# Revisiting Emission-Line Measurement Methods for Narrow-Line Active Galactic
Nuclei

Viraja C. Khatu Department of Physics and Astronomy & Institute of Earth and
Space Exploration, The University of Western Ontario, 1151 Richmond Street,
London, Ontario N6A 3K7, Canada<EMAIL_ADDRESS>Sarah C. Gallagher Department
of Physics and Astronomy & Institute of Earth and Space Exploration, The
University of Western Ontario, 1151 Richmond Street, London, Ontario N6A 3K7,
Canada  Keith Horne School of Physics and Astronomy, University of St Andrews,
North Haugh, St Andrews, KY16 9SS, Scotland, UK  Edward M. Cackett Department
of Physics & Astronomy, Wayne State University, 666 W Hancock Street, Detroit,
Michigan 48201, USA  Chen Hu  Key Laboratory for Particle Astrophysics,
Institute of High Energy Physics, Chinese Academy of Sciences, 19B Yuquan
Road, Beijing 100049, People’s Republic of China  Pu Du Key Laboratory for
Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of
Sciences, 19B Yuquan Road, Beijing 100049, People’s Republic of China  Jian-
Min Wang Key Laboratory for Particle Astrophysics, Institute of High Energy
Physics, Chinese Academy of Sciences, 19B Yuquan Road, Beijing 100049,
People’s Republic of China  Wei-Hao Bian Physics Department, Nanjing Normal
University, Nanjing 210097, People’s Republic of China  Jin-Ming Bai  Yunnan
Observatories, The Chinese Academy of Sciences, Kunming 650011, People’s
Republic of China  Yong-Jie Chen  Key Laboratory for Particle Astrophysics,
Institute of High Energy Physics, Chinese Academy of Sciences, 19B Yuquan
Road, Beijing 100049, People’s Republic of China  Patrick Hall  Department of
Physics and Astronomy, York University, 4700 Keele Street, Toronto, Ontario
M3J 1P3, Canada  Bo-Wei Jiang  Key Laboratory for Particle Astrophysics,
Institute of High Energy Physics, Chinese Academy of Sciences, 19B Yuquan
Road, Beijing 100049, People’s Republic of China  Sha-Sha Li Yunnan
Observatories, The Chinese Academy of Sciences, Kunming 650011, People’s
Republic of China  Yan-Rong Li Key Laboratory for Particle Astrophysics,
Institute of High Energy Physics, Chinese Academy of Sciences, 19B Yuquan
Road, Beijing 100049, People’s Republic of China  Sofia Pasquini Department of
Physics and Astronomy, The University of Western Ontario, 1151 Richmond
Street, London, Ontario N6A 3K7, Canada  Yu-Yang Songsheng  Key Laboratory for
Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of
Sciences, 19B Yuquan Road, Beijing 100049, People’s Republic of China  Chan
Wang  Physics Department, Nanjing Normal University, Nanjing 210097, People’s
Republic of China  Ming Xiao  Key Laboratory for Particle Astrophysics,
Institute of High Energy Physics, Chinese Academy of Sciences, 19B Yuquan
Road, Beijing 100049, People’s Republic of China  Zhe Yu  Key Laboratory for
Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of
Sciences, 19B Yuquan Road, Beijing 100049, People’s Republic of China

(Accepted March 14, 2023)

###### Abstract

Measuring broad emission-line widths in active galactic nuclei (AGN) is not
straightforward owing to the complex nature of flux variability in these
systems. Line-width measurements become especially challenging when signal-to-
noise is low, profiles are narrower, or spectral resolution is low. We
conducted an extensive correlation analysis between emission-line measurements
from the optical spectra of Markarian 142 (Mrk 142; a narrow-line Seyfert
galaxy) taken with the Gemini North Telescope (Gemini) at a spectral
resolution of $185.6\pm 10.2$ km s-1 and the Lijiang Telescope (LJT) at
$695.2\pm 3.9$ km s-1 to investigate the disparities in the measured broad-
line widths from both telescope data. Mrk 142 posed a challenge due to its
narrow broad-line profiles, which were severely affected by instrumental
broadening in the lower-resolution LJT spectra. We discovered that allowing
the narrow-line flux of permitted lines having broad and narrow components to
vary during spectral fitting caused a leak in the narrow-line flux to the
broad component, resulting in broader broad-line widths in the LJT spectra.
Fixing the narrow-line flux ratios constrained the flux leak and yielded the
H$\beta$ broad-line widths from LJT spectra $\sim$54% closer to the Gemini
H$\beta$ widths than with flexible narrow-line ratios. The availability of
spectra at different resolutions presented this unique opportunity to inspect
how spectral resolution affected emission-line profiles in our data and adopt
a unique method to accurately measure broad-line widths. Reconsidering line-
measurement methods while studying diverse AGN populations is critical for the
success of future reverberation-mapping studies. Based on the technique used
in this work, we offer recommendations for measuring line widths in narrow-
line AGN.
Unified Astronomy Thesaurus concepts: Active galactic nuclei (16);
Spectroscopy (1558)
Supporting material: Machine-readable tables and spectra

††journal: PASP††facilities: Gemini North Telescope (GMOS), Lijiang 2.4-meter
Telescope (YFOSC)††software: Python, Astropy (Astropy Collaboration et al.,
2013), prepdataps, PrepSpec, Sherpa (Freeman et al., 2001)

##  1 Introduction

Observing gaps in multi-epoch astronomical data are commonplace. Sparsely
sampled ground-based observations are mainly a result of weather conditions
and pressure from other programs (for queue observatories). Data gaps can
impact the programs requiring frequent visits to the sky, e.g., time-series
observations. One way to work around data gaps is by performing simultaneous
observations with different telescopes. However, using data from various
observatories together in a meaningful way can be challenging because of the
need for sufficient cross-calibration.

Combining spectroscopic observations from different facilities requires
careful consideration of various factors (e.g., exposure time, seeing,
spectral resolution, etc.) affecting the data. When employing multiple
telescopes to observe the same spectral region for a given data set, the
instrument specifications used with different facilities may not be identical.
As an example, if the data from two telescopes were taken with different slit
widths, their spectral resolutions may not match. The wider the slit, the
lower the spectral resolution (depending on the grating used). Instrumental
broadening in lower-resolution spectra causes line features to appear broader
than the true value or sometimes blended with neighboring lines. This
broadening effect can result in inaccurate measurements of the physical
parameters, e.g., full width at half maximum (FWHM) and flux of an emission
line. However, the severity of the effect may be different for different
studies. For objects showing broad-line profiles considerably narrower than
the typical AGN population, e.g., Narrow-Line Seyfert 1 galaxies (NLS1s)
accreting at super-Eddington rates, accounting for instrumental broadening
effects while performing line measurements becomes more critical.

