gaussian profile.

Figure 2 shows the bolometric luminosities of the low redshift AGNs and SDSS
quasars as a function of black hole mass. Most of the AGNs in this work show
an Eddington ratio ranging from 1% to 100%. As shown in Figure 2, the low
redshift AGNs are on average far less massive and luminous ($\rm log\ M_{\rm
BH}$/M⊙ $\sim$ 8.0 and log LBol $\sim$ 44.6) compared with the SDSS quasars
($\rm log\ M_{\rm BH}$/M⊙ $\sim$ 9.0 and log LBol $\sim$ 46.5). Especially,
the low redshift AGN sample uniquely covers the low luminosity range of log
LBol=42.1–45.4, which is $\sim$101-4 times fainter than the lower bound of the
luminosity range of high redshift SDSS quasars and the low black hole mass
(log MBH/M⊙= 6.9–8.0) regime. Together with the SDSS quasars, we can
investigate the relations between the Fe II/Mg II ratio and AGN properties in
the wide dynamic ranges of the AGN properties (i.e., $\sim$6 dex in luminosity
and 3 dex in black hole mass).

Note that, the distributions of black hole mass and AGN bolometric luminosity
of our SDSS quasars are extended by $\sim$0.5 dex to a lower mass and
luminosity, compared with those presented in Paper I. This is due to the
inclusion of lower redshift SDSS quasars (0.46 ¡ z ¡ 0.75), which are likely
less massive and luminous than higher redshift SDSS quasars.

