# Supermassive Black Holes with High Accretion Rates in Active Galactic
Nuclei. XIII. Ultraviolet Time Lag of H$\beta$ Emission in Mrk 142

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  Sofia Pasquini  Department
of Physics and Astronomy, The University of Western Ontario, 1151 Richmond
Street, London, Ontario N6A 3K7, Canada  Patrick Hall  Department of Physics
and Astronomy, York University, 4700 Keele Street, Toronto, Ontario M3J 1P3,
Canada  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  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  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  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  Michael Goad  School of Physics and
Astronomy, University of Leicester, Leicester LE1 7RH, UK  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  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 September 3, 2023)

###### Abstract

We performed a rigorous reverberation-mapping analysis of the broad-line
region (BLR) in a highly accreting ($L/L_{\mathrm{Edd}}=0.74$–3.4) active
galactic nucleus, Markarian 142 (Mrk 142), for the first time using concurrent
observations of the inner accretion disk and the BLR to determine a time lag
for the H$\beta$ $\lambda 4861$ emission relative to the ultraviolet (UV)
continuum variations. We used continuum data taken with the Niel Gehrels Swift
Observatory in the UVW2 band, and the Las Cumbres Observatory, Dan Zowada
Memorial Observatory, and Liverpool Telescope in the g band, as part of the
broader Mrk 142 multi-wavelength monitoring campaign in 2019. We obtained new
spectroscopic observations covering the H$\beta$ broad emission line in the
optical from the Gemini North Telescope and the Lijiang 2.4-meter Telescope
for a total of 102 epochs (over a period of eight months) contemporaneous to
the continuum data. Our primary result states a UV-to-H$\beta$ time lag of
$8.68_{-0.72}^{+0.75}$ days in Mrk 142 obtained from light-curve analysis with
a Python-based Running Optimal Average algorithm. We placed our new
measurements for Mrk 142 on the optical and UV radius-luminosity relations for
NGC 5548 to understand the nature of the continuum driver. The positions of
Mrk 142 on the scaling relations suggest that UV is closer to the “true”
driving continuum than the optical. Furthermore, we obtain
$\log(M_{\bullet}/M_{\odot})$ = $6.32\pm 0.29$ assuming UV as the primary
driving continuum.
Unified Astronomy Thesaurus concepts: Active galactic nuclei (16); Accretion
(14); Spectroscopy (1558)
Supporting material: Machine-readable tables and spectra

††journal: ApJ††facilities: Gemini North Telescope (GMOS), Lijiang 2.4-meter
Telescope (YFOSC), The Neil Gehrels Swift Observatory, Las Cumbres
Observatory, Dan Zowada Memorial Observatory, Liverpool Telescope (Steele et
al., 2004)††software: IRAF, Gemini IRAF, Python, Astropy (Astropy
Collaboration et al., 2013), PrepSpec, Sherpa (Freeman et al., 2001; Burke et
al., 2018), PyROA (Donnan et al., 2021), ICCF (Gaskell & Sparke, 1986; Gaskell
& Peterson, 1987), JAVELIN (Zu et al., 2011, 2013)

##  1 Introduction

Accretion onto supermassive black holes through an accretion disk of ionized
gas powers active galactic nuclei (AGN) at the centers of massive galaxies.
AGN accreting at typical rates (a few percent of the Eddington limit) have a
geometrically thin but optically thick disk – the ‘thin-disk’ model (Shakura &
Sunyaev, 1973). However, theoretical models predict a notably different
structure for the AGN with high accretion rates significantly above the
Eddington limit – super-Eddington AGN (e.g., Abramowicz et al., 1988). The
occurrence of such AGN is likely higher during the peak era of supermassive
black hole growth during cosmic noon (redshifts, $z=1$–3; Brandt & Alexander,
2010; Shen et al., 2020). Understanding the structure of the accretion system
in high-Eddington AGN remains an open issue in accretion physics.

Although models exist for slim-disk systems, observational tests of the
structure of the accretion flow in super-Eddington AGN are rare. At high
accretion rates, radiation pressure is expected to dominate, causing the inner
disk to inflate vertically – now called a ‘slim’ (rather than thin) disk –
with a scale height, $H\leq R$, where R is the disk radius (e.g., Abramowicz
et al., 1988). Photons are trapped in the fast-flowing matter, eventually
falling into the black hole. Given that not all photons escape, the disks in
super-Eddington AGN are underluminous relative to the accretion rates as
compared to thin disks (Jaroszyński et al., 1980). Begelman (2002) proposed an
alternative scenario where the “photon-bubble instability” principle can cause
the disks in super-Eddington AGN to become inhomogeneous at scales much
smaller than the disk scale height.

Reverberation mapping (RM; Blandford & McKee, 1982; Peterson, 1993) provides a
way to observationally study the slim-disk model and broad-line region (BLR)
in super-Eddington AGN. RM takes advantage of the observed continuum
variability of AGN on many time scales (from several days to weeks and years;
e.g, Peterson et al., 1982). The accretion-disk emission illuminates the BLR
on larger scales, and sets the ionization structure and thus the location of
the gas generating the broad emission lines (e.g., H$\beta$). An increase in
continuum emission from the accretion disk results in an increase in broad
emission-line flux after a time lag set by the sum total of the light travel
time between the continuum-emitting region and the BLR (Peterson, 2014), and
the recombination timescale, where the latter is much smaller than the former
for typical BLR densities (and therefore ignored in the time-lag
calculations). RM converts this time lag into a spatial distance, the size of
the BLR. Thus, applying RM to high-accretion rate AGN gives an observational
method to test the structure of the accretion flow and BLR in these systems,
and place super-Eddington AGN on the radius-luminosity (R–L) relationship for
AGN (Kaspi et al., 2005; Bentz et al., 2013).

The Narrow-Line Seyfert 1 (NLS1) class of AGN are considered to have high
accretion rates, and typically display narrow broad emission lines (e.g., the
H$\beta$ line has a full width at half maximum, FWHM $\lesssim 2000$ km s-1)
in comparison to other broad-line objects (and broader than the narrow lines
seen in type 2 objects), strong Fe ii emission lines, and weak [O iii] lines
(e.g., Osterbrock & Pogge, 1987; Boroson & Green, 1992; Boller et al., 1996;
Véron-Cetty et al., 2001) in their spectra. The Super-Eddington Accreting
Massive Black Holes (SEAMBH) campaign has been performing photometric and
spectroscopic monitoring over the past nine years of high accretion-rate AGN
that display spectral characteristics of NLS1s (e.g., Du et al., 2014; Wang et
al., 2014b; Hu et al., 2015; Du et al., 2015, 2016a, 2016b, 2018; Li et al.,
2018, 2021). Du et al. (2016b) showed that the BLRs in super-Eddington AGN are
smaller than those with sub-Eddington accretion rates. In the context of the
slim-disk model, the smaller BLR sizes can be explained as a consequence of
the increased scale height of the inner accretion disk that shields the BLR
from the central ionizing flux (Wang et al., 2014a). H$\beta$, a marker of the
hydrogen ionization front in the BLR, can thus exist at smaller radii than in
thin accretion-disk systems. Fonseca Alvarez et al. (2020) offer an
alternative explanation. In their correlation analysis of the physical and
spectral properties of the Sloan Digital Sky Survey (SDSS) RM AGN, Fonseca
Alvarez et al. (2020) found that the R–L offset (defined as the ratio of the
measured H$\beta$ time lag to the expected time lag from the best-fit R–L such
as that given by Bentz et al. 2013) is positively correlated to the [O iii]
$\lambda 5008$ to H$\beta$ luminosity ratio, which is often used as a proxy
for the number of ionizing photons (e.g., Baldwin et al., 1981). The smaller
BLR sizes are therefore likely a result of the changes in the shape of the
ultraviolet (UV)/optical spectral energy distribution (SED) of AGN (Fonseca
Alvarez et al., 2020).

As the most promising SEAMBH object – a bright target with an extremely super-
Eddington accretion rate ($\dot{M}/\dot{M}_{\mathrm{Edd}}=250$; Li et al.,
2018) and a well-measured H$\beta$ lag – Markarian 142 (Mrk 142 or PG
1022+519, RA = 10h25m31.20s, Dec = +51∘40′34.87″, $z=0.045$) is the target of
our study to probe the structure of its BLR. In the 2012 SEAMBH campaign, Mrk
142 was highly variable with a fractional variability amplitude of
$F_{\rm{var}}=8.1\%$ at 5100 Å over a period of six months. Its variable
nature makes it amenable to RM studies of both accretion-disk structure (from
X-ray/UV/optical continuum time-lag studies) and the BLR structure (from
continuum-emission line time lags). Accretion-disk RM applies the same
principle as BLR RM to the inner and outer regions of the accretion disk to
determine its size and temperature profile (Cackett et al., 2007). The more
energetic X-ray/UV radiation from the inner disk illuminates the disk at
larger radii where the optical photons are generated. Therefore, the lower-
energy emission will respond with a positive time lag to changes in the high
energy radiation giving rise to correlated continuum light curves. Mrk 142 has
a total H$\beta$ time lag ($\tau$) with respect to the 5100 Å continuum
emission of $7.9_{-1.1}^{+1.2}$ days (Du et al., 2015) and a black hole mass
of $\log(M_{\bullet}/M_{\odot})$ = $6.23_{-0.45}^{+0.26}$ (Li et al., 2018).

In this paper, we present Mrk 142 time-lag measurements from two ground-based,
optical spectroscopic RM campaigns of Mrk 142 concurrent with the photometric
monitoring of the target with the Neil Gehrels Swift Observatory (Swift) in a
UV band; and the Las Cumbres Observatory (LCO), Dan Zowada Memorial
Observatory (Zowada), and Liverpool Telescope (Liverpool; Steele et al., 2004)
in an optical band. With our joint campaign, we performed, for the first time,
simultaneous measurements of the inner accretion disk and BLR size in a super-
Eddington AGN. This paper is organized as follows. In Section 2, we provide
details of the observations, and in Section 3, we explain the process of data
reduction. In Section 4, we describe our spectral modeling followed by light-
curve analysis in Section 5. In Section 6, we outline and discuss our results
in the context of previous studies. Section 7 provides closing remarks.
Throughout this work, we use the standard cosmology with $H_{0}=67$ km s-1
Mpc-1, $\Omega_{\Lambda}=0.68$, and $\Omega_{\mathrm{M}}=0.32$ (Planck
Collaboration et al., 2014).

##  2 Observations

We obtained concurrent observations of Mrk 142 with multiple telescopes to
perform RM analysis of the accretion disk and BLR simultaneously. Figure 1
showing the continuum light curves of Mrk 142 highlights the simultaneous
coverage with different telescopes.

Figure 1: Mrk 142 continuum light curves – UVW2 band with Swift (blue upright
triangles, panel a) and the g band with LCO, Zowada, and Liverpool (green
flipped triangles, panel b) from photometric observations; and 5100 Å (purple
diamonds, panel c) inter-calibrated from the spectroscopic observations with
the Gemini North Telescope (Gemini) and the Lijiang Telescope (LJT). The 5100
Å inter-calibrated light curve displays the combined spectroscopic coverage
over 102 epochs. We performed the inter-calibration with a Python-based
Running Optimal Average (PyROA; Donnan et al., 2021) technique (see
introduction to PyROA in Section 5.1).

###  2.1 Gemini North Telescope

We obtained new observations of Mrk 142 long-slit spectra taken with the
Gemini Multi-Object Spectrograph (GMOS; Hook et al., 2004) on the 8.1-m Gemini
North Telescope (Gemini) on Maunakea, Hawai‘i with 33 epochs from February 6
through June 1, 2019. These spectral observations are concurrent with the Mrk
142 photometric data from the Swift telescope comprising 180 epochs of
1-kilosecond exposures at X-ray, UV, and optical wavelengths from January 1
through April 30, 2019 (P.I.: E. Cackett) as well as with the photometric
g-band data from LCO (P.I.: R. Edelson), Zowada (P.I.: E.Cackett), and
Liverpool (P.I.: M. Goad); the photometric data are presented in Cackett et
al. (2020). The Swift observations had a twice-daily cadence until March 19,
and the cadence was decreased to daily from March 20 onward. We required
observations from Gemini in early 2019 with considerable overlap with the
Swift campaign to allow, for the first time, simultaneous measurements of the
UV-emitting accretion disk and the BLR of a super-Eddington AGN. The cadence
of the Gemini observations was set to one day. We obtained data for only two,
sparsely separated epochs in February during the beginning of the observing
period due to weather interruptions. However, observations were more frequent
in March and May, and the daily cadence was achieved in the first week of
April.

The spectra were taken with the GMOS-North Hamamatsu detector and a single
grating, B600 with two different slits, 0.75″ (narrow slit) and 5.00″ (wide
slit), in the two-target acquisition mode, where Mrk 142 and a comparison star
were observed in the same slit. The GMOS-North Hamamatsu detector comprises
three $\sim$2048$\times$4176 pixel chips (full detector size of
6278$\times$4176 pixels, mosaiced) arranged in a row with pixel size of
0.0807″ with two chip gaps 4.88″ wide. The choice of the grating was made to
obtain the broad emission line of interest, H$\beta$ $\lambda 4861$, in the
spectra. The narrow 0.75″ slit was selected to obtain a spectral resolution of
$\sim$1125 (narrow-slit data) required to study the velocity structure of
H$\beta$. Accuracy in spectrophotometric calibration is a key for RM studies,
and therefore, we used the wide slit at a resolution of $\sim$170 (wide-slit
data) to correct for slit losses due to the narrow slit. To satisfy this
calibration requirement, Mrk 142 and a comparison star for flux calibration
(hereafter, calibration star) were placed simultaneously in the same slit. We
achieved this for all observations by fixing the position angle of the slits
at 155.20∘ East of North such that Mrk 142 appeared at the center of the slit.
The selected G-type calibration star (RA = 10h25m36.37s, Dec = +51∘38′52.18″,
r-band magnitude = 15.9 from the SDSS catalog) has a well-calibrated spectrum
and was used for previous LJT campaigns. Flatfield images were taken for every
object (science target and calibration star) with the Gemini Facility
Calibration Unit (GCAL) in the sequence FLAT–OBJECT–OBJECT–FLAT with both
slits. The on-target exposures were 90 s long. We also took daytime arc lamp
spectra with the CuAr lamp, again, for both slits. Binning of 1 in the
spectral (X) direction and 2 in the spatial (Y) direction (1$\times$2) was
used for all data except for the wide-slit arc lamp spectra, which used the
binning of 1$\times$1\. A summary of the GMOS-North science observations is
provided in Table 1. The object spectra from all epochs except the narrow-slit
spectra from epoch 30 were assigned a Pass (“P”) flag.

Table 1: Summary of Mrk 142 GMOS observations from February to June 2019

Epoch | UTaaUT: Universal Time dates Date | MJDbbMJD: Modified Julian Date recorded at the start of the observations for individual exposures. Start Time | Airmass
---|---|---|---
| (YYYY-MM-DD) | 0.75$\arcsec$ slit | 5.00$\arcsec$ slit | 0.75$\arcsec$ slit | 5.00$\arcsec$ slit
1 | 2019-02-06 | 58520.412 | 58520.418 | 1.275 | 1.258
|  | 58520.414 | 58520.420 | 1.270 | 1.254
2 | 2019-02-26 | 58540.415 | 58540.421 | 1.181 | 1.178
|  | 58540.417 | 58540.423 | 1.180 | 1.177
3 | 2019-03-03 | 58545.433 | 58545.439 | 1.178 | 1.181
|  | 58545.435 | 58545.441 | 1.178 | 1.182
4 | 2019-03-09 | 58551.430 | 58551.437 | 1.187 | 1.193
|  | 58551.432 | 58551.438 | 1.188 | 1.194
5 | 2019-03-12 | 58554.550 | 58554.557 | 1.679 | 1.734
|  | 58554.552 | 58554.558 | 1.693 | 1.750
6 | 2019-03-15 | 58557.427 | 58557.433 | 1.200 | 1.209
|  | 58557.428 | 58557.442 | 1.202 | 1.225
7 | 2019-03-16 | 58558.355 | 58558.362 | 1.189 | 1.184
|  | 58558.357 | 58558.363 | 1.188 | 1.183
8 | 2019-03-23 | 58565.281 | 58565.287 | 1.299 | 1.280
|  | 58565.283 | 58565.289 | 1.293 | 1.276
9 | 2019-03-26 | 58568.254 | 58568.260 | 1.365 | 1.341
|  | 58568.256 | 58568.262 | 1.359 | 1.335
10 | 2019-03-27 | 58569.410 | 58569.416 | 1.225 | 1.237
|  | 58569.411 | 58569.418 | 1.228 | 1.241
11 | 2019-03-29 | 58571.233ccScience spectrum assigned SPCALF (see $Note$ below)=0. | 58571.239 | 1.424 | 1.394
|  | 58571.235ddScience spectrum calibrated with the narrow-slit standard star spectrum from exposure 1 and hence assigned SPCALG (see $Note$ below)=B. | 58571.241 | 1.416 | 1.387
12 | 2019-03-31 | 58573.233 | 58573.239 | 1.398 | 1.370
|  | 58573.235 | 58573.241 | 1.390 | 1.364
13 | 2019-04-03 | 58576.457 | 58576.463 | 1.451 | 1.486
|  | 58576.459 | 58576.465 | 1.460 | 1.496
14 | 2019-04-04 | 58577.234 | 58577.240 | 1.350 | 1.327
|  | 58577.235 | 58577.241 | 1.343 | 1.321
15 | 2019-04-05 | 58578.241 | 58578.248 | 1.312 | 1.292
|  | 58578.243 | 58578.249 | 1.306 | 1.287
16 | 2019-04-06 | 58579.236 | 58579.242 | 1.322 | 1.302
|  | 58579.237 | 58579.243 | 1.317 | 1.297
17 | 2019-04-07 | 58580.461 | 58580.467 | 1.543 | 1.585
|  | 58580.463 | 58580.469 | 1.554 | 1.597
18 | 2019-04-08 | 58581.331 | 58581.337 | 1.177 | 1.179
|  | 58581.333 | 58581.339 | 1.177 | 1.180
19 | 2019-04-09 | 58582.432 | 58582.438 | 1.408 | 1.439
|  | 58582.434 | 58582.440 | 1.416 | 1.447
20 | 2019-04-25 | 58598.274 | 58598.280 | 1.175 | 1.176
|  | 58598.276 | 58598.282 | 1.175 | 1.176
21 | 2019-04-27 | 58600.391 | 58600.397ccScience spectrum assigned SPCALF (see $Note$ below)=0. | 1.447 | 1.481
|  | 58600.392 | 58600.398 | 1.456 | 1.491
22 | 2019-05-01 | 58604.338 | 58604.344ccScience spectrum assigned SPCALF (see $Note$ below)=0. | 1.282 | 1.300
|  | 58604.340 | 58604.346 | 1.286 | 1.305
23 | 2019-05-02 | 58605.327 | 58605.333 | 1.259 | 1.275
|  | 58605.329 | 58605.335 | 1.263 | 1.280
24 | 2019-05-07 | 58610.317 | 58610.323 | 1.267 | 1.285
|  | 58610.318 | 58610.324 | 1.272 | 1.289
25 | 2019-05-08 | 58611.361 | 58611.367 | 1.450 | 1.485
|  | 58611.363ccScience spectrum assigned SPCALF (see $Note$ below)=0. | 58611.369ccScience spectrum assigned SPCALF (see $Note$ below)=0. | 1.459 | 1.494
26 | 2019-05-09 | 58612.246 | 58612.253 | 1.177 | 1.179
|  | 58612.248 | 58612.254 | 1.177 | 1.180
27 | 2019-05-12 | 58615.269 | 58615.275 | 1.201 | 1.209
|  | 58615.270 | 58615.276 | 1.203 | 1.212
28 | 2019-05-13 | 58616.320eeScience spectrum likely had a calibration issue and hence was not used for further analysis (see Appendix A for details). | 58616.326 | 1.329 | 1.353
|  | 58616.322 | 58616.328 | 1.335 | 1.359
29 | 2019-05-24 | 58627.266 | 58627.272 | 1.256 | 1.272
|  | 58627.267 | 58627.273 | 1.260 | 1.276
30 | 2019-05-25 | 58628.242ffScience spectrum assigned DQF (see $Note$ below)=U. | 58628.248 | 1.213 | 1.223
|  | 58628.243ffScience spectrum assigned DQF (see $Note$ below)=U. | 58628.249 | 1.216 | 1.227
31 | 2019-05-26 | 58629.251 | 58629.257 | 1.235 | 1.249
|  | 58629.253 | 58629.259 | 1.239 | 1.252
32 | 2019-05-28 | 58631.251 | 58631.257 | 1.246 | 1.261
|  | 58631.252 | 58631.258 | 1.250 | 1.265
33 | 2019-06-01 | 58635.255 | 58635.262 | 1.287 | 1.307
|  | 58635.257 | 58635.263 | 1.292 | 1.312