Historically, reverberation-mapping (RM; Blandford & McKee, 1982; Peterson,
1993) studies have focused mainly on low-redshift AGN ($z<0.3$) that typically
follow sub-Eddington accretion (e.g., Stirpe et al., 1994; Santos-Lleó et al.,
1997; Collier et al., 1998; Dietrich et al., 1998; Kaspi et al., 2000; Bentz
et al., 2006) instead of the more atypical super-Eddington objects (accreting
well above the Eddington limit). RM is a powerful technique that takes
advantage of the variability in AGN over a range of timescales (from several
days to weeks and years; e.g, Peterson et al., 1982) – broad-line region (BLR)
response on larger scales to the continuum variations from the accretion disk,
with a positive time lag – and provides a way to convert the time lag into a
spatial distance, the size of the BLR. The BLR size along with the width of an
emission line is used to obtain black hole masses in AGN. Applying the RM
technique successfully to measure AGN black hole masses thus requires accurate
measurements of the emission-line widths. A majority of the low-redshift AGN
exhibit broad emission lines (e.g., H$\beta$, H$\alpha$, C iv, etc.) with
$\text{FWHM}\geq 2000$ km s-1 in their spectra. Recent efforts by the Super-
Eddington Accreting Massive Black Holes (SEAMBH) collaboration (Du et al.,
2014; Wang et al., 2014; Hu et al., 2015; Du et al., 2015, 2016a, 2016b, 2018)
have successfully identified $\sim$20 highly accreting AGN to date. SEAMBH
objects show spectral features containing narrower H$\beta$ broad lines
(FWHM${}_{\mathrm{\hbox{{\rm H}\kern 0.70004pt{\sc$\beta$}}}}\lesssim 2000$ km
s-1), weak [O iii], and strong optical Fe ii emission lines that appear as a
bumpy pseudo-continuum, similar to other NLS1s (Osterbrock & Pogge, 1987;
Boroson & Green, 1992; Boller et al., 1996; Véron-Cetty et al., 2001). As we
branch out to studying different categories of AGN, and given the importance
of accurate line measurements for RM analysis, we must carefully reconsider:
(1) How does spectral resolution influence the shapes of emission lines in our
data?; and (2) Are the current methods of measuring emission-line properties
sufficient or are they limited in any way to achieving our desired science
goals?

The aim of this paper is to address the above two questions with the optical
spectra of the super-Eddington AGN, Markarian 142 (Mrk 142), taken with the
Gemini North Observatory (Gemini) and the Lijiang Telescope (LJT). As a part
of the broader RM campaign, Cackett et al. (2020) performed overlapping
photometric and spectroscopic observations of Mrk 142 with telescope
facilities worldwide. The goal of the campaign is to study the structure of
the accretion disk and the BLR simultaneously, for the first time, in a super-
Eddington AGN. Because the spectral observations of Mrk 142 with Gemini
suffered with gaps due to unfavourable weather, the Gemini observations were
complemented with simultaneous observations from LJT. With the Gemini+LJT
data, an ultraviolet (UV) continuum to H$\beta$ lag for the object was
measured for the first time (Khatu et al., 2022). The Gemini and LJT spectra
were taken with the same grating but different slit widths – 0.75″ for Gemini
and 2.5″ for LJT; therefore, their spectral resolutions (corresponding to the
instrumental FWHMs) differed – $185.6\pm 10.2$ km s-1 for Gemini and $695.2\pm
3.9$ km s-1 for LJT. Here, the challenge was to accurately measure the
emission lines for spectra at considerably different spectral resolutions for
a narrow-line object. In this paper, we discuss how to address this challenge
with our spectral-fitting procedure. Further, we provide recommendations of
the best strategies for performing accurate emission-line measurements in
narrow-line AGN.

This paper is organized as follows. Section 2 details the process of preparing
the data for correlation analysis and the correlations between the Gemini and
LJT spectral measurements. Section 3 outlines the results. We discuss the
results in Section 4 along with our recommendations. Section 5 summarizes our
findings.

##  2 Methodology

We pre-processed the Gemini and LJT calibrated spectra independently through
PrepSpec111PrepSpec is a spectral analysis software that fits the continuum
and emission lines in the input spectra with a composite model through an
iterative process while correcting for any relative deviations in the
calibrated wavelength and flux scales of the spectra. See Section 2.1 for more
details. (developer: K. Horne) to correct for any relative deviations from
their calibrations. We then modelled the continuum and emission lines in the
spectra with Sherpa222Sherpa is a software application for modeling and
fitting astronomical images and spectra. In this work, the Sherpa v4.10.0
application was used within Coronagraphic Imager with Adaptive Optics (CIAO)
v4.10.0, the X-ray Data Analysis Software designed by the Chandra X-ray
Center. For full documentation of CIAO-Sherpa, see
https://cxc.harvard.edu/sherpa4.14/. (Freeman et al., 2001) v4.10.0 with a
Python wrapper script to examine the correlations between the Gemini and LJT
spectral measurements.

###  2.1 PrepSpec Pre-processing

PrepSpec corrects for differences in relative wavelength and flux calibrations
of the spectra by modeling their continuum, emission lines, and absorption
lines. However, PrepSpec requires that spectra have no gaps in wavelength and
extremely large flux values, for example, resulting from cosmic ray hits. To
prepare the Gemini spectra for PrepSpec, we applied the following corrections:
(1) replaced detector gaps, and residual features from cosmic-ray correction
and sky subtraction with interpolated and simulated data; (2) recovered the
flat spectral regions with zero flux values (resulting from the position angle
of the slit non-parallel to the parallactic angle) and bumpy regions
(resulting from the calibration process) by using a high signal-to-noise (S/N)
mean spectrum as the reference spectrum; and (3) recovered slit losses
(resulting from the 0.75″ narrow slit used for observations) using 5.00″ wide-
slit spectra taken on the same nights. We developed multiple scripts in Python
v3.6.5 to perform the above corrections. All Python scripts are publicly
available in the GitHub repository, prepdataps
(https://github.com/Virachan/prepdataps). Information on the usage and
citation of the scripts is provided in the repository. The LJT spectra had no
gaps and hence were directly processed through PrepSpec after calibration. The
GitHub repository includes the user manual for PrepSpec including a detailed
tutorial with the Mrk 142 Gemini data set.

