# SN 2018gj: A Short-plateau Type II Supernova with Persistent Blue-shifted
$\rm H\alpha$ Emission

Rishabh Singh Teja Indian Institute of Astrophysics, II Block, Koramangala,
Bengaluru-560034, Karnataka, India  Pondicherry University, R.V. Nagar,
Kalapet, Pondicherry-605014, UT of Puducherry, India  Avinash Singh Hiroshima
Astrophysical Science Center, Hiroshima University, Higashi-Hiroshima,
Hiroshima 739-8526, Japan  D.K. Sahu Indian Institute of Astrophysics, II
Block, Koramangala, Bengaluru-560034, Karnataka, India  G.C. Anupama Indian
Institute of Astrophysics, II Block, Koramangala, Bengaluru-560034, Karnataka,
India  Brajesh Kumar Aryabhatta Research Institute of Observational Sciences,
Manora Peak, Nainital-263001, Uttarakhand, India  Tatsuya Nakaoka  Hiroshima
Astrophysical Science Center, Hiroshima University, Higashi-Hiroshima,
Hiroshima 739-8526, Japan  Koji S Kawabata Hiroshima Astrophysical Science
Center, Hiroshima University, Higashi-Hiroshima, Hiroshima 739-8526, Japan
Masayuki Yamanaka Kagoshima University, Amanogawa Galaxy Astronomy Research
Center, 1-21-35, Korimoto, Kagoshima 890-0065, Kyushu-Okinawa, Japan  Takey
Ali National Research Institute of Astronomy and Geophysics (NRIAG), Helwan
11421, Cairo, Egypt  Miho Kawabata Department of Astronomy, Kyoto University,
Kitashirakawa-Oiwake-cho, Sakyo-ku, Kyoto 606-8502, Japan

###### Abstract

We present an extensive, panchromatic photometric (UV, Optical, and NIR) and
low-resolution optical spectroscopic coverage of a Type IIP supernova SN
2018gj that occurred on the outskirts of the host galaxy NGC 6217. From the
$V$–band light curve, we estimate the plateau length to be $\sim$ 70 $\pm$ 2
d, placing it among the very few well-sampled short plateau supernovae (SNe).
With $V$-band peak absolute magnitude $\rm M_{V}\leq-17.0\pm 0.1~{}mag$, it
falls in the middle of the luminosity distribution of the Type II SNe. The
colour evolution is typical to other Type II SNe except for an early elbow-
like feature in the evolution of $V-R$ colour owing to its early transition
from the plateau to the nebular phase. Using the expanding photospheric
method, we present an independent estimate of the distance to SN 2018gj. We
report the spectral evolution to be typical of a Type II SNe. However, we see
a persistent blue shift in emission lines until the late nebular phase, not
ordinarily observed in Type II SNe. The amount of radioactive nickel
($\rm{}^{56}Ni$) yield in the explosion was estimated to be $\rm 0.026\pm
0.007~{}M_{\odot}$. We infer from semi-analytical modelling, nebular spectrum,
and 1-D hydrodynamical modelling that the probable progenitor was a red
supergiant with a zero-age-main-sequence mass $\rm\leq 13~{}M_{\odot}$. In the
simulated hydrodynamical model light curves, reproducing the early optical
bolometric light curve required an additional radiation source, which could be
the interaction with the proximal circumstellar matter (CSM).

Observational astronomy(1145) — Type II supernovae(1731) — Red supergiant
stars(1375) — Hydrodynamical simulations(767)

††facilities: IAO(HCT):2-m, Kanata(HONIR):1.5-m ATLAS, and
Swift(UVOT)††software: Astropy (Astropy Collaboration et al., 2013, 2018,
2022) , emcee (Foreman-Mackey et al., 2013), MESA (Paxton et al., 2011, 2013,
2015, 2018, 2019), STELLA (Blinnikov & Sorokina, 2004; Baklanov et al., 2005;
Blinnikov et al., 2006), matplotlib (Hunter, 2007), pandas (Wes McKinney,
2010; pandas development team, 2020), numpy (Harris et al., 2020), scipy
(Virtanen et al., 2020), Jupyter (Kluyver et al., 2016), and seaborn (Waskom,
2021)

##  1 Introduction

Massive stars ($\geq\rm 8~{}M_{\odot}$) reach their life-cycle termination in
violent explosions termed as Core-Collapse Supernovae (CCSNe). On the basis of
their observable properties, viz., spectral lines and light curves, CCSNe are
further divided into various sub-classes. The absence of Hydrogen Balmer lines
in the spectrum puts a supernova (SN) into the Type I class, whereas the
presence of these features allows it to be classified as a Type II SN. Type I
class is further subdivided with the presence or absence of He I
$\lambda~{}5876$ (Ib or Ic) (Minkowski, 1941; Filippenko, 1997). Based on
their light curve shape, Type IIs are further classified under Type IIP and
IIL sub-classes. A plateau-like constant luminosity period of about 100 d in
the light curve evolution means the SN is of the Type IIP (plateau) class.
While a ‘linear’ decline from maxima in the light curve denotes the SN to be
of Type IIL (linear) class (Barbon et al., 1979). Although there are observed
dissimilarities in the light curves of Type IIP and Type IIL classes, it is
still unsettled if the two classes are intrinsically different. In many sample
studies, it is noticed that the Type II sub-classes (IIP and IIL) form a
continuous sequence (Anderson et al., 2014a; Pessi et al., 2019; Sanders et
al., 2015; Singh et al., 2018; de Jaeger et al., 2019). In contrast, few
studies present subtle differences in these sub-classes both photometrically
and spectroscopically (Arcavi et al., 2012; Faran et al., 2014a, b). Recent
studies with larger samples seem to favour the continuous population of these
events (Galbany et al., 2016; Rubin et al., 2016; Gutiérrez et al., 2017).
Apart from these typical classes, there have been numerous instances where
narrow emission spectral features are superimposed over usual broad emission
features (Stritzinger et al., 2012; Taddia et al., 2013; Smith et al., 2014;
Gangopadhyay et al., 2020; Ransome et al., 2022) in the SN spectra. These
events are interacting SNe and known as IIn supernovae (Filippenko, 1997).

With the advent of various night sky surveys, viz. Zwicky Transient Facility
(ZTF, Bellm et al., 2019), Asteroid Terrestrial-impact Last Alert System
(ATLAS, Tonry et al., 2018), Gaia (Gaia Collaboration et al., 2016), All-Sky
Automated Survey for Supernovae (ASAS-SN, Kochanek et al., 2017), etc., we see
an enormous number of discoveries and extensive follow-up related to SNe. From
the numerous observational (Elmhamdi et al., 2003a; Anderson et al., 2014a)
and theoretical modelling studies (Sukhbold et al., 2016; Curtis et al.,
2021), it is well established that the average plateau length in type IIP SNe
is around 100 d. However, there are cases when the plateau length is found to
be longer ($\geq 120~{}d$, Sahu et al., 2006a; Pastorello et al., 2009; Yang
et al., 2021) or shorter ($\leq\rm 65~{}d$, Hiramatsu et al., 2021; Teja et
al., 2022) than the typical value. SNe with a longer plateau duration are
mostly found to be low-luminosity (LL) IIP. A moderate range of progenitor
masses ($\rm 10-15~{}M_{\odot}$, Spiro et al., 2014) have been deduced by
modelling them, and these masses corroborate with the direct detection of
progenitors (Smartt, 2009). Nevertheless, Type IIP events with plateau lengths
less than 70 d are rare in synthesised models and observations. The occurrence
of short plateau events is very small ($\sim$4% of all type IIP SNe) in binary
population synthesis and single progenitor models (Eldridge et al., 2018;
Hiramatsu et al., 2021). The small number of well-studied short plateau
objects is insufficient to constrain these rates quantitatively. Thus, any
addition to the sample of short plateau events will further improve our
understanding of Type II SNe.

The shorter plateau length in Type IIP SNe is usually explained by
considerable stripping of the hydrogen envelope. The stripping of the outer
hydrogen layer is possible in all mass ranges of red-supergiants (RSGs) via
various mechanisms, viz. wind mass loss, presence of a secondary star,
episodic mass losses, etc. Some theoretical works have shown high mass RSGs as
progenitors of short plateau SNe (Dessart et al., 2010; Sukhbold et al., 2016;
Hiramatsu et al., 2021) as, with the usual single-star evolutionary scenario
with “typical” mass-loss, only the more massive stars are able to achieve
stronger winds required to strip enough Hydrogen to cause a shorter plateau.
However, there are reasons to believe otherwise, where it is possible to get a
shorter plateau if the multiplicity (Eldridge et al., 2018) or extensive mass
loss in lower mass RSG is considered (Teja et al., 2022). In a study by
Sollerman et al. (2021), the progenitor of the short plateau object SN 2020jfo
was solely detected in the F814W band of the Hubble Space Telescope (HST),
estimating its mass to range from 10 to 15 $\rm M_{\odot}$. The lack of
detection of the progenitor in the bluer bands indicated the progenitor as a
cool and red star. Further, the observational upper mass for Type IIP
progenitors is $\lesssim 19~{}\rm M_{\odot}$ (Van Dyk, 2017), although the
masses of RSGs observed in the Local Group galaxies have been found to range
up to 25$\rm~{}M_{\odot}$ (Smartt et al., 2009; Rodríguez, 2022), leading to
the missing mass “RSG problem”. Massive RSGs as progenitors for the short
plateau could address the “RSG problem” (Hiramatsu et al., 2021), although in
general, there is no consensus with regards to the statistical significance of
the RSG problem (Eldridge et al., 2013; Kochanek, 2020; Davies & Beasor,
2020).

With the high cadence of modern sky surveys, quite a few of the short plateau
SNe are discovered soon after the explosion. Early detection of these events
provides essential information about the late-stage evolution of the
progenitor and its immediate surrounding. The ‘flash ionization’ features seen
in some of these events are interpreted as the presence of circumstellar
material (CSM) in their immediate vicinity (Gal-Yam et al., 2014). Flash
ionization feature has been observed in about 18% of the SNe II, at ages $<$ 5
days (Khazov et al., 2016). With the increasing number of supernovae observed
early enough, the fraction of supernovae showing flash ionization features is
also increasing ($>36\%$, Bruch et al., 2022), indicating the presence of CSM
close to the explosion site is common in Type II SNe (Morozova et al., 2018).
Other observational features such as narrow emission lines, high-velocity
absorption features in spectra, and enhanced luminosity in light curves
(Bullivant et al., 2018; Singh et al., 2019; Zhang et al., 2022) also reveal
the presence of spatially confined CSM, most probably originating from
enhanced mass loss from progenitor shortly prior to the explosion.

The evidence of CSM in Type IIP is usually seen early on with ionized lines,
narrow emission lines, high-velocity absorption features in spectra, and
enhanced luminosity in light curves (Bullivant et al., 2018; Singh et al.,
2019; Zhang et al., 2022). Furthermore, it has been established that sometimes
only a few of these features are present while others are missing altogether
(Andrews et al., 2019; Dong et al., 2021). However, alternate pathways
regarding the initial rise times and enhanced luminosity are being studied
theoretically. The detailed studies of the Hydrogen-rich layer in 3D models
(Goldberg et al., 2022) could also reveal the initial behaviour of the peak if
other shreds of evidence are scarce.

This work presents detailed spectroscopic and photometric observations of SN
2018gj along with the analytical and hydrodynamical modelling to infer
properties of probable progenitor. The paper has been divided as follows:
Section 2 briefly describes the data acquisition and reduction process. The
analysis of the apparent and the bolometric light curve is given in Section
3.2. This section also utilizes semi-analytical light curve modelling for
approximate estimates of progenitor properties. The spectral evolution from
the photospheric phase to the nebular phase is presented in Section 4.
Further, in Section 5, we attempt to estimate the progenitor evolution
history, its properties, explosion parameters, etc., using complete 1-D
hydrodynamical modelling. We briefly discuss the implications of our work and
aspects related to consistent blue-shifted emission lines in Section 6 and
provide a conclusion in the subsequent section.

Figure 1: Location of SN 2018gj in the host NGC 6217. The dashed violet line
marks the separation between the host centre and SN. The image is an RGB
colour composite utilising Bessell’s $V$, $R$, and $I$ filters.