Note. — Observations were done with the GMOS-North Hamamatsu detector in the
two-target acquisition mode (Mrk 142 and a comparison star in the same slit)
positioning the slit at 155.20∘ East of North, with the B600 grating (covering
the broad H$\beta$ emission line at $\sim$4862Å) and two slits, 0.75$\arcsec$
(narrow slit) and 5.00$\arcsec$ (wide slit). Two exposures were taken with
every grating/slit combination, each 90 seconds long. A Data Quality Flag
(DQF) of “P” or “U” that stands for Pass or Usable was assigned to all data at
the time of observing. Unless stated otherwise, all science spectra were
assigned a DQF of “P”. SpectroPhotometric CALibration Flag (SPCALF) indicates
whether the science spectra were calibrated (“1”) or not calibrated (“0”)
during spectral reduction (see $\S$3.1.4 for more details). SpectroPhotometric
CALibration Grade (SPCALG) indicates the grade assigned to the
spectrophotometric calibration based on the epoch and exposure of the
calibration star spectrum used for calibrating the science spectra (see
$\S$3.1.4 for more details). All science spectra were assigned an SPCALF of 1
and an SPCALG of “A” unless indicated otherwise.

###  2.2 Lijiang Telescope

To complement the short observing period of 33 epochs with Gemini, we
incorporated supporting observations of Mrk 142 for our study. We observed Mrk
142 with the Yunnan Faint Object Spectrograph and Camera on the Lijiang 2.4-m
Telescope (LJT; Wang et al., 2019) in the two-target acquisition mode with the
same calibration star as used for the Gemini observations. We followed the
same observing procedure as for previous SEAMBH campaigns (e.g., Du et al.,
2014, 2015). We obtained long-slit spectra of the target at 69 epochs from
November 1, 2018 through June 21, 2019, contemporaneously with the Swift,
LCO+Zowada+Liverpool, and Gemini observing campaigns.

Two exposures of 1200 seconds each were taken for each epoch, with Grism 14
and a long slit with a projected width of 2$\farcs$5\. The yielded spectra
cover a wavelength rage of 3800 Å to 7200 Å, with a dispersion of 1.8 Å
pixel-1. The final instrumental broadening is roughly 695 km s-1 in FWHM.
Bias, dome flats, and arc-lamp spectra were taken each night for calibrations,
and spectrophotometric standards were observed in several nights of good
weather conditions.

Table 2 provides a summary of the overlapping photometric and spectroscopic
programs.

Table 2: Summary of Overlapping Photometric and Spectroscopic Observations  Filter/Line | Observatory | Date Range (MJDaaMJD: Modified Julian Date) | Number of Epochs | Mean Cadence
---|---|---|---|---
UVW2 [1928 Å]bbPhotometry | Swift | 58484.349–58603.941 | 149 |  $\sim$twice-daily
g [4770 Å]bbPhotometry | LCO, Zowada, Liverpool | 58422.973–58653.260 | 361 | 2 days
H$\beta$ $\lambda 4861$ccSpectroscopy | Gemini | 58520.414–58635.257 | 33 |  $\sim$3.6 days
H$\beta$ $\lambda 4861$ccSpectroscopy | LJT | 58423.899–58655.549 | 69 |  $\sim$3.4 days

##  3 Spectral Reduction

###  3.1 Gemini Spectral Reduction

The spectral reduction process for all Gemini epochs included four stages (in
the order of appearance below) with the Gemini Image Reduction and Analysis
Facility (Gemini IRAF111Gemini IRAF is an external package that makes use of
IRAF (a software system used for the reduction and analysis of astronomical
data, created and supported by the National Optical Astronomy Observatory in
Tucson, Arizona). See more at https://www.gemini.edu/sciops/data-and-
results/processing-software/description.) reduction package: (1) baseline
calibrations with GCAL flats, two-dimensional (2D) arc lamp spectra, and bias
frames; (2) cleaning of 2D spectra followed by the wavelength calibration and
extraction of one-dimensional (1D) science and calibration-star spectra (in
the same slit); (3) preparing 1D spectra for analysis with PrepSpec (see
introduction to PrepSpec in Section 4.1); and (4) flux calibration of the 1D
science spectra. For each epoch, we first sorted the data into lists of bias
frames, GCAL flats, arc lamp spectra, and object spectra for both the narrow
and the wide slits. We then used the the same reduction script with different
parameter settings for processing the data taken with the two slits.

####  3.1.1 Baseline Calibrations

Baseline calibrations comprised creating a masterbias image, generating a
dispersion solution with the narrow-slit arc lamp spectra, and constructing
masterflat images with both the narrow- and wide-slit flatfield images. For
individual observing nights, we used bias frames with the binning of
1$\times$2 and a full-frame readout from the Gemini Observatory Archive. We
applied an overscan noise correction to all bias images, for a given night,
before combining them into a masterbias image. We then reduced the narrow-slit
arc-lamp spectra with bias subtraction turned off and used them to generate 2D
dispersion solutions with the task gswavelength. Generating dispersion
solutions was a two-step process – fitting the 1D wavelength solution in the
spectral direction and fitting any distortions in the spatial direction. The
reference wavelengths for the arc-lamp spectra were used from the Gemini IRAF
package. Because the re-binned, wide-slit arc-lamp spectra – binned from
1$\times$1 to 1$\times$2 to match the binning of the corresponding GCAL flats
and object spectra – were unable to provide a non-distorted wide-slit
dispersion solution, we used the narrow-slit solution to wavelength calibrate
the wide-slit data. For a given epoch, we combined the two GCAL flats
(including a quantum efficiency correction for each) taken with the two slits
to create a masterflat corrected for the uneven illumination along the GMOS
detector in the long-slit mode.

####  3.1.2 Cleaning, Wavelength Calibration, and Extraction

We corrected the 2D object spectra affected by cosmic-ray hits and performed
their wavelength calibration to then extract the 1D science and calibration-
star spectra. With the task gscrrej, we first selected a fixed square region
surrounding the cosmic-ray affected pixels above a specified threshold and
then replaced them with interpolated values from local noise levels. However,
this method did not correct for all cosmic rays. We applied an additional
correction to the affected pixels that remained uncorrected in the next stage
of the reduction process. We applied the derived narrow-slit dispersion
solutions to both the narrow- and the wide-slit object spectra.

For a given epoch, we extracted 1D science and calibration-star spectra
separately from individual exposures with the task gsextract. We selected a
considerable swath of background for subtraction from both sides of each trace
during the extraction process. The subtraction of bright skylines from the
extracted 1D spectra resulted in some sharp spikes in the spectra owing to
residual noise. We applied additional correction to remove the sharp features
in the 1D spectra in the next stage of reduction (see Section 3.1.3 for
details).

A few of the extracted science and calibration-star spectra showed flat
regions (zero flux values) on the shorter-wavelength (or blue) end ($\sim$3355
Å to $\sim$4325 Å) that do not match the true shape of the continuum, while
some spectra showed bump-like features. The flat regions were a consequence of
the slit position angle not aligned along the parallactic angle, whereas the
bump-like features likely resulted from the flat-fielding process, where a
higher order spline was used to create the masterflat to appropriately trace
detector sensitivity near the chip-gap regions and avoid discontinuities in
the calibrated spectra near the chip edges. We corrected the spectra
containing flat blue ends or bumpy features individually before attempting
flux calibration (see Section 3.1.3 for details).

####  3.1.3 Additional Corrections to 1D Spectra – Preparing Data for PrepSpec

To prepare the spectra for PrepSpec, it was important that each spectrum have
no gaps. Before the flux calibration stage, we trimmed the blue ends of the
spectra shorter than $\sim$4325 Å in the rest frame because they were very
noisy and not required for the purposes of this study. We further processed
the 1D spectra for: (1) flat blue ends (due to the slit position angle) or
bump-like features (from the flat-fielding process) appearing in some spectra;
and (2) spectral regions affected by artefacts from cosmic-ray removal and sky
subtraction as well as chip gaps with no flux. This additional processing was
important for the initial stage of modeling spectra with PrepSpec, the
software tool that corrects spectra for relative calibration differences (see
Section 4.1 for details).

We developed a script to correct flat and bump-like regions in the 1D spectra
in Python222Visit https://www.python.org/ for full documentation on Python.
v3.6.5. A spline function fit to a reference spectrum modeled the true shape
of the affected region. We then modeled the flux over the affected pixels
assuming a Gaussian distribution of data points with standard deviation equal
to the measured standard deviation at the same location in the reference
spectrum. The reference spectrum used for recovery was typically the spectrum
from another exposure taken on the same night (see Appendix A for exceptions).

To correct for spectral regions affected by artefacts and chip-gaps, we
developed another Python script to replace the regions with affected data
points by local median values or interpolated and simulated data. In a given
window of affected points: (1) if the number of pixels was $<$5, the algorithm
replaced every data point by the median value of a range of 5 pixels on either
side of that point with the noise equal to the local median noise; and (2) if
the number of pixels was $\geq$5, the algorithm first linearly interpolated
across the affected region and then replaced the interpolated points with
simulated data assuming a Gaussian distribution with a standard deviation
equal to twice the noise in the interpolated data. The uncertainties for the
corrected pixel regions were assigned to be twice as much as the standard
deviation of the unaffected individual pixel values in the region.

We used the wide-slit science and calibration-star spectra to correct for the
wavelength-dependent slit losses in the narrow-slit spectra with a PyRAF (IRAF
with Python wrapper) script. We employed the IRAF task curfit to fit a spline
function to the ratios of the narrow-slit to the reference spectra. We used a
single reference spectrum: the mean of the bright, wide-slit spectra. Finally,
we updated the starting pixel value of the wavelength scale in the FITS file
headers of the slit-loss corrected spectra to generate the appropriate
wavelength grid for the trimmed spectra.

The Python scripts for performing the above corrections to prepare spectra for
PrepSpec analysis are publicly available on GitHub333Please contact the
corresponding author for further details..

####  3.1.4 Flux Calibration

The flux calibration process included two steps – fitting a sensitivity curve
of the detector response to the flux standard with gsstandard, and applying
the sensitivity solution to the science spectra with the task gscalibrate. For
flux calibration, we used the calibration star captured in the same slit as
the science target except for a handful of spectra for which we used the star
from another exposure of the same epoch (see Appendix A for details).
Accordingly, we assigned a SpectroPhotometric CALibration Flag (SPCALF) of 1
(0) for calibrated (non-calibrated) science spectra (stated in Table 1). Based
on the epoch and exposure of the standard star spectrum used for calibration,
we further assigned a SpectroPhotometric CALibration Grade (SPCALG; see Table
1) to the science spectra as follows.

  * •

SPCALG “A”: Science spectrum calibrated with the standard star spectrum from
the same exposure.

  * •

SPCALG “B”: Science spectrum calibrated with the standard star spectrum from
the same epoch but different exposure.

Appendix A outlines special cases of spectral reduction that were treated
separately.

###  3.2 LJT Spectral Reduction

We first reduced the LJT spectra with IRAF, following the standard procedures
for bias subtraction, flat-field correction, and wavelength calibration. The
spectra of both the target and the calibration star were extracted in a
uniform aperture of 8$\farcs$5\. For those nights with good weather
conditions, the spectra of the calibration star were flux-calibrated using the
spectrophotometric standards. We combined these flux-calibrated spectra to
generate a fiducial spectrum of the calibration star. Then, for each exposure,
a sensitivity function was obtained by fitting the fiducial spectrum to the
extracted spectrum of the comparison star. Finally, we performed flux-
calibration of the target spectrum (see Li et al. 2021 for more details).

###  3.3 Comparison Between Gemini and LJT Spectra

Gemini spectra from 33 epochs and LJT spectra from 69 epochs provided 102
epochs of Mrk 142 spectral observations overlapping with the Swift and
LCO+Zowada+Liverpool photometric campaigns. A mean spectrum allows us to
visualize spectral features in high signal-to-noise (S/N) from the combined
observations, while a root-mean-square (RMS) spectrum signifies the
variability in the spectral features. Figure 2 displays the mean and RMS of
the Gemini (Top) and LJT (Bottom) spectra. The higher-resolution Gemini mean
spectrum shows sharper emission-line profiles (H$\beta$, [O iii], and He i) as
compared to the LJT mean. At lower resolution, LJT spectra are affected by
instrumental broadening which results in the narrow emission lines, e.g., [O
iii], appearing broader than in the Gemini mean. The instrumental broadening
effect also blurs the Fe ii emission (shaded in faint blue) and the coronal
lines (high-ionization forbidden transitions shaded in brown) in the LJT mean
spectrum. In contrast to the Gemini mean, the Fe ii features at $\sim$4925 Å
and $\sim$5030 Å in the LJT mean appear blended with the H$\beta$ wings on the
longer-wavelength (red) side and [O iii] $\lambda 5008$, respectively. The RMS
of the Gemini spectra shows a noisy region blueward of 4750 Å likely dominated
by calibration noise. It is worth noting, however, that the finer wavelength
sampling of the Gemini spectra (owing to the narrow-slit observations) makes
that region appear even noisier. On the other hand, the region towards the
blue end of the LJT RMS spectrum shows clear evidence of variability in the He
ii $\lambda 4687$ line although it is heavily contaminated with Fe ii in the
surrounding region. Variability in H$\beta$ is revealed by both the Gemini and
the LJT RMS spectra. Although no variability in He i is evident from the
Gemini RMS, the LJT RMS shows a weak signature of variability in broad He i. A
very low, broad wave appears from $\sim$5250 Å to $\sim$5450 Å and from
$\sim$5650 Å to $\sim$5950 Å in the LJT RMS spectrum likely resulting from
calibration. The GMOS chip gap region in the Gemini spectrum extends from
$\sim$5350 Å to $\sim$5410 Å, which also appears as a low bump in the RMS
spectrum.

Figure 2: Rest-frame mean (black; panels a and c) and root-mean-square (RMS;
gray; panels b and d) of Mrk 142 Gemini (Top; velocity resolution of $185.6\pm
10.2$ km s-1) and LJT (Bottom; velocity resolution of $695.2\pm 3.9$ km s-1)
spectra highlighting the Regions of Interest – H$\beta$ $\lambda 4861$ and [O
iii] $\lambda\lambda 4960,5008$ (region shaded in green), and He i $\lambda
5877$ (region shaded in pink). Labels enclosed in dashed (dotted) boxes
indicate broad (narrow) lines. The Gemini mean spectrum shows sharp Fe ii
features (shaded in faint blue), which appear blended with the red wings of
H$\beta$ and [O iii] $\lambda 5008$ (blue shaded bars) in the LJT mean. Owing
to the high signal-to-noise of the Gemini spectra, the peculiar shape of the
He i $\lambda 5877$ line is clearly evident. The high-ionization coronal lines
(shaded in brown) also appear sharp in contrast to the LJT spectrum, as a
result. The LJT RMS spectrum shows clear variability in He ii (shaded in
blue). Both RMS spectra indicate variability in the broad H$\beta$. However,
no significant variability is evident in He i over the timescale of Gemini+LJT
observations. The yellow-shaded region in the Gemini spectra indicates the
GMOS chip gap from $\sim$5350 Å to $\sim$5410 Å.
(The reduced and calibrated Mrk 142 Gemini spectra are available in a machine-
readable form.)

##  4 Spectral Analysis

To measure the H$\beta$ and He i emission lines in the calibrated spectra, we
first corrected any discrepancies in the calibrations of the Gemini and LJT
spectra, independently with PrepSpec, and then modeled their spectral features
with Sherpa. For PrepSpec modeling of Gemini spectra, we used the spectral
region from $\sim$4430 Å to $\sim$6300 Å. For LJT spectra, we kept the
spectral region from $\sim$3390 Å to $\sim$6300 Å.