###  2.2 Gemini/LJT Correlation Analysis

We investigated correlations between the Mrk 142 Gemini and LJT emission-line
measurements to study the effect of low spectral resolution on the measured
FWHM values. To fit the H$\beta$ $\lambda 4861$ and He i $\lambda 5877$
Regions of Interest, we initially followed a standard approach. We set the
FWHM, flux, and position of the [O iii] $\lambda 5008$ line to vary during the
fit, and fixed the FWHMs and positions of the narrow components in H$\beta$
and He i relative to the [O iii] $\lambda 5008$ line. We kept the H$\beta$ and
He i narrow-line fluxes as free parameters. Further, we used two Gaussians to
model the broad H$\beta$ and He i emission lines. We fixed the FWHM of the
broader broad H$\beta$ component and allowed the width of the narrower broad
component to be a free parameter to reduce the number of free parameters and
avoid degeneracy in the spectral model. For the He i line, we fixed the FWHMs
of both its broad components with respect to the FWHM of the flexible,
narrower broad H$\beta$ component. We applied the Boroson & Green (1992)
template to fit the Fe ii pseudo-continuum and the Bruzual & Charlot (2003)
host galaxy template with 11 Gyr at $z=0.05$ to correct for the effect of
host-galaxy emission. This approach worked well for the Gemini spectra.
However, the LJT H$\beta$ FWHM measurements were broader than expected,
indicating that the fitting approach failed for the LJT spectra. Figures 1 and
2 show model fits to a single-epoch spectrum from Gemini and LJT,
respectively.

Figure 1: Composite model fit to epoch 24 of the Mrk 142 Gemini data
displaying individual components of the model. Panel a: Composite model (red
solid curve) fit to the data (black solid curve) from 4430 Å to 6300 Å is
shown in the main panel, and the H$\beta$ and He i Regions of Interest are
shown in the Inset panels. The individual components of the model are
displayed at the bottom of the panel: continuum (cyan solid curve); Fe ii I Zw
1 template as a pseudo-continuum (faint blue solid curve); host-galaxy
template (orange solid curve); He ii broad components (blue dashed Gaussians);
H$\beta$ broad components (green dashed Gaussians); He i broad components
(pink dashed Gaussians); narrow-line components of H$\beta$, He i, and [O iii]
(purple solid Gaussians); and high-ionization coronal lines (brown solid
Gaussians). The total broad H$\beta$ and He i profiles are also overplotted
(gray solid curves). Panel b: Residuals of the model with reduced $\chi^{2}$,
${\chi_{\nu}}^{2}=1.183$. The model shows larger residuals around the [O iii]
$\lambda 5008$ line indicating a sub-optimal fit in that region. The noisier
blue end of the spectrum affects the overall fit in that region, thus
resulting in larger residuals compared to the red end of the spectrum.  Figure
2: Composite model fit to epoch 24 of the Mrk 142 LJT data displaying
individual components of the model. See caption of Figure 1 for a description
of the individual model components in Panel a. The red side of the broad
H$\beta$ emission line shows contamination with the Fe ii emission at
$\sim$4923 Å. Similarly, the [O iii] $\lambda 5008$ line shows considerable
blending with the Fe ii feature in its red wing, thus affecting a reliable
measurement of the [O iii] $\lambda 5008$ line. Panel b shows the residuals of
the model with ${\chi_{\nu}}^{2}=1.711$. The smaller residuals indicate an
overall good fit to the spectrum. The model performance drops significantly at
both ends of the spectrum although it does not impact measurements in the
Regions of Interest.

Due to low resolution of the LJT spectrum (695.2 km s-1), emission-line
features appear smeared as compared to the Gemini spectrum (185.6 km s-1). In
H$\beta$, the sharper peak of the narrow component evident in the Gemini
spectrum is not clearly distinguishable in the LJT spectrum. The Fe ii
emission-line component on the red side of H$\beta$ also appears to
contaminate the broader H$\beta$ component. Similarly, the red wing of the [O
iii] $\lambda 5008$ line appears to be blended with the Fe ii emission on its
red side. The possible contamination with Fe ii emission due to low spectral
resolution of the LJT spectra results in a broad FWHM for the [O iii] $\lambda
5008$ line. Further, at the instrumental resolution of the LJT spectrograph,
the [O iii] lines with FWHM $\sim 320$ km s-1 (as measured from the higher-
resolution Gemini spectra) are unresolved. The unresolved [O iii] lines in the
LJT spectra further complicate the measurements of their widths.

####  2.2.1 The Problem – Posed: Why do the broad H$\beta$ FWHMs from the
Gemini and LJT spectra not match?

We found that the FWHM values of the broad H$\beta$ and the [O iii] $\lambda
5008$ lines in the Gemini and LJT spectra did not agree with each other.
Figure 3 displays the differences in the measured FWHMs of the two lines. To
understand the cause of this problem, it is important to consider the
differing instrumental resolutions of Gemini and LJT. We used the spectra of a
G-type comparison star, common for both the Gemini and the LJT data, observed
in the same slit as the target for every exposure to calculate the
instrumental resolutions. The comparison star, similar to the target, appears
point-like in the slit and does not fill the entire slit unlike arc lamp
spectra or sky lines; therefore, unresolved absorption lines in the stellar
spectra can be used to estimate the line spread function of the instrument
more accurately than arc lamp spectra or sky lines. We fit the weak and hence
unresolved H$\beta$ stellar absorption line close to the H$\beta$/[O iii]
complex in the Gemini data using a Gaussian function, where the FWHM of the
Gaussian gave the mean resolution of $185.6\pm 10.2$ km s-1 with reference to
the [O iii] $\lambda 5008$ line. Following the procedure in Du et al. (2016a),
we convolved a higher-resolution stellar template spectrum with a Gaussian
function to obtain the observed stellar spectra in the LJT data; here as well,
the FWHM of the convolved Gaussian provided the mean resolution of $695.2\pm
3.9$ km s-1 for the LJT spectrograph. Considering the difference in the
resolutions of the Gemini and LJT spectra, we expect the FWHM values from LJT
to have 670.0 km s-1 broader effective width (here, defined as the width of
the Gaussian kernel required to smooth the higher-resolution Gemini spectrum
to the lower-resolution LJT spectrum, and given by
$\sqrt{695.2^{2}-185.6^{2}}$ for Gaussian profiles) than the Gemini FWHM
values. The [O iii] $\lambda 5008$ line in the LJT spectra (Figure 3, panel a)
has $\sim$680 km s-1 broader effective widths than the [O iii] $\lambda 5008$
FWHMs measured from the Gemini spectra as expected from the differing
instrumental resolutions of the two telescopes. However, the LJT H$\beta$
broad line shows a much greater effect, $\sim$1450 km s-1 broader effective
widths than those measured from the Gemini spectra. The broad He i FWHM
measurements were affected in the same way as H$\beta$. This implies that
there are multiple factors influencing the FWHM measurements in the LJT
spectra, likely resulting from instrumental broadening.