Figure 2.—  AGN bolometric luminosity as a function of black hole mass.
Symbols are same as those in Figure 1. Dashed lines indicate the Eddington
ratios (100, 10, and 1%).
Table 2Emission line and AGN properties Object | $\rm F_{Fe~{}{\sevenrm II}}$ | $\rm F_{Mg~{}{\sevenrm II}}$ | $\rm Fe~{}{\sevenrm II}/Mg~{}{\sevenrm II}$ | $\sigma_{\rm Mg~{}{\sevenrm II}}$ | log $\rm M_{BH}/M_{\odot}$ | log $\rm L_{3000}$ | log $\rm L_{Bol}/L_{Edd}$
---|---|---|---|---|---|---|---
| ($\rm 10^{-16}\ erg\ s^{-1}\ cm^{-2}$) |  | (km s-1) |  | ($\rm erg\ s^{-1}$) |
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8)
KUG 0003+199 | $145.8\pm 4.6$ | $55.3\pm 1.0$ | $2.64\pm 0.10$ | $1045\pm 42$ | $7.66\pm 0.03$ | $44.02\pm 0.00$ | $-1.02\pm 0.04$
FIRST J0012-1022 | $10.3\pm 2.0$ | $3.9\pm 0.6$ | $2.65\pm 0.70$ | $1846\pm 808$ | $8.50\pm 0.09$ | $44.71\pm 0.01$ | $-1.17\pm 0.15$
PGC 87392 | $31.5\pm 0.5$ | $7.2\pm 0.1$ | $4.36\pm 0.11$ | $793\pm 26$ | $6.96\pm 0.03$ | $43.10\pm 0.00$ | $-1.24\pm 0.03$
ESO 113-45 | $160.6\pm 7.1$ | $104.2\pm 2.0$ | $1.54\pm 0.09$ | $2029\pm 116$ | $8.32\pm 0.05$ | $44.19\pm 0.01$ | $-1.51\pm 0.06$
HE 0132-4313 | $18.4\pm 0.8$ | $3.5\pm 0.1$ | $5.23\pm 0.35$ | $1025\pm 77$ | $8.23\pm 0.05$ | $45.20\pm 0.00$ | $-0.42\pm 0.06$
3C 48.0 | $14.7\pm 2.5$ | $4.2\pm 0.3$ | $3.54\pm 0.30$ | $1281\pm 70$ | $8.56\pm 0.05$ | $45.46\pm 0.01$ | $-0.48\pm 0.05$
SDSS J015530.02-085704.0 | $11.0\pm 1.9$ | $7.4\pm 0.5$ | $1.48\pm 0.30$ | $2320\pm 180$ | $8.63\pm 0.07$ | $44.58\pm 0.01$ | $-1.44\pm 0.06$
AKN 120 | $232.3\pm 7.8$ | $97.7\pm 1.8$ | $2.38\pm 0.11$ | $2300\pm 97$ | $8.41\pm 0.03$ | $44.16\pm 0.00$ | $-1.64\pm 0.04$
PG 0844+349 | $85.6\pm 4.1$ | $19.1\pm 0.5$ | $4.48\pm 0.29$ | $1167\pm 26$ | $7.96\pm 0.02$ | $44.43\pm 0.00$ | $-0.92\pm 0.02$
KUG 0921+525 | $129.5\pm 3.7$ | $70.9\pm 3.1$ | $1.83\pm 0.10$ | $1150\pm 36$ | $7.65\pm 0.03$ | $43.84\pm 0.00$ | $-1.20\pm 0.03$
SDSS J094603.94+013923.6 | $7.3\pm 0.9$ | $2.4\pm 0.2$ | $3.03\pm 0.47$ | $1442\pm 155$ | $7.91\pm 0.09$ | $43.97\pm 0.03$ | $-1.33\pm 0.09$
NGC 3516 | $184.1\pm 7.6$ | $122.4\pm 2.1$ | $1.50\pm 0.08$ | $2381\pm 100$ | $7.92\pm 0.02$ | $43.12\pm 0.00$ | $-2.19\pm 0.04$
MCG 10-16-111 | $11.1\pm 0.7$ | $4.6\pm 0.2$ | $2.44\pm 0.19$ | $1362\pm 117$ | $7.25\pm 0.05$ | $42.75\pm 0.01$ | $-1.89\pm 0.06$
MCG 9-19-073 | $17.4\pm 1.2$ | $16.0\pm 0.9$ | $1.09\pm 0.13$ | $1864\pm 152$ | $7.12\pm 0.08$ | $41.94\pm 0.03$ | $-2.57\pm 0.07$
CGCG 13-24 | $11.2\pm 0.7$ | $7.8\pm 0.4$ | $1.44\pm 0.12$ | $1504\pm 99$ | $6.91\pm 0.06$ | $41.89\pm 0.03$ | $-2.41\pm 0.07$
MARK 50 | $37.2\pm 2.5$ | $17.8\pm 0.6$ | $2.08\pm 0.16$ | $1534\pm 162$ | $7.49\pm 0.03$ | $43.01\pm 0.01$ | $-1.86\pm 0.06$
3C 273 | $407.8\pm 10.2$ | $135.8\pm 7.5$ | $3.00\pm 0.19$ | $1548\pm 77$ | $9.02\pm 0.04$ | $46.06\pm 0.00$ | $-0.35\pm 0.04$
RXS J12517+2404 | $3.8\pm 3.5$ | $5.5\pm 0.4$ | $0.69\pm 0.45$ | $3147\pm 335$ | $8.79\pm 0.08$ | $44.37\pm 0.04$ | $-1.80\pm 0.10$
3C 277.1 | $6.3\pm 0.6$ | $2.4\pm 0.2$ | $2.56\pm 0.19$ | $1332\pm 274$ | $8.27\pm 0.04$ | $44.82\pm 0.01$ | $-0.84\pm 0.09$
NGC 5548 | $92.8\pm 4.5$ | $74.0\pm 1.3$ | $1.26\pm 0.07$ | $2546\pm 103$ | $7.88\pm 0.02$ | $42.91\pm 0.01$ | $-2.35\pm 0.04$
UGC 10120 | $32.2\pm 0.5$ | $11.1\pm 0.8$ | $2.90\pm 0.21$ | $869\pm 35$ | $7.09\pm 0.03$ | $43.21\pm 0.00$ | $-1.27\pm 0.04$
SBS 1701+610 | $3.2\pm 8.5$ | $4.5\pm 0.5$ | $0.71\pm 0.59$ | $3217\pm 524$ | $8.55\pm 0.08$ | $43.85\pm 0.11$ | $-2.09\pm 0.13$
SDSS J171448.50+332738.3 | $5.6\pm 3.0$ | $4.4\pm 0.3$ | $1.27\pm 0.35$ | $2322\pm 236$ | $8.42\pm 0.08$ | $44.15\pm 0.07$ | $-1.65\pm 0.09$
CGCG 229-15 | $29.7\pm 0.7$ | $11.9\pm 0.6$ | $2.49\pm 0.14$ | $1159\pm 63$ | $7.20\pm 0.04$ | $42.92\pm 0.00$ | $-1.66\pm 0.05$
NGC 6814 | $23.7\pm 1.8$ | $12.7\pm 0.6$ | $1.88\pm 0.18$ | $1996\pm 147$ | $6.90\pm 0.06$ | $41.38\pm 0.02$ | $-2.91\pm 0.06$
MARK 509 | $201.7\pm 22.4$ | $174.5\pm 6.1$ | $1.16\pm 0.05$ | $2591\pm 368$ | $8.57\pm 0.10$ | $44.27\pm 0.01$ | $-1.69\pm 0.26$
B2 2201+31A | $57.4\pm 3.5$ | $14.9\pm 0.5$ | $3.85\pm 0.30$ | $1577\pm 49$ | $8.84\pm 0.03$ | $45.67\pm 0.01$ | $-0.56\pm 0.03$
MR 2251-178 | $57.0\pm 3.0$ | $84.9\pm 0.9$ | $0.67\pm 0.04$ | $3903\pm 44$ | $8.98\pm 0.01$ | $44.37\pm 0.00$ | $-1.99\pm 0.01$
NGC 7469 | $236.3\pm 5.8$ | $107.1\pm 1.2$ | $2.21\pm 0.06$ | $1471\pm 25$ | $7.71\pm 0.01$ | $43.52\pm 0.00$ | $-1.57\pm 0.02$
Figure 3.—  Fe II/Mg II ratio as a function of redshift. Symbols are the same
as those in Figure 1.
Figure 4.—  Relations between the Fe II/Mg II ratio and black hole mass
(left), bolometric luminosity (middle), and Eddington ratio (right). Symbols
are same as those in Figure 1.