###  4.1 PrepSpec Modeling

We independently modeled the 64 narrow-slit Gemini spectra and the 69 LJT
spectra with PrepSpec444Find current version of PrepSpec at http://star-
www.st-andrews.ac.uk/~kdh1/lib/prepspec/prepspec.tar.gz. (developer: K. Horne)
to correct for any relative deviations in the calibrated wavelength and flux
scales. PrepSpec models spectra by fitting the continuum and emission lines
with a composite model through an iterative process. We included the following
model components for fitting the Mrk 142 spectra: (1) [A]verage spectrum
(specified by “A”) – mean of the input spectra; (2) [C]ontinuum – variations
in the continuum emission from the accretion disk modeled as a polynomial
defined by $\log{\lambda}$ with time-dependent coefficients; (3) [W]avelength
jitter – inter-spectra shifts in the wavelength scales; (4) [F]lux jitter –
time-dependent photometric corrections to minimize the scatter of narrow
emission-line fluxes relative to their median; and (4) [B]road-line variations
– variability in the broad emission-line features. Modeling emission lines in
PrepSpec takes into account the velocity window half-widths of the broad as
well as the narrow lines, whose initial values were set to 3000 km s-1 and 500
km s-1, respectively. We set the broad H$\beta$ $\lambda 4861$ and He i
$\lambda 5877$ as variable lines for Gemini spectra, and H$\gamma$ $\lambda
4342$, He ii $\lambda 4687$, H$\beta$, and He i $\lambda 5877$ as variable for
LJT spectra. The software uses the I Zwicky 1 (I Zw 1) template model (Véron-
Cetty et al., 2001) to fit Fe ii emission in the mean spectrum. PrepSpec is
not designed to handle gaps in spectra or extremely large flux values, e.g.,
from cosmic-ray hits. Therefore, chip gaps and artefacts from cosmic-ray
correction or sky subtraction in the Gemini spectra were replaced by median or
simulated data (see Section 3.1.3 for details) during spectral reduction.

In the PrepSpec modeling stage, we first corrected the Gemini and LJT spectra
for pixel shifts relative to the [O iii] $\lambda 5008$ line and then modeled
the spectra with a composite model. We observed small pixel shifts ($<$6
pixels) while aligning the spectra along the wavelength axis. The model
components were jointly fit starting with a single component and then adding
components up to the ACWFB composite model for both the Gemini and the LJT
spectra. PrepSpec determines the best-fitting model by accessing the Bayesian
Information Criterion and reduced $\chi^{2}$ ($\chi_{\nu}^{2}$, where $\nu$
stands for degrees of freedom) statistics. The goal of the fitting process is
to use the fewest possible parameters to describe the data while penalizing
the model for the number of parameters used. A good model yields
$\mathrm{\chi_{\nu}^{2}\sim 1}$. Figure 3 displays the final model (dark blue
curve) passing through the black mean spectrum (panel a) and the model (dark
gray curve) to the residual root-mean-square (RMSx) spectrum (panel b) for the
64 narrow-slit Gemini spectra. The RMS spectrum shows that the spectra are
noisier at the bluer end.

Figure 3: Mean (panel a) and the root-mean-square (RMS) spectra for 64 narrow-
slit Mrk 142 Gemini spectra processed through PrepSpec showing model fits with
individual components. In panel a, the composite model (dark blue curve),
including the components shown at the bottom of the plot – average spectrum
(AVG; black), continuum (cont; red), Fe ii (Fe2; faint blue), broad-line
region (BLR; dark blue), and narrow-line region (NLR; orange), is overlaid on
the mean spectrum (black curve). The broad (narrow) emission lines are
indicated with green (orange) dotted vertical lines as well as with green
(orange) solid horizontal dashes. The broad lines of H$\beta$ (blue label) and
He i (purple label) are marked with solid horizontal dashes. In panel b, model
(model; dark gray curve) fit to the residual RMS spectrum (RMSx; blue curve)
includes the components: continuum (cont; red curve) and BLR (green curve at
the bottom of the plot). The raw RMS spectrum is the upper green curve. The
BLR component comprises the broad lines of H$\beta$ (blue bump around
$\sim$4862 Å) and He i (purple bump around $\sim$5877 Å) shown at the bottom
of the plot. The broad He ii emission feature at $\sim$4687 Å (box-like
feature in the model) is contaminated with Fe ii and hence difficult to fit
given the noise in the region. The deviation in the residual RMS spectrum
($\sigma_{\mathrm{RMSx}}$; cyan curve) shows large values in the region of the
GMOS detector chip gap from $\sim$5345 Å to $\sim$5420 Å. In both panels, the
active broad-line windows of H$\beta$ and He i used for PrepSpec modeling are
shown in negative-value space.

Figure 4 shows the final model (panel a) along with the residuals (in the
units of $\sigma$; panel b) in grayscale for the Gemini spectra. The best-fit
model yielded a $\chi_{\nu}^{2}$ value of 0.782, which indicates overfitting
of the data, possibly indicating inaccurate error bars larger than the scatter
in the data. The dark regions in the model highlight the prominent emission-
line features of H$\beta$ $\lambda 4861$ and [O iii] $\lambda\lambda
4960,5008$. The weak fluctuations blueward of $\sim$4700 Å indicate more noise
in that region as compared to the red end of the spectra. The residuals in
grayscale display horizontal wiggles that are strongly evident in some
spectra. We noted that the wiggles appear in the spectral regions replaced by
simulated data to correct for residual features either from cosmic-ray
correction or sky subtraction. The replacement with simulated data may have
resulted in a lower performance of the model in those regions. Another
probable reason for the wiggles is the use of a higher-order spline during
flat-fielding in the spectral reduction process (refer Section 3.1.3 for
details). However, we visually inspected all spectra processed through
PrepSpec and observed no anomalous behavior in the regions with wiggles.
Therefore, the spectra were considered valid for further analysis.

Figure 4: PrepSpec model including all components (panel a) and residuals
($data-model$ in units of standard deviation, $\sigma$; panel b) with a
reduced $\chi^{2}$ ($\chi_{\nu}^{2}$) of 0.782 for 64 narrow-slit Mrk 142
spectra. In panel a, dark regions indicate strong emission lines of H$\beta$
and [O iii], whereas the weaker He i lines and Fe ii emission appears as less
prominent features. In panel b, each row represents a single exposure spectrum
(where multiple exposures at a given epoch are not yet combined). The
horizontal wiggles strongly evident in some spectra are likely the result of
either replacing values with simulated data in those regions or using a higher
order function during flat-fielding (see text for more details). The smeared
region from $\sim$5345 Å to $\sim$5420 Å is one of the chip gaps of the GMOS
detector where simulated data was added during reduction.

PrepSpec modeling of LJT spectra yielded nearly even residuals with a
$\chi_{\nu}^{2}$ value of 0.791. The region redward of 6300 Å in LJT spectra
comprises several blended narrow-line features, which resulted in a sub-
optimal performance of the PrepSpec model. Therefore, we excluded the red side
of the LJT spectra ($\lambda>6300$ Å) during PrepSpec processing.

###  4.2 Spectral Modeling in Sherpa

We modeled the continuum and emission lines in the Gemini and LJT spectra in
Sherpa555Sherpa 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; Burke et al., 2018) v4.10.0 with a Python wrapper
script. We first corrected the Gemini and LJT spectra for Galactic reddening
using $E(B-V)=0.015$ (Schlafly & Finkbeiner, 2011). Averaging the two narrow-
slit Gemini exposures from every night into a single spectrum per epoch (with
exceptions for spectra from epochs 11, 25, and 28, where we only used single
exposures) yielded a total of 33 Gemini spectra. Together with the 69 LJT
spectra, we modeled a total of 102 Mrk 142 spectra.

We developed a composite model with a goal of performing a clean extraction of
the H$\beta$ and He i emission lines from the Gemini and LJT spectra. We
included a power-law fit to the continuum, three Gaussians to model each of
the H$\beta$, He i and He ii emission lines, and a single Gaussian for each of
the [O iii] doublet lines. We adopted the I Zw 1 template model from Boroson &
Green (1992) as a pseudo-continuum to trace the Fe ii emission-line features.
We also experimented with the Fe ii template from Véron-Cetty et al. (2001).
However, it failed to suitably trace the sharp Fe ii features in Mrk 142. With
the Boroson & Green (1992) Fe ii template model, the fits yielded lower
(${\chi_{\nu}}^{2}$) values than with the Véron-Cetty et al. (2001) template.
Following the procedure in Hu et al. (2015), we added single Gaussian profiles
for each of the six coronal lines (Fe vii $\lambda 5160$, Fe vi $\lambda
5177$, Ca v $\lambda 5311$, Fe vii $\lambda 5278$, Fe vii $\lambda 5722$, Fe
vii $\lambda 6088$; see Figure 2). In addition, we included the host-galaxy
template with 11 Gyr at $z=0.05$ from the 2013 updated version of Bruzual &
Charlot (2003) galaxy templates. The host-galaxy template, affecting the
redder part of the spectrum more than the bluer, contributed greatly in
producing a good fit to the He i emission-line region. The fit in the H$\beta$
region was less sensitive to host-galaxy emission. We referred to the Vanden
Berk et al. (2001) rest wavelengths for setting the positions of all emission
lines.

####  4.2.1 Gemini Spectral Analysis

Our goal of spectral fitting was to accurately estimate the H$\beta$, [O iii],
and He i profiles in the Gemini spectra. We aimed at finding a robust and
flexible set of parameters that fit the structure in the spectra over all
epochs. Figure 5 shows the composite model fit to a single-epoch Gemini
spectrum.

Figure 5: 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
${\chi_{\nu}}^{2}=1.183$. 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.

We describe the fitting process as follows. The Gaussian used for each of the
[O iii] doublet lines traces the systemic narrow-line emission peaks. While
fitting the Gemini spectra, the position, FWHM, and flux of the [O iii]
$\lambda 5008$ emission line were freed. However, we fixed the position of the
[O iii] $\lambda 4960$ line relative to the [O iii] $\lambda 5008$ line and
the flux in the [O iii] $\lambda 4960$ line to a factor of 1/3 compared to the
[O iii] $\lambda 5008$ flux. We chose Gaussians over Lorentzians to
appropriately trace the narrower wings of the [O iii] lines. We fixed the
positions of the narrow components of H$\beta$, He i, and He ii relative to
the position of the [O iii] $\lambda 5008$ line, and their widths equal to the
[O iii] $\lambda 5008$ FWHM. Spectral fitting in Sherpa takes into account the
scaling of the FWHM for a given line relative to the calibrator line, which is
the [O iii] $\lambda 5008$ line for this work. The position and flux
parameters of the two broad components of both H$\beta$ and He i were freed.
The width of only one of the H$\beta$ Gaussians was allowed to vary while the
second Gaussian was fixed at twice the width of the first. On the other hand,
the widths of the He i broad components were fixed at factors of 1 and 6 of
the FWHM of the flexible, broad H$\beta$ component. We determined the above
FWHM ratios for the broad H$\beta$ and He i emission lines from the mean
spectrum. The insets in Figure 5 show a closer view of the two Regions of
Interest – H$\beta$ and He i. A single broad component of He ii with position
fixed relative to the flexible, broad H$\beta$ component and width equal to
the FWHM of the same component proved insufficient to trace the broader
emission around $\sim$4650 Å, indicating a plausible blueshifted broad
component of He ii. Adding another blueshifted Gaussian 1.5 times the width of
the flexible, broad H$\beta$ component with flux equal to that of the first
broad He ii component significantly improved the fit in that region. Table 3
lists the emission-line parameters along with their settings as used during
spectral fitting.

Table 3: Emission-Line Fitting Parameters for Gemini and LJT Spectra  Line | Parameter | Fixed | Ratio relative to the fixed line
---|---|---|---
|  | relative to lineaaParameter settings with no data indicate that the parameter was kept flexible during spectral fitting. | Gemini | LJT
| Position |  $\cdots$ |  $\cdots$ |  $\cdots$
[O iii] $\lambda 5008$ | FWHM |  $\cdots$ |  $\cdots$ |  $\cdots$
| Flux |  $\cdots$ |  $\cdots$ |  $\cdots$
| Position | [O iii] $\lambda 5008$ | 0.990 | 0.990
[O iii] $\lambda 4960$ | FWHM | [O iii] $\lambda 5008$ | 1.000 | 1.000
| Flux | [O iii] $\lambda 5008$ | 0.333 | 0.333
| Position | [O iii] $\lambda 5008$ | 0.971 | 0.971
Narrow H$\beta$ $\lambda 4861$ | FWHM | [O iii] $\lambda 5008$ | 1.000 | 1.000
| Flux | [O iii] $\lambda 5008$ |  $\cdots$ | 0.293
| Position |  $\cdots$ |  $\cdots$ |  $\cdots$
Narrower broad H$\beta$ $\lambda 4861$ | FWHM |  $\cdots$ |  $\cdots$ |  $\cdots$
| Flux |  $\cdots$ |  $\cdots$ |  $\cdots$
| Position |  $\cdots$ |  $\cdots$ |  $\cdots$
Broader broad H$\beta$ $\lambda 4861$ | FWHM | Narrower broad H$\beta$ $\lambda 4861$ | 2.000 | 2.500
| Flux |  $\cdots$ |  $\cdots$ |  $\cdots$
| Position | [O iii] $\lambda 5008$ | 1.174 | 1.174
Narrow He i $\lambda 5877$ | FWHM | [O iii] $\lambda 5008$ | 1.000 | 1.000
| Flux | [O iii] $\lambda 5008$ |  $\cdots$ | 0.034
| Position |  $\cdots$ |  $\cdots$ |  $\cdots$
Narrower broad He i $\lambda 5877$ | FWHM | Narrower broad H$\beta$ $\lambda 4861$ | 1.200 | 1.000
| Flux |  $\cdots$ |  $\cdots$ |  $\cdots$
| Position |  $\cdots$ |  $\cdots$ |  $\cdots$
Broader broad He i $\lambda 5877$ | FWHM | Narrower broad H$\beta$ $\lambda 4861$ | 6.000 | 6.000
| Flux |  $\cdots$ |  $\cdots$ |  $\cdots$
| Position | [O iii] $\lambda 5008$ | 0.936 | 0.936
Narrow He ii $\lambda 4687$ | FWHM | [O iii] $\lambda 5008$ | 1.000 | 1.000
| Flux |  $\cdots$ |  $\cdots$ |  $\cdots$
| Position | Narrower broad H$\beta$ $\lambda 4861$ | 0.964 | 0.964
Narrower broad He ii $\lambda 4687$ | FWHM | Narrower broad H$\beta$ $\lambda 4861$ | 1.000 | 1.000
| Flux |  $\cdots$ |  $\cdots$ |  $\cdots$
| Position | Narrower broad H$\beta$ $\lambda 4861$ | 0.956 | 0.956
Blue-shifted broad He ii $\lambda 4687$ | FWHM | Narrower broad H$\beta$ $\lambda 4861$ | 1.500 | 1.500
| Flux | Narrower broad He ii $\lambda 4687$ | 1.000 | 1.000

We followed the Fe ii template fitting procedure described in Hu et al.
(2015), where the Fe ii emission is defined by a convolution of the Boroson &
Green (1992) template with a Gaussian. We applied the Gaussian as a 1D Point
Spread Function (PSF) with a fixed FWHM, and the amplitude of the convolved Fe
ii model was set as a flexible parameter while fitting. Although the Fe ii
model successfully traces the sharp Fe ii features in most parts of the
spectrum, it performs sub-optimally near the Fe ii emission at the red wing of
the [O iii] $\lambda 5008$ line thus resulting in larger residuals in that
region. Further, the model overestimates the emission between the two [O iii]
lines due to the broader wing of Fe ii from the template model.

Modeling individual coronal lines in the spectra considerably improved the fit
in the Fe ii emission region from $\sim$5150 Å to $\sim$5350 Å. In this
region, the Fe coronal lines appeared to be slightly redshifted ($\leq$0.003)
with respect to their rest wavelengths. We set the coronal-line widths to 1.5
times the [O iii] $\lambda 5008$ line width and their flux values to specific
fractions of the [O iii] $\lambda 5008$ flux, as determined from the fit to
the Gemini mean spectrum.

From spectral modeling, we derived, at each epoch, the total FWHM and flux
values of the H$\beta$, He i, and [O iii] lines. We measured the FWHM of the
broad and total (including both the broad and the narrow components) H$\beta$
and He i lines empirically by subtracting all other model components from the
spectra including the narrow lines. To calculate the contribution from the
broad-line and total (again, including both the broad- and the narrow-line)
flux in the H$\beta$ and He i emission profiles, we simply added the
contribution from each of their components. Tables 4, 5, and 6 provide
emission-line measurements for the Gemini spectra from 33 epochs. For epoch
11, the model failed to constrain the broad H$\beta$ emission as the region
blueward of the H$\beta$ line appeared noisier compared to the other epochs.
We therefore excluded epoch 11 from further analysis. Also, due to improper
flux calibration at the location of the H$\beta$ line in epoch 25, the line
appeared unusually broader and brighter than at the other epochs. We therefore
excluded the spectrum from epoch 25 as well.

Table 4: [O iii] $\lambda 5008$ Emission-Line Measurements for Gemini Spectra

Epoch | Position${}_{\hbox{[{\rm O~{}}\kern 0.70004pt{\sc iii}]}\lambda 5008}$ | FWHM${}_{\hbox{[{\rm O~{}}\kern 0.70004pt{\sc iii}]}\lambda 5008}$ | $F_{\hbox{[{\rm O~{}}\kern 0.70004pt{\sc iii}]}\lambda 5008}$ |  $\chi_{\nu}^{2}$[a][a]footnotemark:
---|---|---|---|---
| [Å] | [km s-1] | [10-15 erg s-1 cm-2] |
1 | $5008.21\pm 0.04$ | $313\pm 5$ | $15.7\pm 0.2$ | 1.07
2 | $5008.19\pm 0.05$ | $318\pm 9$ | $15.8\pm 0.3$ | 1.06
3 | $5008.12\pm 0.04$ | $325\pm 6$ | $16.1\pm 0.2$ | 1.23
4 | $5008.19\pm 0.04$ | $303\pm 9$ | $15.7\pm 0.3$ | 1.21
5 | $5008.18\pm 0.05$ | $320\pm 5$ | $16.2\pm 0.3$ | 0.99
6 | $5008.20\pm 0.04$ | $325\pm 3$ | $16.1\pm 0.2$ | 1.08
7 | $5008.23\pm 0.03$ | $311\pm 4$ | $15.5\pm 0.2$ | 1.18
8 | $5008.15\pm 0.04$ | $322\pm 5$ | $16.1\pm 0.2$ | 1.22
9 | $5008.15\pm 0.05$ | $336\pm 7$ | $16.1\pm 0.3$ | 0.97
10 | $5008.11\pm 0.04$ | $326\pm 5$ | $16.0\pm 0.3$ | 1.04
11 | $5008.11\pm 0.07$ | $317\pm 9$ | $15.6\pm 0.5$ | 0.99
12 | $5008.16\pm 0.06$ | $333\pm 10$ | $16.3\pm 0.4$ | 1.08
13 | $5008.19\pm 0.04$ | $304\pm 6$ | $15.6\pm 0.3$ | 1.12
14 | $5008.16\pm 0.04$ | $317\pm 5$ | $15.8\pm 0.2$ | 1.24
15 | $5008.20\pm 0.04$ | $319\pm 4$ | $15.9\pm 0.2$ | 1.20
16 | $5008.19\pm 0.04$ | $311\pm 5$ | $15.6\pm 0.2$ | 1.26
17 | $5008.22\pm 0.04$ | $315\pm 4$ | $16.0\pm 0.2$ | 1.27
18 | $5008.14\pm 0.04$ | $338\pm 6$ | $16.1\pm 0.2$ | 1.33
19 | $5008.22\pm 0.04$ | $312\pm 2$ | $15.8\pm 0.2$ | 1.10
20 | $5008.21\pm 0.03$ | $292\pm 6$ | $15.5\pm 0.2$ | 1.17
21 | $5008.23\pm 0.04$ | $313\pm 6$ | $16.0\pm 0.2$ | 1.28
22 | $5008.18\pm 0.03$ | $308\pm 6$ | $15.8\pm 0.2$ | 1.21
23 | $5008.20\pm 0.03$ | $304\pm 4$ | $15.6\pm 0.2$ | 1.24
24 | $5008.15\pm 0.04$ | $320\pm 3$ | $15.8\pm 0.2$ | 1.18
25 | $5008.20\pm 0.05$ | $307\pm 5$ | $15.9\pm 0.3$ | 1.11
26 | $5008.20\pm 0.05$ | $310\pm 7$ | $15.9\pm 0.3$ | 1.19
27 | $5008.21\pm 0.04$ | $302\pm 5$ | $15.5\pm 0.2$ | 1.24
28 | $5008.34\pm 0.05$ | $301\pm 2$ | $15.3\pm 0.3$ | 1.07
29 | $5008.18\pm 0.04$ | $323\pm 7$ | $16.1\pm 0.3$ | 1.19
30 | $5008.24\pm 0.04$ | $321\pm 4$ | $15.9\pm 0.2$ | 1.35
31 | $5008.27\pm 0.03$ | $306\pm 5$ | $15.7\pm 0.2$ | 1.16
32 | $5008.25\pm 0.04$ | $321\pm 6$ | $16.0\pm 0.3$ | 1.10
33 | $5008.22\pm 0.05$ | $328\pm 4$ | $16.4\pm 0.2$ | 1.05

Note. — This table is available in machine-readable form.