##  2 Data Acquisition and Processing

Figure 2: Photometric data for SN 2018gj spanning $\sim$300 d post-discovery.
Corresponding spectral epochs are marked along the abscissa. [Violet pentagon
markers over-plotted on $V$ and $B$ bands are from Swift $UVV$ and $UVB$
bands, respectively]

The discovery of SN 2018gj, in the outskirts of the barred spiral galaxy NGC
6217 (about 122$\arcsec$ or $\rm\sim 11~{}kpc$ away from the centre of the
host galaxy) (Figure 1) was reported on 2018 January 14 (2458132.91 JD) at
(J2000), $\rm RA,\alpha=16^{\circ}32\arcmin 02\arcsec.40$ and $\rm
Dec,\delta=+78^{\circ}12\arcmin 41\arcsec.13$ (Wiggins, 2018). Immediately
after the discovery, it was classified as a Type IIb SN with the possibility
of it being a Type IIP SN (Bertrand, 2018). Later on, it was classified as a
young Type II SN (Kilpatrick, 2018). We started an extensive follow-up
campaign in optical-NIR photometry and spectroscopy, which continued for about
300 d after the discovery. An imager cum spectrograph, the Himalaya Faint
Object Spectrograph (HFOSC) mounted on the 2-m Himalayan Chandra Telescope
(HCT) of the Indian Astronomical Observatory (IAO) (Prabhu, 2014), Hanle,
India, was used for optical photometry and spectroscopy. It is equipped with a
liquid nitrogen-cooled $2k\times 4k$ pixels SITe CCD chip. With a pixel size
of 15$\mu$m it provides a plate scale of $0.296\arcsec/pixel$. The gain and
readout noise of the CCD are $\rm 1.22~{}e^{-}/ADU$ and $\rm 4.87~{}e^{-}$,
respectively. Near Infrared (NIR) data were acquired with the Hiroshima
Optical and Near-InfraRed Camera (HONIR; Akitaya et al., 2014) installed at
the 1.5-m Kanata Telescope operated by the Hiroshima Astrophysical Science
Center (HASC) of Hiroshima University. The NIR Arm has a HgCdTe VIRGO-2K array
with $2k\times 2k$ pixels (pixel size $\rm 20\times 20~{}\mu m$, plate scale
of $\rm 0.295\arcsec/pixel$) with $\rm 11.6~{}e^{-}/ADU$ and $\rm 24~{}e^{-}$
gain and readout noise, respectively. In addition to the science frames, we
obtained several biases and twilight flat frames.

We pre-processed optical raw data using standard tasks in IRAF implemented
using a custom pipeline RedPipe (Singh, 2021) built upon PyRAF to correct for
bias, flat-field, and cosmic rays. The observed multiple frames were aligned
and co-added in respective bands to improve the signal-to-noise ratio.
Standard star fields PG 1633+009, PG 2213-006, and SA 110 from Landolt (1992)
were observed on four nights under photometric conditions to calibrate
secondary standards in the SN field. We used DAOPHOT 3 (Stetson, 1987) to
perform point spread function (PSF) photometry on the standard fields. The
average atmospheric extinction co-efficient for the site Stalin et al. (2008)
and standard stars with a brightness range of $12.02\leq V\leq 16.25$ mag and
colour range of $-0.22\leq B-V\leq 2.53$ mag, were used for calibration of
secondary standards. As the SN was relatively isolated in its host galaxy, the
supernova magnitude was extracted using PSF photometry. The extracted
magnitudes were then calibrated differentially with respect to the secondary
standard in the supernova field. The supernova magnitude in $UBVRI$ bands are
listed in Appendix A. The NIR data was also reduced using the standard IRAF
tasks. The secondary stars for $J$, $H$ and $Ks$ bands were calibrated using
the magnitudes provided by the 2MASS catalogue (Skrutskie et al., 2006). The
supernova magnitude in $JHKs$ bands are listed in Appendix A.

Further, we supplemented our photometry data using public archive images from
the UltraViolet/Optical Telescope (Roming et al., 2005, $UVOT$) on board Neil
Gehrels Swift Observatory (Gehrels et al., 2004) in the
$UVW2,\,UVM2,\,UVW1,\,UVU,\,UVB,$ and $UVV$ bands. The archival images were
reduced using High Energy Astrophysics Software (HEASOFT, v6.27) package with
the latest calibration database for the $UVOT$ instrument, following the
methods described in Poole et al. (2008) and Brown et al. (2009). The SN
magnitude was extracted using UVOTSOURCE task with an aperture size of
$5\arcsec$ for the source and a similar aperture size to extract the
background counts. The final $UVOT$ magnitudes were obtained in the Vega
system and are tabulated in Table 4. We also obtained photometry in ATLAS-$o$
band (AB-magnitude) from ATLAS forced photometry server (Tonry et al., 2018;
Smith et al., 2020).

The low-resolution spectroscopic ($\sim$ 10 Å) data was obtained with HFOSC
using a setup consisting of $1.92\arcsec$ slit with grisms, Gr7 ($3800-6840$
Å) and Gr8 ($5800-9350$ Å) during 2018 January 14 (JD 2458132.5) to 2018
October 31 (JD 2458423.1). The log of spectroscopic observations is given in
Table 6 and marked in Figure 2. Spectra of arc lamps and spectrophotometric
standards were also obtained for wavelength and flux calibration,
respectively. Standard tasks in IRAF were used for spectral data reduction.
The observed spectroscopic data were corrected for bias, and the 1-D spectra
were extracted using the optimal extraction algorithm (Horne, 1986).
Wavelength calibration was performed using the dispersion solutions obtained
utilizing arc lamp spectra. Night-sky emission lines were used to check the
accuracy of wavelength calibration, and small shifts were applied wherever
necessary. The instrumental response was corrected using the observed spectro-
photometric standards. The response curves obtained during nearby nights were
used for those nights where standard star observations were unavailable. The
flux-calibrated spectrum in both the grisms was combined to obtain a single
flux-calibrated spectrum. The spectra were then scaled to the calibrated
$UBVRI$ magnitudes to bring them to an absolute flux scale.

##  3 Analysis

###  3.1 Host Properties

The preferred redshift (z) and distance (D) of NGC 6217 are $\rm 0.00454\pm
0.00001$ and $\rm 19.61\pm 1.37~{}Mpc$, respectively, and are referenced from
NASA/IPAC Extragalactic Database (NED)111http://ned.ipac.caltech.edu/. Other
distance estimates exist with a great scatter ranging from 15 Mpc to 35 Mpc
(Bottinelli et al., 1984; Tutui & Sofue, 1997). The SN was located in the
outskirts of the probable host NGC 6217 ($\rm 9\arcmin 13\arcsec.8\ ``W"\ and\
47\arcsec.4\ ``N"\ implying\ \sim 2\arcmin$ separation from the host’s
centre). To check the veracity of its association with NGC 6217, an
independent estimate of the distance to the SN was made using the Expanding
Photosphere Method (EPM) (Kirshner & Kwan, 1974; Schmidt et al., 1992; Hamuy
et al., 2001). The detailed methodology and calculations are presented in
Appendix B. The dilution factors were adopted from Hamuy et al. (2001),
Dessart & Hillier (2005), and Vogl et al. (2019). We found that the distances
estimated using constrained explosion epochs and non-constrained explosion
epochs varied as much as by 3 Mpc. The average distances using all three
dilution factors are $\rm 15.7\pm 1.7~{}Mpc$ (non-constrained explosion epoch)
and $\rm 17.5\pm 4.1~{}Mpc$ (constrained explosion epoch). Errors quoted are
due to the scatter in the different measurements for three filter sets and
three dilution factors. The distance of the SN estimated using EPM is in
agreement with the distances given in NED for NGC 6217 and establishes the
association of the SN with NGC 6217.

From IRSA-Galactic Dust Reddening and Extinction map (Schlafly & Finkbeiner,
2011), the Galactic line of sight reddening towards the SN location is given
as $\rm E(B-V)=0.0375\pm 0.0002~{}mag$. Weak Na ID absorption was detected in
the spectra at the redshift of the host galaxy with a pseudo-equivalent width
(pEW) of $\rm 0.36~{}\AA$, averaged over the first five spectra. Using
(Equation 9, Poznanski et al., 2012) we find a host reddening value of $\rm
E(B-V)=0.04\pm 0.02~{}mag$. Hence, throughout this work, we adopt a total line
of sight reddening value $\rm E(B-V)\approx 0.08\pm 0.02~{}mag$.

###  3.2 Light Curve Analysis

The last non-detection of SN 2018gj was on 2018 January 7.9 (JD 2458126.4) in
the Gaia photometry, up to the limiting magnitude of $\sim$21.5 in G-Gaia
filter (AB magnitude system), and was discovered on 2018 January 10.7 (JD
2458129.2). Using this last non-detection and the first detection of SN
2018gj, the explosion epoch is constrained as 2018 January 9.3 ($\sim$JD
2458127.8) $\pm$ 1.4 d. This explosion epoch has been used throughout this
work, and all the phases are reported with respect to it. The panchromatic
light curve evolution of SN 2018gj in UV, optical and NIR bands are presented
in Figure 2. UV light curves in $UVW2$, $UVM2\,$ and $UVW1$ bands span a
period of $\sim$14 d post-explosion, NIR light curves span up to 180 d whereas
the optical light curve extends until $\sim$297 d. In all the light curves, we
find a clear transition from the slowly declining (almost constant) light
curve phase to the radioactive nickel-powered phase towards the end. During
this transition, in visual bands, we see a drop of $\rm\geq 1.5~{}mag$.

During the plateau phase, the light curves decline at different rates in
different wavebands. In the $U$ filter, we observe the sharpest decline with
$\rm 6.44\pm 0.03~{}mag~{}(100~{}d)^{-1}$. As we move towards the redder
wavelengths, we find the decline rate slows down to $\rm 3.39\pm
0.03~{}mag~{}(100~{}d)^{-1}$ in $B$, $\rm 1.26\pm 0.02~{}mag~{}(100~{}d)^{-1}$
in $V$, $\rm 0.79\pm 0.02~{}mag~{}(100~{}d)^{-1}$ in $R$ and $\rm 0.64\pm
0.02~{}mag~{}(100~{}d)^{-1}$ in $I$. The decline is even slower in the near-
infrared wavelength regime with $\rm 0.37\pm 0.02~{}mag~{}(100~{}d)^{-1}$ in
$J$, but the decline rate increases slightly as we go toward redder bands with
$\rm 0.42\pm 0.06~{}mag~{}(100~{}d)^{-1}$ in $H$ and ultimately $\rm 0.50\pm
0.07~{}mag~{}(100~{}d)^{-1}$ in $Ks$ band. We find the slowest decline to be
in the $J$ filter. It is also noteworthy that in the radioactive decay tail
phase, the decline rate trend reverses with the slowest decline observed in
$B$ band $\rm 0.90\pm 0.01~{}mag~{}(100~{}d)^{-1}$ and it is almost the same
in $V$, $R$ and $I$ bands as $\rm 1.33\pm 0.01~{}mag~{}(100~{}d)^{-1}$, $\rm
1.14\pm 0.02~{}mag~{}(100~{}d)^{-1}$ and $\rm 1.26\pm
0.02~{}mag~{}(100~{}d)^{-1}$ respectively. We find the late-phase light curve
decline rates to be much higher in the near-infrared bands as $\rm 1.86\pm
0.07~{}mag~{}(100~{}d)^{-1}$ in $J$, $\rm 2.58\pm 0.11~{}mag~{}(100~{}d)^{-1}$
in $H$ and $\rm 2.12\pm 0.24~{}mag~{}(100~{}d)^{-1}$ in $Ks$ bands. During the
late phase, the light curve in the $H$ band declined at the fastest rate.

###  3.3 V-band Light Curve

Figure 3: $V$-band light curve evolution of SN 2018gj along with other Type II
SNe. Continuous light blue lines are representative of a larger Type II sample
from Anderson et al. (2014a) and Faran et al. (2014a). Estimated light curve
parameters for $V$-band viz. OPTd, Pd, s1, s2, and s3 are also shown.
Supernovae data used in this plot are mentioned in Table 7

After correcting for extinction, the apparent $V$-band magnitudes were
transformed to absolute magnitudes using a distance modulus, $\rm\mu=31.46\pm
0.15~{}mag$ (using the preferred distance of $\rm 19.61\pm 1.37~{}Mpc$ as
given in NED). Even though the initial rise in the bluer bands is missed, we
see the light curve getting brighter during the first two observations in the
$I$ band and, to a similar extent, in the $R$ band. A similar rise is observed
in the NIR $J$ and $Ks$ bands.

In the absence of the rising part of the V-band light curve, the peak absolute
magnitude $\rm M_{V}$, could not be constrained well (Figure 3). However, an
upper bound on the peak $\rm M_{V}\lesssim-17.0\pm 0.1$ mag can be set. The
mean of maximum $\rm M_{V}$ value for a sample of 68 Type II SNe estimated by
Anderson et al. (2014a) is $\rm-16.74\pm 1.01~{}mag$, which puts SN 2018gj
towards the brighter end of Type II SNe. Furthermore, we observe a rapid
decline in magnitude after $\rm+60~{}d$, corresponding to a sharp transition
from the plateau phase to the nebular phase. Using the functional form given
in Elmhamdi et al. (2003a), we could find the transition time at $\rm+79\pm
2~{}d$ and a plateau length (OPTd) of $\rm\approx 70\pm 3~{}d$, placing SN
2018gj in the shorter plateau group of Type IIP SNe. Following the phase
definitions given in Anderson et al. (2014a), we estimated $V$-band light
curve parameters for SN 2018gj. We find s1, s2, and s3 to be $\rm 3.00\pm
0.20~{}mag~{}(100~{}d)^{-1}$, $\rm 1.34\pm 0.02~{}mag~{}(100~{}d)^{-1}$, and
$\rm 1.33\pm 0.01~{}mag~{}(100~{}d)^{-1}$, respectively. The $s1$ and $s2$
decline rates are quite similar to the average values obtained from the Type
II sample, which are $\rm 2.65\pm 1.50~{}mag~{}(100~{}d)^{-1}$, and $\rm
1.27\pm 0.93~{}mag~{}(100~{}d)^{-1}$, respectively. However, the decline in
$s3$ is slower than the average Type II SNe $s3$ decline rate of $\rm 1.47\pm
0.82~{}mag~{}(100~{}d)^{-1}$.

###  3.4 Colours

Figure 4: Mean colour evolution of Type II SNe along with the colour evolution
of SN 2018gj for different bands are shown. The shaded region colour with a
solid line represents the mean colours from a larger Type IIP sample with
$1\,\sigma$ scatter from the mean value. Sources of data have been referenced
in the Table 7.