##  4\. Result

In Figure 3, we present the Fe II/Mg II ratios of the low redshift AGNs and
SDSS quasars as a function of redshift. We find that there is no significant
difference in Fe II/Mg II ratio between the low redshift AGNs (log Fe II/Mg II
= 0.30$\pm$0.24) and SDSS quasars (log Fe II/Mg II = 0.45$\pm$0.15). This may
indicate the lack of redshift dependence of Fe II/Mg II, which is consistent
with the findings in previous works (e.g., Maiolino et al. 2003; De Rosa et
al. 2011; Sameshima et al. 2017; Paper I; Onoue et al. 2020; Sameshima et al.
2020; Schindler et al. 2020).

Comparisons of the Fe II/Mg II ratios and AGN properties are presented in
Figure 4. We find that the Fe II/Mg II ratio correlates with AGN luminosity
and Eddington ratio. Although the strong correlation between the Fe II/Mg II
ratio and Eddington ratio has previously been reported (Dong et al. 2011;
Sameshima et al. 2017; Paper I), the correlation between the Fe II/Mg II ratio
and AGN luminosity has not yet been discovered. Meanwhile, the Fe II/Mg II
ratio and black hole mass shows weak (SDSS quasars) or marginal (low-z AGNs)
correlations, which is inconsistent with their anti-correlation found for
other samples of SDSS quasars (e.g., Dong et al. 2011; Paper I).

For statistical assessment, we perform Spearman’s and Kendall’s correlation
tests for both of the low redshift AGNs and SDSS quasars (Table 3 and 4). As
expected in Figure 4, we statistically confirm the strong (weak) correlation
of the Fe II/Mg II ratio with Eddington ratio (AGN luminosity). In addition,
the correlation coefficients are found to be larger for the low redshift AGNs
than for the SDSS quasars. In terms of the relation between the Fe II/Mg II
and black hole mass, we find no correlation for the low redshift AGNs, but a
weak anti-correlation for the SDSS quasars. Overall, the statistical tests may
indicate that the Fe II/Mg II ratio strongly correlates with Eddington ratio
rather than black hole mass and luminosity. In the appendix, we provide the
fitting results of 5 SDSS quasars with low- and high- Eddington ratio,
respectively, to show how their spectra are different depending on Eddington
ratio. We find that the correlations between the Fe II/Mg II ratio and AGN
properties shown for the SDSS quasars are consistent with those in the
literature (e.g., Dong et al. 2011; Paper I). Note that the AGN properties
presented in Dong et al. (2011) were calculated based on the line width of
H$\beta$ and 5100Å continuum luminosity. This means that the choice of
emission lines between H$\beta$ and Mg II for black hole mass estimation does
not affect the main result.