Table 5: H$\beta$ $\lambda 4861$ Emission-Line Measurements for Gemini Spectra

Epoch | FWHM${}_{\hbox{{\rm H}\kern 0.70004pt{\sc$\beta$}},b}$ | $F_{\hbox{{\rm H}\kern 0.70004pt{\sc$\beta$}},b}$ | FWHM${}_{\hbox{{\rm H}\kern 0.70004pt{\sc$\beta$}},n}$ | $F_{\hbox{{\rm H}\kern 0.70004pt{\sc$\beta$}},n}$ | FWHM${}_{\hbox{{\rm H}\kern 0.70004pt{\sc$\beta$}},t}$ | $F_{\hbox{{\rm H}\kern 0.70004pt{\sc$\beta$}},t}$
---|---|---|---|---|---|---
| [km s-1] | [10-15 erg s-1 cm-2] | [km s-1] | [10-15 erg s-1 cm-2] | [km s-1] | [10-15 erg s-1 cm-2]
1 | $1777\pm 72$ | $112.2\pm 2.4$ | $312\pm 5$ | $5.3\pm 0.4$ | $1445\pm 52$ | $117.5\pm 2.4$
2 | $1681\pm 109$ | $106.3\pm 4.3$ | $317\pm 8$ | $5.5\pm 0.6$ | $1324\pm 83$ | $111.8\pm 4.3$
3 | $1703\pm 69$ | $115.8\pm 5.1$ | $325\pm 5$ | $5.1\pm 0.4$ | $1412\pm 73$ | $120.9\pm 5.1$
4 | $1745\pm 83$ | $110.5\pm 2.7$ | $303\pm 9$ | $4.5\pm 0.4$ | $1478\pm 67$ | $115.0\pm 2.7$
5 | $1555\pm 80$ | $107.5\pm 3.4$ | $319\pm 4$ | $3.1\pm 0.6$ | $1466\pm 96$ | $110.6\pm 3.4$
6 | $1830\pm 77$ | $109.3\pm 3.7$ | $324\pm 3$ | $5.1\pm 0.5$ | $1524\pm 80$ | $114.4\pm 3.7$
7 | $1797\pm 69$ | $112.2\pm 2.2$ | $310\pm 3$ | $4.5\pm 0.4$ | $1525\pm 56$ | $116.7\pm 2.2$
8 | $1697\pm 62$ | $106.5\pm 2.3$ | $321\pm 4$ | $3.5\pm 0.4$ | $1447\pm 62$ | $110.0\pm 2.4$
9 | $1499\pm 83$ | $100.2\pm 3.1$ | $336\pm 6$ | $5.1\pm 0.6$ | $1379\pm 58$ | $105.4\pm 3.2$
10 | $1593\pm 77$ | $103.4\pm 2.7$ | $326\pm 4$ | $5.0\pm 0.4$ | $1328\pm 55$ | $108.4\pm 2.8$
11aaReduced $\chi^{2}$, $\chi_{\nu}^{2}=\chi^{2}/\nu$, where $\nu$ indicates 3897 degrees of freedom, gives the model statistic for individual epochs. | $1637\pm 132$ | $104.3\pm 3.3$ | $317\pm 9$ | $5.7\pm 0.8$ | $1235\pm 165$ | $110.1\pm 3.4$
12 | $1732\pm 120$ | $101.5\pm 5.8$ | $332\pm 10$ | $5.9\pm 0.7$ | $1322\pm 81$ | $107.3\pm 5.8$
13 | $1628\pm 88$ | $101.3\pm 2.5$ | $303\pm 6$ | $3.7\pm 0.5$ | $1354\pm 77$ | $105.0\pm 2.5$
14 | $1707\pm 69$ | $109.1\pm 2.6$ | $316\pm 5$ | $4.2\pm 0.4$ | $1384\pm 56$ | $113.3\pm 2.7$
15 | $1672\pm 104$ | $108.8\pm 2.7$ | $319\pm 3$ | $4.9\pm 0.4$ | $1341\pm 30$ | $113.7\pm 2.7$
16 | $1780\pm 76$ | $103.2\pm 2.3$ | $311\pm 5$ | $4.4\pm 0.4$ | $1412\pm 73$ | $107.6\pm 2.3$
17 | $1623\pm 65$ | $108.4\pm 3.0$ | $315\pm 4$ | $3.8\pm 0.4$ | $1402\pm 60$ | $112.2\pm 3.0$
18 | $1712\pm 72$ | $105.6\pm 2.4$ | $337\pm 5$ | $4.6\pm 0.5$ | $1477\pm 64$ | $110.2\pm 2.4$
19 | $1579\pm 91$ | $106.1\pm 4.2$ | $311\pm 1$ | $6.1\pm 0.5$ | $1348\pm 64$ | $112.2\pm 4.2$
20 | $1558\pm 62$ | $115.2\pm 2.1$ | $291\pm 5$ | $3.4\pm 0.4$ | $1473\pm 42$ | $118.7\pm 2.1$
21 | $1604\pm 43$ | $112.6\pm 2.1$ | $312\pm 5$ | $3.6\pm 0.4$ | $1446\pm 71$ | $116.2\pm 2.1$
22 | $1698\pm 62$ | $109.3\pm 2.8$ | $307\pm 5$ | $4.4\pm 0.4$ | $1442\pm 55$ | $113.7\pm 2.8$
23 | $1590\pm 57$ | $108.3\pm 2.1$ | $304\pm 3$ | $3.7\pm 0.4$ | $1416\pm 52$ | $112.0\pm 2.2$
24 | $1668\pm 77$ | $110.9\pm 2.7$ | $319\pm 3$ | $4.3\pm 0.5$ | $1391\pm 54$ | $115.2\pm 2.7$
25bbDue to a calibration issue at the location of the H$\beta$ emission line, the H$\beta$ profile appeared unusually broader and brighter than in other spectra. Therefore, this epoch was excluded from further analysis. | $1672\pm 73$ | $140.4\pm 3.6$ | $307\pm 5$ | $5.9\pm 0.7$ | $1603\pm 83$ | $146.3\pm 3.7$
26 | $1655\pm 95$ | $107.0\pm 2.6$ | $309\pm 7$ | $4.9\pm 0.4$ | $1297\pm 50$ | $111.9\pm 2.6$
27 | $1649\pm 48$ | $103.4\pm 3.9$ | $301\pm 5$ | $4.6\pm 0.4$ | $1356\pm 59$ | $108.0\pm 3.9$
28 | $1678\pm 96$ | $102.6\pm 3.2$ | $300\pm 2$ | $3.9\pm 0.6$ | $1459\pm 148$ | $106.5\pm 3.3$
29 | $1713\pm 76$ | $94.9\pm 3.1$ | $322\pm 7$ | $4.3\pm 0.4$ | $1410\pm 66$ | $99.2\pm 3.1$
30 | $1754\pm 96$ | $102.7\pm 3.7$ | $321\pm 4$ | $5.5\pm 0.5$ | $1395\pm 92$ | $108.2\pm 3.8$
31 | $1816\pm 81$ | $109.4\pm 4.3$ | $306\pm 5$ | $6.1\pm 0.4$ | $1489\pm 96$ | $115.5\pm 4.3$
32 | $1682\pm 79$ | $109.6\pm 2.3$ | $321\pm 5$ | $4.9\pm 0.4$ | $1423\pm 47$ | $114.5\pm 2.4$
33 | $1699\pm 58$ | $110.0\pm 5.0$ | $328\pm 4$ | $3.8\pm 0.5$ | $1515\pm 78$ | $113.8\pm 5.0$

Note. — The second and the third columns providing the FWHM and flux values,
respectively, for the broad (‘b’) H$\beta$ component include contributions
from both the broad Gaussians defined for the line. The FWHM of the narrow
(‘n’) H$\beta$ is equal to the FWHM of the [O iii] $\lambda 5008$ (see Table
4, third column). The total (‘t’) FWHM and flux include contributions from
both the broad and the narrow components (t = b \+ n).

Note. — This table is available in machine-readable form.

Table 6: He i $\lambda 5877$ Emission-Line Measurements for Gemini Spectra

Epoch | FWHM${}_{\hbox{{\rm He~{}}\kern 0.70004pt{\sc i}},b}$ | $F_{\hbox{{\rm He~{}}\kern 0.70004pt{\sc i}},b}$ | FWHM${}_{\hbox{{\rm He~{}}\kern 0.70004pt{\sc i}},n}$ | $F_{\hbox{{\rm He~{}}\kern 0.70004pt{\sc i}},n}$ | FWHM${}_{\hbox{{\rm He~{}}\kern 0.70004pt{\sc i}},t}$ | $F_{\hbox{{\rm He~{}}\kern 0.70004pt{\sc i}},t}$
---|---|---|---|---|---|---
| [km s-1] | [10-15 erg s-1 cm-2] | [km s-1] | [10-15 erg s-1 cm-2] | [km s-1] | [10-15 erg s-1 cm-2]
1 | $47\pm 37$ | $34.4\pm 0.8$ | $312\pm 5$ | $0.7\pm 0.1$ | $47\pm 95$ | $35.1\pm 0.8$
2 | $53\pm 37$ | $33.4\pm 1.0$ | $317\pm 8$ | $0.6\pm 0.2$ | $53\pm 36$ | $34.0\pm 1.0$
3 | $90\pm 44$ | $41.3\pm 0.9$ | $325\pm 5$ | $0.7\pm 0.1$ | $90\pm 41$ | $42.0\pm 0.9$
4 | $36\pm 25$ | $36.0\pm 0.9$ | $303\pm 9$ | $0.8\pm 0.1$ | $36\pm 20$ | $36.8\pm 0.9$
5 | $335\pm 70$ | $35.2\pm 1.1$ | $319\pm 4$ | $0.3\pm 0.2$ | $335\pm 71$ | $35.5\pm 1.1$
6 | $46\pm 36$ | $35.1\pm 0.9$ | $324\pm 3$ | $0.6\pm 0.1$ | $46\pm 35$ | $35.7\pm 0.9$
7 | $136\pm 170$ | $39.7\pm 0.8$ | $310\pm 3$ | $0.6\pm 0.1$ | $1962\pm 312$ | $40.3\pm 0.8$
8 | $49\pm 65$ | $39.1\pm 0.7$ | $321\pm 4$ | $0.5\pm 0.1$ | $49\pm 59$ | $39.6\pm 0.7$
9 | $34\pm 43$ | $33.1\pm 0.9$ | $336\pm 6$ | $0.7\pm 0.2$ | $34\pm 46$ | $33.7\pm 0.9$
10 | $92\pm 53$ | $36.3\pm 0.8$ | $326\pm 4$ | $0.7\pm 0.2$ | $92\pm 52$ | $37.0\pm 0.8$
11aaBecause the noisy region blueward of the H$\beta$ emission line was unable to well constrain the broad, blue wing of H$\beta$, this epoch was excluded from further analysis. | $153\pm 39$ | $36.6\pm 1.4$ | $317\pm 9$ | $0.4\pm 0.2$ | $153\pm 38$ | $37.1\pm 1.4$
12 | $92\pm 51$ | $31.4\pm 1.3$ | $332\pm 10$ | $0.5\pm 0.2$ | $92\pm 52$ | $32.0\pm 1.3$
13 | $1419\pm 90$ | $35.9\pm 0.9$ | $303\pm 6$ | $0.0\pm 0.2$ | $1419\pm 108$ | $35.9\pm 0.9$
14 | $83\pm 51$ | $41.0\pm 0.8$ | $316\pm 5$ | $0.8\pm 0.1$ | $83\pm 55$ | $41.8\pm 0.8$
15 | $66\pm 41$ | $38.4\pm 0.8$ | $319\pm 3$ | $0.5\pm 0.1$ | $66\pm 41$ | $38.9\pm 0.8$
16 | $152\pm 225$ | $38.8\pm 0.8$ | $311\pm 5$ | $0.6\pm 0.1$ | $1758\pm 497$ | $39.4\pm 0.8$
17 | $1825\pm 303$ | $38.8\pm 0.9$ | $315\pm 4$ | $0.3\pm 0.1$ | $1528\pm 415$ | $39.1\pm 0.9$
18 | $37\pm 32$ | $37.2\pm 0.8$ | $337\pm 5$ | $0.4\pm 0.1$ | $37\pm 181$ | $37.6\pm 0.9$
19 | $1828\pm 42$ | $35.4\pm 0.9$ | $311\pm 1$ | $0.7\pm 0.1$ | $1806\pm 41$ | $36.1\pm 0.9$
20 | $1862\pm 357$ | $42.0\pm 0.7$ | $291\pm 5$ | $0.4\pm 0.1$ | $1829\pm 631$ | $42.4\pm 0.7$
21 | $1798\pm 399$ | $38.4\pm 0.8$ | $312\pm 5$ | $0.9\pm 0.1$ | $1651\pm 647$ | $39.3\pm 0.8$
22 | $1870\pm 654$ | $41.9\pm 0.8$ | $307\pm 5$ | $0.4\pm 0.1$ | $1870\pm 682$ | $42.2\pm 0.8$
23 | $38\pm 189$ | $40.2\pm 0.8$ | $304\pm 3$ | $0.5\pm 0.1$ | $1873\pm 336$ | $40.7\pm 0.8$
24 | $54\pm 84$ | $41.1\pm 0.9$ | $319\pm 3$ | $0.5\pm 0.1$ | $54\pm 132$ | $41.7\pm 0.9$
25bbExcluded from further analysis. See corresponding note in Table 5. | $137\pm 43$ | $38.3\pm 1.3$ | $307\pm 5$ | $0.6\pm 0.2$ | $137\pm 45$ | $38.9\pm 1.3$
26 | $61\pm 53$ | $36.9\pm 0.8$ | $309\pm 7$ | $0.5\pm 0.1$ | $61\pm 110$ | $37.4\pm 0.8$
27 | $114\pm 180$ | $38.7\pm 0.9$ | $301\pm 5$ | $0.5\pm 0.1$ | $1935\pm 389$ | $39.3\pm 0.9$
28 | $81\pm 60$ | $55.6\pm 1.1$ | $300\pm 2$ | $0.1\pm 0.2$ | $81\pm 52$ | $55.7\pm 1.1$
29 | $181\pm 100$ | $36.0\pm 0.8$ | $322\pm 7$ | $0.4\pm 0.1$ | $181\pm 96$ | $36.4\pm 0.8$
30 | $34\pm 86$ | $40.0\pm 1.0$ | $321\pm 4$ | $0.5\pm 0.1$ | $34\pm 125$ | $40.5\pm 1.0$
31 | $66\pm 268$ | $44.6\pm 0.9$ | $306\pm 5$ | $0.9\pm 0.1$ | $66\pm 627$ | $45.5\pm 0.9$
32 | $294\pm 50$ | $41.2\pm 0.9$ | $321\pm 5$ | $0.9\pm 0.1$ | $1631\pm 160$ | $42.1\pm 0.9$
33 | $1537\pm 161$ | $35.3\pm 0.9$ | $328\pm 4$ | $0.3\pm 0.1$ | $1528\pm 267$ | $35.6\pm 0.9$

Note. — The second and the third columns providing the FWHM and flux values,
respectively, for the broad (‘b’) He i component include contributions from
both the broad Gaussians defined for the line. The FWHM of the narrow (‘n’) He
i is equal to the FWHM of the [O iii] $\lambda 5008$ (see Table 4, third
column). The total (‘t’) FWHM and flux include contributions from both the
broad and the narrow components (t = b \+ n).

Note. — This table is available in machine-readable form.

####  4.2.2 LJT Spectral Analysis

We fit the 69 LJT spectra with the same goal of modeling the H$\beta$, [O
iii], and He i lines accurately. Figure 6 shows the fit to a single-epoch LJT
spectrum.

Figure 6: Composite model fit to epoch 24 of the Mrk 142 LJT data displaying
individual components of the model. See caption of Figure 5 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 the end of the spectrum although it does not impact measurements in the
Regions of Interest.

We adopted the same model as for the Gemini spectra with small modifications
to the ratios of certain fixed parameters. We determined the flux ratios for
the coronal lines relative to the [O iii] $\lambda 5008$ line flux from the
fit to the mean LJT spectrum. The width of the fixed broad H$\beta$ Gaussian
was fixed at a factor of 2.5 (instead of 2 for the Gemini spectra). A factor
of 2 for this second H$\beta$ Gaussian in LJT spectra was insufficient to
trace the broad wing of H$\beta$, which also affected the fit to the blended
Fe ii feature at $\sim$4923 Å. Therefore, a broader H$\beta$ component was
required to generate a good fit in that region. This indicates an interplay
between the broad H$\beta$ and Fe ii line emission in the fitting process.
Similarly, the [O iii] $\lambda 5008$ appears to be blended with the Fe ii
emission feature at its red wing. This is caused by the instrumental
broadening in LJT spectra that further resulted in wider [O iii] FWHM
measurements than typically expected for [O iii] in NLS1 objects. To contain
the effect of the “broader” [O iii] FWHM measurements on the H$\beta$ and He i
line measurements, we fixed the narrow-line flux ratios of H$\beta$ to [O iii]
$\lambda 5008$ and He i to [O iii] $\lambda 5008$ from the Gemini spectral
measurements (see Table 3). Tables 7, 8, and 9 provide emission-line
measurements for the LJT spectra from 69 epochs.