In Figure 4, the $U-B$, $B-V$, $V-R$, and $R-I$ colour evolution is shown. To
compare SN 2018gj colours with other Type IIP SNe, a mean colour curve from a
sample of 44 Type IIP SNe, available in the literature, is created (For
reference, see Table 7). We do not consider any epoch on which the number of
available data points is less than five. We apply extinction correction to all
the respective individual band photometry using Cardelli et al. (1989) with
$\rm R_{V}=3.1$. Further, Gaussian smoothing is applied using
scipy.ndimage.gaussian_filter1d. The resultant mean colours, from the sample,
along with $1\,\sigma$ scatter are over-plotted with that of SN 2018gj (see
Figure 4). The colour evolution of SN 2018gj predominantly follows the typical
Type IIP SNe behaviour with slight deviations in early $U-B$, late $B-V$, and
$V-R$ during the transition phase. The initial $U-B$ colour ($\rm<20~{}d$) for
SN 2018gj is redder than the average $U-B$ value for Type IIP SNe whereas the
$B-V$ colour evolution of SN 2018gj starts to deviate after $\rm+110~{}d$ and
becomes bluer than the average sample values. Further, we observe a slightly
redder ‘elbow’ kind of feature in $V-R$ mean colour values around
$\rm+100~{}d$ for the sample, which could signify a mean plateau length
duration of $\rm 100~{}d$ for the sample. In comparison, this break in $V-R$
colour evolution continuity is quite significant in SN 2018gj and is observed
at $\rm+70~{}d$, which later evolves along with the mean colour evolution for
the sample. The $R-I$ colour evolution SN 2018gj is typical of Type IIP SNe.

###  3.5 Bolometric Light Curve

Figure 5: Pseudo-bolometric and bolometric light curves for SN 2018gj obtained
using multiband photometry are shown. The second plot at the bottom shows the
temperature and radius evolution obtained using blackbody fits from the SEDs.

The multi-broadband photometry is used to obtain the bolometric light curve of
SN 2018gj, using the widely employed SuperBol (mnicholl, 2018) code. The code
computes pseudobolometric/bolometric curves by integrating the flux over
observed bands. Further, a complete bolometric curve is estimated using
blackbody extrapolations, additionally providing information about the
evolution of blackbody temperature and radius. The zero points used to convert
magnitudes to fluxes are obtained from Bessell et al. (1998) for UBVRIJHK of
the Johnson-Cousins-Glass system, Tonry et al. (2018) for the ATLAS filters.
Zero points for other filters are obtained from SVO Filter Profile Service
(Rodrigo et al., 2012; Rodrigo & Solano, 2020). To accommodate the missing
epochs, the light curves were linearly interpolated, and if needed, the
extrapolation was achieved using constant colour with respect to the well-
sampled reference band. These objectives are utilized using various tasks in
scipy.

We estimate three different pseudobolometric/bolometric light curves. With
only optical bands a pesudobolometric light curve ($\rm L_{Opt}$) is
generated. Secondly, we include NIR data with optical and obtain OIR
bolometric light curve (see Figure 5). As the UV data is not available
throughout, we include UV data for the initial few days and estimate the
bolometric light curve ($\rm L_{UV+Opt+IR}$). We find that using UVOIR data,
the estimated bolometric light curve very closely traces the blackbody
corrected estimate to the observed light curve ($\rm L_{BB}$). For further
analysis, we use the UVOIR observed bolometric light curve.

We missed the early detection and rise, and therefore cannot constrain the
peak in any of the bands. Hence, we only report the maximum value in the
pseudobolometric/bolometric light curves. For the optical bolometric light
curve, the peak value obtained is $\rm 1.42\pm 0.06\times
10^{42}~{}erg~{}s^{-1}$ and if we include the NIR and UV contributions, the
values obtained are $\rm 1.84\pm 0.06\times 10^{42}~{}erg~{}s^{-1}$ and $\rm
3.18\pm 0.08\times 10^{42}~{}erg~{}s^{-1}$, respectively. We observe that
during the initial phase of $\sim$ 5-15 d, the NIR contribution to the
pseudobolometric light curve is only $\sim 25\%$. It sustains a maximum value
of around $\rm\sim 50\%$ after the transition phase from 80 d to 110 d. The
NIR contribution remains significant during the nebular phase also, with an
average value of $\rm\sim 43\pm 2\%$, which is similar to the values estimated
for other SNe (Patat et al., 2001; Elmhamdi et al., 2003a).

###  3.6 Radioactive $\rm{}^{56}Ni$

Figure 6: Posterior plot for nickel mass and characteristic time estimates for
SN 2018gj using Equation 2.

The $\rm{}^{56}Ni$ decay chain primarily dominates the late-time light curve
evolution of Type II SNe. It is the primary source of energy during the
nebular phase of Type II SNe. We used various methods to estimate the mass of
synthesized $\rm{}^{56}Ni$. We compared the bolometric luminosity of SN 2018gj
in the nebular phase with the bolometric luminosity of SN 1987A. The mass of
$\rm{}^{56}Ni$ in SN 1987A is very well constrained using multiband photometry
and hydrodynamical modelling and can be utilized to estimate mass of
$\rm{}^{56}Ni$ in SN 2018gj. We compare the bolometric luminosity with the
values obtained for SN 1987A at similar epochs and use Equation 1 to get an
estimate on $\rm{}^{56}Ni$ mass.

$M_{Ni}(SN~{}2018gj)\approx
M_{Ni}(SN~{}1987A)\times\frac{L_{1987A}(t)}{L_{2018gj}(t)}$ (1)

From the late time light curve ($\rm>110~{}d$) we estimate the mass of
$\rm{}^{56}Ni$ to be $\rm M_{Ni}=0.024\pm 0.004~{}M_{\odot}$. $\rm{}^{56}Ni$
and characteristic timescale are also estimated using the Equation 2 and
scipy.minimize and emcee packages.

$L_{obs}=L_{0}\times
M_{Ni}\times\left[e^{-(\frac{t-t_{0}}{t_{Co}})}-e^{-(\frac{t-t_{0}}{t_{Ni}})}\right]\times\left(1-e^{(-\frac{t_{c}^{2}}{(t-t_{0})^{2}})}\right)$
(2)

The posterior distribution for the fits is shown in Figure 6. We obtained
$\rm{}^{56}Ni$ mass and characteristic time of $\rm 0.025\pm
0.002~{}M_{\odot}$ and $\rm 269\pm 33~{}d$, respectively.

The steepness parameter (S) described in Elmhamdi et al. (2003a) could also be
used to estimate the mass of $\rm{}^{56}Ni$ synthesized in the explosion.
Applying the refined steepness relation from Singh et al. (2018), we get a
steepness parameter, $\rm S=0.154\pm 0.028$, which translates to $\rm
M_{Ni}=0.028\pm 0.005$. The estimated $\rm{}^{56}Ni$ mass with different
techniques are in good agreement with each other, with an average value of
$\rm M_{Ni}=0.026\pm 0.007~{}M_{\odot}$.

###  3.7 Two-Component Analytical Light Curve Model

Figure 7: Semi-Analytical model fitting for SN 2018gj using two-component
model as described in Nagy & Vinkó (2016). The contributions from the shell
and the core are also shown independently. In the inset, best-fitting
parameters are listed for reference. The evolution of the light curve without
$\gamma-$ray leakage is shown by the cyan dashed line.

Nagy & Vinkó (2016) formulated a two-component progenitor model to fit the
observed bolometric light curves of Type IIP SNe semi-analytically. This
formulation is based on the seminal work by Arnett & Fu (1989) and subsequent
modifications by Popov (1993); Blinnikov & Popov (1993); Nagy et al. (2014).
It could be utilized to get approximate estimates on ejecta mass ($\rm
M_{ej}$), progenitor radius ($\rm R_{0}$), total energy ($\rm E_{tot}$), and
synthesized $\rm{}^{56}Ni$ mass ($\rm M_{Ni}$). The formulation divides the
homologously expanding and spherically symmetric SN ejecta into two
components: an inner faction with a flat (constant) density configuration; an
outer region with power law or exponential density profile (Nagy et al.,
2014). Both these spherically symmetric components have different masses,
radii, energies, and densities but a common centre. The outer region is an
extended envelope (Nagy & Vinkó, 2016). Contribution to bolometric luminosity
($\rm L_{bol}$) is primarily by energy released due to recombination ($\rm
L_{rec}$) and radioactive decay ($\rm L_{Ni}$) of $\rm{}^{56}Ni$. We use the
UVOIR bolometric luminosity to approximate the semi-analytical models. The
best fitting model is shown in Figure 7, and the obtained parameters are
presented in Table 1. For the shell component we found, $\rm
M_{ej_{s}}=0.2~{}M_{\odot}$ confined within a radius of $2.12\times
10^{13}~{}cm$. We find a similar radius value for the core as well ($\rm\sim
2.10\times 10^{13}~{}cm$) with an ejecta mass, $\rm
M_{ej_{c}}=6.6~{}M_{\odot}$. The outer envelope appears not far-extended, and
the density is slightly higher ($\rm\sim 1.0\times 10^{-8}~{}g~{}cm^{-3}$) as
obtained for other Type IIPs in Nagy & Vinkó (2016). For comparison, the radii
obtained are between the values obtained for SN 2005cs ($\rm
R_{shell}=2.0\times 10^{13}~{}cm$ and $\rm R_{core}=1.2\times 10^{13}~{}cm$)
and SN 2012aw ($\rm R_{shell}=4.5\times 10^{13}~{}cm$ and $\rm
R_{core}=3.0\times 10^{13}~{}cm$). The shell densities obtained for both the
cases are $\rm 1.8\times 10^{-8}~{}g~{}cm^{-3}$ and $\rm 5.2\times
10^{-9}~{}g~{}cm^{-3}$ respectively. The values obtained for SN 2018gj are
within similar ranges for other Type IIP SNe with a normal plateau duration.
From the semi-analytical modelling, we get a total ejecta mass, $\rm
M_{ej}\approx 6.8\pm 0.7~{}M_{\odot}$, radius, R$\approx 305\pm
30~{}R_{\odot}$, and $1.9\pm 0.2$ foe as the total energy released after the
explosion.

During the nebular phase, the light curve decline rate of SN 2018gj is
$1.34\pm 0.02$ mag 100$\rm\,d^{-1}$, much faster than $0.98\pm 0.02$ mag
100$\rm\,d^{-1}$, the decay rate of $\rm{}^{56}Co$ to $\rm{}^{56}Fe$ with full
$\gamma-$ray trapping. The faster decline of the late-phase light curve
indicates that the leakage of $\gamma$-rays is significant in SN 2018gj. The
effect of $\gamma-$ray leakage on the late time light curve could be
introduced using the $\rm A_{g}$ parameter. This parameter is the
effectiveness of $\gamma-$ray trapping (Chatzopoulos et al., 2012) whereas in
luminosity equation, it could be shown as $\rm
L_{bol}=L_{Ni}(1-\exp{(-A_{g}/t^{2})})+L_{rec}$. Physically, it is related to
the characteristic time scale ($\rm T_{0}$) of the $\gamma-$rays as $\rm
A_{g}=T_{0}^{2}$. The late phase light curve, powered by the radioactive
decay, is fit by an $\rm A_{g}=65000~{}d^{2}$ and mass of synthesized
$\rm{}^{56}Ni$, ($\rm M_{Ni})=0.025~{}M_{\odot}$. The corresponding $\rm
T_{0}$ value is 255 d, similar to the value obtained in Section 3.5. The $\rm
M_{Ni}$ estimated here corroborates our previous estimates in Section 3.5.
Further, the correlation between ejecta mass and opacity (correlation
coefficient, r $=0.984$, Nagy & Vinkó, 2016) makes it insubstantial to comment
on the possible progenitor mass with certainty up to two orders of magnitudes.
If we consider a proto-neutron star core of mass $\rm\sim 1.5~{}M_{\odot}$,
nominal mass loss due to winds, and the estimated ejecta mass, we could
constrain the lower limit of progenitor mass, which is $\rm\geq
10-11~{}M_{\odot}$, an estimate very similar to another short plateau object
SN 2020jfo (Teja et al., 2022), which had a very similar light curve shape,
but a shorter plateau by $\sim$ 10 days.

Table 1: Parameters for best-fitting two-component model

Parameters∗ | Shell | Core
---|---|---
Ejecta Mass, $\rm M_{ej}$ ($\rm M_{\odot}$) | 0.20 | 6.60
Radius, R ($\rm 10^{13}~{}cm$) | 2.12 | 2.10
Thermal Energy, $\rm E_{th}$ ($\rm 10^{51}~{}erg$) | 0.10 | 0.41
Kinetic Energy, $\rm E_{kin}$ ($\rm 10^{51}~{}erg$) | 0.15 | 1.2
Expansion Velocity, $\rm v_{exp}$ ($\rm 1000~{}km~{}s^{-1}$) | 13.0 | 5.5
Opacity, $\rm\kappa$ ($\rm cm^{2}~{}g^{-1}$) | 0.4 | 0.2

∗ $\rm T_{rec}\approx 6000~{}K$, $\rm A_{g}=6500~{}d^{2}$ and $\rm
M_{Ni}=0.024~{}M_{\odot}$

Figure 8: Spectral time series for SN 2018gj containing 31 epochs spanning 295
d post-explosion. All spectra have been calibrated with photometry for
absolute flux and corrected for host redshift. Some of the prominent spectral
lines have been marked for clarity. (The data used to create this figure are
available.)