Table 3Results of Spearman’s Rank-order correlation test | $M_{\rm BH}/M_{\odot}$ | $L_{\rm Bol}/L_{\odot}$ | $L_{\rm Bol}/L_{\rm Edd}$
---|---|---|---
(1) | (2) | (3) | (4)
Fe II/Mg II (low-z) |  $r_{s}$= –0.121 |  $r_{s}$= 0.342 |  $r_{s}$= 0.776
|  $p$= 0.531 |  $p$= 0.069 |  $p$= 0.000
Fe II/Mg II (SDSS quasars) |  $r_{s}$= –0.250 |  $r_{s}$= 0.192 |  $r_{s}$= 0.502
|  $p$= 0.000 |  $p$= 0.000 |  $p$= 0.000
Table 4Results of Kendall’s Rank-order correlation test | $M_{\rm BH}/M_{\odot}$ | $L_{\rm Bol}/L_{\odot}$ | $L_{\rm Bol}/L_{\rm Edd}$
---|---|---|---
(1) | (2) | (3) | (4)
Fe II/Mg II (low-z) |  $r_{s}$= –0.099 |  $r_{s}$= 0.212 |  $r_{s}$= 0.557
|  $p$= 0.453 |  $p$= 0.101 |  $p$= 0.000
Fe II/Mg II (SDSS quasars) |  $r_{s}$= –0.172 |  $r_{s}$= 0.130 |  $r_{s}$= 0.361
|  $p$= 0.000 |  $p$= 0.000 |  $p$= 0.000

##  5\. Discussion

Figure 5.—  Fe II/Mg II ratios of the low redshift AGNs as a function of
redshift. Color represents black hole mass bins.

###  5.1. Lack of redshift dependence of Fe II/Mg II

Extending the redshift range down to $\sim$0, we confirm that the Fe II/Mg II
ratio is independent of redshift up to z$\sim$7 (Barth et al., 2003; Maiolino
et al., 2003; De Rosa et al., 2011; Mazzucchelli et al., 2017; Shin et al.,
2019; Onoue et al., 2020; Sameshima et al., 2020; Schindler et al., 2020).
However, in Paper I, we discussed that the absence of cosmic evolution of the
Fe II/Mg II ratio may be caused by biased samples in previous works, which
investigated very luminous and massive AGNs. The black hole mass range of the
SDSS quasars presented in Paper I is $\sim$ 10${}^{8-10}M_{\odot}$. With the
assumption of a black hole mass–stellar mass ratio of 0.001–0.01 (e.g.,
Marconi & Hunt, 2003; Peng et al., 2006; Schramm et al., 2008), the
corresponding mass of their host galaxies ranges 10${}^{10-13}M_{\odot}$. At
such high stellar mass regimes, galaxy metallicity evolution is known to be
non-significant as a function of redshift (e.g., Erb et al., 2006; Maiolino et
al., 2008). For example, for galaxies with a stellar mass of
10${}^{11}M_{\odot}$, metallicity increases by only $\sim$0.2 dex between
redshifts 0.4 and 2, which is the range of our SDSS quasars (see Figures 8 and
9 of Maiolino et al. 2008). Therefore, even if the cosmic evolution of the Fe
II/Mg II ratio does exists, it may be difficult to detect the evolution due to
the large scatter of the Fe II/Mg II ratio.