Figure 3: Differences in the full width at half maximum (FWHM) values measured
from the Gemini (blue open circles) and LJT (red open circles) spectra for [O
iii] $\lambda 5008$ (panel a) and broad H$\beta$ (panel b), indicating that
the LJT measurements have a broader effective width of 670.0 km s-1 (see text
for the definition) as expected owing to the Gemini and LJT instrumental
resolutions. In panel a, the purple pluses and maroon crosses represent the
line spread functions (determined from the comparison star observed in the
same slit as the target at each epoch) for the Gemini and LJT data,
respectively. The fitting procedure for both the Gemini and the LJT spectra
incorporated flexible narrow-line ratio of H$\beta$ to [O iii] $\lambda 5008$.

To identify the possible reason(s) for the observed discrepancies in the FWHM
measurements, we considered the narrow-line fluxes in the H$\beta$ and [O iii]
$\lambda 5008$ lines that we allowed to vary during spectral fitting. Figure 4
displays the correlation between the measured fluxes for the two lines. For
the LJT spectra, the fluxes in the narrow H$\beta$ line (red open squares) are
correlated to the [O iii] $\lambda 5008$ line fluxes
($r_{\mathrm{Spearman}}\sim 0.5$) with a large scatter in the measured values
from both lines. However, the fluxes for narrow lines, originating in the
narrow-line region (NLR) of AGN, are not expected to vary relative to the
continuum variations over the timescale of an RM campaign. The constancy of
the narrow-line fluxes is attributed to the NLR being farther away from the
central source (supermassive black hole + accretion disk) than the BLR, which
receives the continuum variations. The correlation observed between the LJT
narrow H$\beta$ and [O iii] $\lambda 5008$ line fluxes is absent in the Gemini
flux values (blue open circles; $r_{\mathrm{Spearman}}\sim 0.1$), which are
also more constrained than the LJT measurements.

Figure 4: Correlations between the narrow H$\beta$ line flux and the [O iii]
$\lambda 5008$ line flux from the Gemini (blue circles) and LJT (red squares)
spectra. Open symbols represent measurements with flexible narrow-line flux
ratios of $F_{\mathrm{\hbox{{\rm H}\kern
0.70004pt{\sc$\beta$}}}}/F_{\mathrm{\hbox{[{\rm O~{}}\kern 0.70004pt{\sc
iii}]~{}$\lambda 5008$}}}$ and $F_{\mathrm{\hbox{{\rm He~{}}\kern
0.70004pt{\sc i}}}}/F_{\mathrm{\hbox{[{\rm O~{}}\kern 0.70004pt{\sc
iii}]~{}$\lambda 5008$}}}$, whereas filled symbols (for LJT only) represent
measurements with fixed narrow-line flux ratios. For fitting the LJT spectra,
we fixed the above narrow-line flux ratios determined from the Gemini spectra
fitting process (0.293 for H$\beta$ to [O iii] $\lambda 5008$ and 0.034 for He
i to [O iii] $\lambda 5008$) as the resolved [O iii] $\lambda 5008$ line in
the Gemini spectra provided reliable measurements of the narrow-line flux
ratios. The weak positive correlation for the LJT measurements with flexible
narrow-line ratios indicates that the “broader” [O iii] $\lambda 5008$ line
results in an excess narrow-line flux for the narrow H$\beta$ component.

####  2.2.2 The Culprit – Pronounced: A “broader” [O iii] $\lambda 5008$ FWHM
leads to a broader broad H$\beta$ FWHM in the LJT spectra.

Integrating the observations from Figures 3 and 4, we concluded that the
“broader” (than expected) [O iii] $\lambda 5008$ line in the LJT spectra
causes the correlation and scatter observed in the H$\beta$ narrow-line
fluxes, consequently leading to the “broader” broad H$\beta$ FWHMs in the LJT
spectra as compared to the narrower broad H$\beta$ in the Gemini spectra. The
lower spectral resolution of the LJT spectra smears the narrow-line profile of
the [O iii] $\lambda 5008$ line causing it to appear broader than usual (see
Figure 2). This effect is amplified in the case of Mrk 142 as it is a NLS1
with narrower and weaker [O iii] lines compared to the more typical broad-line
objects (with narrow-line widths of several hundred km s-1). Also, the likely
contamination from the Fe ii emission at the red wing of [O iii] $\lambda
5008$ (see Figure 2) further complicates the picture. The net result is a
“broader” FWHM measured for the [O iii] line. We interpret this result to mean
the following:
Because the width of the narrow H$\beta$ component is set equal to width of
the [O iii] line, a “broader” [O iii] leads to a “broader” narrow H$\beta$ in
the LJT spectra. The “broader” narrow H$\beta$ collects more flux leaving less
flux for the broad H$\beta$ components, which are kept flexible in the model.
The more the flux in the narrow H$\beta$ line, the lower the peak flux of the
broad H$\beta$ (after subtracting the narrow component), resulting into a
“broader” broad H$\beta$ FWHM.

####  2.2.3 The Solution – Proposed: Tie the flux in narrow H$\beta$ relative
to the flux in [O iii] $\lambda 5008$.

To contain the effect of the “broader” [O iii] $\lambda 5008$ line on the
broad H$\beta$ FWHM measurements in the LJT spectra, we fixed the narrow-line
fluxes as well as the widths of H$\beta$ and He i relative to the [O iii] flux
from the Gemini spectral measurements. At the resolution of the Gemini spectra
(185.6 km s-1), the [O iii] $\lambda 5008$ line is just resolved. Thus, the
FWHM measurements for the [O iii] line in the Gemini spectra are more reliable
than the LJT values. We therefore applied the narrow-line flux ratios,
$F_{\mathrm{\hbox{{\rm H}\kern 0.70004pt{\sc$\beta$}}}}/F_{\mathrm{\hbox{[{\rm
O~{}}\kern 0.70004pt{\sc iii}]~{}$\lambda 5008$}}}=0.293$ and
$F_{\mathrm{\hbox{{\rm He~{}}\kern 0.70004pt{\sc i}}}}/F_{\mathrm{\hbox{[{\rm
O~{}}\kern 0.70004pt{\sc iii}]~{}$\lambda 5008$}}}=0.034$, from the Gemini
spectra to the H$\beta$ and He i lines, respectively, in the LJT spectra.