Table 7: [O iii] $\lambda 5008$ Emission-Line Measurements for LJT Spectra

Epoch | Position${}_{\hbox{[{\rm O~{}}\kern 0.70004pt{\sc iii}]}\lambda 5008}$ | FWHM${}_{\hbox{[{\rm O~{}}\kern 0.70004pt{\sc iii}]}\lambda 5008}$ | $F_{\hbox{[{\rm O~{}}\kern 0.70004pt{\sc iii}]}\lambda 5008}$ |  $\chi_{\nu}^{2}$[a][a]footnotemark:
---|---|---|---|---
| [Å] | [km s-1] | [10-15 erg s-1 cm-2] |
1 | $5007.25\pm 0.09$ | $718\pm 9$ | $16.6\pm 0.2$ | 2.27
2 | $5007.22\pm 0.13$ | $754\pm 22$ | $17.5\pm 0.4$ | 1.45
3 | $5007.25\pm 0.13$ | $741\pm 13$ | $17.2\pm 0.3$ | 2.00
4 | $5007.40\pm 0.12$ | $787\pm 19$ | $17.8\pm 0.4$ | 2.03
5 | $5007.33\pm 0.10$ | $716\pm 18$ | $16.1\pm 0.4$ | 2.07
6 | $5007.43\pm 0.13$ | $740\pm 21$ | $16.4\pm 0.4$ | 1.71
7 | $5007.44\pm 0.16$ | $880\pm 6$ | $19.6\pm 0.4$ | 1.60
8 | $5007.46\pm 0.06$ | $691\pm 13$ | $16.9\pm 0.3$ | 2.56
9 | $5007.42\pm 0.10$ | $679\pm 19$ | $17.1\pm 0.3$ | 1.68
10 | $5007.51\pm 0.17$ | $707\pm 27$ | $17.4\pm 0.6$ | 1.28
11 | $5007.43\pm 0.14$ | $742\pm\cdots$ | $17.6\pm 0.3$ | 1.51
12 | $5007.26\pm 0.09$ | $713\pm 10$ | $16.7\pm 0.3$ | 2.19
13 | $5007.41\pm 0.20$ | $716\pm 27$ | $17.2\pm 0.6$ | 1.51
14 | $5007.49\pm 0.12$ | $757\pm 13$ | $16.8\pm 0.3$ | 1.67
15 | $5007.57\pm 0.14$ | $737\pm 22$ | $16.8\pm 0.4$ | 1.42
16 | $5007.53\pm 0.10$ | $682\pm 16$ | $17.4\pm 0.3$ | 1.66
17 | $5007.44\pm 0.10$ | $682\pm 2$ | $15.7\pm 0.2$ | 1.98
18 | $5007.46\pm 0.15$ | $736\pm 27$ | $16.3\pm 0.5$ | 1.20
19 | $5007.65\pm 0.14$ | $752\pm 15$ | $16.6\pm 0.3$ | 1.93
20 | $5007.45\pm 0.15$ | $727\pm 28$ | $17.2\pm 0.6$ | 1.24
21 | $5007.53\pm 0.14$ | $758\pm 17$ | $17.1\pm 0.4$ | 1.40
22 | $5007.67\pm 0.17$ | $802\pm 16$ | $17.1\pm 0.4$ | 1.47
23 | $5007.16\pm 0.23$ | $772\pm 26$ | $17.7\pm 0.7$ | 1.21
24 | $5007.56\pm 0.10$ | $674\pm 17$ | $16.5\pm 0.3$ | 1.74
25 | $5007.57\pm 0.11$ | $700\pm 26$ | $16.9\pm 0.4$ | 1.66
26 | $5007.55\pm 0.11$ | $733\pm 14$ | $17.1\pm 0.3$ | 1.77
27 | $5007.45\pm 0.09$ | $680\pm 4$ | $16.8\pm 0.3$ | 2.02
28 | $5007.66\pm 0.14$ | $801\pm 6$ | $16.9\pm 0.3$ | 1.45
29 | $5007.48\pm 0.10$ | $785\pm 16$ | $18.6\pm 0.3$ | 1.96
30 | $5007.60\pm 0.14$ | $742\pm 22$ | $17.7\pm 0.5$ | 1.34
31 | $5007.46\pm 0.10$ | $707\pm 11$ | $16.1\pm 0.3$ | 2.25
32 | $5007.38\pm 0.08$ | $699\pm 5$ | $16.3\pm 0.4$ | 1.32
33 | $5007.48\pm 0.13$ | $684\pm 17$ | $16.5\pm 0.4$ | 1.80
34 | $5007.52\pm 0.11$ | $683\pm 17$ | $17.1\pm 0.4$ | 1.76
35 | $5007.38\pm 0.11$ | $776\pm 15$ | $16.8\pm 0.3$ | 2.82
36 | $5007.39\pm 0.06$ | $681\pm 2$ | $16.5\pm 0.2$ | 4.36
37 | $5007.44\pm 0.09$ | $682\pm 0$ | $16.5\pm 0.2$ | 2.13
38 | $5007.66\pm 0.13$ | $810\pm 9$ | $17.3\pm 0.4$ | 1.47
39 | $5007.65\pm 0.24$ | $719\pm 49$ | $17.2\pm 1.0$ | 2.02
40 | $5007.63\pm 0.12$ | $719\pm 16$ | $16.9\pm 0.4$ | 1.71
41 | $5007.56\pm 0.08$ | $728\pm 9$ | $16.9\pm 0.2$ | 4.65
42 | $5007.61\pm 0.09$ | $688\pm 2$ | $16.9\pm 0.2$ | 3.74
43 | $5007.41\pm 0.14$ | $713\pm 27$ | $17.2\pm 0.5$ | 1.52
44 | $5007.48\pm 0.16$ | $712\pm 45$ | $17.4\pm 0.9$ | 1.63
45 | $5007.51\pm 0.13$ | $745\pm 18$ | $18.3\pm 0.4$ | 1.53
46 | $5007.47\pm 0.10$ | $731\pm 14$ | $16.8\pm 0.3$ | 1.98
47 | $5007.57\pm 0.22$ | $744\pm 36$ | $16.5\pm 0.7$ | 1.05
48 | $5007.60\pm 0.12$ | $685\pm 26$ | $16.1\pm 0.5$ | 2.26
49 | $5008.33\pm 0.21$ | $857\pm 30$ | $18.8\pm 0.6$ | 2.06
50 | $5007.51\pm 0.09$ | $691\pm 31$ | $17.1\pm 0.5$ | 3.21
51 | $5007.76\pm 0.08$ | $726\pm 11$ | $16.7\pm 0.2$ | 3.28
52 | $5007.64\pm 0.12$ | $686\pm 31$ | $16.1\pm 0.5$ | 1.61
53 | $5007.44\pm 0.11$ | $707\pm 19$ | $17.1\pm 0.4$ | 1.82
54 | $5007.64\pm 0.11$ | $679\pm 15$ | $16.6\pm 0.4$ | 1.59
55bbThis spectrum appeared very noisy likely due to some disturbance in the field of view at the time of observation. Therefore, we excluded this epoch from further analysis. | $5007.50\pm 0.23$ | $670\pm 26$ | $14.5\pm 0.6$ | 1.97
56 | $5007.40\pm 0.12$ | $646\pm 31$ | $15.8\pm 0.4$ | 1.53
57 | $5007.39\pm 0.08$ | $634\pm 1$ | $16.1\pm 0.2$ | 2.55
58 | $5007.55\pm 0.08$ | $711\pm 8$ | $17.4\pm 0.2$ | 3.54
59 | $5007.62\pm 0.08$ | $724\pm 12$ | $17.7\pm 0.3$ | 3.37
60 | $5007.57\pm 0.16$ | $726\pm 21$ | $17.5\pm 0.5$ | 1.48
61 | $5007.39\pm 0.14$ | $668\pm 27$ | $17.2\pm 0.6$ | 1.50
62 | $5007.60\pm 0.13$ | $750\pm 14$ | $18.6\pm 0.3$ | 2.58
63 | $5007.68\pm 0.09$ | $659\pm 14$ | $16.4\pm 0.3$ | 2.02
64 | $5007.32\pm 0.08$ | $660\pm 11$ | $16.4\pm 0.3$ | 3.39
65 | $5007.70\pm 0.08$ | $727\pm 12$ | $17.4\pm 0.2$ | 3.46
66 | $5007.55\pm 0.09$ | $681\pm 12$ | $17.1\pm 0.3$ | 2.27
67 | $5007.63\pm 0.10$ | $709\pm 14$ | $17.0\pm 0.3$ | 2.03
68 | $5007.70\pm 0.10$ | $756\pm 3$ | $17.4\pm 0.3$ | 1.73
69 | $5007.59\pm 0.17$ | $752\pm 25$ | $17.3\pm 0.4$ | 1.78

Note. — This table is available in machine-readable form.

Table 8: H$\beta$ $\lambda 4861$ Emission-Line Measurements for LJT Spectra

Epoch | FWHM${}_{\hbox{{\rm H}\kern 0.70004pt{\sc$\beta$}},b}$ | $F_{\hbox{{\rm H}\kern 0.70004pt{\sc$\beta$}},b}$ | FWHM${}_{\hbox{{\rm H}\kern 0.70004pt{\sc$\beta$}},n}$ | $F_{\hbox{{\rm H}\kern 0.70004pt{\sc$\beta$}},n}$ | FWHM${}_{\hbox{{\rm H}\kern 0.70004pt{\sc$\beta$}},t}$ | $F_{\hbox{{\rm H}\kern 0.70004pt{\sc$\beta$}},t}$
---|---|---|---|---|---|---
| [km s-1] | [10-15 erg s-1 cm-2] | [km s-1] | [10-15 erg s-1 cm-2] | [km s-1] | [10-15 erg s-1 cm-2]
1 | $1912\pm 52$ | $83.5\pm 1.5$ | $718\pm 9$ | $4.85\pm 0.07$ | $1660\pm 42$ | $88.3\pm 1.5$
2 | $1933\pm 73$ | $82.7\pm 3.5$ | $754\pm 22$ | $5.13\pm 0.13$ | $1702\pm 46$ | $87.8\pm 3.5$
3 | $1951\pm 38$ | $83.3\pm 1.6$ | $741\pm 13$ | $5.03\pm 0.09$ | $1748\pm 48$ | $88.3\pm 1.6$
4 | $1901\pm 52$ | $84.9\pm 2.8$ | $787\pm 19$ | $5.22\pm 0.11$ | $1700\pm 69$ | $90.1\pm 2.8$
5 | $1881\pm 46$ | $80.3\pm 3.8$ | $716\pm 18$ | $4.72\pm 0.10$ | $1706\pm 46$ | $85.0\pm 3.8$
6 | $1958\pm 85$ | $82.2\pm 3.1$ | $740\pm 21$ | $4.80\pm 0.12$ | $1708\pm 47$ | $87.0\pm 3.1$
7 | $2055\pm 86$ | $82.6\pm 2.3$ | $880\pm 6$ | $5.74\pm 0.11$ | $1750\pm 69$ | $88.3\pm 2.3$
8 | $1956\pm 54$ | $81.3\pm 2.4$ | $691\pm 13$ | $4.95\pm 0.09$ | $1804\pm 71$ | $86.3\pm 2.4$
9 | $1884\pm 63$ | $78.3\pm 1.5$ | $679\pm 19$ | $5.02\pm 0.10$ | $1618\pm 33$ | $83.4\pm 1.5$
10 | $1988\pm 85$ | $85.2\pm 4.7$ | $707\pm 27$ | $5.10\pm 0.17$ | $1742\pm 82$ | $90.3\pm 4.7$
11 | $1985\pm 102$ | $78.2\pm 4.9$ | $742\pm\cdots$ | $5.17\pm 0.09$ | $1647\pm 54$ | $83.3\pm 4.9$
12 | $1924\pm 44$ | $82.1\pm 1.8$ | $713\pm 10$ | $4.90\pm 0.08$ | $1703\pm 46$ | $87.0\pm 1.8$
13 | $1981\pm 87$ | $84.8\pm 7.0$ | $716\pm 27$ | $5.03\pm 0.18$ | $1848\pm 48$ | $89.8\pm 7.0$
14 | $2041\pm 64$ | $80.2\pm 1.5$ | $757\pm 13$ | $4.93\pm 0.10$ | $1779\pm 58$ | $85.1\pm 1.5$
15 | $2004\pm 57$ | $78.5\pm 4.3$ | $737\pm 22$ | $4.94\pm 0.12$ | $1684\pm 77$ | $83.4\pm 4.3$
16 | $2017\pm 83$ | $82.3\pm 1.5$ | $682\pm 16$ | $5.11\pm 0.10$ | $1630\pm 61$ | $87.4\pm 1.5$
17 | $1928\pm 64$ | $81.8\pm 1.9$ | $682\pm 2$ | $4.61\pm 0.07$ | $1702\pm 41$ | $86.4\pm 1.9$
18 | $1904\pm 79$ | $82.9\pm 4.6$ | $736\pm 27$ | $4.77\pm 0.14$ | $1678\pm 55$ | $87.7\pm 4.6$
19 | $2024\pm 63$ | $83.0\pm 2.2$ | $752\pm 15$ | $4.87\pm 0.09$ | $1782\pm 52$ | $87.9\pm 2.2$
20 | $1961\pm 91$ | $81.3\pm 4.0$ | $727\pm 28$ | $5.05\pm 0.17$ | $1657\pm 70$ | $86.4\pm 4.0$
21 | $1999\pm 68$ | $77.6\pm 2.0$ | $758\pm 17$ | $5.02\pm 0.12$ | $1696\pm 92$ | $82.7\pm 2.0$
22 | $1878\pm 92$ | $76.6\pm 2.2$ | $802\pm 16$ | $5.01\pm 0.12$ | $1685\pm 55$ | $81.6\pm 2.2$
23 | $1904\pm 60$ | $77.1\pm 13.0$ | $772\pm 26$ | $5.18\pm 0.21$ | $1755\pm 59$ | $82.3\pm 13.0$
24 | $1933\pm 44$ | $77.7\pm 1.5$ | $674\pm 17$ | $4.83\pm 0.09$ | $1653\pm 57$ | $82.6\pm 1.5$
25 | $1885\pm 73$ | $76.8\pm 2.5$ | $700\pm 26$ | $4.96\pm 0.11$ | $1647\pm 61$ | $81.8\pm 2.5$
26 | $2037\pm 49$ | $78.9\pm 1.8$ | $733\pm 14$ | $5.02\pm 0.09$ | $1816\pm 70$ | $83.9\pm 1.8$
27 | $1968\pm 76$ | $79.7\pm 1.6$ | $680\pm 4$ | $4.92\pm 0.08$ | $1735\pm 41$ | $84.6\pm 1.6$
28 | $1976\pm 77$ | $76.7\pm 2.0$ | $801\pm 6$ | $4.94\pm 0.08$ | $1764\pm 58$ | $81.7\pm 2.0$
29 | $1984\pm 45$ | $78.0\pm 3.0$ | $785\pm 16$ | $5.46\pm 0.10$ | $1742\pm 47$ | $83.4\pm 3.0$
30 | $1862\pm 89$ | $75.4\pm 2.7$ | $742\pm 22$ | $5.18\pm 0.14$ | $1698\pm 62$ | $80.6\pm 2.7$
31 | $2007\pm 39$ | $80.2\pm 1.9$ | $707\pm 11$ | $4.71\pm 0.08$ | $1744\pm 42$ | $84.9\pm 1.9$
32 | $2058\pm 96$ | $81.3\pm 2.3$ | $699\pm 5$ | $4.77\pm 0.11$ | $1741\pm 63$ | $86.0\pm 2.3$
33 | $1912\pm 56$ | $82.9\pm 2.1$ | $684\pm 17$ | $4.84\pm 0.11$ | $1688\pm 73$ | $87.7\pm 2.1$
34 | $1936\pm 39$ | $84.7\pm 2.9$ | $683\pm 17$ | $5.00\pm 0.10$ | $1726\pm 50$ | $89.7\pm 2.9$
35 | $1964\pm 29$ | $81.9\pm 1.2$ | $776\pm 15$ | $4.91\pm 0.09$ | $1730\pm 67$ | $86.9\pm 1.2$
36 | $1919\pm 32$ | $84.6\pm 1.0$ | $681\pm 2$ | $4.85\pm 0.05$ | $1702\pm 29$ | $89.5\pm 1.0$
37 | $1895\pm 76$ | $85.5\pm 1.7$ | $682\pm 0$ | $4.82\pm 0.07$ | $1654\pm 34$ | $90.3\pm 1.7$
38 | $1922\pm 72$ | $84.5\pm 1.7$ | $810\pm 9$ | $5.08\pm 0.11$ | $1708\pm 50$ | $89.6\pm 1.7$
39 | $1869\pm 69$ | $85.1\pm 21.5$ | $719\pm 49$ | $5.05\pm 0.29$ | $1655\pm 33$ | $90.1\pm 21.5$
40 | $1911\pm 50$ | $87.1\pm 3.9$ | $719\pm 16$ | $4.94\pm 0.11$ | $1670\pm 68$ | $92.1\pm 3.9$
41 | $1866\pm 45$ | $88.7\pm 0.7$ | $728\pm 9$ | $4.96\pm 0.06$ | $1641\pm 31$ | $93.6\pm 0.7$
42 | $1933\pm 47$ | $87.3\pm 1.9$ | $688\pm 2$ | $4.96\pm 0.06$ | $1682\pm 45$ | $92.2\pm 1.9$
43 | $1836\pm 74$ | $91.0\pm 6.8$ | $713\pm 27$ | $5.03\pm 0.16$ | $1700\pm 34$ | $96.0\pm 6.8$
44 | $1919\pm 58$ | $87.2\pm 8.9$ | $712\pm 45$ | $5.10\pm 0.27$ | $1686\pm 45$ | $92.3\pm 8.9$
45 | $1888\pm 66$ | $86.5\pm 3.0$ | $745\pm 18$ | $5.36\pm 0.12$ | $1676\pm 57$ | $91.8\pm 3.0$
46 | $1943\pm 46$ | $85.2\pm 2.8$ | $731\pm 14$ | $4.94\pm 0.09$ | $1663\pm 43$ | $90.1\pm 2.8$
47 | $1809\pm 133$ | $80.0\pm 4.8$ | $744\pm 36$ | $4.85\pm 0.21$ | $1606\pm 79$ | $84.9\pm 4.8$
48 | $1937\pm 54$ | $82.2\pm 3.2$ | $685\pm 26$ | $4.71\pm 0.13$ | $1700\pm 62$ | $86.9\pm 3.2$
49 | $2129\pm 115$ | $80.4\pm 2.7$ | $857\pm 30$ | $5.51\pm 0.17$ | $1702\pm 127$ | $85.9\pm 2.7$
50 | $2032\pm 39$ | $87.9\pm 1.9$ | $691\pm 31$ | $5.02\pm 0.14$ | $1773\pm 45$ | $92.9\pm 1.9$
51 | $1996\pm 36$ | $85.7\pm 1.8$ | $726\pm 11$ | $4.89\pm 0.07$ | $1749\pm 40$ | $90.6\pm 1.8$
52 | $1921\pm 51$ | $81.7\pm 2.6$ | $686\pm 31$ | $4.73\pm 0.15$ | $1665\pm 56$ | $86.5\pm 2.6$
53 | $1857\pm 43$ | $81.6\pm 1.9$ | $707\pm 19$ | $5.00\pm 0.11$ | $1667\pm 48$ | $86.6\pm 1.9$
54 | $1846\pm 71$ | $80.3\pm 3.6$ | $679\pm 15$ | $4.87\pm 0.11$ | $1627\pm 53$ | $85.1\pm 3.6$
55aaExcluded from further analysis. See corresponding note in Table 5.Reduced $\chi^{2}$, $\chi_{\nu}^{2}=\chi^{2}/\nu$, where $\nu$ indicates 1071 degrees of freedom, gives the model statistic for individual epochs. | $2051\pm 101$ | $98.8\pm 3.2$ | $670\pm 26$ | $4.24\pm 0.17$ | $1837\pm 91$ | $103.0\pm 3.2$
56 | $1900\pm 60$ | $84.4\pm 3.3$ | $646\pm 31$ | $4.64\pm 0.12$ | $1657\pm 35$ | $89.1\pm 3.3$
57 | $1855\pm 32$ | $84.3\pm 1.5$ | $634\pm 1$ | $4.71\pm 0.06$ | $1673\pm 36$ | $89.0\pm 1.5$
58 | $1873\pm 45$ | $85.1\pm 1.1$ | $711\pm 8$ | $5.11\pm 0.06$ | $1648\pm 35$ | $90.3\pm 1.1$
59 | $1880\pm 33$ | $83.1\pm 1.2$ | $724\pm 12$ | $5.18\pm 0.07$ | $1683\pm 33$ | $88.3\pm 1.2$
60 | $1831\pm 79$ | $82.8\pm 4.3$ | $726\pm 21$ | $5.13\pm 0.14$ | $1674\pm 49$ | $87.9\pm 4.3$
61 | $1802\pm 71$ | $79.5\pm 7.3$ | $668\pm 27$ | $5.04\pm 0.17$ | $1536\pm 60$ | $84.5\pm 7.3$
62 | $1943\pm 57$ | $78.1\pm 2.9$ | $750\pm 14$ | $5.44\pm 0.09$ | $1724\pm 43$ | $83.6\pm 2.9$
63 | $1934\pm 51$ | $79.9\pm 2.3$ | $659\pm 14$ | $4.81\pm 0.09$ | $1639\pm 39$ | $84.7\pm 2.3$
64 | $1852\pm 36$ | $77.7\pm 1.7$ | $660\pm 11$ | $4.82\pm 0.07$ | $1653\pm 37$ | $82.5\pm 1.7$
65 | $1893\pm 33$ | $81.0\pm 1.1$ | $727\pm 12$ | $5.11\pm 0.07$ | $1682\pm 46$ | $86.2\pm 1.1$
66 | $1930\pm 47$ | $82.6\pm 1.5$ | $681\pm 12$ | $5.01\pm 0.09$ | $1706\pm 32$ | $87.6\pm 1.5$
67 | $1877\pm 35$ | $83.7\pm 2.2$ | $709\pm 14$ | $4.98\pm 0.09$ | $1695\pm 56$ | $88.7\pm 2.2$
68 | $1838\pm 47$ | $81.5\pm 2.4$ | $756\pm 3$ | $5.11\pm 0.09$ | $1651\pm 43$ | $86.6\pm 2.4$
69 | $1893\pm 67$ | $81.3\pm 3.0$ | $752\pm 25$ | $5.05\pm 0.11$ | $1696\pm 35$ | $86.3\pm 3.0$