To better understand this issue, we investigate the low redshift AGNs since
their black hole masses are down to $\sim$ 10${}^{6.9}M_{\odot}$,
corresponding to a mass of their host galaxies of 10${}^{8.9-9.9}M_{\odot}$
(see Greene et al., 2020, and the references therein). As shown in Figure 3,
the low redshift AGNs do not show any clear redshift evolution of the Fe II/Mg
II ratio, whereas the black hole masses of the low redshift AGNs span two
orders of magnitude. Since galaxy metallicity-redshift relations depend on
stellar mass (see e.g., Maiolino et al., 2008), we may need to take into
account a black hole mass dependency in the Fe II/Mg II-redshift relation. To
this end, we divide the low redshift AGN sample into four groups on the basis
of their black hole masses and investigate the Fe II/Mg II–redshift relation
for each subsample (Figure 5). However, we find no significant evidence for
the redshift evolution of the Fe II/Mg II ratio across all the black hole mass
bins. Although this result potentially confirms the absence of cosmic
evolution in the Fe II/Mg II ratio, it could have been due to the narrow
redshift range of the low redshift AGN sample (i.e., z ¡ $\sim$0.4) and the
large scatter of Fe II/Mg II. It has been observed that galaxy metallicity
increases by less than $\sim$0.2 dex within the redshift range of 0-0.7 (see
e.g., Figure 9 of Maiolino et al., 2008). With this reason, it is possible
that the redshift evolution of the Fe II/Mg II ratio of the low redshift AGNs
is concealed by the large scatter (i.e., $\sim$0.24 dex), which is similar to
that of higher redshift AGNs.

###  5.2. Primary parameter: Eddington ratio?

In Section 4, we confirm that Fe II/Mg II shows a strong dependency on
Eddington ratio using a sample of low redshift AGNs over large dynamic ranges
of black hole mass and luminosity, which is consistent with previous works
(Dong et al. 2011; Sameshima et al. 2017 and Paper I). However, in contrast to
the previous works (Dong et al. 2011 and Paper I), we find that the Fe II/Mg
II ratio exhibits different trends in terms of black hole mass and AGN
luminosity.

We reveal, for the first time, the weak positive correlation between the Fe
II/Mg II ratio and AGN luminosity, which is consistent with previous results
for the BLR metallicity indicators (i.e., N V/C IV, Hamann & Ferland, 1993;
Nagao et al., 2006; Matsuoka et al., 2011; Shin et al., 2013). It can be
postulated that the correlation could have been revealed because of the wider
dynamic range ($\sim$6 dex) of the AGN luminosity than that adopted in the
previous works (i.e., $\sim$1.5 dex, e.g., Dong et al. 2011; Paper I). If we
take into account the large scatter of the Fe II/Mg II ratio (see Figure 4),
it may be difficult to observe the correlation within a narrow dynamic range
of luminosity. Our interpretation can be supported through the weaker
correlation between the Fe II/Mg II ratio and AGN luminosity of the SDSS
quasars, the luminosity range of which is $\sim$2 dex, compared with that of
the low redshift AGNs (see Table 3).

Figure 6.—  Relations between Fe II/Mg II ratio and AGN properties for the
subsamples of the SDSS quasars in different luminosity bins, which are denoted
in the left column. Lowest to highest redshift bins are shown from top to
bottom. Blue and gray symbols indicate a subsample and the whole sample of the
SDSS quasars, respectively. Correlation coefficients between the Fe II/Mg II
ratio and AGN properties for each subsample are shown in each panel.
Figure 7.—  Same as Figure 6 except with subsamples in different black hole
mass bins, which are denoted in the left column.
Figure 8.—  Same as Figure 6 except with subsamples in different Eddington
ratio bins, which are denoted in the right column.

To better understand the relations between the Fe II/Mg II ratio and AGN
properties, we divide our 4,061 SDSS quasars into 5 subsamples based on
luminosity, mass, and Eddington ratio and investigate the relations. Note that
we arbitrarily determine the physical ranges for each subsample to include
$\sim$800 quasars.

First, as shown in Figure 6, the Fe II/Mg II ratio shows a strong correlation
(anti-correlation) with Eddington ratio (black hole mass) within a narrow AGN
luminosity range in each luminosity bin. Interestingly, the correlation
coefficient between the Fe II/Mg II ratio and black hole mass for each
subsamples is much larger than that for the whole sample of SDSS quasars and
low redshift AGNs. On the other hand, the correlation coefficient between the
Fe II/Mg II ratio and Eddington ratio are similar for the subsamples and whole
samples of SDSS quasars. The different behaviors in the relation between the
Fe II/Mg II ratio and black hole mass depending on samples may indicate the
sample selection effect. At a given luminosity, Eddington ratio and black hole
mass are inversely proportional. Therefore, if there is a strong correlation
between the Fe II/Mg II ratio and Eddington ratio, it can lead the strong
anti-correlation between the Fe II/Mg II ratio and black hole mass for each
subsample within a narrow luminosity range.