##  4 Spectral Analysis

Apart from SN classification, detailed spectral studies provides insight into
the ejecta composition, asymmetries, dust formation, and explosive
nucleosynthesis. In this section, we present a detailed optical spectroscopic
analysis of SN 2018gj. The temporal evolution of spectra is presented in
Figure 8, marked with some well-identified hydrogen and metal features. The
spectral sequence is not corrected for telluric absorption lines. Further, all
the spectra have been scaled with photometry for absolute flux calibration and
corrected for the host redshift. We study the spectral evolution spanning 31
epochs over the photospheric phase to the nebular phase beginning $+5~{}d$.

###  4.1 Photospheric/Plateau Phase Spectra

Figure 9: SN 2018gj spectrum during maximum light. Spectra of other Type II
SNe around the maximum is shown for comparison. The comparison sample is drawn
from Table 7.

The early part of spectra before or around the peak for typical Type II SNe is
dominated by a featureless blue continuum along with a hint of formation of
broad and discrete Hydrogen features, predominantly Balmer series ($\rm
H\alpha~{}6563~{}\AA,\ H\beta~{}4861~{}\AA,\ H\gamma~{}4340~{}\AA\ and\
H\delta~{}4102~{}\AA$). The features show a typical P-Cygni profile due to the
expansion of the ejecta. The early spectra of SN 2018gj show these features.
The He I$\rm~{}5876~{}\AA$ appears as early as $\rm+5~{}d$ and seen till
$\rm+16~{}d$ where it gets blended with the Na ID$\rm~{}5890,~{}5896~{}\AA$.
The temperature of the ejecta estimated using SED (Section 3.5) around this
phase is about $\rm\gtrsim 10000~{}K$, as the ejecta expands, it gradually
cools down. With the ejecta cooling, metallic lines are seen, dominating the
blue region of the spectra. All these metallic features show well-defined
P-Cygni profiles. As the SN evolves, the absorption depth increases in
strength and the Fe II multiplet $\rm~{}4924,~{}5018,~{}5169~{}\AA$ lines are
clearly seen at $+$24 d. The near-infrared region of the spectrum evolves with
conspicuous Ca II triplet ($\rm~{}8498,~{}8542~{},~{}8662~{}\AA$) that is
visible during the same phase and becomes prominent as it evolves further.
Towards the end of the plateau around $\rm\sim+64~{}d$, the Na ID line
develops prominently.

The spectral evolution covers the transition from the plateau phase to the
nebular phase very well. We obtained four spectra during the transition period
from $\rm+72~{}d$ to $\rm+88~{}d$. We find increased flux in the redder side
with the increased strength of Ca II triplet. Similarly, other features become
more prominent with an increase in their strengths. Apart from the increasing
strength of earlier Hydrogen features, other lines, viz. Ba
I$\rm~{}6142~{}\AA$, He I$\rm~{}7065~{}\AA$, and O I$\rm~{}7774~{}\AA$ develop
and are observed clearly (Figure 8). This could be either due to the
temperature change or because we can probe deep inside the ejecta as the
hydrogen layer becomes transparent to the radiation from these parts.
Nevertheless, from the SED fitting, we find the temperature fairly consistent
within this phase. So this is primarily due to the decreased opacity of the
hydrogen layer. We do not find other stark differences during the transition
phase.

When we compare the spectral features of SN 2018gj with other Type II SNe, we
find that these features are fairly typical and are observed in all sorts of
Type II SNe whether they show plateau or decline linearly both in the early
phase (Figure 9) as well as photospheric phase (Figure 10). The primary
distinction is broadly the strength and spread of these features. During
maximum light, the absorption trough of lines observed in SN 2018gj lies in-
between other SNe used for comparison. For archetypal Type IIP SNe, SN 1999em
(Hamuy et al., 2001; Leonard et al., 2002a; Elmhamdi et al., 2003b) and SN
2004et (Sahu et al., 2006a), we find the strength of Balmar features is more
prominent around the similar phase. However, even for normal Type IIP SNe,
e.g., SN 2005cs (Pastorello et al., 2006; Faran et al., 2014a) and SN 2013ab
(Bose et al., 2015) the strength could vary. Although the early spectrum of SN
2020jfo (Teja et al., 2022), another short plateau event, appears very similar
to the spectrum of SN 2018gj except toward the shorter wavelengths, especially
around H$\gamma$. There was the presence of ionized He in the early spectra of
SN 2020jfo. Spectral comparison around mid plateau for SN 2018gj reveals the
lack of metallic or fully developed features, which are more prominent in
other SNe viz. SN 2020jfo, SN 2013ej, SN 2005cs, SN 2004et, and SN 1999em.
Furthermore, it is observed that the hydrogen and other metallic features in
SN 2018gj are weak as compared to normal Type II SNe but similar to SN 2009kr
and SN 2013ab. SN 2013ab shows many similarities with SN 2018gj around the
same phase.

Figure 10: Spectrum of SN 2018gj during plateau phase is shown in comparison
with other Type II SNe. The comparison sample is drawn from Table 7.

###  4.2 Ejecta Velocity

In Figure 11, we show the expansion velocities estimated using the non-blended
absorption minima of various species. The absorption minimum is estimated by
fitting a Gaussian profile, and the expansion velocities are measured with
respect to the rest frame wavelengths. A peculiar velocity evolution of
Hydrogen features is seen for the initial few days. It first rises and then
declines. The rising part of the ejecta velocity has not been observed for
other SNe. While the estimation of an initial lower velocity may indeed be
true, the absorption features during this phase are very broad and associated
with higher measurement uncertainty. A shallow absorption feature is seen
around 6200Å during the early phases (until $\sim 40$ d). It could be
attributed to a high velocity (HV) H$\alpha$ feature (Dessart & Hillier,
2022), at a velocity of $\sim 15000$ km s-1. Figure 11 also shows a comparison
of the SN 2018gj velocities with the mean expansion velocities obtained from a
large sample of Type II SNe (Gutiérrez et al., 2017). The expansion velocities
for SN 2018gj are towards the higher end of $1-\sigma$ scatter from the mean.
It continues to follow this higher velocity trend even after transitioning
from the plateau phase to the nebular phase. The expansion velocity inferred
from Fe II features is found to be higher than the mean value initially;
however, later, it follows a trend similar to the mean of the sample.

Figure 11: Temporal velocity evolution of various lines identified in the
spectra using the absorption minimum is shown here. The velocities have been
compared with the sample from Gutiérrez et al. (2017) where the solid lines
are the mean values from the sample and the shaded area around it in similar
colour represents the 1$-\sigma$ scatter from the mean velocities.

From various absorption features, we estimate that the layers of the ejecta
are moving with velocities higher than $\rm 10000~{}km~{}s^{-1}$. Although the
temperature around a similar phase estimated for SN 1999em is similar to SN
2018gj, the H$\alpha$ velocity inferred was much higher ($\sim$ 16000 $\rm
km~{}s~{}^{-1}$) (Elmhamdi et al., 2003b). In the case of SN 2013ej (Valenti
et al., 2014) and SN 2020jfo, the expansion velocities are around
$\rm~{}13000~{}km~{}s^{-1}$ and comparable to that of SN 2018gj. As the ejecta
evolves with time, it starts to slow down ($\rm<9000~{}km~{}s^{-1}$ around +20
d) and cool to a lower temperature ($\rm\leq 8000~{}K$ around +20 d).

During the photospheric phase, the expansion velocities continue to follow the
declining trend and reach $\sim$8000 $\rm km~{}s^{-1}$ around +40 d.
Afterwards, the decline is very slow and does not follow the average trend.
The expansion velocities estimated using Hydrogen features are on the higher
side for the Type II SNe. For SN 1999em around +40 d, typical temperatures are
5000–6000 K and H$\alpha$ velocity of about 6000$\rm~{}km~{}s^{-1}$ (Elmhamdi
et al., 2003b). In 2005cs velocities are much lower around +40 d and are
estimated as $\rm\leq 4000~{}km~{}s^{-1}$ and $\rm 2000~{}km~{}s^{-1}$ for
H$\alpha$ and metal lines, respectively (Pastorello et al., 2006). Around
similar phase H$\alpha$ and metal velocities for SN 2004et are 7500 $\rm
km~{}s^{-1}$ and 4500 $\rm km~{}s^{-1}$, respectively. In case of SN 2009kr,
SN 2013by and SN 2020jfo, H$\alpha$ velocities are $\rm\leq
7000~{}km~{}s^{-1}$ whereas for SN 2018gj it is close to the velocities
estimated for SN 2013ab (8000 $\rm km~{}s^{-1}$) and SN 2013ej (8500 $\rm
km~{}s^{-1}$).

Similar observations are true for velocities estimated using metal lines.
Typical expansion velocities around the plateau phase start at $\rm
6000~{}km~{}s^{-1}$ and slow down to $\rm\sim 3000~{}km~{}s^{-1}$ towards the
end of the plateau phase.

###  4.3 Nebular Phase Spectra

When the receding photosphere reaches the base of the outer envelope, the
plateau/photospheric phase ends, and the supernova transitions to the nebular
phase. Continuous expansion reduces temperature, column density, and optical
depth (Jerkstrand, 2017). The ejecta is optically thin, and the inner ejecta
layers are probed. Supernova in this phase is still optically bright, and the
prominent energy source is the radioactive decay chain of $\rm{}^{56}Ni$
synthesized in the explosion. The midpoint of transition happens around +80 d,
and several metal lines originating from forbidden transitions, e.g. [Ca
II]$~{}7291,~{}7324~{}\AA$ start appearing. The strength of Na ID
$~{}5893~{}\AA$ and Ca I triplet keeps on increasing as the ejecta evolves
with time. Other forbidden lines viz. [Fe
II]$~{}\rm~{}6118,~{}7155,~{}7172~{}\AA$, [O I]$~{}\rm 6300,~{}6364~{}\AA$
also start to appear in the spectra. Blue-ward of Ca triplet, we identify the
O I$~{}\rm 7774~{}\AA$. The presence of H$\alpha$ continues during the nebular
phase and is the dominant line in the spectrum, although much narrower.

Figure 12: Spectral comparison of SN2018gj with other Type II SNe around
similar epochs during the nebular phase.

Figure 12 shows the comparison of nebular phase spectra for SN 2018gj with
several other Type II SNe. The O I$~{}\rm 7774~{}\AA$ line in SN 2018gj is
found to be weakest in comparison to other Type II SNe except for SN 2013by.
Apart from certain features common in Type II SNe, we find a hint of stable
[Ni II] $\rm 7378~{}\AA$ with emission feature having an intrinsic velocity
similar to other emission features starting from $+112~{}d$ (Figure 8). This
feature was observed in SN 2020jfo $\sim$ $\rm+196~{}d$ as presented in Teja
et al. (2022). However, it is quite possible that in SN 2020jfo, the stable Ni
was present from an earlier epoch, but due to its proximity to the Sun, the
first nebular spectrum could be obtained $\sim$ $\rm+196~{}d$. This feature is
very prominent in SN 2020jfo but weak in SN 2018gj.

###  4.4 Blue-shifted Emission From Photospheric Phase To Nebular Phase

Figure 13: Focused view of spectral time series for H$\alpha$ line in SN
2018gj. The black line marked is the rest wavelength for H$\alpha$. The
spectra are corrected for host redshift, and it is evident that the peak of
emission features never reaches the rest wavelength.

We observed blueshift in the emission peaks in the spectral evolution of SN
2018gj. In Figure 13, the region around H$\alpha$ has been plotted, showcasing
this persistent blue shift in the H$\alpha$ emission peak. The H$\alpha$
emission peak is shifted by $\rm\sim\,4500~{}km~{}s^{-1}$ around +10 d, which
decreases monotonically till the end of the plateau around +75 d where it
reaches a value $\rm\sim\,500~{}km~{}s^{-1}$ but never reaches rest
wavelengths (Figure 14). Instead, we observed the shift to increase during the
transition phase and settle on a value of $\rm-1000~{}km~{}s^{-1}$. The blue
shift is seen till the last available spectrum ($+$295 d). The shift is not
only observed in the H$\alpha$ but is also seen in other lines with similar
values.

Figure 14: Velocity evolution of blue-shifted $\rm H\alpha$ emission peak.
Velocity evolution for emission features obtained using other ions has also
been plotted.

###  4.5 Progenitor Mass Estimates Using Nebular Lines

Figure 15: Late phase (+295 d) spectrum of SN 2018gj compared with the model
spectra around similar phase to estimate the initial mass of the progenitor.
The model spectra are obtained from Jerkstrand, Anders (2017).

In addition to light curve modelling, there are other independent methods for
determining the progenitor’s mass. One such approach is to utilize the nebular
phase spectra, which can provide insight into the metallic lines that arise
from stellar nucleosynthesis. Jerkstrand et al. (2014) demonstrated that the
late-phase lines of [O I] $~{}6300,\,6364\,\AA$ and [Ca II]
$~{}7291,\,7324\,\AA$ can serve as proxies for progenitor mass. To constrain
the progenitor mass of SN 2018gj, we compared the nebular phase spectrum at
+295 d with model spectra from Jerkstrand, Anders (2017). The model spectra
for progenitor masses of 12, 15, 19, and 25 $\rm M_{\odot}$ have been scaled
for the $\rm{}^{56}Ni$ mass and the distance of SN 2018gj (in contrast to 5.5
Mpc for the model spectra) (Figure 15). To account for the difference in phase
between the model spectra and the observed spectrum, the observed spectrum was
scaled by the brightness difference due to dissimilarity in phases determined
from the characteristic time scale ($t_{c}$) obtained from the
$\rm{}^{56}Ni$-decay powered phase of the light curve using
$f_{corr}=f_{obs}/(1-e^{-(t_{c}/phase)})$ (Singh et al., 2019).