Tying the LJT narrow-line flux ratios confined the flux measured for the
H$\beta$ narrow component as compared to the H$\beta$ narrow-line flux
measured when the narrow-line flux ratios were kept flexible. Figure 4
displays the fixed H$\beta$ narrow-line fluxes from the LJT spectra (red
filled squares) as exactly correlated ($r_{\mathrm{Spearman}}=1.0$) to the LJT
[O iii] $\lambda 5008$ fluxes. The large scatter in the narrow H$\beta$ line
fluxes from flexible line ratios for the LJT spectra (red open squares;
$\sigma^{2}=4.631$) is considerably reduced after adopting fixed narrow-line
ratios ($\sigma^{2}=0.042$). This reduction in scatter signifies that the
H$\beta$ narrow-line fluxes in the LJT spectra are now well constrained.
The applied flux ratios along with fixed widths for the narrow lines helped
constrain the narrow H$\beta$ flux. With a fixed width and constrained flux of
the narrow H$\beta$ component, the “excess” flux is directed back to the broad
components. The more the broad H$\beta$ flux, the higher the peak flux
measured for the broad H$\beta$, resulting into a narrower broad H$\beta$
FWHM.

##  3 Results

We studied the effect of the LJT spectral resolution (695.2 km s-1) on the
measured H$\beta$ FWHMs by correlating the emission-line measurements in the
Mrk 142 Gemini and LJT spectra. We identified that the “broader” FWHM
measurements of the unresolved [O iii] $\lambda 5008$ line in the LJT spectra
lead to an overestimation of the H$\beta$ narrow-line fluxes by a factor of
two, ultimately resulting in H$\beta$ FWHM values with $\sim$1450 km s-1
broader effective width than the H$\beta$ FWHM values from the Gemini spectra.
To correct for this effect, we adapted our spectral fitting procedure for the
LJT spectra by fixing the narrow-line ratios of H$\beta$ and He i with respect
to the [O iii] $\lambda 5008$ line based on our spectral measurements for the
Gemini spectra containing resolved [O iii] lines. We present our results
below.

Applying narrow-line flux ratios for fitting the lower-resolution LJT spectra
significantly reduces the scatter in the narrow-line fluxes of the H$\beta$
and He i broad lines. Figure 5 displays the fluxes of the narrow component in
H$\beta$ (panel a) and He i (panel b) before and after applying the flux
ratios for the LJT spectra. Before fixing the narrow-line fluxes, the higher
H$\beta$ to [O iii] $\lambda 5008$ and He i to [O iii] $\lambda 5008$ flux
ratios for the lower-resolution LJT spectra result from the “excess” flux
gathered under the narrow H$\beta$ and He i lines owing to the narrow H$\beta$
and He i line widths set equal to the width of the “broader” [O iii] $\lambda
5008$ line. After fixing the narrow-line flux ratios, the H$\beta$ and He i
line measurements are more consistent, with values similar to the narrow-line
fluxes from the Gemini data. The higher resolution of the Gemini spectra,
providing resolved [O iii] lines, allowed precise measurements of [O iii] line
widths and fluxes, thus resulting in the smaller scatter in the H$\beta$ and
He i narrow-line fluxes. In addition, we expect the narrow-line fluxes to be
constant over the length of our campaign. However, the H$\beta$ and He i
narrow-line fluxes from the LJT spectra are unreliable when the narrow-line
ratios are free parameters due to the large uncertainties and scatter in the
measured values. The constant H$\beta$ and He i narrow-line flux is clearly
evident after fixing the narrow-line ratios for the LJT spectra.

Figure 5: Narrow H$\beta$ (panel a) and He i (panel b) light curves measured
from the Gemini (blue circles) and LJT (red squares) spectra fit with flexible
(open symbols) and fixed (filled symbols) narrow-line flux ratios. Fixing the
H$\beta$ and He i narrow-line flux ratios of 0.293 and 0.034, respectively,
relative to the [O iii] $\lambda 5008$ line flux considerably reduced the
scatter in the LJT measurements as well as resulted in lower uncertainties.
With fixed narrow-line flux ratios, the new fluxes for the narrow H$\beta$ and
He i lines from the LJT spectra are closer to the Gemini measurements.

We found that the constrained H$\beta$ narrow-line fluxes in the LJT spectra
yield narrower FWHMs for the H$\beta$ broad component, and Figure 6 displays
this result. Flexible narrow-line flux ratios in the LJT spectra result in a
large scatter in the broad H$\beta$ FWHMs (red open squares) with a mean value
of $\sim$2220 km s-1. After fixing the narrow-line flux ratios, the
constrained narrow-line flux in H$\beta$ re-allocates the “excess” flux to the
broad components. As a result of the higher broad-line peak flux, the half-
maximum point increases, thus measuring a narrower H$\beta$ broad-line
profile. Figure 7 explicitly shows the dependence of the measured H$\beta$
FWHM on the peak flux of the line. With flexible narrow-line ratios for the
lower-resolution LJT spectra, the measured broad H$\beta$ FWHMs are strongly
negatively correlated ($r_{\mathrm{Spearman}}=-0.789$) with the peak fluxes of
the line. This correlation is weaker ($r_{\mathrm{Spearman}}=-0.449$) with the
fixed narrow-line flux ratios for the LJT spectra and also similar to the
correlation observed for the Gemini spectra ($r_{\mathrm{Spearman}}=-0.487$).
The remaining dependence of the broad H$\beta$ FWHM on its peak flux can be
attributed to the contamination in the H$\beta$ line from the nearby Fe ii
emission (also discussed below). The new measurements of the broad H$\beta$
FWHM, obtained after fixing the narrow-line flux ratios for the LJT spectra,
have a mean of $\sim$1930 km s-1, $\sim$54% closer to the Gemini H$\beta$ mean
FWHM. The new broad H$\beta$ FWHM values also show a scatter of $\sim$340 km
s-1, similar to the scatter in the Gemini H$\beta$ FWHM values (see Figure 6).

Figure 6: Correlations between the broad H$\beta$ full width at half maximum
(FWHM) and the narrow H$\beta$ flux from the Gemini (blue circles) and LJT
(red squares) spectra fit with flexible (open symbols) and fixed (filled
symbols) narrow-line flux ratios. The scatter in the LJT measurements with
flexible narrow-line ratios (orange shaded region) is considerably reduced
(red shaded region) after fixing the narrow-line ratios. Fixed ratios
nullified the strong correlation that is evident in the LJT measurements with
flexible ratios.  Figure 7: Dependence of the full width at half maximum
(FWHM) on the peak flux of the broad H$\beta$ line from the Gemini (blue
circles) and LJT (red squares) spectra fit with flexible (open symbols) and
fixed (filled symbols) narrow-line flux ratios. Fixed ratios nullified the
strong correlation that is evident in the LJT measurements with flexible
ratios.