Second, in each mass bin, there are strong correlations of the Fe II/Mg II
ratio with both of AGN luminosity and Eddington ratio (Figure 7). At a given
black hole mass, AGN luminosity and Eddington ratio are proportional.
Therefore, the strong correlation between the Fe II/Mg II and AGN luminosity
in each subsample can be also caused by the strong correlation between the Fe
II/Mg II ratio and Eddington ratio.

Third, Figure 8 shows that the Fe II/Mg II ratio is marginally correlated with
both of black hole mass and AGN luminosity in each Eddington ratio bin. These
results potentially confirm that the Fe II/Mg II ratio–black hole mass and Fe
II/Mg II ratio–AGN luminosity relations are subject to sample selection,
suggesting that the reported anti-correlation between the Fe II/Mg II ratio
and black hole mass may be artificial. Meanwhile, regardless of the sample
selection, Eddington ratio shows a strong correlation with the Fe II/Mg II
ratio.

In conclusion, the Fe II/Mg II ratio is primarily related to Eddington ratio,
and not black hole mass, which is related to the global properties of galaxies
(i.e., galaxy mass). This trend is consistent with previous results for the
BLR metallicity indicators (e.g., Shemmer et al., 2004; Shin et al., 2013) and
other emission line ratios (i.e., Fe II/H$\beta$, e.g., Netzer & Trakhtenbrot,
2007; Dong et al., 2011), implying the physical connection between the metal
enrichment at the nuclear region of galaxies and the accretion activity of
AGNs (e.g., Dong et al. 2011; Shin et al. 2013, 2017; Paper I).

###  5.3. Physical meaning of the Fe II/Mg II ratio

Several line ratios (i.e., N V/C IV and Fe II/H$\beta$) including the Fe II/Mg
II ratio, correlate with Eddington ratio. Interestingly, the Fe II/H$\beta$
ratio (Panda et al., 2018, 2019a) and N V/C IV ratio (Hamann & Ferland, 1992,
1993; Nagao et al., 2006) have been suggested to be associated with BLR
metallicity. Therefore, the correlation between the Fe II/Mg II ratio and
Eddington ratio may suggest that the Fe II/Mg II ratio is also related to BLR
metallicity, also supported by theoretical studies (Verner et al., 2003;
Sarkar et al., 2021).

A physical connection between the Fe II/Mg II ratio and BLR metallicity can be
understood in terms of metal enrichment from star formation. As a proxy of the
Fe/Mg abundance ratio, we can track the change of the Fe II/Mg II ratio as a
function of time from the onset of star formation based on an enrichment delay
(tens of Myr to a few Gyrs, Matteucci & Recchi, 2001) between alpha elements
and iron which are produced mainly from Type II and Type Ia supernovae,
respectively. If we simply consider a single episode of star formation, the Fe
II/Mg II will be constant from the onset of star formation until Type II SNe
explode. Once Type II SNe begin to explode (a few tens of Myrs from the onset
of star formation), the Fe II/Mg II will decrease due to the enrichment of
alpha elements during other few tens of Myrs until all of Type II SNe explode.
After then, iron will be enriched by Type Ia SNe; hence the Fe II/Mg II ratio
will increase as a function of time for a few Gyrs. Therefore, except for a
short time period ($\sim$a few tens of Myr), it can be expected that the Fe
II/Mg II ratio increases as a function of time.

On the other hand, metallicity increases as a function of time from the onset
of star formation due to the enrichment of metals from stellar evolution. In
this sense, the possible connection between the Fe II/Mg II ratio and BLR
metallicity can be considered. We note that there were reports that the Fe
II/Mg II ratio is not only determined by the Fe/$\alpha$ abundance ratio but
also other physical parameters of BLR cloud (i.e., gas density and
microturbulence Verner et al., 2003; Sameshima et al., 2017). With this
reason, the Fe II/Mg II may not be a direct indicator of metallicity, while it
can still be an indirect indicator of metallicity as we discussed.

In conclusion, the correlation between several line flux ratios tracing the
chemical properties of the BLR and Eddington ratio can be considered as the
relation between the BLR metallicity and accretion activity of AGN. In the
next section, we further discuss the origin for the relation between the BLR
metallicity and Eddington ratio.