The comparison of [O I] 6300 Å, 6364 Å line fluxes of the observed spectra
with the spectral models suggests a progenitor of mass $\rm\leq$ 15 $\rm
M_{\odot}$. However, the observed $\rm H\alpha$ flux is relatively weak as
compared to the 15 $\rm M_{\odot}$ progenitor, indicating a partially stripped
hydrogen envelope in SN 2018gj. In core-collapse SNe, the mass of calcium
synthesized in the explosion is insensitive to the progenitor’s zero-age main-
sequence mass, whereas the mass of synthesized oxygen depends on it. Hence,
the [Ca II] / [O I] flux ratio is a useful indicator of the progenitor mass
(Fransson & Chevalier, 1989). The lower the value of the ratio, the heavier
the progenitor. As seen in the model spectra presented in Figure 15, the [Ca
II]$~{}7291,\,7324\,\AA$ line from different mass models have similar line
strength whereas it is differentiable in the case of [O I]
$~{}6300,\,6364\,\AA$ and increases with the progenitor masses. In the case of
SN 2018gj, the [Ca II] lines are stronger than the model spectra, whereas [O
I] lines are much weaker. Therefore the [Ca II] / [O I] line flux ratio is
much larger than one indicating a low mass progenitor.

##  5 Hydrodynamical Modelling

Table 2: Parameters for pre-SN/Explosion progenitor models evolved from MESA that were used to generate model light curves in STELLA Pre-Supernova Parameters | Explosion Parameters
---|---
$M_{i}$ | $\alpha_{Dutch}$ | $\rm M_{f}$ | $\rm M_{H-rich}$ | $\rm M_{He-core}$ | $\rm M_{Fe-core}$ | $\rm logT_{eff}$ | $\rm logL$ | Age | Radius | $E_{Exp}$ | $M_{Ni}$
($\rm M_{\odot}$) |  | ($\rm M_{\odot}$) | ($\rm M_{\odot}$) | ($\rm M_{\odot}$) | ($\rm M_{\odot}$) | $\rm T_{eff}(K)$ | $\rm L(erg~{}s^{-1})$ | (Myr) | ($\rm R_{\odot}$) | $\rm(10^{51}~{}erg)$ | ($\rm M_{\odot}$)
13 | 3.0 | 9.1 | 5.35 | 3.75 | 1.50 | 3.57 | 4.83 | 16.7 | 620 | 0.4 | 0.025
4.0 | 8.2 | 4.54 | 3.63 | 1.53 | 3.57 | 4.80 | 16.7 | 609 | 0.4 | 0.025
4.5 | 7.3 | 3.66 | 3.65 | 1.48 | 3.51 | 4.77 | 16.7 | 773 | 0.4 | 0.030
5.0 | 6.9 | 3.26 | 3.60 | 1.52 | 3.51 | 4.80 | 16.8 | 794 | 0.2 | 0.027
5.0 | 6.9 | 3.26 | 3.60 | 1.52 | 3.51 | 4.80 | 16.8 | 794 | 0.3 | 0.027
| 5.0 | 6.9 | 3.26 | 3.60 | 1.52 | 3.51 | 4.80 | 16.8 | 794 | 0.4 | 0.028
| 5.5 | 6.3 | 2.69 | 3.57 | 1.61 | 3.52 | 4.72 | 16.9 | 705 | 0.3 | 0.025

Figure 16: Temporal evolution of pseudo-equivalent width (pEW) for Fe II
$\rm~{}5169~{}\AA$ line obtained using optical spectra. Other markers
represent the pEWs obtained from models given in Dessart et al. (2013). The
solid blue line and the shaded region around it represent the mean pEW and the
corresponding 1-$\sigma$ scatter about the mean for a larger sample of Type II
SNe given in Gutiérrez et al. (2017).

Figure 17: Top: One dimensional representation of mass fractions for 13 $\rm
M_{\odot}$ ZAMS model with final mass 7.3 $\rm M_{\odot}$. The elements are
part of the nuclear reaction rates network used in the model’s evolution. The
abscissa is shown till 4 $\rm M_{\odot}$ as the trend followed beyond it is
the same for the outer hydrogen envelope. Bottom: Effect of mixing with the
implementation of Duffell RTI on the ejecta structure just before the breakout
is shown for some of the prominent elements for the same model as in the Top
panel.

The lower bound for progenitor mass obtained using the semi-analytical light
curve modelling and the independent progenitor mass estimated using the
nebular spectrum comparison with model spectra suggest that SN 2018gj resulted
from a low-mass RSG progenitor with ZAMS mass ranging from 10-15 $\rm
M_{\odot}$. Model light curves of normal Type IIP SNe have been extensively
studied (Dessart et al., 2010; Sukhbold et al., 2016; Eldridge et al., 2018),
and in some cases, refined analytical equations are provided to get estimates
on the progenitor properties (Goldberg et al., 2019). We compare the
observables obtained for SN 2018gj with the analytical equations (Goldberg et
al., 2019) obtained for Type IIP and find that for a specific radius range of
RSG ($\rm 300-1200~{}R_{\odot}$), the equations hint at a shallow ejecta mass
($\rm~{}0.5-2.5~{}M_{\odot}$) and explosion energy ($\rm 0.4-0.03~{}foe$) (see
Appendix C). These ejecta masses are in disagreement with our previous
estimates obtained using semi-analytical modelling and nebular spectra
comparisons. Even if we use radii obtained from the semi-analytical modelling
in the scaling relation, the values obtained for the ejecta mass and explosion
energy are not similar to those obtained from the semi-analytical modelling.
But as we go for much smaller radii ($\sim$200 R$\odot$), the ejecta mass (4.5
M$\odot$) and explosion energy ($~{}\rm\sim 1~{}foe$) increase reaching closer
to the values obtained using semi-analytical modeling. However, it is noted
here that the analytical equations are calibrated for the SNe IIP that show a
normal plateau of $\sim 100$ days and may not necessarily be valid for short
plateaus as also indicated by Hiramatsu et al. (2021).

Figure 18:  Variations in 13 $\rm M_{\odot}$ ZAMS model using different
parameters to achieve a shorter plateau length. Zoomed out a plot in the
bottom left shows the variation in explosion energy for different model light
curves around the plateau transition. The second plot in the right inset shows
the corresponding Fe 5169 velocities obtained using models. The thicker line
represents the model where the expansion velocity could be matched with the
observed velocities.

A more robust way forward is to perform a complete hydrodynamical modelling to
better understand the progenitor, its evolution history, and other SN
explosion parameters. We perform the modelling using the Modules for
Experiments in Stellar Astrophysics (MESA version r-15140, Paxton et al.,
2011, 2013, 2015, 2018, 2019) and STELLA (Blinnikov & Sorokina, 2004; Baklanov
et al., 2005; Blinnikov et al., 2006) packaged within MESA. It was compiled
using MESA SDK (version x86_64-linux-20.12.1, Townsend, 2020). The modelling
setup follows the values prescribed in Farmer et al. (2016). In lower mass
models, we had increased the $max\\_model\\_number$ in each $inlists$ to
accommodate longer evolution times. We fixed the overshooting values to
default settings ($f=0.01,f_{0}=0.005$). We set the
$varcontrol\\_target=10^{-4}$ for the convergence of models with higher mass
loss. Some other basic setup parameters are as follows: the nuclear reaction
rates network used ‘approx21_cr60_plus_co56.net’, provided within MESA. These
rates are primarily from the Nuclear Astrophysics Compilation of Reaction
rates, (NACRE, Angulo, 1999) and the Joint Institute for Nuclear Astrophysics,
JINA reaction rates (REACLIB, Cyburt et al., 2010). The mixing length
parameter (MLT_option) defaults to $Henyey$ Henyey et al. (1965), with
$\rm\alpha_{MLT}=1.5-2.0$, where $\rm\alpha_{MLT}$ is the ratio of mixing
length to the pressure scale height ($\rm=P/g\rho$). Other than the models
with 19 $\rm M_{\odot}$ and 13 $\rm M_{\odot}$ ($\rm\alpha_{dutch}=3.0$) where
$\rm\alpha_{MLT}$ is set to default value of 1.5, we set it to 2.0 for the
remaining models. Cool and hot wind schemes ($\alpha_{dutch}$) for the Red
Giant Branch or Asymptotic Giant Branch phase are considered ‘Dutch’,
combining works by many Dutch authors. The primary combination chosen is based
on the work by Glebbeek et al. (2009). Typically, if the surface H has a mass
fraction $<$ 0.4 and a $\rm T_{eff}$ $>$ $\rm 10^{4}\,K$, the scheme used is
from Vink et al. (2001), otherwise, it is from Nugis & Lamers (2000). The
default $Ledoux$ criterion is used to determine the position of the convective
boundaries.

The light curve modelling in MESA+STELLA was achieved in the broad steps:
progenitor evolution, synthetic explosion, shock propagation, shock breakout
and ejecta evolution. In the first step, we used "make_pre_ccsnIIp" example
provided in test suites to evolve a pre-main sequence star until the
development of the iron core further leading to its rapid infall. Given that
there is no solution to achieve a spontaneous explosion in MESA, the test
suite, namely "ccsnIIp", provides an alternative methodology to achieve the
desired explosion. Primarily, a thin layer (mass $\rm\sim 0.01~{}M_{\odot}$)
at the inner boundary is injected with a tremendous amount of energy over a
brief period (5 ms) to achieve the synthetic explosion. Finally, the shock is
propagated with various layers, and the structure and hydrodynamical
parameters are obtained just before the shock breakout as input to the STELLA
(Paxton et al., 2018). Further details of the steps adopted and the parameters
adjusted from evolution to explosion and handover to STELLA could be obtained
from (Farmer et al., 2016; Teja et al., 2022). We used 400 zones for STELLA
with 40 extra zones in case of CSM. For the case of bolometric light curves,
we used 40 frequency bins. However, in the case of UBVRI light curves, we had
estimated 13$\rm M_{\odot}$ cases for 120 frequency bins for better
resolution. Another parameter crucial in modelling is the metallicity which
could affect wind-driven mass losses, the mass of the hydrogen envelope, and
the line-profile signatures in Type II SNe (Dessart et al., 2013). Metallicity
becomes more significant in the case of short plateaus due to extensive wind
mass losses and smaller hydrogen envelopes. Since SN 2018gj is far from its
host galaxy centre, we tried to image the region around the SN in search of
possible nearby H II using a narrow band H$\alpha$ filter. Unfortunately, we
could not detect any such region for sufficiently long exposures. To crudely
estimate metallicity, we utilized the pseudo-equivalent width (pEW) evolution
of Fe II$\rm~{}\lambda~{}5169~{}\AA$. We compared it with the models presented
in the Dessart et al. (2013). Figure 16 shows the time evolution of pEW of Fe
II$\rm~{}\lambda~{}5169~{}\AA$ along with the models presented in Dessart et
al.. It also shows the mean and 1$-\sigma$ scatter in corresponding values for
a larger Type II SNe sample (Gutiérrez et al., 2017). From these models, we
found that two models with 0.5$\rm~{}Z_{\odot}$ and $\rm Z_{\odot}$ matched
with the pEW obtained in the case of SN 2018gj. Hence, we fix the metallicity
of all the models to be of solar values.

Figure 19: Optical bolometric luminosities obtained using MESA+STELLA are
plotted along with the optical bolometric light curve of SN 2018gj. The
initial rise is not fitting well in the optical regime.

We tried to evolve progenitors with zero-age-main-sequence (ZAMS) masses 13
$\rm M_{\odot}$ and 14 $\rm M_{\odot}$ and extracted their pseudo-
bolometric/bolometric light curve evolution after they explode. We checked for
higher mass models also (see Appendix D) We found out that with standard mass
loss by winds, none of the models was able to reproduce a short plateau. In
most cases, the plateau duration was typical of normal Type IIP SNe. However,
we could get shorter plateaus as we enhanced the mass loss rate through winds
using the  wind scaling factor, $\alpha_{dutch}=3.0-5.5$. As the plateau
duration primarily depends on the hydrogen envelope mass, achieving shorter
plateaus from each of these progenitor masses with the correct mass loss was
possible. However, the simultaneous match to the expansion velocities was not
achieved in the models for 14 $\rm M_{\odot}$ progenitors. In the case of 13
$\rm M_{\odot}$ models, we were able to match the light curve and expansion
velocities up to the initial 50 days. Figure 17 gives the final composition
for one of the 13 $\rm M_{\odot}$ models representing the elements used in the
progenitor structure. It also shows the mixing effect on the ejecta
composition with the implementation of Duffell RTI in MESA (Duffell, 2016).
The mass fractions beyond 4 $\rm M_{\odot}$ are very similar with no
recognizable changes and, therefore, are not shown in the top panel of Figure
17. Although elements are mixed at different mass coordinates, the core and
outer structure fairly consist of iron and hydrogen, respectively. From the
current understanding of single star evolution, high mass RSG
($\rm>20~{}M_{\odot}$), with enough mass loss, could give a smaller plateau as
obtained in the works by Dessart et al. (2010); Hiramatsu et al. (2021). To
explore the possibility of a high mass progenitor, we also attempted to
generate models using 19 $\rm M_{\odot}$ progenitors, as this is the upper
limit for directly detected progenitors. It is possible to obtain smaller
plateau lengths with lower mass loss rates, but these models failed to
reproduce the velocity evolution of the ejecta [Appendix D]. Properties of
some of the pre-SN progenitors are provided in Table 2, giving details of the
initial and final masses of the progenitors.