We also examined the correlation between the strength of Fe ii
($R_{\mathrm{\hbox{{\rm Fe~{}}\kern 0.70004pt{\sc ii}}}}$, defined as the
ratio of equivalent width of Fe ii in the 4434–4684 Å region to that of broad
H$\beta$) and the FWHM of broad H$\beta$, shown in Figure 8. The
$R_{\mathrm{\hbox{{\rm Fe~{}}\kern 0.70004pt{\sc
ii}}}}$–FWHM${}_{\mathrm{\hbox{{\rm H}\kern 0.70004pt{\sc$\beta$}},broad}}$
correlation reiterates the issue of the broader H$\beta$ FWHM measurements in
a different context. The LJT H$\beta$ FWHM values with flexible narrow-line
ratios (red open squares) are weakly correlated to $R_{\mathrm{\hbox{{\rm
Fe~{}}\kern 0.70004pt{\sc ii}}}}$. This correlation vanishes after fixing the
narrow-line flux ratio of H$\beta$ to [O iii] $\lambda 5008$. The new broad
H$\beta$ measurements (red filled squares) are closer to the values measured
from the Gemini spectra; however, an offset is still present. At the low
spectral resolution of the LJT spectra, the Fe ii emission around the H$\beta$
line likely contaminates the H$\beta$ broad-line emission (see Figure 2). The
remainder offset noted above can likely be a result of the potential Fe ii
contamination with the broad H$\beta$ line in the LJT spectra. Therefore,
understanding any interplay between the two lines is crucial. In addition, we
note that the $R_{\mathrm{\hbox{{\rm Fe~{}}\kern 0.70004pt{\sc ii}}}}$
measurements from the LJT spectra are smaller as compared to those from the
Gemini spectra, likely due to the lower resolution of the LJT data.

Figure 8: Correlations between the strength of Fe ii (ratio of equivalent
width of Fe ii in the [4434–4684 Å] region to that of broad H$\beta$) and the
full width at half maximum (FWHM) of the broad H$\beta$ from the Gemini (blue
circles) and LJT (red squares) spectra fit with flexible (open symbols) and
fixed (filled symbols) narrow-line flux ratios. Fixing the narrow-line flux
ratios moved the mean H$\beta$ FWHM from the LJT data closer to the mean of
the Gemini H$\beta$ FWHM measurements. There is an unexplained offset between
the Gemini and the new LJT measurements likely due to the Fe ii emission
contaminating the broad H$\beta$ line in the LJT spectra.

##  4 Discussion

We correlated emission-line measurements from Mrk 142 spectra taken with
Gemini and LJT at different resolutions (185.6 km s-1 for the former and 695.2
km s-1 for the latter) to study the discrepancies observed in the measured
FWHM values of broad H$\beta$. Given the NLS1 nature of Mrk 142, its broad
H$\beta$ profile is narrower as compared to the more typical broad-line
Seyfert 1s, and therefore challenging to accurately measure in lower-
resolution spectra. Accurate measurements of the narrow-line fluxes are
critical to measure broad emission-line widths, which in turn are used to
derive the black hole masses in AGN.

Our adopted method of measuring the broad H$\beta$ FWHM decreased the FWHM
values measured from the LJT spectra significantly, thus bringing them closer
to the Gemini measurements as well as reducing the scatter in the measured
values. The smaller scatter in the H$\beta$ FWHMs from the LJT spectra was an
improvement by a factor of $\sim$2.6 as compared to the measurements with
flexible narrow-line ratios. Although we significantly improved our
measurements from the LJT spectra, the new H$\beta$ FWHM values do not exactly
match with those from the Gemini spectra. There is an offset of $\sim$250 km
s-1 between the mean FWHM values from the two data sets that is perhaps a
consequence of the Fe ii emission contaminating the broad, red wing of
H$\beta$. At lower resolution, the strong Fe ii lines in the LJT spectra are
smeared as compared to the sharper features in the Gemini spectra (see Figures
1 and 2), resulting in weaker Fe ii measured from the LJT spectra (see Figure
8). Therefore, there likely exists cross-talk between the two broad lines
affecting the measurements of both the Fe ii emission and the broad H$\beta$
wings.

We also caution that our method does not affect the [O iii] line measurements
from the LJT spectra although it restores the broad-line flux measured for the
H$\beta$ line. Figure 9 makes this explicit. The [O iii] fluxes measured from
the LJT spectra are approximately the same (red filled squares) before fixing
the narrow-line flux ratios (see in Figure 9, panel a). The [O iii] fluxes
remain unchanged because the [O iii] $\lambda 5008$ flux was freed during
spectral fitting. In contrast, an increase in flux is clearly seen in the
broad H$\beta$ light curve (red filled squares in Figure 9, panel b). Fixing
the narrow-line flux ratios resulted in an increase of $\lesssim$10% in the
H$\beta$ broad-line flux in the LJT spectra – a difference that is greater
than or similar to the H$\beta$ flux uncertainties in a majority of the LJT
epochs. Our proposed method here can be used with spectral data sets having
different resolutions from either different gratings or different slit widths.
However, it does not test the effect on line fluxes, e.g., the offset observed
in the broad H$\beta$ line fluxes from Gemini and LJT (see Figure 9, panel b).
Such an offset may result from varying slit widths or orientation of the slit
or a combined effect of both. The orientation effect can be especially
concerning for extended sources in which the [O iii] emission emerging from
the NLR on larger spatial scales and the broad H$\beta$ emission from the BLR
closer to the central black hole can fill the slit differently. However, the
size of the central source in Mrk 142 is $3\arcsec\times 3\arcsec$ (and the
apparent size of the host galaxy is $15\arcsec\times 15\arcsec$), where the
issue of H$\beta$/[O iii] emission filling the slit differently on a spatial
scale is likely negligible. Nevertheless, we note that testing our proposed
method with different slit widths and orientations will help understand the
effects on measured line widths and fluxes in greater detail.

Figure 9: [O iii] $\lambda 5008$ (panel a) and broad H$\beta$ (panel b) light
curves from the Gemini (blue circles) and LJT (red squares) spectra fit with
flexible (open symbols) and fixed (filled symbols) narrow-line flux ratios.
Because the [O iii] $\lambda 5008$ line flux is kept flexible even while
fitting with fixed narrow-line flux ratios, the measured fluxes before and
after fixing narrow-line ratios are similar for the [O iii] line. However,
there is $\sim$10% increase in the the broad H$\beta$ flux from the LJT
spectra fit with fixed narrow-line ratios.

