# SN 2021wvw: A core-collapse supernova at the sub-luminous, slower, and
shorter end of Type IIPs

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  Jared A. Goldberg Center
for Computational Astrophysics, Flatiron Institute, 162 5th Ave, New York, NY
10010, USA  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  Avinash Singh Oskar Klein Centre, Department of Astronomy, Stockholm
University, Albanova University Centre, SE-106 91 Stockholm, Sweden  Hiroshima
Astrophysical Science Center, Hiroshima University, Higashi-Hiroshima,
Hiroshima 739-8526, Japan  Vishwajeet Swain Department of Physics, Indian
Institute of Technology Bombay, Powai, Mumbai 400076  Varun Bhalerao
Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai
400076

###### Abstract

We present detailed multi-band photometric and spectroscopic observations and
analysis of a rare core-collapse supernova SN 2021wvw, that includes
photometric evolution up to 250 d and spectroscopic coverage up to 100 d post-
explosion. A unique event that does not fit well within the general trends
observed for Type II-P supernovae, SN 2021wvw shows an intermediate luminosity
with a short plateau phase of just about 75 d, followed by a very sharp
($\sim$10 d) transition to the tail phase. Even in the velocity space, it lies
at a lower velocity compared to a larger Type II sample. The observed peak
absolute magnitude is $-16.1$ mag in $r$-band, and the nickel mass is well
constrained to $0.020\pm 0.006~{}M_{\odot}$. Detailed hydrodynamical modeling
using MESA+STELLA suggests a radially compact, low-metallicity, high-mass Red
Supergiant progenitor ($M_{ZAMS}=18~{}M_{\odot}$), which exploded with
$\rm\sim 0.2\times 10^{51}~{}erg~{}s^{-1}$ leaving an ejecta mass of
$M_{ej}\approx 5~{}M_{\odot}$. Significant late-time fallback during the shock
propagation phase is also seen in progenitor+explosion models consistent with
the light curve properties. As the faintest short-plateau supernova
characterized to date, this event adds to the growing diversity of
transitional events between the canonical $\sim$100 d plateau Type IIP and
stripped-envelope events.

Core-collapse supernovae (304); Type II supernovae(1731); Supernova dynamics
(1664); Red supergiant stars(1375); Supernovae (1668); Observational
astronomy(1145)

††facilities: HCT: 2-m, GIT: 0.7-m, ZTF, ATLAS††software: astropy (Astropy
Collaboration et al., 2013, 2018, 2022), ds9 (Smithsonian Astrophysical
Observatory, 2000), emcee (Foreman-Mackey et al., 2013), IRAF (Tody, 1993),
Jupyter-notebook (Kluyver et al., 2016), matplotlib (Hunter, 2007), MESA,
numpy (Harris et al., 2020), pandas (Wes McKinney, 2010; pandas development
team, 2020), plot_atlas_fp.py (Young, 2020) scipy (Virtanen et al., 2020),
STELLA, SYNAPPS

##  1 Introduction

Stars with mass $\rm\gtrsim 8~{}M_{\odot}$ end their lives as energetic cosmic
explosions called core-collapse supernovae (CCSNe). Depending on factors such
as the initial mass, rotation, evolutionary track, retained envelope,
immediate surroundings, and explosion energy, their light curves come in
various shapes and brightness, and there are differences in their spectral
features as well. Persistent hydrogen features in the spectra indicate a Type
II class SN; otherwise, a Type I SN (Filippenko, 1997). There is a further
distinction in the light curve evolution of the Type IIs, with either a linear
decline (Type IIL) or with a slow, plateau-like decline (Type IIP) followed by
a linear decline (Barbon et al., 1979). Although appearing distinct, it is
becoming increasingly evident that there is no clear boundary between the IIP
and IIL subclasses, and these are merely a continuous sequence of the Type II
class (Anderson et al., 2014; Pessi et al., 2019).

Within the Type IIP subclass, there appears to be a certain amount of
inhomogeneity concerning the plateau length. In most cases, the plateau length
is, on an average, 100 d. However, recent observations have shown several
events that deviate from this 100 d plateau length on either side, from the
shorter end of the plateau ($\sim 4\%$, Eldridge et al., 2018; Hiramatsu et
al., 2021) to the long plateau phase ($\rm\sim 0.35\%~{}for~{}>140~{}d$,
Eldridge et al., 2018). A few examples of the short plateau SNe are SN 2006Y
(55 d), SN 2006ai (60 d) (Hiramatsu et al., 2021), SN 2020jfo (65 d)
(Sollerman et al., 2021; Teja et al., 2022), and SN 2018gj (70 d) (Teja et
al., 2023a), while SN 2005cs (110 d) (Tsvetkov et al., 2006; Pastorello et
al., 2009), SN 2018hwm (130 d) (Reguitti et al., 2021), and SN 2020cxd (120
d), SN 2021aai (140 d), (Valerin et al., 2022) had a longer plateau duration.
In addition, there is also a very heterogeneous distribution in the brightness
space for this subclass (Valenti et al., 2016). With more discoveries and
extensive follow-up in recent times, many events are found to be intrinsically
fainter compared to typical Type II SNe (mean $\rm M_{Vmax}\sim-16.7$,
Anderson et al., 2014) and are termed as low ($\rm M_{V}\geq-15~{}mag$) or
intermediate ($\rm M_{V}\approx-16~{}mag$) luminosity SNe. These
low/intermediate luminosity SNe also predominantly show a plateau length of
100 d or more (for instance $\geq 140$ d in SN 2016bkv, Nakaoka et al., 2018;
Valerin et al., 2022; Fang et al., 2024). Current understanding attributes
these SNe to originate from weak explosions of the lower mass end of the red
supergiant (RSG) stars, typically less than 15 $\rm M_{\odot}$ with low
$\rm{}^{56}Ni$ mass production (Pumo et al., 2017; Lisakov et al., 2018).