Note. — The second and the third columns providing the FWHM and flux values,
respectively, for the broad (‘b’) H$\beta$ component include contributions
from both the broad Gaussians defined for the line. The FWHM of the narrow
(‘n’) H$\beta$ is equal to the FWHM of the [O iii] $\lambda 5008$ (see Table
7, third column). The total (‘t’) FWHM and flux include contributions from
both the broad and the narrow components (t = b \+ n).

Note. — This table is available in machine-readable form.

Table 9: He i $\lambda 5877$ Emission-Line Measurements for LJT Spectra

Epoch | FWHM${}_{\hbox{{\rm He~{}}\kern 0.70004pt{\sc i}},b}$ | $F_{\hbox{{\rm He~{}}\kern 0.70004pt{\sc i}},b}$ | FWHM${}_{\hbox{{\rm He~{}}\kern 0.70004pt{\sc i}},n}$ | $F_{\hbox{{\rm He~{}}\kern 0.70004pt{\sc i}},n}$ | FWHM${}_{\hbox{{\rm He~{}}\kern 0.70004pt{\sc i}},t}$ | $F_{\hbox{{\rm He~{}}\kern 0.70004pt{\sc i}},t}$
---|---|---|---|---|---|---
| [km s-1] | [10-15 erg s-1 cm-2] | [km s-1] | [10-15 erg s-1 cm-2] | [km s-1] | [10-15 erg s-1 cm-2]
1 | $3321\pm 340$ | $56.5\pm 1.3$ | $718\pm 9$ | $0.56\pm 0.01$ | $3233\pm 310$ | $57.0\pm 1.3$
2 | $4215\pm 487$ | $54.0\pm 1.9$ | $754\pm 22$ | $0.59\pm 0.01$ | $3719\pm 432$ | $54.6\pm 1.9$
3 | $2677\pm 393$ | $53.4\pm 1.5$ | $741\pm 13$ | $0.58\pm 0.01$ | $2640\pm 335$ | $54.0\pm 1.5$
4 | $3526\pm 460$ | $51.2\pm 1.6$ | $787\pm 19$ | $0.61\pm 0.01$ | $3472\pm 439$ | $51.8\pm 1.6$
5 | $3672\pm 430$ | $50.7\pm 1.5$ | $716\pm 18$ | $0.55\pm 0.01$ | $2955\pm 380$ | $51.2\pm 1.5$
6 | $4021\pm 559$ | $53.0\pm 1.7$ | $740\pm 21$ | $0.56\pm 0.01$ | $3358\pm 509$ | $53.6\pm 1.7$
7 | $2800\pm 413$ | $56.6\pm 1.9$ | $880\pm 6$ | $0.67\pm 0.01$ | $2652\pm 370$ | $57.3\pm 1.9$
8 | $2393\pm 429$ | $59.9\pm 1.8$ | $691\pm 13$ | $0.57\pm 0.01$ | $2390\pm 356$ | $60.5\pm 1.8$
9 | $3007\pm 395$ | $51.5\pm 1.5$ | $679\pm 19$ | $0.58\pm 0.01$ | $3002\pm 377$ | $52.1\pm 1.5$
10 | $3440\pm 567$ | $57.7\pm 2.4$ | $707\pm 27$ | $0.59\pm 0.02$ | $3384\pm 534$ | $58.3\pm 2.4$
11 | $3742\pm 464$ | $50.2\pm 2.0$ | $742\pm\cdots$ | $0.60\pm 0.01$ | $3336\pm 414$ | $50.8\pm 2.0$
12 | $3707\pm 394$ | $52.6\pm 1.3$ | $713\pm 10$ | $0.57\pm 0.01$ | $3234\pm 349$ | $53.1\pm 1.3$
13 | $2031\pm 523$ | $58.0\pm 3.7$ | $716\pm 27$ | $0.58\pm 0.02$ | $2020\pm 440$ | $58.6\pm 3.7$
14 | $4636\pm 499$ | $54.8\pm 1.7$ | $757\pm 13$ | $0.57\pm 0.01$ | $3448\pm 477$ | $55.3\pm 1.7$
15 | $3570\pm 482$ | $51.3\pm 2.1$ | $737\pm 22$ | $0.57\pm 0.01$ | $3392\pm 451$ | $51.9\pm 2.1$
16 | $3777\pm 455$ | $52.6\pm 1.6$ | $682\pm 16$ | $0.59\pm 0.01$ | $2817\pm 387$ | $53.2\pm 1.6$
17 | $3086\pm 433$ | $55.4\pm 1.5$ | $682\pm 2$ | $0.53\pm 0.01$ | $3061\pm 378$ | $55.9\pm 1.5$
18 | $2644\pm 473$ | $49.8\pm 2.2$ | $736\pm 27$ | $0.55\pm 0.02$ | $2584\pm 432$ | $50.4\pm 2.2$
19 | $3681\pm 401$ | $54.9\pm 1.5$ | $752\pm 15$ | $0.56\pm 0.01$ | $3607\pm 366$ | $55.4\pm 1.5$
20 | $3500\pm 533$ | $52.3\pm 2.2$ | $727\pm 28$ | $0.59\pm 0.02$ | $3260\pm 504$ | $52.9\pm 2.2$
21 | $2511\pm 515$ | $45.0\pm 1.9$ | $758\pm 17$ | $0.58\pm 0.01$ | $2479\pm 447$ | $45.6\pm 1.9$
22 | $4378\pm 683$ | $57.8\pm 2.1$ | $802\pm 16$ | $0.58\pm 0.01$ | $3636\pm 586$ | $58.4\pm 2.1$
23 | $3628\pm 556$ | $53.8\pm 3.7$ | $772\pm 26$ | $0.60\pm 0.02$ | $3230\pm 523$ | $54.4\pm 3.7$
24 | $3526\pm 399$ | $52.0\pm 1.4$ | $674\pm 17$ | $0.56\pm 0.01$ | $3148\pm 367$ | $52.6\pm 1.4$
25 | $3227\pm 518$ | $51.5\pm 1.7$ | $700\pm 26$ | $0.58\pm 0.01$ | $3101\pm 485$ | $52.1\pm 1.7$
26 | $3575\pm 504$ | $53.0\pm 1.6$ | $733\pm 14$ | $0.58\pm 0.01$ | $3365\pm 459$ | $53.5\pm 1.6$
27 | $4302\pm 565$ | $53.1\pm 1.4$ | $680\pm 4$ | $0.57\pm 0.01$ | $4133\pm 484$ | $53.6\pm 1.4$
28 | $3591\pm 602$ | $52.1\pm 1.7$ | $801\pm 6$ | $0.57\pm 0.01$ | $3578\pm 529$ | $52.6\pm 1.7$
29 | $3724\pm 551$ | $49.4\pm 1.5$ | $785\pm 16$ | $0.63\pm 0.01$ | $3287\pm 540$ | $50.0\pm 1.5$
30 | $2501\pm 565$ | $53.2\pm 2.1$ | $742\pm 22$ | $0.60\pm 0.02$ | $2342\pm 479$ | $53.8\pm 2.1$
31 | $4400\pm 518$ | $50.7\pm 1.4$ | $707\pm 11$ | $0.55\pm 0.01$ | $4224\pm 445$ | $51.3\pm 1.4$
32 | $3186\pm 487$ | $57.9\pm 2.0$ | $699\pm 5$ | $0.55\pm 0.01$ | $3123\pm 437$ | $58.4\pm 2.0$
33 | $3456\pm 555$ | $58.8\pm 1.8$ | $684\pm 17$ | $0.56\pm 0.01$ | $3362\pm 519$ | $59.3\pm 1.8$
34 | $2880\pm 373$ | $57.8\pm 1.9$ | $683\pm 17$ | $0.58\pm 0.01$ | $2793\pm 302$ | $58.4\pm 1.9$
35 | $3257\pm 410$ | $55.0\pm 1.3$ | $776\pm 15$ | $0.57\pm 0.01$ | $3217\pm 374$ | $55.6\pm 1.3$
36 | $3778\pm 482$ | $55.3\pm 0.9$ | $681\pm 2$ | $0.56\pm 0.01$ | $3648\pm 431$ | $55.8\pm 0.9$
37 | $3369\pm 351$ | $57.0\pm 1.4$ | $682\pm 0$ | $0.56\pm 0.01$ | $3007\pm 302$ | $57.5\pm 1.4$
38 | $3024\pm 428$ | $52.6\pm 2.0$ | $810\pm 9$ | $0.59\pm 0.01$ | $3009\pm 400$ | $53.2\pm 2.0$
39 | $2901\pm 389$ | $53.0\pm 4.1$ | $719\pm 49$ | $0.59\pm 0.03$ | $2809\pm 349$ | $53.5\pm 4.1$
40 | $3124\pm 489$ | $57.3\pm 1.8$ | $719\pm 16$ | $0.57\pm 0.01$ | $3069\pm 431$ | $57.9\pm 1.8$
41 | $4761\pm 506$ | $57.8\pm 1.0$ | $728\pm 9$ | $0.58\pm 0.01$ | $3452\pm 380$ | $58.4\pm 1.0$
42 | $3699\pm 399$ | $61.1\pm 1.2$ | $688\pm 2$ | $0.58\pm 0.01$ | $3664\pm 382$ | $61.7\pm 1.2$
43 | $2720\pm 318$ | $56.2\pm 2.4$ | $713\pm 27$ | $0.58\pm 0.02$ | $2658\pm 296$ | $56.8\pm 2.4$
44 | $3220\pm 447$ | $51.5\pm 2.4$ | $712\pm 45$ | $0.59\pm 0.03$ | $3184\pm 440$ | $52.1\pm 2.4$
45 | $3481\pm 491$ | $53.9\pm 2.0$ | $745\pm 18$ | $0.62\pm 0.01$ | $3422\pm 444$ | $54.5\pm 2.0$
46 | $3367\pm 428$ | $50.9\pm 1.4$ | $731\pm 14$ | $0.57\pm 0.01$ | $3317\pm 417$ | $51.5\pm 1.4$
47 | $3618\pm 841$ | $54.1\pm 3.2$ | $744\pm 36$ | $0.56\pm 0.02$ | $3612\pm 762$ | $54.6\pm 3.2$
48 | $2302\pm 454$ | $51.5\pm 1.7$ | $685\pm 26$ | $0.55\pm 0.02$ | $2300\pm 404$ | $52.0\pm 1.7$
49 | $3621\pm 1008$ | $56.9\pm 2.6$ | $857\pm 30$ | $0.64\pm 0.02$ | $3598\pm 876$ | $57.6\pm 2.6$
50 | $3405\pm 461$ | $55.3\pm 1.4$ | $691\pm 31$ | $0.58\pm 0.02$ | $2868\pm 423$ | $55.9\pm 1.4$
51 | $2974\pm 379$ | $50.9\pm 1.1$ | $726\pm 11$ | $0.57\pm 0.01$ | $2512\pm 286$ | $51.4\pm 1.1$
52 | $3095\pm 465$ | $49.0\pm 1.6$ | $686\pm 31$ | $0.55\pm 0.02$ | $3061\pm 412$ | $49.6\pm 1.6$
53 | $3560\pm 386$ | $55.2\pm 1.5$ | $707\pm 19$ | $0.58\pm 0.01$ | $2853\pm 361$ | $55.8\pm 1.5$
54 | $4011\pm 529$ | $54.9\pm 1.8$ | $679\pm 15$ | $0.56\pm 0.01$ | $3867\pm 475$ | $55.4\pm 1.8$
55aaExcluded from further analysis. See note a in Table 7. | $1713\pm 519$ | $56.2\pm 2.9$ | $670\pm 26$ | $0.49\pm 0.02$ | $1708\pm 510$ | $56.6\pm 2.9$
56 | $3026\pm 343$ | $50.5\pm 1.7$ | $646\pm 31$ | $0.54\pm 0.01$ | $2986\pm 363$ | $51.0\pm 1.7$
57 | $3362\pm 424$ | $49.0\pm 1.2$ | $634\pm 1$ | $0.55\pm 0.01$ | $2803\pm 397$ | $49.6\pm 1.2$
58 | $3533\pm 224$ | $52.5\pm 1.1$ | $711\pm 8$ | $0.59\pm 0.01$ | $3401\pm 203$ | $53.1\pm 1.1$
59 | $4223\pm 565$ | $51.4\pm 1.1$ | $724\pm 12$ | $0.60\pm 0.01$ | $2775\pm 415$ | $52.0\pm 1.1$
60 | $2515\pm 545$ | $50.3\pm 2.4$ | $726\pm 21$ | $0.60\pm 0.02$ | $2515\pm 480$ | $50.8\pm 2.4$
61 | $3274\pm 521$ | $50.4\pm 2.2$ | $668\pm 27$ | $0.59\pm 0.02$ | $3129\pm 497$ | $51.0\pm 2.2$
62 | $3352\pm 421$ | $51.9\pm 1.7$ | $750\pm 14$ | $0.63\pm 0.01$ | $3337\pm 419$ | $52.5\pm 1.7$
63 | $3756\pm 487$ | $53.0\pm 1.4$ | $659\pm 14$ | $0.56\pm 0.01$ | $3257\pm 447$ | $53.6\pm 1.4$
64 | $4127\pm 1067$ | $49.8\pm 1.2$ | $660\pm 11$ | $0.56\pm 0.01$ | $3030\pm 761$ | $50.3\pm 1.2$
65 | $4321\pm 452$ | $57.7\pm 1.2$ | $727\pm 12$ | $0.59\pm 0.01$ | $3535\pm 420$ | $58.3\pm 1.2$
66 | $5320\pm 693$ | $57.0\pm 1.4$ | $681\pm 12$ | $0.58\pm 0.01$ | $3285\pm 608$ | $57.6\pm 1.4$
67 | $3695\pm 507$ | $56.9\pm 1.5$ | $709\pm 14$ | $0.58\pm 0.01$ | $3549\pm 504$ | $57.5\pm 1.5$
68 | $3375\pm 481$ | $52.8\pm 1.7$ | $756\pm 3$ | $0.59\pm 0.01$ | $2925\pm 432$ | $53.4\pm 1.7$
69 | $3431\pm 465$ | $53.3\pm 1.7$ | $752\pm 25$ | $0.59\pm 0.01$ | $2660\pm 385$ | $53.9\pm 1.7$

aafootnotetext: Excluded from further analysis. See note a in Table 7.

