# [O III] 5007Å Emission Line Width as a Surrogate for $\sigma_{*}$ in Type 1
AGNs?

Huynh Anh N. Le (黎阮黄英) 1,2,∗ Yongquan Xue (薛永泉) 1,2,∗ Xiaozhi Lin (林晓鸷) 1,2
Yijun Wang (王倚君) 3,4 1 CAS Key Laboratory for Research in Galaxies and
Cosmology, Department of Astronomy, University of Science and Technology of
China, Hefei 230026, China<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>
2 School of Astronomy and Space Science, University of Science and Technology
of China, Hefei 230026, China  3 Department of Astronomy, Nanjing University,
Nanjing 210093, China<EMAIL_ADDRESS>
4 Key Laboratory of Modern Astronomy and Astrophysics (Nanjing University),
Ministry of Education, Nanjing 210093, China

###### Abstract

We present a study of the relation between the [O III] 5007Å emission line
width ($\rm\sigma_{[OIII]}$) and stellar velocity dispersion ($\sigma_{*}$),
utilizing a sample of 740 type 1 active galactic nuclei (AGNs) with high-
quality spectra at redshift z $<$ 1.0. We find the broad correlation between
the core component of [O III] emission line width ($\rm\sigma_{[OIII,core]}$)
and $\sigma_{*}$ with a scatter of 0.11 dex for the low redshift (z $<$ 0.1)
sample; for redshift (0.3 $<$ z $<$ 1.0) AGNs, the scatter is larger, being
0.16 dex. We also find that the Eddington ratio ($\rm L_{bol}/L_{Edd}$) may
play an important role in the discrepancies between $\rm\sigma_{[OIII,core]}$
and $\sigma_{*}$. As the $\rm L_{bol}/L_{Edd}$ increases,
$\rm\sigma_{[OIII,core]}$ tends to be larger than $\sigma_{*}$. By classifying
our local sample with different minor-to-major axis ratios, we find that
$\sigma_{*}$ is larger than $\rm\sigma_{[OIII,core]}$ for those edge-on spiral
galaxies. In addition, we also find that the effects of outflow strength
properties such as maximum outflow velocity ($\rm V_{max}$) and the broader
component of [O III] emission line width and line shift
($\rm\sigma_{[OIII,out]}$ and $\rm V_{[OIII,out]}$) may play a major role in
the discrepancies between $\rm\sigma_{[OIII,core]}$ and $\sigma_{*}$. The
discrepancies between $\rm\sigma_{[OIII,core]}$ and $\sigma_{*}$ are larger
when $\rm V_{max}$, $\rm V_{[OIII,out]}$, and $\rm\sigma_{[OIII,out]}$
increase. Our results show that the outflow strengths may have significant
effects on the differences between narrow-line region gas and stellar
kinematics in AGNs. We suggest that caution should be taken when using
$\rm\sigma_{[OIII,core]}$ as a surrogate for $\sigma_{*}$. In addition, the
substitute of $\rm\sigma_{[OIII,core]}$ for $\sigma_{*}$ could be used only
for low luminosity AGNs.

###### Subject headings:

galaxies: active – galaxies: kinematics and dynamics – quasars: emission lines

††slugcomment: Accepted for publication in ApJ**affiliationtext: Author to
whom any correspondence should be addressed.

##  1\. INTRODUCTION

Black-hole mass (MBH) is a fundamental driving factor in active galactic
nuclei (AGNs). The study of the correlations between MBH and properties of
their host galaxies is important in understanding the physical nature and the
growth history of AGNs. Over the last two decades, there have been many
studies for investigating the co-evolution between supermassive black holes
and their host galaxies (e.g., Ferrarese & Merrit, 2000; Gebhardt et al.,
2000; McLure & Jarvis, 2002; Tremaine et al., 2002; Woo et al., 2006, 2010;
Xue et al., 2010; Kormendy & Ho, 2013; Le et al., 2014; Sun et al., 2015;
Shankar et al., 2016; Xue, 2017; Shankar et al., 2019; Le & Woo, 2019; Woo et
al., 2019; Lin et al., 2022; Ayubinia et al., 2022). The tight correlations
between MBH and their host galaxies suggest that black holes and their hosts
are co-evolving and regulating each other. These scaling relations could be
explained by either mutual merger processes or AGN feedback (Silk & Rees,
1998; Peng et al., 2006).

In spite of the tight correlations between black holes and their host
galaxies, it is difficult for us to measure the host galaxy properties due to
AGNs often outshining their host galaxies. In particular, the measurement of
stellar velocity dispersions ($\sigma_{*}$) is challenging because of the
contamination of AGN continuum and emission lines in the observed spectra
(particularly for high redshift AGNs). To overcome this issue, some studies
have suggested using the line width of [O III] 5007Å ($\rm\sigma_{[OIII]}$) as
a surrogate for the stellar velocity dispersion ($\sigma_{*}$) by assuming
that the ionized gas kinematics of the narrow-line region (NLR) is followed
the gravitational potential of the bulge of the host galaxy (e.g., Wilson &
Heckman, 1985; Terlevich, Diaz & Terlevich, 1990; Whittle, 1992; Nelson &
Whittle, 1996; Nelson, 2000; Boroson, 2003; Shields et al., 2003; Greene & Ho,
2005; Rice et al., 2006; Netzer & Trakhtenbrot, 2007; Salviander et al., 2007;
Salviander & Shields, 2013). By analyzing in detail the [O III] kinematics,
Wilson & Heckman (1985) is the first study which found that
$\rm\sigma_{[OIII]}$ is correlated well with $\sigma_{*}$. Later on, using a
large sample of 75 Seyfert galaxies, Nelson & Whittle (1996) found that there
is a strong correlation between $\sigma_{*}$ and [O III] profile. By using 21
radio-quiet quasars, Bonning et al. (2005) found that $\rm\sigma_{[OIII]}$ is
on average consistent with $\sigma_{*}$, converted from the Faber-Jackson
relation. Using a large sample from the Sloan Digital Sky Survey (SDSS, York
et al., 2000), Salviander, Shields & Bonning (2015) found a similar result as
that of Bonning et al. (2005), supporting for the use of $\rm\sigma_{[OIII]}$
as a surrogate for $\sigma_{*}$ in statistical studies.

The use of $\rm\sigma_{[OIII]}$ to replace for $\sigma_{*}$ is appealing
because it is easy for us to detect and measure $\rm\sigma_{[OIII]}$ for low
and high redshift AGNs. Thus, the [O III] emission line plays an important
role in the study of cosmic evolution between MBH and their host galaxies.
However, some studies have also found that the [O III] emission line often
shows an asymmetric profile (e.g., the blue wing component) which could be
interpreted as signatures of the non-gravitational potential such as outflows
(e.g., Heckman et al., 1984; Bae & Woo, 2014; Woo et al., 2016; Le et al.,
2017). Because of this reason, some studies have suggested using only the core
component of [O III] emission line ($\rm\sigma_{[OIII,core]}$) as a surrogate
for $\sigma_{*}$ (e.g., Greene & Ho, 2005; Komossa & Xu, 2007; Bennert et al.,
2018). Greene & Ho (2005) found that after correcting for the blue wing
component in the [O III] profile, $\sigma_{*}$ is traced well by
$\rm\sigma_{[OIII]}$, albeit with large scatter. In addition, some other
studies also proposed to use other NLR emission lines which have lower
ionization potential compared to that of [O III], suffering less from outflow
effects, such as [O II] 3727Å, [N II] 6583Å and [S II] 6716Å,3731Å (e.g.,
Phillips et al., 1986; Greene & Ho, 2005; Komossa & Xu, 2007; Ho, 2009;
Bennert et al., 2018). However, the use of those emission lines as a surrogate
for $\sigma_{*}$ also shows large scatter as the case of using
$\rm\sigma_{[OIII,core]}$. Although the correlation between
$\rm\sigma_{[OIII,core]}$ and $\sigma_{*}$ has been investigated by many
studies, the driving factor for the large scatter between both components is
still unclear.

Most of the studies of comparison between $\rm\sigma_{[OIII]}$ and
$\sigma_{*}$ are carried out by indirect comparison between the
MBH$-$$\rm\sigma_{[OIII]}$ and MBH$-$$\rm\sigma_{*}$ relations (e.g., Nelson,
2000; Boroson, 2003; Komossa & Xu, 2007; Grupe & Mathur, 2004; Wang & Lu,
2001). Until now, there are a few studies in which the authors directly and
simultaneously compare $\rm\sigma_{[OIII]}$ and $\sigma_{*}$. Using 1749 type
2 Seyfert galaxies, Greene & Ho (2005) studied the direct comparison between
$\rm\sigma_{[OIII]}$ and $\sigma_{*}$. They found that
$\rm\sigma_{[OIII,core]}$ is consistent with $\sigma_{*}$ after removing for
the asymmetric blue wing in the [O III] profile, and the ratio
$\rm\sigma_{[OIII]}$$/$$\sigma_{*}$ is larger as the Eddington ratio
increases. Rice et al. (2006) analyzed 24 low redshift targets of mostly type
2 AGNs using spatially resolved spectra of Hubble Space Telescope and found
that the scatter between $\rm\sigma_{[OIII]}$ and $\sigma_{*}$ is complicated
and cannot be corrected by using a simple relation. Ho (2009) did a similar
study as that of Greene & Ho (2005) but for the [N II] 6583Å emission line by
using 345 galaxies from the Palomar spectroscopy survey, and found consistent
results as those of Greene & Ho (2005). For a larger sample, Woo et al. (2016)
used 39,000 type 2 AGNs at z $<$ 0.3 to compare directly $\rm\sigma_{[OIII]}$
and $\sigma_{*}$. They found that $\rm\sigma_{[OIII]}$ fitted with double
Gaussian is larger than $\sigma_{*}$ by a factor of 1.3-1.4, suggesting that
the non-gravitational component (e.g., outflows) is relatively comparable to
the gravitational potential. Recently, by using the SDSS sample of 611 hidden
type 1 AGNs, Eun, Woo & Bae (2017) investigated that $\sigma_{*}$ is
consistent with velocity dispersions of [N II] and $\rm\sigma_{[OIII,core]}$.
Bennert et al. (2018) used 59 long-slit, high signal-to-noise (S/N) and
spatially resolved Keck spectra to have a direct comparison of the
relationship between $\rm\sigma_{[OIII,core]}$ and $\sigma_{*}$. They found
large scatter in the correlation between $\rm\sigma_{[OIII,core]}$ and
$\sigma_{*}$ in their sample and suggested that the use of
$\rm\sigma_{[OIII,core]}$ as a surrogate for $\sigma_{*}$ should take caution
when applied for individual targets.