Further, masses of helium and iron core present during evolution are also
mentioned in the table. In addition to the used parameters, Table 2 also lists
the various properties of the pre-SN star, viz. effective temperature,
luminosity, age, and radius. We only show those models where we could achieve
smaller plateau lengths. Detailed descriptions and analyses of these
individual models are beyond the scope of this work. As expected from the
initial mass of the progenitor models, there are not many differences in the
pre-SN structure apart from the mass difference of the hydrogen envelope. All
the models with the same initial mass have similar evolution times, effective
temperatures, core masses, and luminosities.

We attempted to generate the model light curves to match the observed UVOIR
bolometric luminosity. After achieving a desired plateau length in the model
light curves, the mass of synthesized nickel and explosion energy were
constrained by varying the nickel mass ($x\\_ctrl(12)$) and explosion energy
($inject\\_until\\_reach\\_model\\_with\\_total\\_energy$) parameters during
the explosion and shock propagation. Figure 18 shows all the models for 13
$\rm M_{\odot}$ with plateau lengths $\rm 80\pm 10~{}d$. The bolometric
luminosity of SN 2018gj is over-plotted. In the model, the explosion energy
and nickel mass are well constrained, however, the initial peak (s1) is
slightly under-luminous. Instead of comparing the bolometric luminosity, we
compare the observed pseudo (optical) bolometric luminosity with modelled
pseudo-bolometric luminosity ($\rm L_{UBVRI}$), which reveals the under-
luminous s1 phase more prominently. We discuss the possible presence of CSM
interaction in the subsequent section. The nickel mass obtained with the
hydrodynamical modelling corroborates the earlier mass estimates through
various techniques. The explosion energy obtained is slightly less than the
semi-analytical modelling estimates.

##  6 Discussion

###  6.1 Blueshifted Emission

As described earlier in Section 4.4, we observed the emission peaks were
blueshifted, and these shifts were observed till the late phase. The blue-
shifted emission during the photospheric phase has been observed and discussed
explicitly in many works (Andrews et al., 2011; Bose et al., 2015; Dastidar et
al., 2018). It has been established in Anderson et al. (2014b) that this
feature is typical to Type IIP SNe during the early/photospheric phase. It was
concluded by Chugai (1988) that these blue-shifted emission peaks during the
photospheric phase are due to the diffuse reflection of the photosphere’s
resonance radiation. Primarily in all the cases, the shifts are only present
up to the late photospheric phase or early nebular phase except in the case of
SN 2007it (Andrews et al., 2011) where it has been observed till 150 d post-
explosion. Anderson et al. (2014b) utilizing the Type IIP modelled spectra
from Dessart et al. (2013) showed the shifts in emission peaks vanish after
photospheric phase and the emission peaks are observed at rest wavelengths.
Interestingly, the shifted peak is reported for H$\alpha$ and not any other
lines.

The blue shift in the emission peaks observed in the spectral evolution of SN
2018gj is a typical feature for Type IIP SNe during the photospheric phase.
But the intriguing aspect is the presence of these shifts until the late
nebular phase and are not just limited to the prominent H$\alpha$ feature.
Observance of such shifts during the late nebular phase is rare in most of the
usual Type IIP SNe studied in the literature. The blueward shift might not be
physical but apparent and can be explained from the argument presented in
Anderson et al. (2014b) regarding ejecta geometry and its composition. One of
the critical factors is the changes in the opacity values. Opacity within the
photosphere and above depends on various physical processes, viz. density,
composition, and degree of ionization within the ejecta (Sim, 2017). During
the photospheric phase, the density structure in Type IIP ejecta is much
steeper. It enhances the confinement of the emission/absorption line. Further,
it aggravates the concealment of the receding portion of the ejecta, hence
biasing the blueward line emission for a distant observer during photospheric
phase(Anderson et al., 2014b).

But the above reasoning might not be valid during the nebular phase when the
ejecta behaves like an emission line nebulae. Other radiative transfer effects
might come into play, especially due to free electrons, photo-ionization, or
the presence of dust (Jerkstrand, 2017). During the nebular phase, the amount
of electron scattering is relatively low, with an optical depth of
$\tau_{e}\leq 1$. Most photons will not be scattered or will only be scattered
once. As a result, the distortions in the line profile are not significant
(Jerkstrand, 2017). However, the scattering does cause a slight blue shift of
the peak. For instance, when $\tau_{e}=1$, the shift is approximately
$\Delta\lambda/\lambda_{0}(V_{max}/c)=-0.13$, which corresponds to a velocity
shift of $\rm 390~{}kms^{-1}$ for a line that is $\rm 3000kms^{-1}$ wide
Jerkstrand (2017). The blueshift observed in the spectra is much larger than
the values obtained for typical opacity. Hence, this might not be the cause of
the observed shifts.

The continuous absorptive opacity or the photon destruction (continuous
absorption) by dust or photo-ionization could also cause a significant blue
shift. For $\tau_{e}=1$, the shift is approximately
$\Delta\lambda/\lambda_{0}(V_{max}/c)=-0.31$, which corresponds to a velocity
shift of $\rm\approx 900~{}kms^{-1}$ (Jerkstrand, 2017) which is significant
and close to the observed values. But for these effects, the presence of dust
or enough optically thick material is required. As a considerable fraction of
the hydrogen envelope is removed from the progenitor of SN 2018gj, the
presence of optically thick material also does not seem plausible. However,
the presence of pre-existing dust or early dust formation in the ejecta could
be a possibility. We do not find a convincing signature for the presence of
dust in the ejecta. During the nebular phase, the light curve in the optical
band is found to decline faster than the $\rm{}^{56}Co$ decay rate, which
could be due to the light absorption by dust. In such a scenario, due to
reprocessing of light by the dust particles, the light curve decline in the
redder bands is expected to be slower. However, on the contrary, in SN 2018gj,
light curves in the redder bands are found to decline much faster (Section
3.2).

Since the supernova occurred in the outskirts of the host galaxy, the
intrinsically high velocity of the progenitor star towards the line of sight
could also be the possibility. Although it is rare to find such high-mass
hyper-velocity stars going rogue but could be possible, as observed in Evans &
Massey (2015).

###  6.2 CSM Interaction?

A piece of substantial evidence has been found in favour of early CSM
interaction having a signature in the light curves. However, we do not see any
interaction feature in the spectral evolution. When we try to fit pseudo
bolometric luminosity with UBVRI bolometric luminosity from the models (see
Figure 19), we could see that the initial part does not fit that well until we
introduce CSM interaction (see Figure 20).

In Figure 20, we introduce three CSM profiles with different wind evolution
time and mass loss rates giving total masses 0.1, 0.15, 0.20 $\rm M_{\odot}$
with different extents. We observe that the initial light evolution could be
explained with less than 0.15 $\rm M_{\odot}$ of CSM, which is close to the
progenitor. The enhanced pre-SN wind was activated 10-20 years before the
explosion.

Figure 20: The effect of adding CSM around the progenitor is prominently seen
in the early stage and can explain the initial excess in the individual light
curves in redder bands. The thicker dashed lines represent the light curves
obtained using 120 frequency bins.

Since there is no evidence in spectra to corroborate the presence of CSM
around the progenitor. Either the lack of CSM interaction evidence in spectra
is due to some non-spherical geometry, or it might be the intrinsic feature of
these SNe and warrant a further understanding of these light curve rise times.

##  7 Conclusion

In this work, we presented a detailed investigation of a short plateau Type II
supernova SN 2018gj, which exhibited a plateau lasting for $\rm\sim 70~{}d$ in
its light curve. This plateau duration is significantly less than the
characteristic plateau length of $\rm\sim 100~{}d$ for Type IIP SNe. We
carried out detailed photometric observations in UV, optical, and NIR
wavelengths and the detailed optical spectroscopic evolution from the
photospheric phase to the nebular phase ($\sim$ 300 d from the explosion). The
various light curve parameters were estimated, and the peak $V$-band magnitude
was estimated as $\rm-17.0\pm 0.1~{}mag$. Using the bolometric light curve
mass of synthesized radioactive $\rm{}^{56}Ni$ is estimated as $\rm 0.026\pm
0.007~{}M_{\odot}$. Spectroscopic comparison of SN 2018gj with other Type II
SNe indicated it to be a normal Type II SN but with high H$\alpha$ velocities.
Further, blueshift in the emission features during the late nebular phase is
also reported. We carried out semi-analytical modelling, nebular phase
spectral comparisons, and complete 1-D hydrodynamical modelling to ascertain
ejecta mass, explosion energy, synthesized nickel mass, and details about the
progenitor. The models favoured a low mass progenitor of ZAMS mass of
$\rm<13~{}M_{\odot}$, contrary to the higher mass RSG channels available in
the literature. We found the mass of the hydrogen envelope to be only $\rm\sim
2.5-3.0~{}M_{\odot}$ and a total pre-SN mass $\rm\leq 7~{}M_{\odot}$.

## Data Availability

The majority of data are presented in tables. The spectra files are provided
as data behind the figure. The inlists used for creating MESA models and
associated models are available on Zenodo under an open-source Creative
Commons Attribution license: https://doi.org/10.5281/zenodo.7994631 (catalog
doi:10.5281/zenodo.7994631).

Other data files, models, etc., will be shared with users upon reasonable
request.

We are grateful to the anonymous referee for a thorough evaluation of the
manuscript that helped in improving it. We thank the staff of IAO, Hanle, and
CREST, Hosakote, that made these observations possible. The facilities at IAO
and CREST are operated by the Indian Institute of Astrophysics, Bangalore.
This research has made use of the High-Performance Computing (HPC)
resources222https://www.iiap.res.in/?q=facilities/computing/nova made
available by the Computer Center of the Indian Institute of Astrophysics,
Bangalore. This research made use of
RedPipe333https://github.com/sPaMFouR/RedPipe (Singh, 2021), an assemblage of
data reduction and analysis scripts written by AS. This work was supported by
the Joint Research Project, Grant number JPJSBP120227709. AT acknowledges
support from the Egyptian Science, Technology and Innovation Funding Authority
(STDF) under the grant number 45779. DKS acknowledges the support provided by
DST-JSPS under grant number DST/INT/JSPS/P 363/2022. This work was also partly
supported by JSPS KAKENHI Grant Numbers JP50645512. This research has also
made use of the NASA/IPAC Extragalactic Database
(NED444https://ned.ipac.caltech.edu

), which is funded by the National Aeronautics and Space Administration and
operated by the California Institute of Technology. This work has used data
from the Asteroid Terrestrial-impact Last Alert System (ATLAS) project. The
Asteroid Terrestrial-impact Last Alert System (ATLAS) project is primarily
funded to search for near-earth asteroids through NASA grants NN12AR55G,
80NSSC18K0284, and 80NSSC18K1575; byproducts of the NEO search include images
and catalogues from the survey area. This work was partially funded by
Kepler/K2 grant J1944/80NSSC19K0112 and HST GO-15889, and STFC grants
ST/T000198/1 and ST/S006109/1. The ATLAS science products have been made
possible through the contributions of the University of Hawaii Institute for
Astronomy, the Queen’s University Belfast, the Space Telescope Science
Institute, the South African Astronomical Observatory, and The Millennium
Institute of Astrophysics (MAS), Chile.

##  Appendix A DATA

Table 3: The $UBVRI$ photometric magnitudes of SN 2018gj.