Note. — The second and the third columns providing the FWHM and flux values,
respectively, for the broad (‘b’) He i component include contributions from
both the broad Gaussians defined for the line. The FWHM of the narrow (‘n’) He
i is equal to the FWHM of the [O iii] $\lambda 5008$ (see Table 7, third
column). The total (‘t’) FWHM and flux include contributions from both the
broad and the narrow components (t = b \+ n).

Note. — This table is available in machine-readable form.

##  5 Light Curve Analysis

We used the Mrk 142 Gemini and LJT spectral measurements to generate light
curves for the broad H$\beta$ and He i emission-line profiles. We obtained the
total broad-line light curves by integrating the flux under the two broad
components (see green dashed Gaussians for H$\beta$ and pink dashed Gaussians
for He i in Figures 5 and 6) for the two emission lines.

We scaled the broad H$\beta$ light curve from Gemini to the broad H$\beta$
light curve from LJT to generate an inter-calibrated light curve. The H$\beta$
light curves from Gemini and LJT were offset by $\sim$25% from each other
although they displayed similar fluctuations in their patterns. The offset can
be attributed to various factors – different seeing conditions at Gemini and
LJT or even the difference in the calibrations from the two telescopes.
Because we are interested in measuring a time shift in the pattern with
reference to the continuum variations, scaling and combining the light curves
is valid for our purpose. Figure 7 shows the scaled broad H$\beta$ light curve
plotted with the original Gemini and LJT light curves. We then inter-
calibrated the original H$\beta$ light curve from LJT and the scaled H$\beta$
light curve from Gemini with PyROA (see Section 5.1) to use the combined light
curve to determine the time lag between the continuum and emission-line
variability.

Figure 7: Broad H$\beta$ light curve from Gemini (dark blue open circles)
scaled down (faint blue open circles) to the broad H$\beta$ light curve from
LJT (red solid squares). The scaling factor of 0.77 was determined such that
the Gemini data points are distributed evenly above and below the LJT light
curve. The two light curves show similar behavior except at Modified Julian
Date $\sim$58540, where the LJT light curve increases in flux while the Gemini
light curve appears fainter.

###  5.1 Cross Correlation Time Lags

We cross-correlated the broad H$\beta$ Gemini+LJT inter-calibrated light curve
with the UVW2 light curve from Swift to measure the reverberation lag of the
BLR response to the continuum variability from the accretion disk, which is at
smaller size scales than the BLR. Following Cackett et al. (2020), we chose
the UVW2 because we aim to measure the response of H$\beta$ line-emitting gas
to the UV continuum and the UVW2 was the shortest wavelength available from
the photometric monitoring of Mrk 142. During cross-correlation, we also
included the LCO+Zowada+Liverpool/g, the inter-calibrated 5100 Å continuum
from Gemini and LJT data, and the LJT broad H$\beta$ light curves to use
maximum available information for a reliable measurement of the variability
pattern.

We employed Python-based Running Optimal Average (PyROA; Donnan et al., 2021)
to calculate cross-correlation time lags. PyROA666See PyROA code and
documentation at https://github.com/FergusDonnan/PyROA. uses a running optimal
average (ROA) calculated with a window function (defined by a Gaussian by
default) of a certain width to estimate light-curve behavior while fitting all
input light curves simultaneously. The width of the window function controls
the flexibility of the model in deriving the driving light curve – a narrower
window function traces the fluctuating pattern of a highly variable light
curve more appropriately than a wider window, which behaves more rigidly. The
code uses priors to initiate the modeling process, and the performance of the
model is evaluated using Bayesian Information Criterion. PyROA offers a robust
treatment for outliers with an extra variance parameter and a standard
deviation threshold. The extra variance adds in quadrature to the nominal
uncertainties of the input light curves, and the threshold set by the user
allows further inflation of the uncertainties to mitigate the influence of
large outliers. Figure 8 shows the cross-correlation results with reference to
the Swift/UVW2 band.

Figure 8: Time-lag measurements with reference to the Swift/UVW2 band (top
row) with lag distributions modeled as Log-Gaussians. Left: Top three panels
show continuum light curves – Swift/UVW2 (blue), LCO+Zowada+Liverpool/g
(green), and inter-calibrated Gemini+LJT/5100 Å – in units of 10-15 erg s-1
cm-2 Å-1. Bottom two panels show the broad H$\beta$ light curves – LJT only
(pink) and Gemini+LJT inter-calibrated (olive) – in units of 10-14 erg s-1
cm-2 Å-1. Right: Time-lag distributions (colored histograms for the mean lag
and gray shaded uncertainty estimates from a Log-Gaussian lag distribution) of
the light curves on the left with reference to the Swift/UVW2 band, which has
a fixed lag of 0.00 days. Insets in the second and the third panels show a
close view of the time-lag distributions for LCO+Zowada+Liverpool/g and
Gemini+LJT/5100 Å light curves, respectively. For each of the echo light
curves, the black solid vertical line marks the lag measurement, given by the
median lag of the colored distribution

and the black dashed vertical lines (on either sides of the solid line) mark
the corresponding uncertainty.

In addition to the H$\beta$ time lag for the Gemini+LJT inter-calibrated light
curve ($8.68_{-0.72}^{+0.75}$ days), PyROA provided lag measurements for other
input light curves ($0.73_{-0.10}^{+0.10}$ days for LCO+Zowada+Liverpool/g,
$0.79_{-0.29}^{+0.27}$ days for Gemini+LJT/5100 Å, and $8.14_{-0.80}^{+0.82}$
days for LJT/H$\beta$) with reference to the Swift/UVW2 band. With respect to
the shorter-wavelength UVW2 emission, we expect to measure positive lags for
the longer-wavelength emission in the g-band, at 5100 Å, and for the H$\beta$
emission line. We thus modeled the distribution of time lags as a Log-Gaussian
function that imposes positive lags with reference to UVW2, whose lag is fixed
at 0.00 days (see Figure 8). In addition to measuring the time shift in the
light-curve pattern, the width of the Log-Gaussian model also accounts for the
amount of blurring applied to the reference light curve (here, UVW2) to match
the response in the echo light curves. This becomes important for BLR RM,
where the emission-line variations, emerging farther away from the central
engine and from a more spatially extended structure (size scale $\sim$1
parsec) than the accretion disk, are smoother compared to the continuum
variations closer to the center. In PyROA, the width of the time-lag
distribution quantifies the blurring determined for each of the echo light
curves: $0.28_{-0.18}^{+0.19}$ days for LCO+Zowada+Liverpool/g,
$0.88_{-0.48}^{+0.62}$ days for Gemini+LJT/5100 Å, $4.88_{-0.90}^{+1.16}$ days
for LJT/H$\beta$), and $5.47_{-0.89}^{+1.06}$ days for Gemini+LJT/H$\beta$. We
also performed light-curve analysis with the Interpolated Cross-Correlation
Function (ICCF; Gaskell & Sparke, 1986; Gaskell & Peterson, 1987) and Just
Another Vehicle for Estimating Lags In Nuclei (JAVELIN; Zu et al., 2011, 2013,
using a top-hat time-lag distribution function) for comparison with the PyROA
results. Table 10 displays the time-lag measurements with all three methods.

Table 10: Time-Lag Measurements

Time Lag [days] | PyROA∗ | ICCF | JAVELIN
---|---|---|---
UVW2-to-g | $0.73_{-0.10}^{+0.10}$ | $0.7_{-0.2}^{+0.2}$ | $0.54_{-0.08}^{+0.08}$
UVW2-to-5100 Å | $0.79_{-0.29}^{+0.27}$ | $1.7_{-1.2}^{+1.8}$ | $0.78_{-0.38}^{+0.42}$
UVW2-to-H$\beta$,LJT | $8.14_{-0.80}^{+0.82}$ | $8.8_{-3.5}^{+2.5}$ | $6.95_{-0.46}^{+0.69}$
UVW2-to-H$\beta$,Gemini+LJT | $8.68_{-0.72}^{+0.75}$ | $8.7_{-9.1}^{+4.2}$ | $11.38_{-4.49}^{+0.51}$

**footnotetext: We consider these as the most robust time-lag measurements of
the three methods. See Section 6 for further details.

###  5.2 He i Light Curves

The peculiar, asymmetrical shape of the He i line – narrow-line emission and a
broad, asymmetrical component (modeled by a Gaussian six times the width of
the broad H$\beta$ line in our spectra fitting procedure) – is clearly evident
in the high S/N Gemini mean spectrum. The asymmetry in the broad component due
to the stronger blueshifted emission feature likely indicates a wind component
in the BLR. However, the cause of such a disk-wind component is not clear.
Leighly (2004) performed CLOUDY simulations to model 10 high- and low-
ionization emission lines observed in NLS1s. She suggested that the
blueshifted emission evident in the high-ionization lines in NLS1s arises from
a wind moving towards us. Interestingly, the plausible broad, blueshifted
component for He ii in the spectral model may also be a result of such a wind
emission. Further analysis of the He ii line is needed to draw firm inferences
in this regard. In addition to the blueshifted wind, Leighly (2004) found that
the high-ionization Ly$\alpha$ was dominated by emission in the accretion-disk
atmosphere or at the low-velocity base of the broad-line wind. The very broad,
flattened emission feature in He i may be indicative of a disk-wind feature as
noted for Ly$\alpha$. Furthermore, Leighly (2004) derived a small covering
fraction for the BLR. She argued that in an object with a small black hole
mass, as in the case of Mrk 142
($M_{\bullet}=3.89~{}\times~{}10^{6}~{}M_{\odot}$[7771 $M_{\odot}$ = 1 Solar
mass]), a small covering fraction can result from an emission-line region
closer to the plane of the disk. Li et al. (2018) performed velocity-resolved
RM of Mrk 142, where the authors concluded that the two-zone BLR model (Wang
et al., 2014a) best fit the Mrk 142 BLR with an opening angle ($\theta$) of
10–30∘ (representing a disk-like BLR). Estimating the covering fraction from
the opening angle as $\theta/90^{\circ}$ yields a value of 0.1–0.3 for the
covering fraction; however, these small values do not confirm the presence of
a disk wind in Mrk 142. To understand the components that form the atypical
Mrk 142 BLR system or the kind of BLR geometry in a super-Eddington that can
show a broad, blueshifted emission feature similar to the He i line feature,
we would need further investigation of BLR models and data for super-Eddington
AGN.

Although the LJT RMS spectrum of Mrk 142 shows a weak variable feature for He
i, the variability is not usefully quantifiable given the timescale and S/N of
our current Gemini+LJT spectroscopic campaigns. Figure 9 displays the
individual and total broad-line components of He i emission from both the
Gemini and the LJT observations. The offset observed in the narrower broad
component is similar to that observed in the broad H$\beta$, where the light
curve from Gemini appears at higher flux values than the LJT light curve.
Interestingly, the broader broad component is brighter in LJT than in Gemini
likely resulting from the blueshifted disk-wind component broadened due to the
wider slit used for LJT data.

Figure 9: He i light curves highlighting the contributions from the individual
broad components (referred to as broader and narrower) to the total broad
components from Gemini (open circles) and LJT (solid squares) data. Smaller
(larger) size of the markers represents narrower (broader) components. It is
interesting to note that the broader He i light curve from the LJT spectra is
brighter than the broader He i component from the Gemini spectra likely due to
the blue wing of He i (traced primarily by the broader component) in the LJT
data affected by instrumental broadening.

##  6 Results and Discussion

We present the first results on the lag of the broad H$\beta$ line with
respect to the UV continuum in Mrk 142 from optical spectroscopic observations
from Gemini+LJT with simultaneous monitoring in the photometric Swift/UVW2 and
LCO+Zowada+Liverpool/g bands.

We applied a spectral model with same number of components but different
parameter settings to the Gemini and LJT spectra to derive H$\beta$ and He i
light curves. We noted that a profile composed of one narrow + two broad
Gaussians sufficiently traced both the H$\beta$ and the He i lines, where the
widths and positions of the narrow components were tied to those of the [O
iii] $\lambda 5008$ line. The use of Gaussians for fitting broad lines such as
H$\beta$ in our data does not comply with the Wang et al. (2014a) line-profile
predictions for a super-Eddington AGN, where self-shadowing effects due to a
slim-disk structure in super-Eddington AGN could result in the broad-line
profiles appearing more Lorentzian than Gaussian. We recognize that our Mrk
142 spectral fitting model does not align the Wang et al. (2014a); however,
our results are not sufficient evidence to rule out the self-shadowing
hypothesis. A detailed analysis of spectral line profiles for a larger sample
of super-Eddington AGN is required to build a robust understanding of how the
accretion-disk behavior affects the observed broad-line profiles in these
objects. We employed fixed 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$}}}$ and $F_{\mathrm{\hbox{{\rm
He~{}}\kern 0.70004pt{\sc i}}}}/F_{\mathrm{\hbox{[{\rm O~{}}\kern
0.70004pt{\sc iii}]~{}$\lambda 5008$}}}$ for the LJT spectral model
(determined from flexible flux ratios for the Gemini spectra) due to the
instrumental broadening in the LJT spectra affecting emission-line
measurements. Although the LJT RMS spectrum shows a weak feature at the He i
location, PrepSpec modeling and light-curve analysis suggested that there is
no adequate variability in the line that is measurable with the current
Gemini+LJT data. However, we acknowledge that the He i emission line shows a
peculiar profile evident from the high S/N of the Gemini spectra. The broader
Gaussian used for the line indicates stronger blueshifted emission than the
redshifted side of the line. Also, the He ii line specifically required a
broad, blueshifted component to accurately trace the emission in that region.
Followed by spectral analysis, we empirically measured the FWHM values as well
as calculated the narrow- and broad-line flux values of the H$\beta$ and He i
lines to obtain their light curves.

Applying PyROA, we performed cross-correlation analysis with continuum
(Swift/UVW2, LCO+Zowada+Liverpool/g, and Gemini+LJT/5100 Å) and broad H$\beta$
light curves (LJT and Gemini+LJT inter-calibrated) with a goal of determining
reverberation time lag for the Gemini+LJT inter-calibrated H$\beta$ light
curve. PyROA provided an improvement in quantifying the uncertainties compared
to previous studies. Most early RM studies have extensively applied the ICCF
method for time-lag measurements which makes it a good comparison standard.
However, ICCF struggles with non-uniformly sampled data, which is true for our
Gemini+LJT campaigns similar to most other studies, and uses linear
interpolation to estimate the light-curve behavior in the regions with data
gaps. Consequently, the uncertainties reported for ICCF-based measurements are
typically conservative compared to JAVELIN and PyROA, as noted in this work
for the 5100 Å continuum as well as the H$\beta$ emission from LJT and
Gemini+LJT inter-calibrated data (see Table 10). In the context of the
uncertainties on time-lag measurements, JAVELIN has been shown to perform
better. For instance, Edelson et al. (2019) reported uncertainties from ICCF
to be twice as large as those from JAVELIN which is also evident from the
results in this work (see Table 10). JAVELIN uses damped random walk (DRW) to
estimate the light-curve pattern in the regions where data are not available.
DRW closely characterizes the variability observed in AGN, plausibly leading
to smaller uncertainties in the final lag measurements. However, JAVELIN
requires a good estimation of uncertainties in data. For sub-optimally
calibrated uncertainties, JAVELIN can sometimes fail to deliver reliable lag
measurements (Donnan et al., 2021). This is likely the reason the LJT/H$\beta$
and Gemini+LJT/H$\beta$ emission-line light curves, which have larger
calibrated uncertainties than the continuum light curves, show time-lag
measurements differing from those reported by PyROA. PyROA offers an
improvement over JAVELIN – the ROA along with a robust error treatment not
only prevents the outlier points from disrupting the estimation of the driving
light curve but also applies a valid algorithm for resolving data gaps.

We measured a time lag of $8.68_{-0.72}^{+0.75}$ days for the Gemini+LJT
inter-calibrated H$\beta$ emission with reference to the UVW2 continuum. We
also obtained a lag of $0.79_{-0.29}^{+0.27}$ days for the 5100 Å continuum
with reference to the UVW2 band (that is consistent, within uncertainties,
with the time lag–wavelength relationship in Cackett et al., 2020), and a lag
of $7.89\pm 0.80$ days for the H$\beta$ emission with respect to the 5100 Å
continuum. From here, we report a black hole mass of
$\log(M_{\bullet}/M_{\odot})$ = $6.28\pm 0.29$ derived using Equation 1,

$M_{\bullet}=\frac{f~{}c~{}\tau_{\text{\hbox{{\rm H}\kern
0.70004pt{\sc$\beta$}}}}~{}V_{\text{FWHM,\hbox{{\rm H}\kern
0.70004pt{\sc$\beta$}}}}^{2}}{G}$ (1)

where we used a $\log(f)$ value of $-0.36_{-0.54}^{+0.33}$ from the dynamical
modeling of the Mrk 142 BLR by Li et al. (2018). It is possible that the value
of $\log(f)$ has a large uncertainty, which depends on the BLR’s dynamical
model or the calibration using the $M-\sigma_{*}$ relation for classical
bulges and pseudobulges (e.g. Ho & Kim, 2014; Li et al., 2018; Yu et al.,
2020). For $V_{\mathrm{FWHM}}$, we used the mean H$\beta$ FWHM of $1680\pm 14$
km s-1 from the Gemini spectra. Here, we chose the Gemini spectra due to their
higher resolution providing a more reliable measurement of the narrower
H$\beta$ broad-line profile than the LJT spectra. We also considered the mean
FWHM from the spectra as against the H$\beta$ RMS profiles as the RMS spectra
from Gemini were noisier blueward of the blue wing of the H$\beta$ line. We
further measured mean luminosities of $\log(L_{\text{UVW2}})=43.832\pm 0.001$,
$\log(L_{5100})=43.643\pm 0.002$, and $\log(L_{\mathrm{\hbox{{\rm H}\kern
0.70004pt{\sc$\beta$}}}})=41.621\pm 0.002$. For the $L_{5100}$ and
$L_{\mathrm{\hbox{{\rm H}\kern 0.70004pt{\sc$\beta$}}}}$ measurements, we
adopted the mean flux value from our Gemini+LJT inter-calibrated light curves
as their respective Gemini light curves alone were insufficient to provide a
reliable flux scale due to the shorter observing timescale.

Our results agree with previously published measurements of Mrk 142 (Du et
al., 2015; Li et al., 2018). From the previous six-month SEAMBH campaign, Du
et al. (2015) reported a time lag of $7.9_{-1.1}^{+1.2}$ days for H$\beta$
with reference to 5100 Å. We measured an optical lag of $7.89\pm 0.80$ days
for H$\beta$ in agreement with the Du et al. (2015) value within
uncertainties. Furthermore, the derived black hole mass for Mrk 142 in this
work, $\log(M_{\bullet}/M_{\odot})$ = $6.28\pm 0.29$, agrees with the value
reported in the recent velocity-resolved RM analysis by Li et al. (2018),
$6.23_{-0.45}^{+0.26}$, within uncertainty limits. Table 11 summarizes the
measured quantities in this work and shows their comparison with the values
from previous studies.