Besides the studies of comparison between $\rm\sigma_{[OIII]}$ and
$\sigma_{*}$, studying the velocity offset of [O III] emission line ($\rm
V_{[OIII]}$) is an interesting topic for exploring AGN-driven outflows. Many
works have investigated $\rm V_{[OIII]}$ with respect to the systemic velocity
of the host galaxy or lower ionization lines such as [O II] or [S II] (e.g.,
Crenshaw & Kraemer, 2000; Zamanov et al., 2002; Eracleous & Halpern, 2004;
Boroson, 2005; Hu et al., 2008; Komossa et al., 2008; Zhang et al., 2011; Bae
& Woo, 2014). Using high-quality spatially resolved spectra, Crenshaw &
Kraemer (2000) studied the acceleration radial velocity based on the peak of
[O III] emission line and interpreted their results using the AGN-driven
biconical radial outflow model. Using single-aperture spectra, the velocity
offset of the peak of [O III] has been investigated statistically (Zamanov et
al., 2002; Eracleous & Halpern, 2004; Boroson, 2005; Hu et al., 2008). Boroson
(2005) found that more than half of their sources show blueshifted of the [O
III] peaks with respect to the systemic velocity based on other lower
ionization lines. They suggested that the blueshifted $\rm V_{[OIII]}$ may be
governed by AGN-properties such as MBH and Eddington ratio. Interestingly, the
blueshifts of higher ionization lines such as [O III] are larger compared to
that of lower ionization lines, e.g., [O II], [S II], [N II] (Eracleous &
Halpern, 2004; Boroson, 2005; Hu et al., 2008). By using a small sample of
narrow-line Seyfert 1 galaxies with strong blueshifted [O III], Komossa et al.
(2008) found that the velocity shift of the core component of [O III] emission
line ($\rm V_{[OIII,core]}$) shows a moderate correlation with Eddington ratio
and optical Fe II strength. Zhang et al. (2011) found similar results but a
weak correlation between $\rm V_{[OIII,core]}$ and Eddington ratio by using
homogenous samples of radio-quiet Seyfert 1 galaxies. Using a large sample,
$\sim$23,000 type 2 AGNs, Bae & Woo (2014) found that half of their sources
show $\rm V_{[OIII]}$ ¿ 20 km s-1, and the fractions of such $\rm V_{[OIII]}$
in type 1 and type 2 AGNs are similar after considering orientation effects.
In short, the velocity of [O III] emission line does show some offset with
respect to the systemic velocity. Particularly, the core component of [O III]
also shows some offset and has weak or moderate correlations with AGN
properties (e.g., Eddington ratio). It is therefore important that we should
consider analyzing $\rm V_{[OIII]}$ when studying the correlation between
$\rm\sigma_{[OIII,core]}$ and $\sigma_{*}$. $\rm V_{[OIII]}$ with respect to
the systemic velocity may have impacts on the discrepancies between
$\rm\sigma_{[OIII,core]}$ and $\sigma_{*}$.

In general, the correlations between $\rm\sigma_{[OIII,core]}$ and
$\sigma_{*}$ mean that they are tracing the same velocity field of the
gravitational potential. However, there is large scatter in these correlations
and the driving factors for these discrepancies are still unclear. Therefore,
a detailed study using a high S/N spectral sample is necessary for robust
measurements of both $\rm\sigma_{[OIII]}$ and $\sigma_{*}$, and crucial for
understanding the physically driven properties of gas and stellar kinematics
in type 1 AGNs. In particular, for high redshift AGNs, we often utilize
$\rm\sigma_{[OIII]}$ as a surrogate for $\sigma_{*}$ since it is challenging
to measure $\sigma_{*}$ for high redshift objects. It is necessary to have a
proper study for the relations between $\rm\sigma_{[OIII]}$ and $\sigma_{*}$
for high redshift AGNs.

In this paper, we present a detailed comparison between $\rm\sigma_{[OIII]}$
and $\sigma_{*}$ for not only local AGNs but also for high redshift AGNs. For
local AGNs (z $<$ 0.1), the sample from Bennert et al. (2018) with long-slit
and high-quality spatially resolved $\sigma_{*}$ is a suitable sample for
studying the relation between $\rm\sigma_{[OIII]}$ and $\sigma_{*}$ that has
robust measurements of both quantities. In this study, by using the 59 local
AGNs from Bennert et al. (2018), we investigate in detail the discrepancy
between $\rm\sigma_{[OIII]}$ and $\sigma_{*}$ as a function of AGN properties.
Then, we apply the same approach for studying the local sample which has
integrated spectra, observed with a larger aperture size (3$\arcsec$) by SDSS,
including 611 hidden type 1 AGNs from Eun, Woo & Bae (2017). For high redshift
AGNs (0.3 $<$ z $<$ 1.0), we select 18 high S/N Keck spectra (Woo et al.,
2006, 2008) and 52 co-added high S/N spectra from the SDSS Reverberation
Mapping (SDSS-RM) project (Shen et al., 2015). Finally, our sample includes
740 targets at redshift z $<$ 1.0, covering the broad dynamic ranges of
$\mathrm{\lambda L_{5100}\sim 10^{41.5}-10^{46.0}}$ erg s-1and 6.5 $<$
$\log($MBH) $<$ 9.5. The high-quality spectra of this sample enable robust
measurements of $\rm\sigma_{[OIII]}$ and $\sigma_{*}$, hence providing us a
good opportunity for studying in detail the direct relationship between both
components and investigating for the physically driving factors of the
discrepancies between them.

In Section 2, we describe the sample selection. Sections 3 and 4 present the
measurements and results, respectively. The discussions and summary are
presented in Sections 5 and 6, respectively. The following cosmological
parameters are used throughout the paper: $H_{0}=70$ km s-1 Mpc-1,
$\Omega_{\rm m}=0.30$, and $\Omega_{\Lambda}=0.70$.

##  2\. Sample Selection

In this work, we combined the aforementioned low and high redshift samples (z
$<$ 1.0) which allow for robust measurements of $\sigma_{*}$ and the [O III]
emission line widths ($\rm\sigma_{[OIII,core]}$ and
$\rm\sigma_{[OIII,broad]}$) to have a detailed study on the correlations
between gas and stellar kinematics not only for local AGNs but also for high
redshift ones.

Firstly, for the local AGN sample (z $<$ 0.1), we selected 59 targets of
Bennert et al. (2018) which have observed using Low Resolution Imaging
Spectrometer (LRIS, Oke et al., 1995) at the Keck telescope. Those targets
have high S/N spectra which provide robust measurements of spatially resolved
$\sigma_{*}$ within the bulge radius (Harris et al., 2012). In addition, for
studying the relation between $\sigma_{*}$ and $\rm\sigma_{[OIII,core]}$
measured from the integrated SDSS spectra (aperture size 3$\arcsec$), we
utilized 611 hidden type 1 AGNs (hereafter, local SDSS sample) from Eun, Woo &
Bae (2017) which have reliable measurements of $\sigma_{*}$ and
$\rm\sigma_{[OIII,core]}$.

Secondly, for high redshift AGNs (0.3 $<$ z $<$ 1.0), we chose 18 sources from
Woo et al. (2006, 2008). The sample was also observed using LRIS-Keck, and has
high S/N spectra which allowed for subtracting the contamination of AGN
continuum component in the stellar feature, leading to reliable estimation of
$\sigma_{*}$. To enlarge the dynamic range of AGN luminosity, we selected 88
co-added sources with co-added high S/N spectra from the SDSS-RM project (Shen
et al., 2015) which have robust measurements of $\sigma_{*}$. Among them, we
removed 36 sources which have large noisy distortion surrounding the [O III]
and H$\beta$ emission line profiles. Then, the remaining SDSS-RM sample has 52
sources which have reliable determinations of both $\sigma_{*}$ and
$\rm\sigma_{[OIII]}$. In total, we obtained 70 AGNs (hereafter, high redshift
sample) which have a unique broad luminosity dynamic range and are suitable
for studying the relation between $\sigma_{*}$ and $\rm\sigma_{[OIII,core]}$
at redshift 0.3 $<$ z $<$ 1.0. With the advantages of high-quality spectral
sample observed with LRIS-Keck and co-added high S/N SDSS-RM spectra, we carry
out a detailed study of the direct relation between $\sigma_{*}$ and
$\rm\sigma_{[OIII,core]}$ for high redshift AGNs.

Finally, our sample included 740 local and high redshift AGNs, covering the
broad dynamic ranges of $\mathrm{\lambda L_{5100}\sim 10^{41.5}-10^{46.0}}$
erg s-1 and 6.5 $<$ $\log($MBH) $<$ 9.5 (see Section 3.1). Figure 1 shows the
distributions of $\mathrm{M_{\rm BH}}$ and continuum luminosity
$\mathrm{L_{5100}}$ of our sample.

Figure 1.— Distributions of continuum luminosity at 5100 Å (left panel) and
black-hole mass (right panel). The magenta, black, blue, and red histograms
show the distributions of the samples of Eun, Woo & Bae (2017), Bennert et al.
(2018), Woo et al. (2006, 2008), and Shen et al. (2015), respectively.

##  3\. Measurements

###  3.1. Spectral Analysis and AGN property measurements

In our study, we have four different subsamples of Woo et al. (2006, 2008),
Shen et al. (2015), Eun, Woo & Bae (2017) and Bennert et al. (2018). In this
section, we describe the spectral analysis processes of those subsamples to
obtain pure emission spectra for measuring AGN properties.

Similar to 18 targets of Woo et al. (2006, 2008), 59 AGNs from Bennert et al.
(2018) were also observed with LRIS-Keck. So, the data reduction and spectral
analysis of both samples were similar to each other. In our previous work in
Woo et al. (2018), we have updated the multi-component spectral analysis of 18
sources in Woo et al. (2006, 2008) following the proredure of Park et al.
(2015). Similarly, Bennert et al. (2018) also applied the method of Park et
al. (2015) in their spectral analysis. Here, we briefly describe the recipe of
our optical spectral analysis. A model with a combination of the pseudo-
continuum including a single power law and an Fe II component based on the I
Zw 1 Fe II template (Boroson & Green, 1992), as well as a host-galaxy
component adopted from the stellar template of the Indo-US spectral library in
Valdes et al. (2004) was applied to fit the observed optical spectra within
the wavelength ranges of 4430Å $-$ 4770Å and 5080Å $-$ 5450Å. The best-fit
model was determined using the $\chi^{2}$ minimization from MPFIT. After
subtracting the pseudo-continuum from the observed spectra, a sixth order
Gauss-Hermite series was applied to fit the broad component of the H$\beta$
emission line. The narrow component of H$\beta$ was modeled separately by
using the [O III] 5007Å best-fit model. From the best-fit model, we measured
line width ($\rm FWHM_{H\beta}$), line dispersion ($\rm\sigma_{H\beta}$), the
luminosity of the H$\beta$ line ($\rm L_{H\beta}$), and the monochromatic
luminosity at 5100Å ($\rm L_{5100}$). The updated measured properties of 18
targets in Woo et al. (2006, 2008) can be found in Table 1 of Woo et al.
(2018), and the resulting measurements of 59 sources of Bennert et al. (2018)
are shown in Table 1 of Bennert et al. (2015).

For 52 sources from Shen et al. (2015), the authors have provided the co-added
integrated spectra in their public catalog. To obtain the pure emission line
spectra from the provided co-added spectra, we performed multi-component
spectral analysis for 52 SDSS-RM spectra similarly as that for targets
observed with LRIS-Keck. Figure 2 shows an example of multi-component fitting
results for a target from the SDSS-RM sample.

The spectral analysis of the local SDSS sample is presented in detail in
Section 2 of Eun, Woo & Bae (2017). This sample is basically selected from the
type 2 AGN catalog of Bae & Woo (2014). After subtracting the SDSS spectra
from the best-fit stellar population model using the penalized pixel-fitting
code (pPXF, Cappellari & Emsellem, 2004), the authors identified the hidden
type 1 AGNs among the type 2 AGNs based on a careful analysis of the broad
component of H$\alpha$ emission line.