Date | JD | Phase∗ | $U$ | $B$ | $V$ | $R$ | $I$
---|---|---|---|---|---|---|---
(yyyy-mm-dd) | 2458000+ | (d) | (mag) | (mag) | (mag) | (mag) | (mag)
2018-01-14 | 132.5 |  $+$4.7 | 14.07 $\pm$ 0.01 | 14.75 $\pm$ 0.01 | 14.71 $\pm$ 0.01 | 14.55 $\pm$ 0.01 | 14.43 $\pm$ 0.01
2018-01-16 | 134.5 |  $+$6.7 | 14.18 $\pm$ 0.01 | 14.84 $\pm$ 0.01 | 14.75 $\pm$ 0.01 | 14.54 $\pm$ 0.01 | 14.40 $\pm$ 0.01
2018-01-18 | 136.5 |  $+$8.7 | 14.24 $\pm$ 0.01 | 14.87 $\pm$ 0.01 | 14.79 $\pm$ 0.01 | 14.56 $\pm$ 0.01 | 14.46 $\pm$ 0.01
2018-01-21 | 139.5 |  $+$11.7 | 14.47 $\pm$ 0.01 | 15.00 $\pm$ 0.01 | 14.92 $\pm$ 0.01 | 14.68 $\pm$ 0.01 | 14.55 $\pm$ 0.01
2018-01-24 | 142.5 |  $+$14.7 | 14.66 $\pm$ 0.01 | 15.06 $\pm$ 0.01 | 14.92 $\pm$ 0.01 | 14.65 $\pm$ 0.01 | 14.54 $\pm$ 0.01
2018-01-25 | 143.5 |  $+$15.7 | 14.76 $\pm$ 0.01 | 15.14 $\pm$ 0.01 | 14.97 $\pm$ 0.01 | 14.68 $\pm$ 0.01 | 14.55 $\pm$ 0.01
2018-01-27 | 145.5 |  $+$17.7 | 14.92 $\pm$ 0.02 | 15.21 $\pm$ 0.01 | 14.99 $\pm$ 0.01 | 14.68 $\pm$ 0.01 | 14.55 $\pm$ 0.01
2018-02-02 | 151.5 |  $+$23.7 | 15.45 $\pm$ 0.02 | 15.49 $\pm$ 0.01 | 15.05 $\pm$ 0.01 | 14.70 $\pm$ 0.01 | 14.56 $\pm$ 0.01
2018-02-03 | 152.5 |  $+$24.7 | 15.50 $\pm$ 0.01 | 15.50 $\pm$ 0.01 | 15.05 $\pm$ 0.01 | 14.69 $\pm$ 0.01 | 14.56 $\pm$ 0.01
2018-02-06 | 155.5 |  $+$27.7 | 15.76 $\pm$ 0.02 | 15.61 $\pm$ 0.01 | 15.05 $\pm$ 0.01 | 14.69 $\pm$ 0.01 | 14.51 $\pm$ 0.01
2018-02-10 | 159.5 |  $+$31.7 | 16.09 $\pm$ 0.02 | 15.78 $\pm$ 0.01 | 15.14 $\pm$ 0.01 | 14.74 $\pm$ 0.01 | 14.57 $\pm$ 0.01
2018-02-13 | 162.5 |  $+$34.7 | 16.21 $\pm$ 0.02 | 15.86 $\pm$ 0.01 | 15.14 $\pm$ 0.01 | 14.74 $\pm$ 0.01 | 14.57 $\pm$ 0.01
2018-02-16 | 165.5 |  $+$37.7 | 16.43 $\pm$ 0.02 | 15.99 $\pm$ 0.01 | 15.23 $\pm$ 0.01 | 14.81 $\pm$ 0.01 | 14.62 $\pm$ 0.01
2018-02-18 | 167.5 |  $+$39.7 | 16.53 $\pm$ 0.02 | 16.05 $\pm$ 0.01 | 15.25 $\pm$ 0.01 | 14.82 $\pm$ 0.01 | 14.63 $\pm$ 0.01
2018-02-25 | 174.5 |  $+$46.7 | 16.93 $\pm$ 0.01 | 16.23 $\pm$ 0.01 | 15.33 $\pm$ 0.01 | 14.88 $\pm$ 0.01 | 14.66 $\pm$ 0.01
2018-03-07 | 184.5 |  $+$56.7 | 17.40 $\pm$ 0.01 | 16.51 $\pm$ 0.01 | 15.48 $\pm$ 0.01 | 15.00 $\pm$ 0.01 | 14.85 $\pm$ 0.01
2018-03-14 | 191.5 |  $+$63.7 | – | 16.70 $\pm$ 0.02 | 15.65 $\pm$ 0.01 | 15.12 $\pm$ 0.02 | 14.89 $\pm$ 0.01
2018-03-15 | 192.5 |  $+$64.7 | 17.99 $\pm$ 0.04 | 16.80 $\pm$ 0.01 | 15.65 $\pm$ 0.01 | 15.15 $\pm$ 0.02 | 14.88 $\pm$ 0.01
2018-03-18 | 195.5 |  $+$67.7 | 18.14 $\pm$ 0.03 | 16.94 $\pm$ 0.01 | 15.74 $\pm$ 0.01 | 15.23 $\pm$ 0.01 | 14.95 $\pm$ 0.01
2018-03-23 | 200.5 |  $+$72.7 | 18.69 $\pm$ 0.02 | 17.28 $\pm$ 0.01 | 15.99 $\pm$ 0.01 | 15.40 $\pm$ 0.01 | 15.10 $\pm$ 0.01
2018-03-30 | 207.5 |  $+$79.7 | – | 18.12 $\pm$ 0.02 | 16.66 $\pm$ 0.01 | 15.98 $\pm$ 0.01 | 15.58 $\pm$ 0.01
2018-04-02 | 210.5 |  $+$82.7 | – | 18.61 $\pm$ 0.02 | 17.11 $\pm$ 0.01 | 16.34 $\pm$ 0.01 | 15.93 $\pm$ 0.01
2018-04-03 | 211.5 |  $+$83.7 | – | 18.73 $\pm$ 0.02 | 17.20 $\pm$ 0.01 | 16.44 $\pm$ 0.02 | 16.10 $\pm$ 0.01
2018-04-07 | 215.5 |  $+$87.7 | 20.07 $\pm$ 0.05 | 18.87 $\pm$ 0.02 | 17.36 $\pm$ 0.01 | 16.58 $\pm$ 0.02 | 16.15 $\pm$ 0.02
2018-04-12 | 220.5 |  $+$92.7 | – | 18.91 $\pm$ 0.01 | 17.51 $\pm$ 0.01 | 16.67 $\pm$ 0.01 | 16.22 $\pm$ 0.01
2018-04-15 | 223.5 |  $+$95.7 | – | – | 17.53 $\pm$ 0.01 | 16.72 $\pm$ 0.01 | 16.30 $\pm$ 0.02
2018-04-21 | 229.5 |  $+$101.7 | – | 19.02 $\pm$ 0.01 | 17.60 $\pm$ 0.01 | 16.79 $\pm$ 0.01 | 16.37 $\pm$ 0.02
2018-04-27 | 235.5 |  $+$107.7 | – | 19.11 $\pm$ 0.03 | 17.70 $\pm$ 0.01 | 16.88 $\pm$ 0.01 | 16.44 $\pm$ 0.02
2018-04-28 | 236.5 |  $+$108.7 | – | 19.10 $\pm$ 0.03 | 17.68 $\pm$ 0.02 | 16.85 $\pm$ 0.03 | 16.43 $\pm$ 0.02
2018-04-29 | 237.5 |  $+$109.7 | – | 19.10 $\pm$ 0.02 | 17.68 $\pm$ 0.02 | 16.86 $\pm$ 0.01 | 16.46 $\pm$ 0.02
2018-05-13 | 251.5 |  $+$123.7 | – | – | 17.89 $\pm$ 0.01 | 17.02 $\pm$ 0.02 | 16.62 $\pm$ 0.03
2018-05-19 | 257.5 |  $+$129.7 | – | – | 17.98 $\pm$ 0.01 | 17.09 $\pm$ 0.01 | 16.68 $\pm$ 0.02
2018-05-28 | 266.5 |  $+$138.7 | – | 19.31 $\pm$ 0.03 | 18.13 $\pm$ 0.02 | 17.19 $\pm$ 0.02 | 16.79 $\pm$ 0.02
2018-06-07 | 276.5 |  $+$148.7 | 20.60 $\pm$ 0.05 | 19.47 $\pm$ 0.02 | 18.24 $\pm$ 0.01 | 17.30 $\pm$ 0.01 | 16.90 $\pm$ 0.02
2018-06-11 | 280.5 |  $+$152.7 | – | – | 18.32 $\pm$ 0.01 | 17.37 $\pm$ 0.01 | 16.91 $\pm$ 0.02
2018-06-24 | 293.5 |  $+$165.7 | – | 19.60 $\pm$ 0.02 | 18.49 $\pm$ 0.02 | 17.49 $\pm$ 0.01 | 17.05 $\pm$ 0.02
2018-06-27 | 296.5 |  $+$168.7 | – | 19.62 $\pm$ 0.02 | 18.41 $\pm$ 0.03 | 17.57 $\pm$ 0.01 | 17.12 $\pm$ 0.02
2018-06-30 | 299.5 |  $+$171.7 | – | – $\pm$ – | 18.59 $\pm$ 0.01 | 17.54 $\pm$ 0.01 | 17.11 $\pm$ 0.02
2018-07-05 | 304.5 |  $+$176.7 | – | 19.68 $\pm$ 0.03 | 18.59 $\pm$ 0.01 | 17.60 $\pm$ 0.01 | 17.20 $\pm$ 0.02
2018-08-03 | 334.3 |  $+$206.5 | – | 19.93 $\pm$ 0.04 | 19.02 $\pm$ 0.04 | 18.02 $\pm$ 0.02 | 17.60 $\pm$ 0.03
2018-10-12 | 403.5 |  $+$275.7 | – | – $\pm$ – | 19.85 $\pm$ 0.03 | 18.86 $\pm$ 0.04 | 18.60 $\pm$ 0.03
2018-10-31 | 423.1 |  $+$295.3 | – | 20.78 $\pm$ 0.03 | 20.17 $\pm$ 0.02 | 19.23 $\pm$ 0.05 | 19.01 $\pm$ 0.04

∗ With reference to the explosion date (JD 2458127.8).

Table 4: Swift/UVOT photometry for SN 2018gj

Date | JD | Phase∗ | $UVW2$ | $UVM2$ | $UVW1$ | $UVU$ | $UVB$ | $UVV$
---|---|---|---|---|---|---|---|---
(yyyy-mm-dd) | 2458000+ | (d) | (mag) | (mag) | (mag) | (mag) | (mag) | (mag)
2018-01-16 | 134.6 |  $+$6.8 | 14.11 $\pm$ 0.03 | 13.92 $\pm$ 0.03 | 13.75 $\pm$ 0.03 | 13.70 $\pm$ 0.03 | 14.82 $\pm$ 0.03 | 14.72 $\pm$ 0.04
2018-01-18 | 136.6 |  $+$8.8 | 14.55 $\pm$ 0.03 | 14.33 $\pm$ 0.04 | 14.08 $\pm$ 0.03 | 13.81 $\pm$ 0.03 | 14.83 $\pm$ 0.03 | 14.78 $\pm$ 0.04
2018-01-20 | 139.1 |  $+$11.3 | 15.01 $\pm$ 0.04 | 14.98 $\pm$ 0.06 | 14.51 $\pm$ 0.04 | 13.96 $\pm$ 0.04 | 14.89 $\pm$ 0.04 | 14.90 $\pm$ 0.06
2018-01-22 | 141.4 |  $+$13.6 | 15.50 $\pm$ 0.03 | 15.49 $\pm$ 0.04 | 14.91 $\pm$ 0.03 | 14.20 $\pm$ 0.03 | 14.95 $\pm$ 0.03 | 14.85 $\pm$ 0.04
2018-01-24 | 142.7 |  $+$14.9 | – | – | – | 14.34 $\pm$ 0.03 | 15.05 $\pm$ 0.03 | 14.87 $\pm$ 0.05

∗ With reference to the explosion date (JD 2458127.8).

Table 5: The $JHKs$ photometric magnitudes of SN 2018gj.