###  5.4. Physical implication of the relation between the BLR metallicity and
Eddington ratio

For the last few decades, the connection between the BLR metallicity and
Eddington ratio has long been discussed, while it has not been fully
understood. From a number of optical studies on AGN (e.g., Boroson & Green,
1992; Sulentic et al., 2000a, b; Marziani et al., 2001; Boroson, 2002; Shen &
Ho, 2014), the Fe II/H$\beta$ ratio and Eddington ratio are known to be
related to the AGN Eigenvector 1. It means that the BLR metallicity and
Eddington ratio can play important roles in AGN physics since the Fe
II/H$\beta$ ratio is associated with the BLR metallicity. Understanding
physical connection between the BLR metallicity and Eddington ratio can
therefore shed light on the AGN physics.

In previous works, nuclear starburst has been discussed as the origin for the
relation because it can enrich BLR metallicity as well as increase accretion
rate of AGNs (Shemmer et al., 2004; Netzer & Trakhtenbrot, 2007; Shin et al.,
2013, 2017; Panda et al., 2019b). Indeed, the connection between nuclear
starburst and the accretion activity of AGNs has been discussed (e.g.,
Imanishi & Wada, 2004; Woo et al., 2012; Esquej et al., 2014) with a delay
time of 50–100 Myr between the two activities (Davies et al., 2007). However,
no strong correlation was found between the nuclear star formation rate and
Eddington ratio (Davies et al., 2007; Woo et al., 2012). For example, in
Davies et al. (2007), Circinus galaxy, NGC 3783, and IRAS 05189-2524 show
similar nuclear star formation rates (30-70 M⊙/yr) and starburst ages (i.e.,
60–80 Myr), while their Eddington ratios are quiet different by factors of up
to $\sim$50\. This result suggests that star formation rate and the accretion
rate of AGNs may be not directly related, meaning that the nuclear starburst
may not be the origin for the correlation between the chemical properties in
the BLR and Eddington ratio. We note that, however, it is also possible that
the no clear relation between the nuclear star formation rate and Eddington
ratio is due to AGN variability (e.g., Hickox et al., 2014).

Alternatively, we can discuss metal cooling as a possible mechanism to explain
the connection between the chemical properties in the BLR and Eddington ratio.
Since the efficiency of radiative cooling is a function of metallicity (e.g.,
Sutherland & Dopita, 1993; Wang et al., 2014), more efficient radiative
cooling due to higher BLR metallicity (and also the Fe/$\alpha$ abundance
ratio, see e.g., Hamann & Ferland 1993) can cause stronger gas inflows (i.e.,
higher gas density) in the BLR as well as higher accretion rate of AGNs. This
scenario is supported by a simulation based study (Mayer et al., 2015),
finding that the metal cooling enhances the gas inflows into the central pc
scale region of galaxies. We note that, based on CLOUDY photoionization
modeling (Ferland et al., 2017), Sameshima et al. (2017) discussed an anti-
correlation between hydrogen gas density of BLR clouds and Eddington ratio,
which is opposite to our scenario. However, their modeled emission line
strengths of Fe II and Mg II are found to be largely inconsistent ($\sim$1
dex) with the observed line strengths (see Figures 4 and 9 of Sameshima et al.
2017), which indicates that their result may not be reliable. The
inconsistency can be because their adopted atomic 371-level Fe+ model (Verner
et al., 1999) may be not accurate (see e.g., Verner et al., 2003; Smyth et
al., 2019; Sarkar et al., 2021) and/or their parameter space may not reflect
the nature of the BLR. Therefore, to confirm the relation between gas density
and Eddington ratio, further investigations are required.

##  6\. Summary

In this work, we investigate the relations between the Fe II/Mg II ratio and
AGN properties of type 1 AGNs at z ¡ 2 in a large dynamic range of AGN
properties. The main results are summarized below.

$\bullet$ The Fe II/Mg II ratios of the low redshift AGNs (z ¡ $\sim$0.4) show
no clear dependence on redshift, which is consistent with previous results for
higher redshift AGNs (up to z$\sim$7), suggesting no cosmic evolution of the
Fe II/Mg II ratios.

$\bullet$ In contrast to previous works, we reveal a weak positive correlation
between the Fe II/Mg II ratio and AGN luminosity over a wide dynamic range of
AGN luminosity ($\sim$ 6 dex). This result is consistent with the previous
studies of BLR metallicity indicators (i.e., N V/C IV).