To have a consistent measurement of MBH for all sources in our sample, we
applied the single-epoch method, using the virial theorem and H$\beta$ size-
luminosity relation based on the result of Bentz et al. (2013) (see equation 1
in Le, Woo & Xue, 2020) for calculating MBH for the high redshift sample (Woo
et al., 2006, 2008 and Shen et al., 2015). As in our previous work, we chose
$\rm\sigma_{H\beta}$ and the monochromatic luminosity at 5100Å ($\rm
L_{5100}$) for determining $\rm M_{BH}$ (Le, Woo & Xue, 2020). We used the
virial factor (f = 4.47) from Woo et al. (2015) for the masses based on
$\rm\sigma_{H\beta}$. From MBH measurements, we determined Eddington ratio for
our sample. The bolometric luminosity is calculated from the monochromatic
luminosity at 5100Å ($\rm L_{bol}$ = 10$\times$$\rm L_{5100}$). For MBH
measurements of the local SDSS sample, Eun, Woo & Bae (2017) used the single-
epoch method to determine MBH for their sample using H$\beta$ and H$\alpha$
emission lines. We simply adopted their measurements in our analysis. Figure 3
displays the distributions of MBH, $\rm L_{bol}$, and Eddington ratio for all
subsamples of Bennert et al. (2018), Eun, Woo & Bae (2017), Woo et al. (2006,
2008) and Shen et al. (2015), respectively.

Figure 2.— Example of multi-component fitting result for the SDSS spectrum,
SDSS J141115.19$-$515209.0 from the sample of Shen et al. (2015). The rest-
frame SDSS spectrum is in thick black. The total model (green) includes power-
law continuum (blue), Fe II model (purple), and stellar model (cyan). The
continuum subtracted emission line is displayed in gray and the H$\beta$ line
broad and narrow models are presented in red and pink, respectively.

Figure 3.— Distributions of MBH, $\rm L_{bol}$, and Eddington ratio for those
subsamples of Bennert et al. (2018), Eun, Woo & Bae (2017), Woo et al. (2006,
2008) and Shen et al. (2015), repsectively. The dash lines indicate different
Eddington ratios.

###  3.2. Stellar Velocity Dispersion and Velocity Shift

With the high S/N spectra of our selected sample, $\sigma_{*}$ has been
robustly measured by previous works of Woo et al. (2006, 2008), Shen et al.
(2015), Eun, Woo & Bae (2017), and Bennert et al. (2018). Basically, the
authors used similar approaches for estimating $\sigma_{*}$ by comparing in
the pixel space between the observed spectra and the Gaussian-broadened
stellar template spectra (G and K giants). Therefore, in this work, we simply
adopted those measurements for our analysis. Here, we briefly explain their
measurements.

Woo et al. (2006, 2008) measured $\sigma_{*}$ for their sample by using
stellar absorption lines around Mg b (5175Å) and Fe (5270Å). After subtracting
the AGN Fe emission, the authors compared in the pixel space the pure observed
spectra with five Gaussian-broadened stellar template spectra (G8, G9, K0, K2,
and K5 giants). Then the final $\sigma_{*}$ estimations were based on the
best-fit template.

For SDSS-RM targets, Shen et al. (2015) used the vdispfit package and the
direct-pixel-fitting code Penalized Pixel-Fitting (pPXF) to measure
$\sigma_{*}$. The measurement was obtained within the wavelength range of
4125-5350 Å containing the G band (4304Å), Mg Ib (5167Å, 5173Å, 5184Å), and Fe
(5270Å). Given the advantage of high S/N co-added spectra, the authors
obtained robust measurements for 88 targets among the total of 212 AGNs used
in their sample. We neglected some sources which have noisy distortion
surrounding the H$\beta$ and [O III] emission lines for a reliable comparison
with $\sigma_{*}$. Finally, we selected 52 targets from Shen et al. (2015) in
our study.

Similar to Woo et al. (2006, 2008), Bennert et al. (2018) compared their
observed spectra with the Gaussian-broadened stellar templates of G, K, A0,
and F2 stars from the Indo-US survey within three spectral regions of Ca H and
Ca K (3969Å and 3934Å), Mg Ib (5167Å, 5173Å, 5184Å) and Ca II (8498Å, 8542Å,
8662Å). From the high-quality long-slit spectra of LRIS-Keck, the sample of
Bennert et al. (2018) allowed for the robust measurements of spatially
resolved $\sigma_{*}$ within the bulge radius (obtained from the surface
photometry fitting of SDSS image, Harris et al., 2012).

Finally, for the local SDSS hidden type 1 AGN sample, Eun, Woo & Bae (2017)
used $\sigma_{*}$ available from the MPA-JHU (Abazajian et al., 2009) catalog.
We adopted those $\sigma_{*}$ values in our analysis.

All of the $\sigma_{*}$ used in this work were corrected for the instrumental
resolution of LRIS-Keck ($\sim$58 km s-1) and SDSS ($\sim$65 km s-1),
respectively.

The high S/N spectra of our selected samples also allow us to measure the
stellar absorption line velocity ($\rm V_{*}$) accurately and provide a
reliable systemic velocity for analyzing the kinematics of [O III] emission
line. Therefore, we adopted $\rm V_{*}$ as systemic velocity in this work. We
used the provided $\rm V_{*}$ from Woo et al. (2006, 2008), Shen et al.
(2016), and Eun, Woo & Bae (2017). For 59 targets of Bennert et al. (2018),
since the authors did not provide $\rm V_{*}$, we adopted the measured $\rm
V_{*}$ of this sample (high S/N spectra, 38 sources) from Sexton et al. (2020)
using the SDSS spectra. Sexton et al. (2020) developed the Bayesian
decomposition analysis for SDSS spectra (BADASS) using Python. BADASS is a
powerful fitting package for obtaining all spectral components of SDSS spectra
simultaneously and accurately by utilizing a Markov-Chain Monte Carlo (MCMC)
fitting technique.

###  3.3. Gas Emission Line Kinematics

In this section, we present the fitting model to measure $\rm\sigma_{[OIII]}$
and $\rm V_{[OIII]}$. In addition, we also measure outflow strength
properties, e.g., maximum outflow velocity ($\rm V_{max}$), to study the
effects of outflow strength on the relations between $\rm\sigma_{[OIII]}$ and
$\sigma_{*}$ .

####  3.3.1 Line Width and Line Shift Measurements

Following the results of Bennert et al. (2018), a double Gaussian is the best
approach to fit the [O III] emission line. In this fitting, a Gaussian is
fitted to the narrow (core) component of the [O III] line
($\rm\sigma_{[OIII,core]}$). While, another Gaussian is modeled for the
broader (outflow) component of the [O III] profile ($\rm\sigma_{[OIII,out]}$).
Based on the best-fit model of the [O III] emission line, we calculated the
second moment ($\rm\sigma_{[OIII]}$) as follows:

$\sigma_{\rm[OIII]}^{2}=\frac{\int\lambda^{2}f_{\lambda}d\lambda}{\int
f_{\lambda}d\lambda}-\lambda_{0}^{2},$ (1)

Here, $f_{\lambda}$ is the flux at each wavelength. $\rm\lambda_{0}$ is the
first moment (centroid wavelength) of the emission line which is calculated as
follows:

$\lambda_{0}=\frac{\int\lambda f_{\lambda}d\lambda}{\int
f_{\lambda}d\lambda},$ (2)

In our analysis, after subtracting the pseudo-continuum from the observed
spectra, we also applied a double Gaussian to model the [O III] emission line
for 18 targets of Woo et al. (2006, 2008) and 52 targets of Shen et al.
(2015). However, in some targets, if the peak of the broader component model
of the [O III] emission line is lower than the noise level in the continuum
(i.e., the amplitude peak-to-noise ratio ¡ 3), we discarded the broad
component as noise and used a single Gaussian function to fit the [O III]
profile. Figure 4 presents examples of [O III] fitting models of S06 and SDSS
J141324.28$+$530527.0 from the samples of Woo et al. (2006, 2008) and Shen et
al. (2015), respectively. The measured [O III] dispersions
$\rm\sigma_{[OIII,core]}$ and $\rm\sigma_{[OIII,out]}$ were also corrected for
the instrumental resolution of LRIS-Keck ($\sim$58 km s-1) and SDSS ($\sim$65
km s-1), respectively.

As mentioned in Section 3.2, we adopted $\rm V_{*}$ as the systemic velocity.
We measured the velocity shifts based on the peaks of the core ($\rm
V_{[OIII,core]}$) and the broad ($\rm V_{[OIII,out]}$) components of [O III]
emission line.

Similar to our analysis, Eun, Woo & Bae (2017) used a double Gaussian to model
the [O III] emission line for the local SDSS sample. Section 3.1 of Eun, Woo &
Bae (2017) presents their emission line fitting model in detail. We adopted
the measurements in their provided catalog in our study.

For the 59 targets of Bennert et al. (2018), since the authors did not release
the spectra, we simply adopted their measurements of $\rm\sigma_{[OIII,core]}$
(see Table 1 in Bennert et al., 2018). In addition, we also used the measured
[O II] dispersion from Bennert et al. (2018) for further analysis in Section
4. For the velocity shift measurements, we adopted the measured $\rm
V_{[OIII,core]}$ and $\rm V_{[OIII,out]}$ with respect to the stellar systemic
velocity of this sample from Sexton et al. (2020) using the SDSS spectra.
Among the 59 targets of Bennert et al. (2018), Sexton et al. (2020) measured
$\rm V_{[OIII,core]}$ and $\rm V_{[OIII,out]}$ for 38 targets which show
strong outflow signatures in their [O III] emission line profiles.

Figure 4.— Examples of [O III] 5007Å fitting models for S06 and SDSS
J141324.28$+$530527.0 from the samples of Woo et al. (2006, 2008) and Shen et
al. (2015), respectively. The total model is shown in red. The core component
of [O III] is fitted by a Gaussian model and displayed in pink. The broader
component (blue) is also fitted by a Gaussian function. The dash-line shows
the rest-frame position of [O III] at 5007Å.

####  3.3.2 Maximum Outflow Velocity

$\rm\sigma_{[OIII,out]}$ is often considered as a tracer of outflow signatures
in AGNs (e.g., Greene & Ho, 2005, Bae & Woo, 2014, Woo et al., 2016, Le et
al., 2017). In our analysis, we determined the outflow strengths of our sample
such as $\rm\sigma_{[OIII,out]}$ and $\rm V_{max}$.

Following the relation from Harrison et al. (2014), we determined $\rm
V_{max}$ from the [O III] fitting models of our sample as follows:

$\rm V_{max}=\rm\Delta V+\rm\frac{W_{80}}{2},$ (3)

$\rm\Delta V$ is the measured velocity offset of the broader component with
respect to that of the core component of the [O III] emission line. A negative
value of $\rm\Delta V$ means that the broad component is blueshifted, while a
positive value shows the redshifted offset. $\rm W_{80}$ presents the width of
80$\%$ of the Gaussian flux of the broad component of [O III] emission line,
$\rm W_{80}$ $=$ 1.09 $\times$ $\rm FWHM_{[OIII,out]}$.

Since we do not have the spectra for 59 targets of Bennert et al. (2018), we
adopted the measured outflow velocities of this sample from Sexton et al.
(2020) using the SDSS spectra.

For the samples of Woo et al. (2006, 2008), Shen et al. (2015), and Eun, Woo &
Bae (2017), we measured $\rm V_{max}$ for 262 sources which show the broad
components in the [O III] profiles. Totally, we measured $\rm V_{max}$ for 300
sources in our sample. Table 1 shows the targets and measured properties for
the sample of Woo et al. (2006, 2008) and Shen et al. (2015).

Following the assumption of uncertainties from Bennert et al. (2018), we
adopted 0.4 dex for the uncertainty of black-hole mass measurements. For other
measured properties, we applied 0.04 dex as the uncertainties.