In general, the root-mean-square (RMS) spectra do not suffer from the blending
of broad- and narrow-line features because the variable part of the spectrum
is exclusively from the BLR. However, RMS spectra are noisier as compared to
the spectra from individual epochs; the emission-line widths obtained from RMS
spectra have higher uncertainties. Therefore, we considered measuring H$\beta$
broad-line widths from individual-epoch Gemini and LJT spectra.

###  4.1 Comparison to Previous Studies

We compared our methodology to the techniques used in previous studies. In a
previous SEAMBH monitoring campaign with LJT (Du et al., 2014; Hu et al.,
2015), Mrk 142 spectra were taken with the same instrument settings as used
for the data set in this work. Hu et al. (2015) describe the spectral fitting
technique adopted for measuring H$\beta$ FWHM from the previous campaign. They
followed a two-step process: (1) Assuming no narrow-line contribution in the
H$\beta$ emission and given that the narrow lines do not vary at the short
variability timescales of the broad-line gas, they modeled the H$\beta$
profile with a Gauss-Hermite function. (2) They modeled the H$\beta$ narrow
line with a Gaussian whose width was set equal to that of the [O iii] $\lambda
5008$ line and its position fixed relative to the [O iii] line. They ran their
fits in two cycles – first, assuming 10% of the [O iii] $\lambda 5008$ flux
for the narrow H$\beta$ component, and the value of the broad H$\beta$ FWHM
was used from this run; and second, assuming 20% narrow-line flux, and the
uncertainty on the FWHM measurement was used from this run in addition to the
uncertainty from the Gauss-Hermite fit for the line. While the calibration of
the uncertainties on the measured H$\beta$ FWHMs from the two-cycle fits and
Gauss-Hermite fits appears sufficient, the flux ratio of the H$\beta$ to [O
iii] narrow lines is somewhat arbitrarily defined. As the narrow-line flux
ratios can be different for different objects, using arbitrary ratios or even
the same ratios for different objects can result in a systematic
overestimation or underestimation of the broad H$\beta$ FWHM values. With the
opportunity of using Mrk 142 spectra at two different resolutions, we applied
the more reliable narrow-line flux ratios determined from the higher-
resolution and high S/N Gemini spectra to the lower-resolution LJT spectra for
the H$\beta$ FWHM measurements from the latter.

Two of the proposed methods of correcting for the effect of different spectral
resolution on line-width measurements include: (1) fitting a difference
spectrum between an input spectrum, whose flux scale factor (or flux ratio) is
to be determined, and a reference spectrum, typically a high S/N spectrum (van
Groningen & Wanders, 1992); and (2) subtracting the RMS width of the line
spread function of the spectrograph from the observed line profile (Fausnaugh
et al., 2017). In the method by van Groningen & Wanders (1992), if the input
and reference (at higher resolution) spectra have different resolutions, the
algorithm first finds a convolution factor to degrade the reference spectrum
and then determines the scale factor by fitting a simple, analytical function
to the difference spectrum that is non-variable over the spectral regions of
narrow lines. However, the success rate of determining the scale factor for
the correct input spectrum decreases as the difference in the spectral
resolution decreases. For the latter case, the method suggested in this work
provides a robust way of measuring the line width by first calculating the
flux scale factor from a higher-resolution spectrum and then applying it to
lower-resolution spectra without confusing between spectra with less
dissimilar resolutions. An alternative method by (Fausnaugh et al., 2017)
attempts to first determine the line spread function of the spectrograph to
subtract from an observed profile so that the intrinsic line width is measured
more accurately, especially for low-resolution spectra. However, determination
of a spectrograph’s line spread function relies on a prior measurement of a
narrow-line profile for at least one of the objects in the data set (e.g., the
Whittle 1992 database used by Fausnaugh et al., 2017). Furthermore, using a
previous database value to correct for spectrograph’s line spread function
does not necessarily catch the temporal variations in the instrument behavior,
where narrow-line ratios from high-resolution spectra taken on the same night
of the low-resolution spectra, as in this work, are beneficial for accurate
measurement of the line width.

Additionally, past studies discuss the use of different line-width measures
for reliable black hole mass estimates (Liu & Bian, 2022). Peterson et al.
(2004) conducted a time-series analysis of 35 AGN to test the effectiveness of
different line-width measures for calculating black hole masses. They conclude
that the line dispersion ($\sigma_{\mathrm{line}}$; or the RMS width
calculated from the second moment of a line profile) is a more robust measure
of the variable line profile than FWHM, especially in objects with strong
narrow lines. However, Bian et al. (2008) argue that $\sigma_{\mathrm{line}}$
strongly depends on the contribution from the wings of broad lines. They
analyzed 329 NLS1s from the Sloan Digital Sky Survey catalog to determine
their black hole masses using $\sigma_{\mathrm{line}}$. They infer that in the
cases where the H$\beta$ broad profile is defined by two broad components (as
for Mrk 142 spectra in this work), the black hole mass measurements using
$\sigma_{\mathrm{line}}$ are about 0.5 dex larger than those obtained from
FWHM measurements.

In another study, Collin et al. (2006) characterized the broad H$\beta$
emission-line profiles of all reverberation-mapped AGN to then based on the
ratio of $\mathrm{FWHM}/\sigma_{\mathrm{line}}$[333The nature of a broad-line
profile determines the relationship between the FWHM and
$\sigma_{\mathrm{line}}$, where $\mathrm{FWHM}/\sigma_{\mathrm{line}}=2.35$
for a Gaussian profile.], separating the AGN with narrower broad H$\beta$
profiles ($\mathrm{FWHM}/\sigma_{\mathrm{line}}<2.35$) from those with broader
H$\beta$ ($\mathrm{FWHM}/\sigma_{\mathrm{line}}>2.35$). In their analysis of
the virial product ($VP=M_{\bullet}/f$, where f is scale factor) with FWHM and
$\sigma_{\mathrm{line}}$ from both mean and RMS spectra, they showed: (1)
although $\sigma_{\mathrm{line}}$ yields consistent results for scale factors
from both the mean and the RMS spectra for objects with narrower as well as
broader broad H$\beta$ profiles, $\sigma_{\mathrm{line}}$ from the mean
spectrum is on average $\sim$20% broader in the mean than the RMS spectra; and
(2) for the narrower broad H$\beta$ population (including NLS1s), although the
scale factors from FWHM are larger by a factor of $\sim$3 from both mean and
RMS spectra, FWHM is only $\sim$10% broader in the mean than the RMS spectra.
It is worth noting from the above discussions that both the FWHM and the
$\sigma_{\mathrm{line}}$ are typically measured to be broader in the mean than
the RMS spectra.