Date | JD | Phase∗ | $Ks$ | $H$ | $J$
---|---|---|---|---|---
(yyyy-mm-dd) | 2458000+ | (d) | (mag) | (mag) | (mag)
2018-01-17 | 136.3 | +8.5 | 14.05 $\pm$ 0.09 | – | 14.28 $\pm$ 0.03
2018-01-19 | 138.4 | +10.6 | 13.97 $\pm$ 0.04 | 14.15 $\pm$ 0.03 | 14.20 $\pm$ 0.03
2018-01-30 | 149.3 | +21.5 | 13.88 $\pm$ 0.03 | 14.08 $\pm$ 0.03 | 14.20 $\pm$ 0.02
2018-02-03 | 153.3 | +25.5 | 13.91 $\pm$ 0.03 | 14.10 $\pm$ 0.02 | 14.23 $\pm$ 0.02
2018-02-06 | 156.3 | +28.5 | 13.85 $\pm$ 0.03 | 14.08 $\pm$ 0.02 | 14.13 $\pm$ 0.02
2018-02-07 | 157.3 | +29.5 | 13.84 $\pm$ 0.02 | 14.02 $\pm$ 0.02 | 14.15 $\pm$ 0.02
2018-02-08 | 157.9 | +30.1 | 13.83 $\pm$ 0.03 | 14.05 $\pm$ 0.02 | 14.16 $\pm$ 0.02
2018-02-14 | 164.3 | +36.5 | 13.90 $\pm$ 0.04 | 14.05 $\pm$ 0.03 | 14.21 $\pm$ 0.02
2018-02-16 | 166.2 | +38.4 | 14.00 $\pm$ 0.04 | 14.08 $\pm$ 0.02 | 14.23 $\pm$ 0.02
2018-02-21 | 171.2 | +43.4 | 14.06 $\pm$ 0.04 | 14.14 $\pm$ 0.03 | 14.18 $\pm$ 0.02
2018-02-26 | 176.3 | +48.5 | 13.92 $\pm$ 0.04 | 14.09 $\pm$ 0.03 | 14.24 $\pm$ 0.02
2018-02-27 | 177.0 | +49.2 | – | – | 14.24 $\pm$ 0.02
2018-03-01 | 179.2 | +51.4 | 14.01 $\pm$ 0.03 | 14.19 $\pm$ 0.02 | 14.32 $\pm$ 0.02
2018-03-09 | 187.3 | +59.5 | 14.02 $\pm$ 0.03 | 14.23 $\pm$ 0.02 | 14.31 $\pm$ 0.02
2018-03-11 | 189.3 | +61.5 | 13.96 $\pm$ 0.04 | 14.12 $\pm$ 0.03 | 14.29 $\pm$ 0.02
2018-03-12 | 190.3 | +62.5 | 14.07 $\pm$ 0.04 | 14.19 $\pm$ 0.03 | 14.34 $\pm$ 0.02
2018-03-17 | 195.2 | +67.4 | 14.15 $\pm$ 0.04 | 14.30 $\pm$ 0.02 | 14.41 $\pm$ 0.02
2018-03-22 | 200.1 | +72.3 | 14.13 $\pm$ 0.03 | 14.43 $\pm$ 0.02 | 14.57 $\pm$ 0.02
2018-03-25 | 203.2 | +75.4 | 14.30 $\pm$ 0.04 | 14.51 $\pm$ 0.03 | 14.66 $\pm$ 0.02
2018-03-28 | 206.1 | +78.4 | 14.45 $\pm$ 0.05 | 14.62 $\pm$ 0.03 | 14.87 $\pm$ 0.02
2018-03-30 | 208.1 | +80.4 | 14.72 $\pm$ 0.04 | 14.85 $\pm$ 0.03 | 15.06 $\pm$ 0.02
2018-04-01 | 210.2 | +82.4 | – | 15.03 $\pm$ 0.04 | 15.31 $\pm$ 0.04
2018-04-02 | 211.2 | +83.4 | 14.98 $\pm$ 0.08 | 15.09 $\pm$ 0.04 | 15.38 $\pm$ 0.04
2018-04-07 | 216.3 | +88.5 | 15.19 $\pm$ 0.05 | 15.50 $\pm$ 0.03 | 15.77 $\pm$ 0.03
2018-04-08 | 217.2 | +89.4 | – | 15.47 $\pm$ 0.04 | 15.74 $\pm$ 0.03
2018-04-12 | 221.3 | +93.5 | 15.28 $\pm$ 0.05 | 15.56 $\pm$ 0.04 | 15.9 $\pm$ 0.04
2018-04-15 | 224.3 | +96.5 | 15.25 $\pm$ 0.09 | 15.62 $\pm$ 0.05 | 15.93 $\pm$ 0.04
2018-04-17 | 226.3 | +98.5 | 15.37 $\pm$ 0.09 | 15.57 $\pm$ 0.04 | 15.91 $\pm$ 0.03
2018-04-21 | 230.3 | +102.5 | – | 15.69 $\pm$ 0.05 | 15.94 $\pm$ 0.04
2018-04-22 | 231.3 | +103.5 | 15.43 $\pm$ 0.09 | 15.63 $\pm$ 0.05 | 15.98 $\pm$ 0.04
2018-04-28 | 237.2 | +109.4 | 15.48 $\pm$ 0.10 | 15.79 $\pm$ 0.07 | 16.08 $\pm$ 0.06
2018-04-30 | 239.2 | +111.4 | 15.47 $\pm$ 0.13 | 15.82 $\pm$ 0.07 | –
2018-05-09 | 248.2 | +120.4 | 15.74 $\pm$ 0.11 | 16.08 $\pm$ 0.06 | 16.36 $\pm$ 0.03
2018-05-11 | 250.1 | +122.3 | 15.68 $\pm$ 0.12 | 16.05 $\pm$ 0.05 | 16.38 $\pm$ 0.05
2018-05-12 | 251.2 | +123.4 | – | – | 16.42 $\pm$ 0.05
2018-05-21 | 260.1 | +132.3 | 15.87 $\pm$ 0.16 | 16.48 $\pm$ 0.05 | 16.57 $\pm$ 0.04
2018-05-23 | 262.2 | +134.4 | 15.91 $\pm$ 0.12 | 16.50 $\pm$ 0.07 | 16.66 $\pm$ 0.04
2018-05-31 | 270.2 | +142.4 | 16.17 $\pm$ 0.11 | 16.67 $\pm$ 0.07 | 16.79 $\pm$ 0.06
2018-06-04 | 274.2 | +146.4 | 16.23 $\pm$ 0.27 | – | 16.76 $\pm$ 0.08
2018-06-16 | 286.1 | +158.3 | 16.84 $\pm$ 0.20 | 17.02 $\pm$ 0.12 | 16.91 $\pm$ 0.04
2018-07-12 | 312.1 | +184.3 | – | 17.64 $\pm$ 0.23 | –
2018-08-01 | 332.0 | +204.2 | – | – | 17.97 $\pm$ 0.09

∗ With reference to the explosion date (JD 2458127.8).

Table 6: Log of spectroscopic observations of SN 2018gj.

Date | JD | Phase | Range
---|---|---|---
(yyyy-mm-dd) | (2458000+) | (d) | (Å)
2018-01-14 | 132.5 |  $+$4.7 | 3500–9250
2018-01-16 | 134.5 |  $+$6.7 | 3500–9250
2018-01-18 | 136.5 |  $+$8.7 | 3500–9250
2018-01-21 | 139.5 |  $+$11.7 | 3500–9250
2018-01-24 | 142.5 |  $+$13.7 | 3500–9250
2018-01-25 | 143.5 |  $+$15.7 | 3500–9250
2018-01-27 | 145.5 |  $+$17.7 | 3500–9250
2018-02-02 | 151.5 |  $+$23.7 | 3500–9250
2018-02-03 | 152.5 |  $+$24.7 | 3500–9250
2018-02-06 | 155.5 |  $+$27.7 | 3500–9250
2018-02-13 | 162.5 |  $+$34.7 | 3500–9250
2018-02-16 | 165.5 |  $+$37.7 | 3500–9250
2018-02-18 | 167.5 |  $+$39.7 | 3500–9250
2018-02-20 | 169.5 |  $+$41.7 | 3500–9250
2018-02-25 | 174.5 |  $+$46.7 | 3500–9250
2018-03-14 | 191.5 |  $+$63.7 | 3500–9250
2018-03-15 | 192.5 |  $+$64.7 | 3500–9250
2018-03-18 | 195.5 |  $+$67.7 | 3500–9250
2018-03-23 | 200.5 |  $+$72.7 | 3500–9250
2018-03-30 | 207.5 |  $+$79.7 | 3500–9250
2018-04-02 | 210.5 |  $+$82.7 | 3500–9250
2018-04-07 | 215.5 |  $+$87.7 | 3500–9250
2018-04-15 | 223.5 |  $+$95.7 | 3500–7800
2018-04-21 | 229.5 |  $+$101.7 | 3500–9250
2018-04-27 | 235.5 |  $+$107.7 | 3500–9250
2018-05-01 | 239.5 |  $+$111.7 | 3500–9250
2018-05-28 | 266.5 |  $+$138.7 | 3500–9250
2018-06-11 | 280.5 |  $+$152.7 | 3500–7800
2018-06-29 | 297.5 |  $+$168.7 | 3500–9250
2018-10-04 | 396.1 |  $+$268.3 | 5200–9250
2018-10-31 | 423.1 |  $+$295.3 | 3500–7800

∗ With reference to the explosion date (JD 2458127.8).

Table 7: Type II SN data used in comparison and estimating mean colour
evolution.

S.No | SN | Reference | S.No. | SN | Reference | S.No. | SN | Reference
---|---|---|---|---|---|---|---|---
1 | 1992H | Clocchiatti et al. (1996) | 16 | 2006au | Taddia et al. (2012) | 31 | 2013by | $\dagger$
2 | 1992af | * | 17 | 2007it | * | 32 | 2013fs | $\dagger$
3 | 1992ba | * | 18 | 2007pk | Inserra et al. (2013) | 33 | LSQ13dpa | $\dagger$
4 | 1997D | Hamuy (2003) | 19 | 2008gz | Roy et al. (2011) | 34 | 2013hj | Bose et al. (2016)
5 | 1999em | * | 20 | 2008in | * | 35 | 2014G | $\dagger$
6 | 1999gi | Leonard et al. (2002b) | 21 | 2009E | Pastorello et al. (2012) | 36 | 2014cx | $\dagger$
7 | 2000cb | Kleiser et al. (2011) | 22 | 2009N | * | 37 | 2014dw | $\dagger$
8 | 2002hx | * | 23 | 2009bw | Inserra et al. (2012) | 38 | ASASSN-14ha | $\dagger$
9 | 2003gd | * | 24 | 2009ib | Takáts et al. (2015) | 39 | 2016X | Huang et al. (2018)
10 | 2004dj | Zhang et al. (2006) | 25 | 2009md | Fraser et al. (2011) | 40 | 2016bkv | Nakaoka et al. (2018)
11 | 2004et | Sahu et al. (2006b) | 26 | 2012A | Inserra et al. (2012) | 41 | 2017eaw | Tsvetkov et al. (2018)
12 | 2004fx | * | 27 | 2012aw | Bose et al. (2013) | 42 | 2018ivc | Bostroem et al. (2020)
13 | 2005af | * | 28 | 2012ec | Barbarino et al. (2015) | 43 | 2018zd | Zhang et al. (2020)
14 | 2005cs | Pastorello et al. (2006) | 29 | 2013K | Tomasella et al. (2018) | 44 | 2020jfo | Teja et al. (2022)
15 | 2006V | Taddia et al. (2012) | 30 | 2013ab | $\dagger$ | - | - | -

* Anderson et al. (2014a), $\dagger$Valenti et al. (2016)

##  Appendix B EPM distance to SN 2018gj

Figure 21: EPM distance estimates for various filter sets and different
dilution factors from Hamuy et al. (2001), Dessart & Hillier (2005) and Vogl
et al. (2019)

The implementation of expanding photosphere method (EPM) was followed as per
the details given in (Hamuy et al., 2001) and (Dessart & Hillier, 2005). This
formalism involves the measurements of two radii associated with SN i) a
photometric angular radius ($\theta$) and ii) a spectroscopic physical radius
(R). With the aid of these two radii, the distance to SN could be derived. The
angular radius ($\theta$) is given as:

$\rm\theta=\frac{R}{D}=\sqrt{\frac{f_{\lambda}}{\pi
B_{\lambda}(T)10^{-0.4A(\lambda)}\zeta_{\lambda}^{2}}},$

where, D is the distance to the SN. $B_{\lambda}(T)$ is the Planck function at
the colour temperature of the blackbody radiation, $f_{\lambda}$ is the
apparent flux density, A($\lambda$) is the dust extinction, and
$\zeta_{\lambda}$ is the dilution factor to account for the deviation from a
black body (Hamuy et al., 2001). The above equation could be transformed in
terms of apparent magnitudes ($m_{\lambda}$) for multiband photometry as:

$\rm
m_{\lambda}=-5log(\zeta_{\lambda})-5log(\theta)+A_{\lambda}+b_{\lambda}(T),$

Now, for different filters set (S) above equation was minimized with
$b_{\lambda}$ values being taken from Hamuy et al. (2001), and dilution
factors have been considered from three different works viz. Hamuy et al.
(2001), Dessart & Hillier (2005) and Vogl et al. (2019). The quantity that was
minimized is as follows:

$\rm\varepsilon=\sum_{\lambda\epsilon
S}\left[m_{\lambda}+log(\theta_{S}\zeta_{S})-A_{\lambda}-b_{\lambda}(T_{S})\right]^{2}$

Finally, using the expansion velocity ($v$) measured using spectra could be
used in the following equation:

$\frac{\theta_{i}}{v_{i}}\approx\frac{(t_{i}-t_{0})}{D}$

, where subscript i implies for each epoch available. A straight line could be
fit for multiple epochs, and the resulting slope is used to get estimates of
the distance.

##  Appendix C Scaling relation for probable progenitor

Scaling relations obtained in the Goldberg et al. (2019) that give a set of
probable explosions which could yield observed bolometric light curve can be
used for initial model guess in MESA models. These relations are solved to
obtain $\rm M_{ej}$ and $\rm E_{exp}$ as a function of $\rm M_{Ni}$, $\rm
L_{50}$, $\rm t_{p}$, and $\rm R$ as:

$\rm\log(E_{51})=-0.728+2.148\log(L_{42})-0.280\log(M_{Ni})+2.091\log(t_{p,2})-1.632\log(R_{500})$
(C1)

, and

$\rm\log(M_{10})=-0.947+1.474\log(L_{42})-0.518\log(M_{Ni})+3.867\log(t_{p,2})-1.120\log(R_{500})$
(C2)

where $\rm E_{51}$ is explosion energy in the units $\rm 10^{51}~{}ergs$, $\rm
M_{10}$ is the ejecta mass in the units $\rm 10~{}M_{\odot}$, $\rm M_{Ni}$ has
$\rm M_{\odot}$ unit, $\rm L_{42}=$ Luminosity at 50 days/$\rm
10^{42}~{}erg~{}s^{-1}$, $\rm R_{500}=$ Progenitor Radius/500 $\rm R_{\odot}$,
and $\rm t_{p,2}=$ Plateau length/100 d.

Figure 22: Scaling relations (Goldberg et al., 2019) in the context of Type
IIP SNe as applicable to SN 2018gj.

##  Appendix D Model Light curves and velocity evolution for 19 $\rm
M_{\odot}$ Models

Figure 23: Variations in 19 $\rm M_{\odot}$ ZAMS model using different
parameters to achieve a shorter plateau length. Zoomed out a plot in the
bottom left shows the variation in explosion energy for different model light
curves around the plateau transition. The second plot in the right inset shows
the corresponding Fe 5169 velocities obtained using models. All the 19 $\rm
M_{\odot}$ models underestimate the velocity evolution.

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