##  4\. Results

In this section, we study the direct relation between the gas emission line
widths ($\rm\sigma_{[OIII,core]}$ and $\rm\sigma_{[OII]}$), and
$\rm\sigma_{*}$. For a detailed study of the difference between those
components, we compared the ratios of $\rm\sigma_{[OIII,core]}$$/$$\sigma_{*}$
and $\rm\sigma_{[OII]}$$/$$\sigma_{*}$ as a function of AGN properties such as
black-hole mass, bolometric luminosity, Eddington ratio, and $\rm\sigma_{*}$.
In addition, we also examined the effects of outflow strength (e.g., $\rm
V_{max}$) and velocity shifts ($\rm V_{[OIII,core]}$ and $\rm V_{[OIII,out]}$)
on the discrepancies between $\rm\sigma_{[OIII,core]}$ and $\rm\sigma_{*}$.

###  4.1. Gas Emission Line Width vs. Stellar Velocity Dispersion

Figure 5 shows the comparison between $\rm\sigma_{*}$ and the gas emission
line-widths of $\rm\sigma_{[OIII,core]}$ and $\rm\sigma_{[OII]}$. The local
sample from Bennert et al. (2018) is a proper sample to study the direct
relations between gas emission line widths and $\rm\sigma_{*}$ because those
targets have the long-slit high-quality spatially resolved spectra which allow
for robust measurements of $\rm\sigma_{[OIII,core]}$, $\rm\sigma_{[OII]}$ and
$\rm\sigma_{*}$. In Figure 5, we found $\rm\sigma_{[OIII,core]}$ and
$\sigma_{*}$ are correlated with a scatter of 0.11 dex. Similarly,
$\rm\sigma_{[OII]}$ and $\sigma_{*}$ show a correlation with a scatter of 0.12
dex. There are three outliers whose double Gaussian model fitting cannot
resolve the [O II] doublet emission lines (3726Å, 3729Å), leading to
overestimation of $\rm\sigma_{[OII]}$ (see Section 4.3 of Bennert et al.,
2018). In the comparison, we displayed our sample color-coded according to
$\rm L_{bol}$. We found that the relation between $\rm\sigma_{[OIII,core]}$,
$\rm\sigma_{[OII]}$ and $\sigma_{*}$ is better correlated for those low
luminosity objects than for higher luminosity sources. When the luminosities
of targets increase, the scatters of the correlations between
$\rm\sigma_{[OIII,core]}$, $\rm\sigma_{[OII]}$ and $\sigma_{*}$ also grow.

As the aperture size of SDSS is 3$\arcsec$, the integrated spectra of SDSS
cover a radius size of $\sim$2.5 kpc of the center of the galaxies with
redshift z $\sim$ 0.1. For the higher redshift sample, the SDSS radius size
includes $\sim$3.3-7.8 kpc within redshift of z $\sim$ 0.2-1.0. Woo et al.
(2006, 2008) extracted their LRIS-KECK spectra within 4-5 pixels (1$\arcsec$,
$\sim$3-5 kpc at redshift z $\sim$ 0.3-0.5). Since the aperture size of SDSS
is large, it is hard to judge whether the measurements of $\rm\sigma_{*}$ and
$\rm\sigma_{[OIII,core]}$ are within the bulge radius or also have
contribution from the disk component of the galaxy. Without spatially resolved
spectra, it is difficult to check the true measurements of $\rm\sigma_{*}$ and
$\rm\sigma_{[OIII,core]}$. We will discuss further this issue in Section 5
that our measurements are reliable within uncertainties. In this section, we
simply check the comparison between $\rm\sigma_{*}$ and
$\rm\sigma_{[OIII,core]}$ for the local SDSS sample and high redshift sources
(Figure 5). Due to the limitation of S/N, we did not obtain
$\rm\sigma_{[OII]}$ for those sources. For the local SDSS sample, we found
that $\rm\sigma_{[OIII,core]}$ and $\sigma_{*}$ show a correlation with a
scatter of 0.12 dex. This result is consistent with that of the high S/N long-
slit spatially resolved spectral sample of Bennert et al. (2018). For the high
redshift targets, the correlation displays a scatter of 0.16 dex, indicating a
large discrepancy in the relation between $\rm\sigma_{*}$ and
$\rm\sigma_{[OIII,core]}$ for high redshift sources. Similar to the local SDSS
sample, the low luminosity high redshift sources have smaller scatters between
$\rm\sigma_{*}$ and $\rm\sigma_{[OIII,core]}$ compared to that of higher
luminosity sources.

Figure 5.— Top panels: Comparison between $\rm\sigma_{*}$ and
$\rm\sigma_{[OIII,core]}$ (left panel) and $\rm\sigma_{[OII]}$ (right panel)
for the sample of Bennert et al. (2018), respectively. Bottom panels:
Comparison between $\rm\sigma_{*}$ and $\rm\sigma_{[OIII,core]}$ for the local
SDSS sample (Eun, Woo & Bae, 2017) and high redshift targets of Woo et al.
(2006, 2008) and Shen et al. (2015). $\rm L_{bol}$ color-scale is displayed.
The dash-line shows the one-to-one relation.

###  4.2. Gas and Stellar Kinematics vs. AGN Properties

For studying the relation between gas emission line width and $\sigma_{*}$ in
more detail, we explored the differences between $\rm\sigma_{[OIII,core]}$ and
$\sigma_{*}$ as a function of AGN properties.

Figure 6 shows the comparisons between
$\rm\sigma_{[OIII,core]}$$/$$\sigma_{*}$ and $\rm M_{BH}$, $\rm
L_{bol}/L_{Edd}$, $\rm L_{bol}$ and $\sigma_{*}$ for the long-slit spatially
resolved spectral sample of Bennert et al. (2018). The logrithmic scale ratio
of $\rm\sigma_{[OIII,core]}$$/$$\sigma_{*}$ is broadened, $\sim$-0.3$-$0.3
within a range of $\log\sigma_{*}$ = 1.8$-$2.6 (i.e., 60$-$400 km s-1). We
found that the good correlation with small scatter is shown between
$\rm\sigma_{[OIII,core]}$ and $\sigma_{*}$ for those targets which have small
MBH and low $\rm L_{bol}$ i.e., $\rm\log(L_{bol}$) $<$ $\sim$43.5. While, the
scatter is significantly broader when MBH and $\rm L_{bol}$ of targets
increase. In addition, we also found that for those targets which have higher
$\rm L_{bol}/L_{Edd}$, $\rm\sigma_{[OIII,core]}$ tends to be larger than
$\sigma_{*}$. Similar to the case of [O III] emission line, we found the good
correlation between $\rm\sigma_{[OII]}$ and $\sigma_{*}$ for those targets
which have small MBH and low $\rm L_{bol}$. As $\rm L_{bol}/L_{Edd}$
increases, $\rm\sigma_{[OII]}$$/$$\sigma_{*}$ also grows (see Figure 7).

Figure 8 presents the comparisons of $\rm\sigma_{[OIII,core]}$ and
$\sigma_{*}$ for the local SDSS sample. We found that those sources with low
$\rm L_{bol}$ show the good correlation, while high bolometric luminosity
sources show large discrepancy ($\sim$-0.4$-$0.4). Similar to the case of the
long-slit spatially resolved sample of Bennert et al. (2018),
$\rm\sigma_{[OIII,core]}$$/$$\sigma_{*}$ tends to increase as $\rm
L_{bol}/L_{Edd}$ increases. Also, for those targets which have larger MBH and
higher $\rm L_{bol}$, $\rm\sigma_{[OIII,core]}$$/$$\sigma_{*}$ tends to be
smaller when $\rm L_{bol}/L_{Edd}$ are low in those targets.

In the case of the high redshift sample, the scatter is large between
$\rm\sigma_{[OIII,core]}$ and $\sigma_{*}$ ($\sim$-0.4$-$0.4). Similar to the
local objects, the low bolometric luminosity sources show small scatters
between $\rm\sigma_{[OIII,core]}$ and $\sigma_{*}$ compared to those high
luminosity sources. And, for sources which have higher $\rm L_{bol}/L_{Edd}$,
$\rm\sigma_{[OIII,core]}$$/$$\sigma_{*}$ tends to be larger (see Figure 9).

The large scatters for those high bolometric luminosity objects may indicate
the difficulty in the measurement of $\rm\sigma_{*}$ for sources with large
contribution of AGN emission in the center or may also illustrate an
additional significant effect which broadens the [O III] emission profile
(e.g., outflows), leading to large uncertainty in measuring the gravitational
component such as $\rm\sigma_{[OIII,core]}$ in the [O III] profile.
Particularly, $\rm L_{bol}/L_{Edd}$ seems to play an important role in the
relations between NLR gas and stellar velocity dispersions.

Figure 6.— Difference between $\rm\sigma_{[OIII,core]}$ and $\rm\sigma_{*}$ as
a function of AGN properties, i.e., $\rm M_{BH}$, $\rm L_{bol}/L_{Edd}$, $\rm
L_{bol}$, and $\rm\sigma_{*}$ for the sample of Bennert et al. (2018). The
color-scale is indicated in each color map panel. The dash-line shows the one-
to-one relation.

Figure 7.— Difference between $\rm\sigma_{[OII]}$ and $\rm\sigma_{*}$ as a
function of AGN properties, i.e., $\rm M_{BH}$, $\rm L_{bol}/L_{Edd}$, $\rm
L_{bol}$, and $\rm\sigma_{*}$ for the sample of Bennert et al. (2018). The
color-scale is indicated in each color map panel. The dash-line shows the one-
to-one relation.

Figure 8.— Same as Figure 6 but for the local SDSS sample of Eun, Woo & Bae
(2017).

Figure 9.— Same as Figure 6 but for the high redshift sample of Woo et al.
(2006, 2008) and Shen et al. (2015).

###  4.3. Gas and Stellar Kinematics vs. Velocity Shifts and Outflow Strengths

To study the driving factor of the discrepancy between
$\rm\sigma_{[OIII,core]}$ and $\rm\sigma_{*}$, we compared the ratio
$\rm\sigma_{[OIII,core]}$$/$$\sigma_{*}$ with [O III] velocity shifts ($\rm
V_{[OIII,core]}$ and $\rm V_{[OIII,out]}$) and outflow strengths such as $\rm
V_{max}$ and $\rm\sigma_{[OIII,out]}$.

Figure 10 presents the comparison between $\rm V_{[OIII,core]}$ and $\rm
V_{[OIII,out]}$ with respect to the systemic velocity as a function of $\rm
M_{BH}$ and $\rm L_{bol}$. For the sources which have low $\rm M_{BH}$ and
$\rm L_{bol}$, $\rm V_{[OIII,core]}$ and $\rm V_{[OIII,out]}$ are small. And,
for the sources which have higher $\rm M_{BH}$ and $\rm L_{bol}$, $\rm
V_{[OIII,core]}$ and $\rm V_{[OIII,out]}$ tend to be larger with large
scatter. Interestingly, the line shifts of the broad component of [O III] show
blueshifted with an average velocity of $-$135$\pm$150 km s-1; while, the line
shifts of the core component display a smaller offset with an average velocity
of $-$14$\pm$47 km s-1. This result may indicate that the kinematics of the
core component of [O III] and stellar absorption lines are quite close to each
other, but the offsets become larger for higher $\rm M_{BH}$ and $\rm L_{bol}$
sources which have stronger outflow signatures (with larger $\rm
V_{[OIII,out]}$).

In Figure 10, we also show the comparison between $\rm V_{max}$, $\rm M_{BH}$
and $\rm L_{bol}$. $\rm V_{max}$ indicates the maximum strength of the outflow
component in the [O III] profile. It shows how large offset of the broad
component compared to that of the core component of the [O III] emission line.
We found that when $\rm L_{bol}$ increases, $\rm V_{max}$ also grows. For
those targets which have small $\rm M_{BH}$ and low $\rm L_{bol}$, $\rm
V_{max}$ is low. In contrast, $\rm V_{max}$ tends to be larger for objects
which have higher $\rm M_{BH}$ and higher $\rm L_{bol}$. This result may
indicate that the AGN accretion plays a major role in outflow physical
properties.