Table 11: Comparison of Measurements to Previous SEAMBH Studies

Measured Quantity | This Work | Value From Previous SEAMBH Studies
---|---|---
$\tau_{\mathrm{UVW2-to-\hbox{{\rm H}\kern 0.70004pt{\sc$\beta$}}}}^{*}$ |  $8.68_{-0.72}^{+0.75}$ days |  $\cdots$
$\tau_{\mathrm{5100~{}\AA-to-\hbox{{\rm H}\kern 0.70004pt{\sc$\beta$}}}}$ |  $7.89\pm 0.80$ days |  $7.9_{-1.1}^{+1.2}$ days (Du et al., 2015)
$\log(M_{\bullet}/M_{\odot})$ | $6.28\pm 0.29$ |  $6.23_{-0.45}^{+0.26}$ (Li et al., 2018)
$\log(L_{\mathrm{UVW2}})$∗ | $43.832\pm 0.001$ |  $\cdots$
$\log(L_{\mathrm{5100}})$ | $43.643\pm 0.002$ |  $43.56\pm 0.06$ (Du et al., 2015)
$\log(L_{\mathrm{\hbox{{\rm H}\kern 0.70004pt{\sc$\beta$}}}})$ | $41.621\pm 0.002$ |  $43.56\pm 0.06$ (Du et al., 2015)

**footnotetext: New measurements

To visualize our results in the broader context of reverberation-mapped AGN,
we placed the measured size of the H$\beta$ line-emitting region on various
R–L scaling relations. Comparisons are discussed below.

Figure 10 shows the $R_{\mathrm{\hbox{{\rm H}\kern
0.70004pt{\sc$\beta$}}}}$–$L_{\mathrm{5100}}$ (panel a) and
$R_{\mathrm{\hbox{{\rm H}\kern
0.70004pt{\sc$\beta$}}}}$–$L_{\mathrm{\hbox{{\rm H}\kern
0.70004pt{\sc$\beta$}}}}$ (panel b) relations with the red star representing
the Mrk 142 measurements from this work. In agreement with the findings from
previous SEAMBH campaigns (black circles in Figure 10; see references in the
figure caption), the red Mrk 142 star appears to depart from the general trend
observed for typical RM objects, especially in the $R_{\mathrm{\hbox{{\rm
H}\kern 0.70004pt{\sc$\beta$}}}}$–$L_{\mathrm{5100}}$ relation (green circles,
panel a; see the entire reference list in the figure caption). Comparatively,
the departure of Mrk 142 from the Kaspi et al. (2005) best-fit relation (panel
b) is less obvious. We quantified these Mrk 142 departures in terms of time
lag (along the vertical axis) relative to the standard deviation of the
departures of the typical RM sample from both best-fit relations
($\sigma_{\mathrm{departure}}$). While the departure of Mrk 142 from the Bentz
et al. (2013) relation (15.7 light-days) is 1.15$\sigma_{\mathrm{departure}}$
(where $\sigma_{\mathrm{departure}}=13.7$ light-days), its departure from the
Kaspi et al. (2005) relation (4.08 light-days) is
$<<$1$\sigma_{\mathrm{departure}}$ (where $\sigma_{\mathrm{departure}}=26.8$
light-days). The latter implies that $R_{\mathrm{\hbox{{\rm H}\kern
0.70004pt{\sc$\beta$}}}}$–$L_{\mathrm{\hbox{{\rm H}\kern
0.70004pt{\sc$\beta$}}}}$ is a tighter relationship for AGN than
$R_{\mathrm{\hbox{{\rm H}\kern 0.70004pt{\sc$\beta$}}}}$–$L_{\mathrm{5100}}$.
The position of Mrk 142 in the $R_{\mathrm{\hbox{{\rm H}\kern
0.70004pt{\sc$\beta$}}}}$–$L_{\mathrm{5100}}$ relationship (panel ar),
considerably below the best-fit line, reiterates the characteristic of super-
Eddington AGN exhibiting smaller BLR sizes in contrast to the sub-Eddington
population at the same luminosities (Du et al., 2016b). Du et al. (2015)
tested this deviation of high accretion-rate AGN from the
$R_{\mathrm{\hbox{{\rm H}\kern 0.70004pt{\sc$\beta$}}}}$–$L_{\mathrm{5100}}$
relationship. Studying the differences in the BLR sizes for AGN with low
($\dot{M}/\dot{M}_{\mathrm{Edd}}<3$) and high
($\dot{M}/\dot{M}_{\mathrm{Edd}}\geq 3$) mass-accretion rates, Du et al.
(2015) inferred that $\dot{M}$ influences the size scales observed in super-
Eddington AGN while such a correlation is absent in the low mass-accretion
rate objects.

Figure 10: Radius-luminosity (R–L) scaling relations for H$\beta$ in the
optical including results from this work (red star). Panel a:
$R_{\mathrm{\hbox{{\rm H}\kern 0.70004pt{\sc$\beta$}}}}$–$L_{\mathrm{5100}}$
relation showing Mrk 142 from this work close to the Du et al. (2015)
measurement (blue square). Panel b: $R_{\mathrm{\hbox{{\rm H}\kern
0.70004pt{\sc$\beta$}}}}$–$L_{\mathrm{\hbox{{\rm H}\kern
0.70004pt{\sc$\beta$}}}}$ relation showing Mrk 142 from this work overlapping
with the measured value in Du et al. (2015). The SEAMBH objects (black
squares; Du et al., 2014; Wang et al., 2014b; Hu et al., 2015; Du et al.,
2015; Li et al., 2018; Zhang et al., 2019; Li et al., 2021) appear on the
lower right of the grey solid lines, which represent the best-fit R–L
relations from Bentz et al. (2013) with $L_{5100}$ (panel a) and Kaspi et al.
(2005) with $L_{\hbox{{\rm H}\kern 0.70004pt{\sc$\beta$}}}$ (panel b),
indicating a smaller size for the broad-line region in highly accreting AGN
compared to the more typical, sub-Eddington AGN mapped in previous studies
(green circles, panel a and grey circles, panel b; Stirpe et al., 1994;
Santos-Lleó et al., 1997; Collier et al., 1998; Dietrich et al., 1998;
Peterson et al., 1998; Kaspi et al., 2000; Santos-Lleó et al., 2001; Kaspi et
al., 2005; Bentz et al., 2006; Collin et al., 2006; Denney et al., 2006; Bentz
et al., 2007, 2009a, 2009b; Denney et al., 2010; Dietrich et al., 2012; Grier
et al., 2012; Barth et al., 2013; Bentz et al., 2013, 2014; Pei et al., 2014;
Peterson et al., 2014, 2002, and references therein) at same luminosities. In
particular, the departure of Mrk 142 from the Bentz et al. (2013) best-fit
relation in panel a is more apparent than the deviation from the Kaspi et al.
(2005) relation in panel b (see text for additional details).

Figure 11 shows the $R_{\mathrm{\hbox{{\rm H}\kern
0.70004pt{\sc$\beta$}}}}$–$L_{\mathrm{5100}}$ and $R_{\mathrm{\hbox{{\rm
H}\kern 0.70004pt{\sc$\beta$}}}}$–$L_{\mathrm{1350}}$ scaling relations for
NGC 5548 over time with optical lag measurements for H$\beta$, and
luminosities at 5100 Å and 1350 Å ($L_{1350}$) from Eser et al. (2015). Again,
the red star in both panels represents the Mrk 142 point from this work. Eser
et al. (2015) formulated a conversion from $L_{5100}$ to $L_{1350}$ for NGC
5548 (see their Equation 4) from all RM campaigns of the object from 1988 to
2008 (Peterson et al., 2002; Bentz et al., 2007, 2009b; Denney et al., 2010).
We applied that conversion to calculate $L_{1350}$ for NGC 5548 and generated
the $R_{\mathrm{\hbox{{\rm H}\kern
0.70004pt{\sc$\beta$}}}}$–$L_{\mathrm{1350}}$ plot (Figure 11, panel b). Here,
we extrapolated the Cackett et al. (2020) UV/optical imaging data – mean flux
densities – in different bands assuming power-law behavior to estimate a
luminosity of $\log(L_{1350})=44.13\pm 0.03$ for Mrk 142 in this work (see
Figure 12). The shift in the position of Mrk 142 from panel a to b, closer to
the R–L scaling relation in the UV, indicates that the UV emission is a better
proxy for the ionizing continuum than the 5100 Å optical emission.

Figure 11: Multi-epoch NGC 5548 radius-luminosity (R–L) scaling relations for
H$\beta$ in the optical and UV including luminosities from Eser et al. (2015)
and results from this work (red star). Panel a: NGC 5548
$R_{\mathrm{\hbox{{\rm H}\kern 0.70004pt{\sc$\beta$}}}}$–$L_{\mathrm{5100}}$
relation from Eser et al. (2015, green circles) on which Mrk 142 from this
work is located to the right at higher luminosities. This follows the similar
deviation from the entire RM sample that is observed in Figure 10, panel a. RM
measurements for NGC 5548 post 2015 (Lu et al., 2016; Pei et al., 2017; De
Rosa et al., 2018; Lu et al., 2022, black circles) are also included for
completeness. Panel b: $R_{\mathrm{\hbox{{\rm H}\kern
0.70004pt{\sc$\beta$}}}}$–$L_{\mathrm{1350}}$ relation for NGC 5548, including
Mrk 142 from this work. From its position to the right of the Eser et al.
(2015) best-fit R–L relation (grey solid line) with $L_{5100}$ in panel a, Mrk
142 has moved closer to the Eser et al. (2015) best-fit R–L relation with
$L_{1350}$ in panel b, suggesting the UV as a better proxy for the driving
continuum than the optical. In general, the offset of the SEAMBHs may reflect
a different

spectral energy distribution.

To further understand the comparison between the $R_{\mathrm{\hbox{{\rm
H}\kern 0.70004pt{\sc$\beta$}}}}$–$L_{\mathrm{1350}}$ relations of Mrk 142 (a
super-Eddington Seyfert 1 galaxy) and NGC 5548 (a normal Seyfert 1 galaxy), we
compared their SEDs from the National Aeronautics and Space
Administration/Infrared Processing and Analysis Center (NASA/IPAC)
Extragalactic Database (NED) and recent studies, including Cackett et al.
(2020). Figure 12 shows the SEDs for the above two AGN from NED along with the
derived optical-to-X-ray spectral slope ($\alpha_{\mathrm{ox}}$) of $-1.35\pm
0.01$ for Mrk 142 from the Cackett et al. (2020) observations (purple
triangles representing mean flux densities in different bands). To derive the
$\alpha_{\mathrm{ox}}$ value, we: (1) fit the local SED around the 2500 Å data
point assuming power-law behavior, (2) calculated the dereddened X-ray flux
density at 2 keV, and (3) used Equation 1 for $\alpha_{\mathrm{ox}}$ from Just
et al. (2007). For NGC 5548, Merritt (2022) obtained an $\alpha_{\mathrm{ox}}$
of $-1.30\pm 0.04$ from simultaneous X-ray/UV/optical observations (see
Chapter 2 therein). A less negative $\alpha_{\mathrm{ox}}$ for NGC 5548
compared to Mrk 142 suggests a harder ionizing SED for the normal Seyfert 1
galaxy, likely due to the soft X-ray excess observed in the object (e.g.,
Mehdipour et al., 2015), than the super-Eddington AGN. However, the soft
excess in NGC 5548 was not evident in 2013, when an obscurer heavily absorbed
its soft X-ray flux (Mehdipour et al., 2015). Most Seyferts/quasars have some
sort of soft X-ray excess; the debate for years has been over the origin
(ionized disk reflection, warm Comptonized emission, a mixture or both). The
implication from Tortosa et al. (2023) is that for super-Eddington AGN,
ionized disk reflection can model the soft excess in this class of AGN well.
It is interesting to witness that despite their distinct types, the SED shapes
of Mrk 142 and NGC 5547 are similar as their $\alpha_{\mathrm{ox}}$ values
agree within uncertainties – a plausible explanation for the tighter
$R_{\mathrm{\hbox{{\rm H}\kern 0.70004pt{\sc$\beta$}}}}$–$L_{\mathrm{1350}}$
correlation than $R_{\mathrm{\hbox{{\rm H}\kern
0.70004pt{\sc$\beta$}}}}$–$L_{\mathrm{5100}}$ noted in both the objects.
Future accretion-disk modeling efforts can help understanding such comparisons
of R–L relationships between normal and super-Eddington AGN.

Figure 12: Spectral energy distributions (SEDs) of Mrk 142 from the National
Aeronautics and Space Administration/Infrared Processing and Analysis Center
(NASA/IPAC) Extragalactic Database (NED, blue squares), and from Cackett et
al. (2020, mean flux density in each band represented with purple triangles);
and NGC 5548 from NED (orange circles) showing similar SED shapes for the two
objects. We derived the optical-to-X-ray slope ($\alpha_{\mathrm{ox}}$) for
the Mrk 142 data from Cackett et al. (2020) regarding a power-law behavior
(fit indicated in black solid line) for the SED around the 2500 Å data point
(purple open triangle). Results indicate a softer ionizing SED for Mrk 142
($\alpha_{\mathrm{ox}}=-1.35$) than NGC 5548 ($\alpha_{\mathrm{ox}}=-1.30$;
Merritt, 2022); see text for a detailed discussion. The fit to the Cackett et
al. (2020) SED is extended to indicate the estimated 1350 Å data point (black
open triangle) used in Figure 11.

If UV emission is closer to the driving continuum as seen in Figure 11, this
will affect the black hole mass of Mrk 142 derived from the 5100 Å to H$\beta$
time lag. Recently, Cackett et al. (2020) performed the accretion-disk RM
analysis for Mrk 142 with data from Swift, LCO, Zowada, Liverpool, and other
ground-based observatories, simultaneous to the Gemini+LJT data taken as a
part of the same broader RM campaign. Cackett et al. (2020) pointed that if
the UVW2 band represents the driving continuum, then the black hole mass
derived from the H$\beta$ optical lag is underestimated by $\sim$10%. We used
the UVW2 to H$\beta$ time lag result from this work to calculate the black
hole mass in Mrk 142. We obtained a mass of $\log(M_{\bullet}/M_{\odot})$ =
$6.32\pm 0.29$ based on the UVW2 to H$\beta$ time lag. This value is $\sim$10%
greater than the black hole mass derived by assuming 5100 Å as the driving
continuum band, and thus verifies the discrepancy estimated by Cackett et al.
(2020). This discrepancy would be as high as $\sim$40% if X-rays, instead of
UV, were the driving continuum (Cackett et al., 2020). However, our work does
not propose any new implications to the accretion-disk structure of Mrk 142. A
robust H$\beta$ lag measurement with reference to the X-ray continuum from
future studies will help understand how X-rays play a role in driving the
continuum variability in Mrk 142 and shape its inner accretion disk.

##  7 Conclusion

We performed BLR RM analysis of Mrk 142 with medium- and low-resolution
optical spectra from Gemini and LJT, simultaneous to the Swift and
LCO+Zowada+Liverpool photometric campaigns reported by Cackett et al. (2020)
to measure the UV lag for H$\beta$ emission line. With PrepSpec analysis, we
corrected calibration discrepancies for both the Gemini and the LJT spectra
individually. From spectral modeling in Sherpa, we measured FWHM and fluxes
for [O iii] $\lambda\lambda 4960,5008$; H$\beta$ $\lambda 4861$; and He i
$\lambda 5877$ emission lines. To combine the 5100 Å and H$\beta$ light curves
from Gemini and LJT, we inter-calibrated the respective light curves from the
two telescopes in PyROA. Applying PyROA for time-lag analysis, we measured a
UV time lag for H$\beta$ and further derived refined black hole masses.
Placing our results on various R–L scaling relations, we verified that our
results are consistent with previously published values for Mrk 142. We
summarize our main findings below.

  1. 1.

PyROA, using Bayesian Information Criterion to evaluate model performance
along with a rigorous treatment of uncertainties, provided a robust method for
measuring cross-correlation time lags. This project is one of the early works
employing PyROA technique for measuring RM time lags with real data. In this
process, the longer timescale of LJT spectra nicely complemented the gaps in
the Gemini observations.

  2. 2.

We measured, for the first time, a UV time lag of $8.68_{-0.72}^{+0.75}$ days
for H$\beta$ in Mrk 142, with simultaneous photometry in the Swift/UVW2 band
and optical spectroscopy with Gemini and LJT. Assuming the UV continuum as the
primary driver of the observed variability, we derived a black hole mass of
$\log(M_{\bullet}/M_{\odot})$ = $6.32\pm 0.29$.

  3. 3.

We obtained a 5100 Å to H$\beta$ time lag of $7.89\pm 0.80$ days, consistent
with the measured value from previous SEAMBH campaigns (Du et al., 2015). From
this lag measurement, we also derived a black hole mass for Mrk 142 of
$\log(M_{\bullet}/M_{\odot})$ = $6.28\pm 0.29$, in agreement with the mass
reported by Li et al. (2018).

  4. 4.

We placed the 5100 Å to H$\beta$ time lag with measured $L_{1350}$ on the
$R_{\mathrm{\hbox{{\rm H}\kern 0.70004pt{\sc$\beta$}}}}$–$L_{\mathrm{1350}}$
relation for NGC 5548 (Eser et al., 2015). Mrk 142 falls closer to the
$R_{\mathrm{\hbox{{\rm H}\kern 0.70004pt{\sc$\beta$}}}}$–$L_{\mathrm{1350}}$
scaling relation than the $R_{\mathrm{\hbox{{\rm H}\kern
0.70004pt{\sc$\beta$}}}}$–$L_{\mathrm{5100}}$ relation indicating that the UV
is closer to the “true” driving continuum as opposed to 5100 Å band.

In addition, we also recorded supplementary results. Our spectral analysis
indicated blueshifted, broad components for the He i and He ii emission lines
suggestive of wind components in these higher-ionization lines. To infer the
cause of such disk+wind components, we need more higher-resolution data and
BLR modeling efforts for super-Eddington AGN. We intend to study the He i and
He ii lines in further detail in our future work. Furthermore, BLR RM analysis
with the concurrent X-ray data available from Swift can better inform our
understanding of the measured H$\beta$ time lags with respect to the UV
continuum. We aim to explore this in our future study.

##  8 acknowledgments

We recognize the support of Rick Edelson in taking the g-band data from Las
Cumbres Observatory. V.C.K. acknowledges the support of Joel Roediger and the
Gemini Observatory staff during the planning of observations and reduction of
the Gemini data. 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. E.M.C. gratefully acknowledges support for analysis of the Swift
data from NASA through grant 80NSSC19K0150, and support for analysis of the
Zowada Observatory data from the NSF through grant AST-1909199. C.H.