$\bullet$ We find a marginal correlation between the Fe II/Mg II ratio and
black hole mass, which is inconsistent with the anti-correlation found for
SDSS quasars in the literature. Based on a test using various subsamples of
SDSS quasars, we interpret that the previous finding of the anti-correlation
was caused by the narrow luminosity range and there may be no physical
relation between the Fe II/Mg II ratio and black hole mass.

$\bullet$ Consistent with previous results, we find a strong correlation
between the Fe II/Mg II ratio and Eddington ratio. With regard to this, we
discuss metal cooling, which can enhance gas inflows as well as high accretion
rate of AGNs.

We thank the anonymous referee for valuable comments and suggestions that
significantly improved the quality of the paper. This research was supported
by Basic Science Research Program through the National Research Foundation of
Korea (NRF) funded by the Ministry of Education (2016R1A2B3011457 and
2019R1A6A3A01093189). JS and MK were supported by the National Research
Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No.
2020R1A2C4001753). TN was financially supported by the Japan Society for the
Promotion of Science (JSPS) KAKENHI grant Nos. 19H00697 and 20H01949. Based on
observations made with the NASA/ESA Hubble Space Telescope, and obtained from
the Hubble Legacy Archive, which is a collaboration between the Space
Telescope Science Institute (STScI/NASA), the Space Telescope European
Coordinating Facility (ST-ECF/ESAC/ESA) and the Canadian Astronomy Data Centre
(CADC/NRC/CSA). Funding for the SDSS and SDSS-II has been provided by the
Alfred P. Sloan Foundation, the Participating Institutions, the National
Science Foundation, the U.S. Department of Energy, the National Aeronautics
and Space Administration, the Japanese Monbukagakusho, the Max Planck Society,
and the Higher Education Funding Council for England. The SDSS Web Site is
http://www.sdss.org/. The SDSS is managed by the Astrophysical Research
Consortium for the Participating Institutions. The Participating Institutions
are the American Museum of Natural History, Astrophysical Institute Potsdam,
University of Basel, University of Cambridge, Case Western Reserve University,
University of Chicago, Drexel University, Fermilab, the Institute for Advanced
Study, the Japan Participation Group, Johns Hopkins University, the Joint
Institute for Nuclear Astrophysics, the Kavli Institute for Particle
Astrophysics and Cosmology, the Korean Scientist Group, the Chinese Academy of
Sciences (LAMOST), Los Alamos National Laboratory, the Max-Planck-Institute
for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New
Mexico State University, Ohio State University, University of Pittsburgh,
University of Portsmouth, Princeton University, the United States Naval
Observatory, and the University of Washington.
In Figure A1, we provide fitting results of five randomly selected SDSS
quasars with low (log LBol/LEdd¡-1) and high Eddington ratio (log
LBol/LEdd¿0), respectively (Figure A1). As expected from Figure 4, the high
Eddington ratio quasars show larger Fe II/Mg II ratios than the low Eddington
ratio quasars. We find one difference between the two groups that low
Eddington ratio AGNs show much broader Mg II line than high Eddington ratio
AGNs. This trend can be expected from i) a strong anti-correlation between the
line width of H$\beta$ and Eddington ratio Netzer & Trakhtenbrot (2007); Xu et
al. (2012) and ii) a linear relationship between the linewidths of H$\beta$
and Mg II (e.g., McGill et al., 2008; Woo et al., 2018; Le et al., 2020). This
trend also can be analytically explained. Based on the single epoch method,
black hole mass is proportional to L${}^{\sim 0.5}\times\ \sigma^{\sim 2}$.
Since Eddington ratio is determined by the ratio between bolometric luminosity
and black hole mass, it is proportional to L${}^{\sim 0.5}\times\
\sigma^{\sim-2}$, which means a strong inverse dependency of Eddington ratio
on the line width of H$\beta$ or Mg II.

Figure A1.—  Examples of fitting results of SDSS quasars with low- (left) and
high- Eddington ratio (right). In each panel, raw spectrum (black), the best-
fit model (red), power-law continuum (blue), Balmer pseudo continuum (orange),
Fe II (magenta), Mg II (green), and the residual spectrum (gray) are shown.
The Fe II/Mg II ratio of each quasar is also shown at the top right corner of
each panel.

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