Figure 11 shows the comparison of $\rm\sigma_{[OIII,core]}$-$\sigma_{*}$ with
$\rm V_{max}$, $\rm\sigma_{[OIII,out]}$, $\rm V_{[OIII,core]}$ and $\rm
V_{[OIII,out]}$, respectively. We found that when $\rm V_{max}$ increases, the
discrepancy between $\rm\sigma_{[OIII,core]}$ and $\rm\sigma_{*}$ tends to be
larger. Similarly, as $\rm\sigma_{[OIII,out]}$ is larger, the difference
between $\rm\sigma_{[OIII,core]}$ and $\rm\sigma_{*}$ is also larger; when
$\rm V_{[OIII,core]}$ and $\rm V_{[OIII,out]}$ increase, the difference
between $\rm\sigma_{[OIII,core]}$ and $\rm\sigma_{*}$ also grows.

The difference between $\rm\sigma_{[OIII,core]}$ and $\rm\sigma_{*}$ is well
connected with $\rm V_{max}$, $\rm\sigma_{[OIII,out]}$, $\rm V_{[OIII,core]}$
and $\rm V_{[OIII,out]}$. This result may indicate that outflows play a
significant role in the discrepancy between $\rm\sigma_{[OIII,core]}$ and
$\rm\sigma_{*}$.

##  5\. Discussions

###  5.1. Outflow Strength Effect

The main question in our work is: what are the physically driven factors for
the scatters between ionized gas kinematics in the NLR and stellar velocity
dispersions? If we assume that the gas kinematics in the NLR is governed by
the gravitational potential of the bulge of the host galaxy, then we expect
that the velocity field of NLR emission lines should trace the same velocity
field as that of the stellar velocity dispersions. However, from previous
studies, many authors found that $\rm\sigma_{[OIII]}$ and $\sigma_{*}$ show
correlations but with large scatters. So, what are the factors for these
substantial scatters between $\rm\sigma_{[OIII]}$ and $\sigma_{*}$? As
discussed in Greene & Ho (2005), the authors found that there is a strong
correlation between the $\rm\sigma_{[OIII]}$$/$$\sigma_{*}$ ratio as a
function of Eddington ratio, indicating that the gas kinematics of the NLR is
not also governed by the primary role of the gravitational potential of the
bulge but also followed by a secondary role of AGN activity such as outflows.
Similar to Greene & Ho (2005), Ho (2009) found the same conclusion by
analyzing the line width of the [N II] emission line. Later on, in the study
of narrow-line Seyfert 1 sample, Komossa & Xu (2007) found that after
correcting for the wing component in the [O III] profile, there is consistency
between $\rm\sigma_{[OIII]}$ and $\sigma_{*}$. However, is there any caution
in the validity of using $\rm\sigma_{[OIII,core]}$ as a surrogate for
$\sigma_{*}$? To test this question, Bennert et al. (2018) used high-quality
long-slit spatially resolved spectra from a sample of 52 Seyfert 1 galaxies to
have a direct and simultaneous comparison between $\rm\sigma_{[OIII,core]}$
and $\sigma_{*}$. They found the large discrepancy in the comparison between
object and object. So, even we use $\rm\sigma_{[OIII,core]}$ to replace
$\sigma_{*}$, there is a large uncertainty to be considered.

In our study, we found the broad correlations with large scatters between
$\rm\sigma_{[OIII,core]}$ and $\sigma_{*}$ for the local SDSS sample of Eun,
Woo & Bae (2017). For the high redshift sample from Woo et al. (2006, 2008)
and Shen et al. (2015), the correlation shows somewhat larger scatter compared
to that of the local SDSS sample. By comparing the differences between
$\rm\sigma_{[OIII,core]}$ and $\rm\sigma_{*}$ as a function of AGN properties,
we found that $\rm\sigma_{[OIII,core]}$ and $\rm\sigma_{*}$ show small scatter
in those targets which have low $\rm L_{bol}$. However, the scatter increases
when $\rm L_{bol}$ grows. Particularly, we found that when $\rm
L_{bol}/L_{Edd}$ increases, $\rm\sigma_{[OIII,core]}$ tends to be larger than
$\rm\sigma_{*}$.

In addition, we also tested the effects of velocity shifts ($\rm
V_{[OIII,core]}$ and $\rm V_{[OIII,out]}$) and outflow strengths
($\rm\sigma_{[OIII,out]}$ and $\rm V_{max}$) on the scatter between
$\rm\sigma_{[OIII,core]}$ and $\sigma_{*}$. In Figures 10 and 11, we found
that $\rm V_{[OIII,core]}$, $\rm V_{[OIII,out]}$, and $\rm V_{max}$ are
connected with MBH and $\rm L_{bol}$. As expected, we found that the
discrepancy between $\rm\sigma_{[OIII,core]}$ and $\rm\sigma_{*}$ is also
connected with $\rm V_{[OIII,core]}$ and $\rm V_{[OIII,out]}$, as well as $\rm
V_{max}$ and $\rm\sigma_{[OIII,out]}$.

We also perform a Spearman’s rank-order correlation to test the relationships
between [O III] vs. stellar kinematics and AGN properties. Table 2 shows the
Spearman’s rank-order coefficients (r) and the p-values of the null hypothesis
that the two quantities are not correlated. We found that the discrepancy
between $\rm\sigma_{[OIII,core]}$ and $\rm\sigma_{*}$ has mild correlations
with Eddington ratio (r = 0.16) and $\rm V_{max}$ (r = 0.17). The correlations
are stronger when compared with the broad component of [O III] such as
$\rm\sigma_{[OIII,out]}$ (r = 0.31) and $\rm V_{[OIII,out]}$ (r = $-$0.33).
And, we also found that in comparison with $\rm\sigma_{[OIII,core]}$ and
$\rm\sigma_{*}$, the discrepancy between $\rm\sigma_{[OIII,out]}$ and
$\rm\sigma_{*}$ has a stronger correlation with outflow strengths such as
Eddington ratio (r = 0.25) and $\rm V_{max}$ (r = 0.80). In addition, there
are mild correlations when comparing the discrepancy between $\rm
V_{[OIII,core]}$ and $\rm V_{*}$ with Eddington ratio (r = $-$0.24),
$\rm\sigma_{[OIII,out]}$ (r = $-$0.20), and $\rm V_{max}$ (r = 0.06). In the
case of $\rm V_{[OIII,out]}$ and $\rm V_{*}$, the correlations tend to be
stronger with Eddington ratio (r = $-$0.29), $\rm\sigma_{[OIII,out]}$ (r =
$-$0.34), and $\rm V_{max}$ (r = 0.46). Our results for the correlations
between velocity shifts and Eddington ratio are in agreement with that of
Zhang et al. (2011). By using homogenous samples of 383 radio-quiet Seyfert 1
galaxies, they also found that there are weak correlations between $\rm
V_{[OIII,core]}$ and $\rm V_{[OIII,out]}$ with AGN properties such as $\rm
L_{5100}$, MBH, and Eddington ratio. They interpreted results that although
AGN activities are responsible for launching initial outflows, the surrounding
interstellar medium (ISM) environment (e.g., density profile) may also have an
impact on the later speed of outflow gas after their launch, and this may lead
to the diversity of [O III] properties in AGNs.

Figure 10.— Comparison between $\rm M_{BH}$ and $\rm V_{[OIII,core]}$ $-$ $\rm
V_{*}$ (top panel), $\rm M_{BH}$ and $\rm V_{[OIII,out]}$ $-$ $\rm V_{*}$
(middle panel), and $\rm M_{BH}$ and $\rm V_{max}$ (bottom panel). The color
scale is displayed for $\rm L_{bol}$. The samples of Bennert et al. (2018),
Eun, Woo & Bae (2017), Woo et al. (2006, 2008), and Shen et al. (2015) are
plotted as circle, star, square, and triangle symbols, respectively. The
vertical dashed lines indicate the mean velocity shifts.

Our results are consistent with those of Greene & Ho (2005) and Ho (2009) that
although gas kinematics of the NLR mainly follows the gravitational potential
of the bulge of the host galaxy, AGN activities such as outflows may also have
impact on the gas kinematics of the NLR. For those targets with high $\rm
L_{bol}$, we expect that the AGN activity is high, and there may be strong
outflows acting on the gas kinematics of the NLR, leading to the large scatter
between $\rm\sigma_{[OIII,core]}$ and $\rm\sigma_{*}$. As discussed in Ho
(2009), the kinematics of the NLR emission gas and stars are expected to be
similar if both quantities are governed by the bulge gravitational potential.
In the cases that the gas and stars suffer collisional hydrodynamic drags by
the surrounding ISM, we may expect to see the results that the gas velocity
dispersions are lower than that of the stars. However, if there is additional
action from the AGN activity (i.e., outflows) on the relations between the gas
and stars, the additional energy may accelerate the gas, then lead to the
results that the gas velocity dispersions are comparable or larger than that
of the stars.

Figure 11.— Difference between $\rm\sigma_{[OIII,core]}$ and $\rm\sigma_{*}$
as a function of $\rm\sigma_{[OIII,out]}$ (top left), $\rm V_{max}$ (top
right), $\rm V_{[OIII,out]}$ \- $\rm V_{*}$ (bottom left), and $\rm
V_{[OIII,core]}$ \- $\rm V_{*}$ (bottom right). The samples of Bennert et al.
(2018), Eun, Woo & Bae (2017), Woo et al. (2006, 2008), and Shen et al. (2015)
are plotted as circle, star, square, and triangle symbols, respectively.

###  5.2. The Limitation of Double Gaussian Approach

Regarding the large scatters between $\rm\sigma_{[OIII,core]}$ and
$\sigma_{*}$ for high luminosity objects, we may need to consider the details
of measurement of the [O III] line width. As suggested by previous studies
(e.g., Greene & Ho, 2005, Bennert et al., 2018), a double Gaussian is the best
choice for fitting the [O III] profile and $\rm\sigma_{[OIII,core]}$ could be
used as a surrogate for $\sigma_{*}$. But what is the true value of the gas
kinematics following the gravitational potential of the stars and not
disturbed by outflow effects? We have simply assumed the correction by
removing the wing component in the [O III] profile. But for those high
luminosity AGNs in which the fraction of AGN accretion is large, the
measurement of the true $\rm\sigma_{[OIII,core]}$ as a surrogate for
$\sigma_{*}$ may have high uncertainty even when we have corrected for non-
gravitational effects by removing the broad wing component in the [O III]
profile.

In general, we suggest that it should be cautionary to use
$\rm\sigma_{[OIII,core]}$ as a surrogate for $\sigma_{*}$ for individual
sources (particularly for high luminosity AGNs). The replacement of
$\rm\sigma_{[OIII,core]}$ for $\sigma_{*}$ could be applied for statistical
studies albeit with large scatters.

###  5.3. Aperture and Rotational Broadening Effects

Both gas and stellar velocity dispersions may vary with different extraction
radius measurements. As we mentioned in Section 4.1, within the large aperture
size of SDSS (3$\arcsec$), the extracted spectra of SDSS cover a size of
$\sim$5.4 kpc in the center of the galaxy at redshift z $\sim$ 0.1. For the
higher redshift sample at z $\sim$ 0.3-1.0, the radius size covers
$\sim$3.3-7.8 kpc in the center of the galaxy. Within the large aperture size,
it may be possible that integrated spectra of SDSS may not only extract the
region within the bulge radius of the galaxy but also contain the disk
component of the galaxy, then overestimate the measured velocity dispersion.
Therefore, it is important to check whether the measurements of
$\rm\sigma_{*}$ are well extracted within the bulge radius of the galaxy.
Similarly, for the gas emission line, we should check whether the extraction
radius for the [O III] emission is well defined within the NLR or not.