###  4.2 Recommendations for Line-Width Measurements in Narrow-Line AGN

The discrepancies highlighted by previous studies emphasize that accurately
measuring broad-line widths in narrow-line objects, e.g., NLS1s, is not
straightforward. As demonstrated in this work, the flux leak from the broad-
line to the narrow-line components can significantly affect the measured FWHM
of the broad lines, e.g., H$\beta$, in NLS1s. The flux leak from Fe ii around
H$\beta$ can also affect the H$\beta$ FWHM measurements. A consistent watch on
how the quality of the data and measurement methods influence each other is
essential. H$\beta$, surrounded by Fe ii emission in the optical and the [O
iii] $\lambda\lambda 4960,5008$ lines, is challenging to measure; however, it
is accessible to most of the ground-based observatories over a considerably
wide redshift range and therefore prominently used for RM studies. Based on
our analysis in this work, we provide recommendations on measuring emission-
line widths in narrow-line AGN.

We strongly recommend both higher- and lower-resolution observations for RM
analysis of narrow-line AGN. In RM, the nearest neighboring narrow line is
typically used for relative flux calibration of the broad lines of interest,
e.g., [O iii] $\lambda 5008$ is used as a calibrator line for measuring
H$\beta$. Therefore, a completely resolved calibrator line is essential. We
regard this as the primary requirement for accurately measuring the broad-line
widths in narrow-line AGN. Then, while measuring line profiles, applying
narrow-line flux ratios (relative to the calibrator line) determined from the
higher-resolution spectra will allow more accurate measurements of line widths
with the mean spectra. If only lower-resolution spectra are available, we
recommend using higher-resolution spectra from archival observations to
determine the appropriate narrow-line flux ratios. If no archival higher-
resolution spectra exist, we highly recommend scheduling at least one higher-
resolution spectrum along with lower-resolution spectra at each epoch. RM
analysis of narrow-line AGN will benefit extensively with simultaneous higher-
and lower-resolution observations.

##  5 Conclusion

We performed a detailed correlation analysis of the spectral measurements from
the Mrk 142 data taken with Gemini at higher resolution (185.6 km s-1) and LJT
at lower resolution (695.2 km s-1) to understand the effect of different
spectral resolutions on the measured physical properties of emission lines.
The FWHMs measured for the broad H$\beta$ from the Gemini and LJT spectra did
not overlap. Through our analysis, we identified that the “broader”,
unresolved [O iii] $\lambda 5008$ in the LJT spectra affected the H$\beta$
FWHM measurements during spectral fitting. We corrected for the LJT H$\beta$
FWHM values by fixing the narrow-line flux ratio of H$\beta$ to the [O iii]
$\lambda 5008$ line flux as determined from the Gemini spectral fits. Adopting
this procedure, the mean H$\beta$ FWHM reduced from $\sim$2220 km s-1 to
$\sim$1930 km s-1, an improvement of $\sim$54% in the mean value. We summarize
our main results below.

  1. 1.

In Mrk 142, lower-resolution spectra with an unresolved [O iii] $\lambda 5008$
line, a fixed width (equal to the [O iii] line width) but flexible line flux
for the narrow H$\beta$ caused a flux leak from the broad to the narrow
component, resulting in a lower peak flux for the broad-line profile and
therefore a broader broad H$\beta$ FWHM as compared to the higher-resolution
spectra with a resolved [O iii] $\lambda 5008$ line.

  2. 2.

Fixing the narrow-line flux ratio of H$\beta$ to [O iii] $\lambda 5008$ while
measuring the H$\beta$ broad-line profile in the LJT spectra nullified the
correlation of the broad H$\beta$ FWHM with the [O iii] $\lambda 5008$ flux as
well as reduced the scatter in the FWHM values by a factor of 2.6, equal to
the scatter in the H$\beta$ FWHMs measured from the Gemini spectra.
Consequently, the mean of the H$\beta$ FWHM values decreased by $\sim$54% or
an effective width of $\sim$1000 km s-1. The remaining offset is likely from
Fe ii.

  3. 3.

Considering the impact of a resolved [O iii] $\lambda 5008$ on the H$\beta$
FWHM measurements, we strongly recommend using both higher- and lower-
resolution spectra for measuring line profiles in narrow-line AGN.

We leveraged the access to both the Gemini and the LJT spectra of Mrk 142 for
RM analysis – while the LJT observations expanded the time baseline and filled
the gaps in Gemini observations, the Gemini spectra at higher resolution
allowed more precise H$\beta$ line measurements from the LJT spectra. We
emphasize that measuring broad-line profiles in objects with narrower broad
lines than the typical AGN population is not straightforward. Branching out to
diverse populations for RM studies perhaps needs a revisit to emission-line
measurement methods.

##  6 acknowledgments

V.C.K. thanks T. A. Boroson, who provided the Fe ii template to C.H. for the
spectral modeling process. We acknowledge the support of the Natural Sciences
and Engineering Research Council of Canada (NSERC), Discovery Grant
RGPIN/04157. V.C.K. acknowledges the support of the Ontario Graduate
Scholarships. C.H. acknowledges support from the National Science Foundation
of China (12122305). P.D. acknowledges financial support from National Science
Foundation of China grants NSFC-12022301, -11873048, and -11991051. The
research of V.C.K. was partially supported by the New Technologies for
Canadian Observatories, an NSERC CREATE program. We acknowledge the support of
the National Key R&D Program of China No. 2021YFA1600404, and the National
Science Foundation of China (11991054, 11833008, 11991051, 11973029). V.C.K.
also acknowledges Jonathan Trump, Martin Houde, Stanimir Metchev, and Charles
McKenzie for their valuable feedback and discussions.

This research was based on observations obtained at the Gemini Observatory,
which is managed by the Association of Universities for Research in Astronomy
(AURA) under a cooperative agreement with the National Science Foundation on
behalf of the Gemini Observatory partnership: the National Science Foundation
(United States), National Research Council (Canada), Agencia Nacional de
Investigación y Desarrollo (Chile), Ministerio de Ciencia, Tecnología e
Innovación (Argentina), Ministério da Ciência, Tecnologia, Inovações e
Comunicações (Brazil), and Korea Astronomy and Space Science Institute
(Republic of Korea). This work was enabled by observations made from the
Gemini North telescope, located within the Maunakea Science Reserve and
adjacent to the summit of Maunakea. We are grateful for the privilege of
observing the Universe from a place that is unique in both its astronomical
quality and its cultural significance.

This research used observations from the Lijiang 2.4-meter Telescope funded by
the Chinese Academy of Sciences (CAS) and the People’s Government of Yunnan
Province.

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