Greene & Ho (2005) examined the extraction aperture size of SDSS for their
study based on the local type 2 AGN sample. By using the relation between the
NLR radius and the [O III] luminosity, they estimated that the typical size of
the NLR for their objects at z $=$ 0.1 is $\sim$0.25-1.2 kpc within the
angular size of $\sim$0.14$\arcsec$-0.67$\arcsec$. This angular size is well
defined within the SDSS aperture size. Following their method, we estimated
the NLR size for our local SDSS and high redshift samples by using the size-
luminosity relation (e.g., Bae et al., 2017, Le et al., 2017). Based on the
bolometric luminosity of our sample, we estimated the [O III] luminosity of
our local SDSS and high redshift samples to be in the range of
$\mathrm{L_{OIII}\sim 10^{41.5}-10^{43}}$ erg s-1($\rm L_{bol}=700\times
L_{OIII}$, LaMassa et al., 2009). This luminosity range corresponds to the
physical size of $\sim$0.25-3.5 kpc, well defined within the SDSS aperture
size at redshift of z $\sim$ 0.1-1.0. Therefore, the measurements of the
$\rm\sigma_{[OIII]}$ of our local and high redshift SDSS samples are well
defined within the NLR.

As for the extraction size of $\sigma_{*}$, as discussed by Greene & Ho
(2005), using the fundamental plane relation from Bernardi (2003), a median
$\rm\sigma_{*}$ of 150 km s-1 corresponds to an effective radius of $\sim$4.5
kpc. For the local SDSS sample, the integrated spectra of SDSS cover the size
of $\sim$5.4 kpc at redshift of z $\sim$ 0.1. Therefore, for the local SDSS
sample, the extraction size of $\rm\sigma_{*}$ is well defined within the size
of the bulge of the galaxy. For the high redshift sample, the SDSS radius size
includes $\sim$3.3-7.8 kpc at redshift of z $\sim$ 0.2-1.0. For the sample at
high redshift z $>$ 0.5, the measurements of $\rm\sigma_{*}$ contain the light
from both the bulge and disk components (see Section 4 in Shen et al., 2015),
we expect that this may lead to the large scatters between
$\rm\sigma_{[OIII,core]}$ and $\rm\sigma_{*}$ for the high redshift AGNs. As
mentioned in Shen et al. (2015), rotational velocity could bias their measured
$\rm\sigma_{*}$ ($<$16$\%$).

Greene & Ho (2005) checked the effect of rotational broadening in their
sample. Based on their analysis, rotational broadening effect could
overestimate the observed gas and stellar velocity dispersions in their sample
by $\sim$12-15$\%$ at z $\sim$ 0.1. Accordingly, we expect that the rotational
broadening effect could bias our measured gas and stellar velocity dispersions
but with small fractions compared to the large scatters between
$\rm\sigma_{[OIII,core]}$ and $\rm\sigma_{*}$.

For the local SDSS sample, Eun, Woo & Bae (2017) classified 221 spiral
galaxies among 611 objects in their sample. Based on the minor-to-major axis
ratio (b/a) obtained from the SDSS-DR7, those sources are classified into
face-on (b/a $>$ 0.5) and edge-on (b/a $<$ 0.5) spiral galaxies. Figure 12
shows the comparison of $\rm\sigma_{[OIII,core]}$ and $\rm\sigma_{*}$ for the
221 spiral galaxies from the local SDSS sample. Interestingly, for those edge-
on targets, we found that $\rm\sigma_{*}$ is on average ($\sim$50 km s-1)
larger than $\rm\sigma_{[OIII,core]}$. While for those face-on sources,
$\rm\sigma_{[OIII,core]}$ and $\sigma_{*}$ are comparable with a scatter of
$\sim$0.12 dex. Eun, Woo & Bae (2017) found that $\sigma_{*}$ for edge-on
targets may be overestimated due to the contribution of the rotational
velocity of the disk galaxy. In addition, for those face-on targets, the
rotational velocity is relatively small compared to that of the edge-on
objects. This may explain why $\sigma_{*}$ is larger than
$\rm\sigma_{[OIII,core]}$ for those edge-on spiral galaxies in the local SDSS
sample. Also, the rotational broadening effect may contribute less to the
velocity dispersions of the NLR gas than to $\sigma_{*}$.

Figure 12.— Comparison between $\rm\sigma_{*}$ and $\rm\sigma_{[OIII,core]}$
for the local SDSS sample (z $<$ 0.1) of Eun, Woo & Bae (2017). The red
symbols indicate edge-on targets (b/a ¡ 0.5), while, face-on targets are shown
in blue symbols (b/a ¿ 0.5).

##  6\. Summary

We constructed our sample based on four different samples at redshift z $<$
1.0. For local AGNs (z $<$ 0.1), we selected 59 high-quality long-slit Keck
spectra (Bennert et al., 2018) and 611 local hidden type 1 SDSS spectra of
Eun, Woo & Bae (2017). For the higher redshift sample (0.3 $<$ z $<$ 1.0), we
chose the sample which is based on 18 high S/N Keck spectra (Woo et al., 2006,
2008) and 52 co-added high S/N spectra from the SDSS-RM project (Shen et al.,
2015). Consequently, our sample has the broad dynamic range of
$\mathrm{\lambda L_{5100}\sim 10^{41.5}-10^{46.0}}$ erg s-1and 6.5 $<$
$\log($MBH) $<$ 9.5. In addition, the high S/N spectra of our sample allow us
to achieve reliable measurements for $\sigma_{*}$ and $\rm\sigma_{[OIII]}$. We
took advantage of this unique sample to test the validity of using
$\rm\sigma_{[OIII,core]}$ as a surrogate for $\sigma_{*}$ not only for local
AGNs but also for high redshift AGNs. We summarize our main results as
follows:

(1) From the comparisons of $\sigma_{*}$ and $\rm\sigma_{[OIII,core]}$, we
found the broad correlation between $\rm\sigma_{[OIII,core]}$ and $\sigma_{*}$
with a scatter of 0.11 dex for the local objects, while, the scatter is
somewhat larger for the high redshift targets, being $\sim$0.16 dex.

(2) We found that $\rm\sigma_{[OIII,core]}$ and $\sigma_{*}$ are well
correlated for the low luminosity objects, while, for the targets which have
higher luminosity ranges, the scatters of correlation between
$\rm\sigma_{[OIII,core]}$ and $\sigma_{*}$ become larger.

(3) We found that the Eddington ratio plays an important role in the
differences between $\rm\sigma_{[OIII,core]}$ and $\sigma_{*}$. For the
targets which have high Eddington ratios, $\rm\sigma_{[OIII,core]}$ tends to
be larger than $\sigma_{*}$. Also, we found that outflow strengths (i.e., $\rm
V_{max}$, $\rm V_{[OIII,out]}$, and $\rm\sigma_{[OIII,out]}$) have significant
effects on the differences between $\rm\sigma_{[OIII,core]}$ and $\sigma_{*}$.
The discrepancies between $\rm\sigma_{[OIII,core]}$ and $\sigma_{*}$ are
larger when $\rm V_{max}$, $\rm V_{[OIII,out]}$, and $\rm\sigma_{[OIII,out]}$
increase.

(4) For the local SDSS sample, $\sigma_{*}$ is on average larger than
$\rm\sigma_{[OIII,core]}$ for the edge-on spiral galaxies. The result may
indicate that the rotational broadening effect has large contribution to
$\sigma_{*}$ compared to $\rm\sigma_{[OIII]}$.

Our results show that the Eddington ratios and outflow strengths may have
significant effects on the discrepancies between the gas and stellar
kinematics in AGNs. Therefore, using $\rm\sigma_{[OIII,core]}$ as a surrogate
for $\sigma_{*}$ should be adopted with caution, and the validity of using
$\rm\sigma_{[OIII,core]}$ to replace $\sigma_{*}$ is warranted only for the
low luminosity AGNs.

We thank the anonymous referee for valuable suggestions and comments, which
improved the paper. We thank Prof. Jong-Hak Woo and Ashraf Ayubinia for
thoughtful discussions. This work has been supported by the National Natural
Science Foundation of China (NSFC-12003031, NSFC-11890693, NSFC-12025303,
NSFC-12203047), National Key R&D Program of China No. 2022YFF0503401, the K.C.
Wong Education Foundation, and the science research grants from the China
Manned Space Project with NO. CMS-CSST-2021-A06. H. A. N. Le acknowledges the
support from the ”Fundamental Research Funds for the Central Universities”.

Table 1Targets and Measured Properties

Target | z | $\rm\lambda L_{5100}$ | $\rm\sigma_{H\beta}$ | $\rm\log(M_{BH})$ | $\rm\sigma_{*}$ | $\rm\sigma_{[OIII,core]}$ | $\rm\sigma_{[OIII,out]}$ | $\rm V_{max}$ | $\rm V_{[OIII,core]}$ | $\rm V_{[OIII,out]}$ | S/N
---|---|---|---|---|---|---|---|---|---|---|---
|  | ($\rm 10^{44}\ erg~{}s^{-1}$) | ($\rm km~{}s^{-1}$) | ($\rm M_{\odot}$) | ($\rm km~{}s^{-1}$) | ($\rm km~{}s^{-1}$) | ($\rm km~{}s^{-1}$) | ($\rm km~{}s^{-1}$) | ($\rm km~{}s^{-1}$) | ($\rm km~{}s^{-1}$) |
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11) | (12)
S01……………………… | 0.3590 | 1.37 | 2194 | 8.22 | 132 | 121 | 314 | -500 | -62 | -368 | 72
S04……………………… | 0.3579 | 1.19 | 1749 | 7.99 | 186 | 180 | 466 | 1196 | -8 | -8 | 46
S05……………………… | 0.3530 | 2.23 | 3333 | 8.70 | 132 | 118 | 391 | -850 | 81 | -72 | 119
S06……………………… | 0.3684 | 1.10 | 1413 | 7.79 | 169 | 143 | 412 | -944 | -2 | -117 | 31
S07……………………… | 0.3517 | 1.81 | 2547 | 8.42 | 145 | 175 | 423 | -934 | 22 | -208 | 105
S08……………………… | 0.3585 | 1.59 | 1217 | 7.75 | 187 | 138 | 303 | -586 | -97 | -288 | 54
S09……………………… | 0.3542 | 1.76 | 1748 | 8.08 | 187 | 115 | 181 | 581 | -62 | 52 | 39
S11……………………… | 0.3558 | 1.57 | 1354 | 7.84 | 127 | 137 | 242 | -467 | -88 | -241 | 115
S12……………………… | 0.3574 | 1.82 | 4256 | 8.87 | 173 | 130 | 579 | -1327 | 175 | -207 | 40
S23……………………… | 0.3511 | 1.78 | 4251 | 8.86 | 172 | 145 | 416 | -990 | -2 | -120 | 106
S24……………………… | 0.3616 | 1.49 | 2635 | 8.40 | 214 | 141 | 241 | -161 | -10 | -466 | 103
S26……………………… | 0.3691 | 0.83 | 1914 | 7.99 | 128 | 101 | 302 | -661 | -20 | -134 | 50
S28……………………… | 0.3678 | 0.97 | 2532 | 8.27 | 210 | 129 | 379 | 1014 | -47 | -6 | 74
W09……………………… | 0.5654 | 2.64 | 2747 | 8.57 | 289 | 184 | 519 | 1543 | -140 | 35 | 63
W11……………………… | 0.5650 | 0.78 | 2026 | 8.02 | 126 | 182 | 503 | -1255 | 52 | -89 | 18
W14……………………… | 0.5617 | 5.56 | 2616 | 8.70 | 228 | 284 | 506 | -1263 | 25 | -222 | 77
W17……………………… | 0.5617 | 0.86 | 2483 | 8.22 | 165 | 169 | 429 | -956 | 4 | -141 | 25
W22……………………… | 0.5622 | 4.65 | 2654 | 8.67 | 144 | 338 | 692 | -932 | -65 | -910 | 82
141359.51+531049.3 | 0.8982 | 0.97 | 1817 | 7.98 | 121 | 157 | 0 | 0 | -222 | 0 | 15
141324.28+530527.0 | 0.4559 | 1.07 | 2080 | 8.12 | 191 | 127 | 342 | -739 | -67 | -205 | 381
141323.27+531034.3 | 0.8492 | 1.97 | 3299 | 8.66 | 166 | 261 | 0 | 0 | 172 | 0 | 14
141532.36+524905.9 | 0.7147 | 1.76 | 1005 | 7.60 | 182 | 126 | 285 | -387 | 180 | -165 | 33
141522.54+524421.5 | 0.5263 | 0.63 | 1229 | 7.54 | 119 | 146 | 187 | 4 | -60 | -543 | 48
141417.69+532810.8 | 0.8077 | 1.55 | 1927 | 8.14 | 232 | 340 | 0 | 0 | -175 | 0 | 32
141151.78+525344.1 | 0.5165 | 1.16 | 2817 | 8.40 | 128 | 208 | 591 | -952 | -147 | -630 | 62
141408.76+533938.3 | 0.1919 | 0.32 | 1188 | 7.36 | 82 | 132 | 248 | -430 | -58 | -265 | 291
141324.66+522938.2 | 0.8122 | 1.36 | 2941 | 8.48 | 114 | 231 | 403 | -550 | 0 | -483 | 75
141724.59+523024.9 | 0.4818 | 0.90 | 2398 | 8.20 | 172 | 176 | 0 | 0 | -29 | 0 | 129
141721.80+534102.6 | 0.1934 | 0.54 | 1025 | 7.35 | 137 | 115 | 215 | 551 | 307 | 307 | 163
141645.58+534446.8 | 0.4418 | 0.47 | 971 | 7.27 | 152 | 129 | 338 | -660 | -12 | -219 | 72
141018.04+532937.5 | 0.4696 | 0.41 | 2077 | 7.90 | 130 | 102 | 236 | -536 | -33 | -102 | 97
141751.14+522311.1 | 0.2806 | 0.13 | 3407 | 8.07 | 181 | 124 | 311 | -730 | 6 | -63 | 124
141112.72+534507.1 | 0.5872 | 1.35 | 1585 | 7.94 | 97 | 133 | 356 | -638 | -72 | -348 | 39
140943.01+524153.1 | 0.4211 | 0.40 | 2268 | 7.97 | 184 | 219 | 0 | 0 | 33 | 0 | 108
141409.44+535648.2 | 0.8251 | 1.36 | 1264 | 7.74 | 95 | 88 | 357 | -778 | -65 | -203 | 195
141941.11+533649.6 | 0.6457 | 3.52 | 1767 | 8.25 | 109 | 142 | 261 | -531 | -19 | -157 | 93
142010.25+524029.6 | 0.5477 | 0.91 | 3681 | 8.58 | 177 | 237 | 0 | 0 | -14 | 0 | 68
141004.27+523141.0 | 0.5266 | 1.28 | 2248 | 8.23 | 150 | 173 | 159 | 754 | -77 | 268 | 147
142038.52+532416.5 | 0.2647 | 0.24 | 2633 | 7.98 | 66 | 137 | 0 | 0 | -73 | 0 | 183
141658.28+521205.1 | 0.6018 | 2.01 | 3184 | 8.64 | 158 | 227 | 719 | -1276 | -231 | -783 | 63
141514.15+540222.9 | 0.8488 | 1.97 | 2910 | 8.55 | 201 | 190 | 324 | -694 | 109 | -29 | 60
142043.53+523611.4 | 0.3368 | 0.24 | 2034 | 7.76 | 115 | 133 | 289 | -535 | -65 | -272 | 167
141320.05+520527.9 | 0.5998 | 0.87 | 2590 | 8.26 | 313 | 182 | 0 | 0 | -1 | 0 | 378
142124.36+532312.5 | 0.8255 | 1.21 | 1813 | 8.03 | 225 | 203 | 0 | 0 | -71 | 0 | 40
142112.29+524147.3 | 0.8425 | 1.52 | 1818 | 8.09 | 77 | 161 | 734 | -1491 | -99 | -444 | 91
141031.33+521533.8 | 0.6076 | 1.14 | 1388 | 7.78 | 187 | 186 | 348 | -687 | -106 | -313 | 149
141049.76+540040.6 | 0.8343 | 1.16 | 1247 | 7.69 | 154 | 149 | 364 | -521 | -18 | -432 | 23
142209.14+530559.8 | 0.7542 | 4.35 | 3532 | 8.91 | 106 | 203 | 0 | 0 | 93 | 0 | 11
141058.78+520712.2 | 0.3910 | 0.26 | 3249 | 8.18 | 93 | 170 | 477 | 1224 | -113 | -113 | 224
141852.64+520142.8 | 0.4398 | 0.31 | 1713 | 7.67 | 96 | 126 | 331 | 850 | -26 | -26 | 52
141553.09+541816.5 | 0.7305 | 1.86 | 1218 | 7.78 | 80 | 126 | 584 | -1113 | 122 | -361 | 32
140904.43+540344.2 | 0.6585 | 0.87 | 3478 | 8.52 | 215 | 318 | 0 | 0 | -99 | 0 | 31
141115.19+515209.0 | 0.5716 | 1.45 | 1822 | 8.08 | 123 | 189 | 565 | 1420 | -115 | -115 | 37
141135.89+515004.5 | 0.6500 | 1.30 | 1365 | 7.80 | 119 | 247 | 343 | -397 | 170 | -313 | 19
140715.49+535610.2 | 0.6827 | 2.02 | 2851 | 8.54 | 119 | 177 | 719 | -1528 | 33 | -244 | 78
140551.99+533852.1 | 0.4548 | 0.64 | 2291 | 8.08 | 197 | 150 | 662 | 1625 | -50 | 19 | 139
140923.42+515120.1 | 0.8532 | 1.07 | 1915 | 8.05 | 379 | 172 | 337 | -520 | 184 | -161 | 8
141419.84+533815.3 | 0.1645 | 0.70 | 1446 | 7.71 | 98 | 134 | 663 | -1284 | 10 | -404 | 91
140915.70+532721.8 | 0.2584 | 0.35 | 3147 | 8.22 | 172 | 195 | 0 | 0 | -73 | 0 | 86
141253.92+540014.4 | 0.1871 | 0.09 | 2431 | 7.68 | 117 | 158 | 0 | 0 | -9 | 0 | 191
140759.07+534759.8 | 0.1725 | 0.40 | 1995 | 7.86 | 130 | 139 | 418 | 796 | -61 | -337 | 146
140812.09+535303.3 | 0.1161 | 0.07 | 3076 | 7.83 | 112 | 160 | 0 | 0 | -3 | 0 | 274
142103.53+515819.5 | 0.2634 | 0.35 | 1521 | 7.59 | 105 | 146 | 317 | -675 | -62 | -200 | 107
141318.96+543202.4 | 0.3623 | 0.98 | 1592 | 7.87 | 130 | 113 | 399 | -956 | -123 | -192 | 82
141644.17+532556.1 | 0.4253 | 0.43 | 1843 | 7.81 | 114 | 163 | 462 | 1185 | -92 | -92 | 127
141729.27+531826.5 | 0.2374 | 0.31 | 2695 | 8.06 | 204 | 186 | 465 | -844 | -100 | -445 | 86
142100.04+532139.6 | 0.6766 | 1.57 | 1657 | 8.01 | 89 | 129 | 390 | -862 | -13 | -151 | 27
141308.10+515210.4 | 0.2882 | 0.54 | 1307 | 7.56 | 104 | 130 | 329 | -638 | -78 | -285 | 68
141645.15+542540.8 | 0.2439 | 0.25 | 2733 | 8.02 | 164 | 134 | 465 | 1323 | -55 | 83 | 118
142225.62+533426.3 | 0.7569 | 0.57 | 2717 | 8.21 | 144 | 183 | 0 | 0 | 77 | 0 | 10

Note. — Col. (1): Name of target. Col. (2): Redshift. Col. (3): Continuum
luminosity at 5100Å. Col. (4): Line dispersion of $\rm{H\beta}$ emission line.
Col. (5): Black-hole mass. Col (6): Stellar velocity dispersion. Col. (7):
Line dispersion of the core component of [O III] emission line. Col. (8): Line
dispersion of the broader component of [O III] emission line. Col. (9):
Outflow velocity. Col. (10): Velocity shift of the core component of [O III]
emission line with respect to the stellar systemic velocity. Col. (11):
Velocity shift of the broader component of [O III] emission line with respect
to the stellar systemic velocity. Col. (12): Signal-to-noise ratio of spectra
at 5100Å continuum. Error values are 0.04 dex for all measured properties
(except that black-hole mass uncertainty is 0.4 dex).

Table 2Spearman’s rank-order Correlation Results between [O III] vs. Stellar
Kinematics and AGN Properties

| $\rm\log(M_{BH})$ | $\rm\log(L_{Bol}/L_{Edd})$ |  $\rm\log(\lambda L_{5100}$) | $\rm V_{max}$ | $\rm\sigma_{[OIII,out]}$ |  $\rm V_{[OIII,out]}$ \- $\rm V_{*}$ |  $\rm V_{[OIII,core]}$ \- $\rm V_{*}$ |  $\rm\sigma_{[OIII,core]}$ \- $\rm\sigma_{*}$ |  $\rm\sigma_{[OIII,out]}$ \- $\rm\sigma_{*}$
---|---|---|---|---|---|---|---|---|---
| ($\rm M_{\odot}$) |  | ($\rm 10^{44}\ erg~{}s^{-1}$) | ($\rm km~{}s^{-1}$) | ($\rm km~{}s^{-1}$) | ($\rm km~{}s^{-1}$) | ($\rm km~{}s^{-1}$) | ($\rm km~{}s^{-1}$) | ($\rm km~{}s^{-1}$)
| (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9)
$\rm\sigma_{[OIII,core]}$ $-$ $\rm\sigma_{*}$ |  $-$0.11 (5e$-$03) | 0.16 (9e$-$06) |  $-$0.08 (3e$-$02) | 0.17 (3e$-$03) | 0.31 (4e$-$08) |  $-$0.33 (6e$-$09) |  $-$0.09 (1e$-$02) | 1.00 (0e+00) | 0.53 (8e$-$23)
$\rm\sigma_{[OIII,out]}$ $-$ $\rm\sigma_{*}$ | 0.29 (3e$-$07) | 0.25 (1e$-$05) | 0.35 (5e$-$10) | 0.80 (3e$-$67) | 0.94 (2e$-$140) |  $-$0.34 (2e$-$09) |  $-$0.20 (6e$-$04) | 0.53 (8e$-$23) | 1.00 (0e+00)
$\rm V_{[OIII,core]}$ $-$ $\rm V_{*}$ | 0.03 (4e$-$01) |  $-$0.24 (1e$-$10) |  $-$0.11 (3e$-$03) | 0.06 (3e$-$01) |  $-$0.20 (6e$-$04) | 0.30 (1e$-$07) | 1.00 (0e+00) |  $-$0.09 (1e$-$02) |  $-$0.20 (6e$-$04)
$\rm V_{[OIII,out]}$ $-$ $\rm V_{*}$ |  $-$0.15 (9e$-$03) |  $-$0.29 (4e$-$07) |  $-$0.31 (5e$-$08) | 0.46 (2e$-$17) |  $-$0.34 (2e$-$09) | 1.00 (0e+00) | 0.30 (1e$-$07) |  $-$0.33 (6e$-$09) |  $-$0.34 (2e$-$09)

Note. — Col. (1): Black-hole mass. Col. (2): Eddington ratio. Col. (3):
Continuum luminosity at 5100Å. Col. (4): Outflow velocity. Col. (5): Line
dispersion of the broader component of [O III] emission line. Col (6):
Velocity shift of the broader component of [O III] emission line with respect
to the stellar systemic velocity. Col. (7): Velocity shift of the core
component of [O III] emission line with respect to the stellar systemic
velocity. Col. (8): Line dispersion of the core component of [O III] emission
line with respect to the stellar dispersion. Col. (9): Line dispersion of the
broad component of [O III] emission line with respect to the stellar
dispersion. The p-values of the null hypothesis that the two quantities are
not correlated are shown in parentheses, following the Spearman’s rank-order
coefficients. The outflow velocities are used in absolute values for comparing
with the line dispersions. The numbers of the sources in the correlation
calculations for the core and broad components of [O III] emission line are
740, and 300, respectively.

## References

  * Abazajian et al. (2009) Abazajian, K. N., Adelman-McCarthy, J. K., Agüeros, M. A., et al. 2009, ApJS, 182, 543
  * Ayubinia et al. (2022) Ayubinia, A., Xue, Y. Q., Woo, J-.H. et al. 2022, Universe, in press
  * Bae & Woo (2014) Bae, H.-J., & Woo, J.-H. 2014, ApJ, 795, 30
  * Bae et al. (2017) Bae, H-J., Woo, J.-H., Karouzos, M. et al. 2017, ApJ, 837, 91
  * Bernardi (2003) Bernardi, M. 2003, AJ, 125, 1866
  * Bennert et al. (2018) Bennert V. N. et al., 2018, MNRAS, 481, 138
  * Bennert et al. (2015) Bennert V. N. et al., 2015, ApJ, 809, 20
  * Bennert et al. (2010) Bennert, V. N., Treu, T., Woo, J.-H., et al. 2010, ApJ, 708, 1507
  * Bentz et al. (2006) Bentz, M. C., Peterson, B. M., Pogge, R. W., Vestergaard, M., & Onken, C. A. 2006, ApJ, 644, 133
  * Bentz et al. (2009a) Bentz, M. C., Peterson, B. M., Netzer, H., Pogge, R. W., & Vestergaard, M. 2009, ApJ, 697, 160
  * Bentz et al. (2013) Bentz, M. C., Denney, K. D., Grier, C. J., et al. 2013, ApJ, 767, 149
  * Boroson (2003) Boroson, T. A., 2003, ApJ, 585, 647
  * Boroson & Green (1992) Boroson, T. A., & Green, R. F. 1992, ApJS, 80, 109
  * Boroson (2005) Boroson, T. 2005, AJ, 130, 381
  * Bonning et al. (2005) Bonning, E.W., Shields, G. A., Salviander, S., McLure, R. J., 2005, ApJ, 626, 89
  * Cappellari & Emsellem (2004) Cappellari, M., & Emsellem, E. 2004, PASP, 116, 138
  * Crenshaw & Kraemer (2000) Crenshaw, D. M., & Kraemer, S. B. 2000, ApJL, 532, L101
  * Eun, Woo & Bae (2017) Eun, D., Woo, J.-H. & Bae, H.-J. 2017, ApJ, 842, 5
  * Eracleous & Halpern (2004) Eracleous, M. & Halpern, J. P. 2004, ApJS, 150, 181
  * Ferrarese & Merrit (2000) Ferrarese, L., & Merritt, D. 2000, ApJ, 539, L9
  * Gebhardt et al. (2000) Gebhardt, K., Bender, R., Bower, G., et al. 2000, ApJ, 539, L13
  * Greene & Ho (2005) Greene, J. E., & Ho, L. C. 2005a, ApJ, 627, 721
  * Grupe & Mathur (2004) Grupe, D. & Mathur, S., 2004, ApJ, 606, L41
  * Harris et al. (2012) Harris, C. E., Bennert V. N., Auger M. W., Treu T., Woo J.-H., Malkan M. A., 2012, ApJS, 201, 29
  * Harrison et al. (2014) Harrison, C. M., Alexander, D. M., Mullaney, J. R., Swinbank, A. M., 2014, MNRAS, 441, 3306
  * Heckman et al. (1984) Heckman, T. M., Miley, G. K., & Green, R. F. 1984, ApJ, 281, 525
  * Ho (2009) Ho, L. C. 2009, ApJ, 699, 638
  * Hu et al. (2008) Hu, C., Wang, J. M., Ho, L. C. et al. 2008, ApJ, 687, 78
  * Komossa & Xu (2007) Komossa, S. & Xu, D., 2007, ApJ, 667, L33
  * Komossa et al. (2008) Komossa, S., Xu, D., Zhou, H., Storchi-Bergmann, T., & Binette, L. 2008, ApJ, 680, 926
  * Kormendy & Ho (2013) Kormendy, J., & Ho, L. C. 2013, ARA&A, 51, 511
  * LaMassa et al. (2009) LaMassa, S. M., Heckman, T. M., Ptak, A., et al. 2009, ApJ, 705, 568
  * Le et al. (2014) Le, H. A. N., Pak, S., Im, M., et al. 2014, JASR, 54, 6
  * Le et al. (2017) Le, H. A. N., Woo, J-.H., Karouzos, M. et al. 2017, ApJ, 851, 8
  * Le & Woo (2019) Le, H. A. N. & Woo, J-.H. 2019, ApJ, 887, 246
  * Le, Woo & Xue (2020) Le, H. A. N., Woo, J-.H., & Xue, Y. Q. 2020, ApJ, 901, 35
  * Lin et al. (2022) Lin, X., Xue, Y. Q., Fang, G. et al. 2022, RAA, 22, 015010
  * McLure & Dunlop (2004) McLure, R. J., & Dunlop, J. S. 2004, MNRAS, 352, 1390
  * McLure & Jarvis (2002) McLure, R. J., & Jarvis, M. J. 2002, MNRAS, 337, 109
  * Nelson & Whittle (1996) Nelson, C. H. & Whittle, M., 1996, ApJ, 465, 96
  * Nelson (2000) Nelson, C. H., 2000, ApJ, 544, 91
  * Netzer & Trakhtenbrot (2007) Netzer, H., Trakhtenbrot, B., 2007, ApJ, 654, 754
  * Oke et al. (1995) Oke, J. B., Cohen, J. G., Carr, M., et al. 1995, PASP, 107, 375
  * Park et al. (2015) Park, D., Woo, J.-H., Bennert, V. et al. 2015, ApJ, 799, 164
  * Peng et al. (2006) Peng, C. Y., Impey, C. D., Rix, H.-W., et al. 2006, ApJ, 649, 616
  * Phillips et al. (1986) Phillips, M. M., Jenkins, C. R., Dopita, M. A., Sadler, E. M., & Binette, L. 1986, AJ, 91, 1062
  * Rice et al. (2006) Rice, M., Martini, P., Greene J. E., Pogge, R. W., Shields J. C., Mulchaey, J. S., Regan, M. W., 2006, ApJ, 636, 654
  * Salviander et al. (2007) Salviander, S., Shields, G. A., Gebhardt, K., & Bonning, E. W. 2007, ApJ, 662, 131
  * Salviander & Shields (2013) Salviander, S. & Shields, G. A, 2013, ApJ, 662, 13
  * Salviander, Shields & Bonning (2015) Salviander, S., Shields, G. A., Bonning, E. W., 2015, ApJ, 799, 173
  * Shankar et al. (2016) Shankar, F., Bernardi, M., Sheth, R. K., et al. 2016, MNRAS, 460, 3119
  * Shankar et al. (2019) Shankar, F., Weinberg, D. H., Marsden, C. et al. 2019, MNRAS, 493, 1500
  * Shen et al. (2015) Shen, Y. et al. 2015, ApJ, 805, 96
  * Shen et al. (2016) Shen, Y. et al. 2016, ApJ, 831, 7
  * Shields et al. (2003) Shields, G. A., Gebhardt, K., Salviander, S., Wills, B. J., Xie, B., Brotherton, M. S., Yuan, J., & Dietrich, M. 2003, ApJ, 583, 124
  * Silk & Rees (1998) Silk, J., & Rees, M. J. 1998, A&A, 331, L1
  * Sexton et al. (2020) Sexton, R. O., Matzko, W., Darden, N., Canalizo, G., & Gorjian, V. 2020, MNRAS, 500, 2871
  * Sun et al. (2015) Sun, M., Trump, J. R., Brandt, W. N., et al. 2015, ApJ, 802, 14
  * Terlevich, Diaz & Terlevich (1990) Terlevich, E., Diaz, A. I., Terlevich, R., 1990, MNRAS, 242, 271
  * Trakhtenbrot & Netzer (2012) Trakhtenbrot, B., & Netzer, H. 2012, MNRAS, 427, 3081
  * Tremaine et al. (2002) Tremaine, S., Gebhardt, K., Bender, R., et al. 2002, ApJ, 547, 2
  * Valdes et al. (2004) Valdes, F., Gupta, R., Rose, J. A., Singh, H. P., & Bell, D. J. 2004, ApJS, 152, 251
  * Wang & Lu (2001) Wang, T. & Lu, Y. 2001, A&A, 377, 52
  * Wilson & Heckman (1985) Wilson, A. S., & Heckman, T. M. 1985, in Astrophysics of Active Galaxies and Quasi-Stellar Objects, ed. J. S. Miller (Mill Valley: University Science Books), 39
  * Whittle (1992) Whittle, M., 1992, ApJ, 387, 109
  * Woo et al. (2006) Woo, J.-H., Treu, T., Malkan, M. A., & Blandford, R. D. 2006, ApJ, 645, 900
  * Woo et al. (2008) Woo, J.-H., Treu, T., Malkan, M. A., & Blandford, R. D. 2008, ApJ, 681, 925
  * Woo et al. (2010) Woo, J.-H., Treu, T., Barth, A. J., et al. 2010, ApJ, 716, 269
  * Woo et al. (2015) Woo, J.-H., Yoon, Y., Park, S. et al. 2015, ApJ, 801, 38
  * Woo et al. (2016) Woo, J.-H., Bae, H.-J., Son, D., & Karouzos, M. 2016, ApJ, 817, 108
  * Woo et al. (2018) Woo, J.-H., Le, H. A. N., Karouzos, M., et al. 2018, ApJ, 859, 138
  * Woo et al. (2019) Woo, J.-H., Cho, H., Gallo, E., et al. 2019, Nature Astronomy, 3, 755
  * Xue et al. (2010) Xue, Y. Q., Brandt, W. N., Luo, B., et al. 2010, ApJ, 720, 368
  * Xue (2017) Xue, Y. Q. 2017, NewAR, 79, 59
  * York et al. (2000) York, D. G., Adelman, J., Anderson, Jr., J. E., et al. 2000, AJ, 120, 1579
  * Zamanov et al. (2002) Zamanov, R., Marziani, P., Sulentic, J. W., et al. 2002, ApJL, 576, L9
  * Zhang et al. (2011) Zhang, K., Dong, X-. B., Wang, T-. G. & Gaskell, C. M. 2011, ApJ, 737, 71