On the other hand, several short-plateau SNe (50 - 80 d) studies show these to
be brighter than the typical Type IIP SNe (Hiramatsu et al., 2021; Teja et
al., 2022), with the low-luminosity, short plateau events being infrequent.
Type II SNe with short plateau also tend to decline faster during their
plateau phase (Hiramatsu et al., 2021). The favored mechanism for these short
plateau SNe is still debated. A common trend is that the lightcurve properties
require a small but non-negligible H-rich envelope ($\approx$ a few
$M_{\odot}$) at the time of explosion (Hiramatsu et al., 2021). Single-star
evolutionary scenarios tend to favor moderate to high initial mass RSGs, as
stronger winds in more massive progenitors provide a channel for stars to lose
the majority but not the entirety of their H-rich envelope (see, e.g. Dessart
et al., 2010; Sukhbold et al., 2016; Curtis et al., 2021). Other theoretical
works remain agnostic to the mass-loss mechanism or directly link low envelope
mass with binary interaction (e.g. Morozova et al., 2015; Paxton et al., 2018;
Dessart et al., 2024), and a growing body of observational works investigate
potential low-mass RSG origins as well (Teja et al., 2022, 2023a; Utrobin &
Chugai, 2024) with one being a direct detection (Sollerman et al., 2021). In
both progenitor-mass regimes, the envelope mass lost by the progenitor is
high.

The occurrence of the short plateau events is relatively low. While the low
luminosity ones might suffer from an observational bias, this cannot be said
about most short plateau events since they are usually bright. Even taking
binarity into account, population-focused studies (e.g. Eldridge et al., 2018;
Ercolino et al., 2024) nonetheless indicate their rates are expected to be low
($\sim 4\%$).

This work presents comprehensive optical spectroscopic and photometric
observations of SN 2021wvw, a distinctive short plateau Type IIP supernova. SN
2021wvw (other names: PS21jnb, ZTF21abvcxel, ATLAS21bgtz, Gaia21eqm) was
discovered on August 24, 2021 14:32.6UT (JD=2459451.1) in UGC 02605 (Jones et
al., 2021) with 17.93 ABMag in the $i-P1$ filter. Subsequently, it was
classified as Type II with a strong blue continuum having P-Cygni H$\alpha$
and H$\beta$ emissions (Hinkle, 2021). The first detection in ZTF-$g$ filter
(19.34 mag) was on JD 2459449.95 and the last non-detection in ZTF-$r$ filter
(19.15 mag) was on JD 2459449.91. Using this, we obtain JD $2459449.93\pm
0.02$ as the explosion epoch. A similar epoch, shifted by $+$0.2 d, is
obtained using data from ATLAS forced photometry server with 5-$\sigma$ last
non-detection ($>$18.89 mag) on JD 2459449.1 and first detection
(18.10$\pm$0.08 mag) on JD 2459451.1 both in ATLAS-$o$ filter. The non-
detections in both ZTF-$r$ and ATLAS-$o$ are at a similar epoch, hence we
consider this as the last non-detection, and the first detection in ZTF-$g$
band. Using this we obtain $t_{exp}=2459449.9\pm 0.3$ as the explosion epoch
and use this throughout. The location of SN 2021wvw in its host galaxy is
marked in Figure 1.

The structure of this paper is as follows: Section 2 provides details of
various data sources utilized. The light curves and spectra are analyzed and
compared in Section 3 and 4 respectively along with estimating $\rm{}^{56}Ni$
mass and expansion velocities. Section 5 explores the probable progenitor
using various models, including complete hydrodynamical modeling, followed by
a general discussion in Section 6. Eventually, we summarize this work in
Section 7.

Figure 1: RGB color composite finder chart for SN2021wvw utilizing
Bessell-$BVR$ filters from HCT.

##  2 Photometry and Spectroscopy: Data sources

Table 1: Log of spectroscopic observations of SN 2021wvw obtained from HCT.

Date | JD | Phase† | Range
---|---|---|---
(yyyy-mm-dd) | (2459000+) | (d) | (Å)
2021-08-28 | 455.4 | 5.5 | 4000-7700
2021-09-13 | 471.3 | 21.4 | 4000-8900
2021-09-18 | 476.3 | 26.3 | 4000-8900
2021-09-19 | 477.4 | 27.4 | 4000-7700
2021-09-29 | 487.3 | 37.3 | 4000-8900
2021-10-02 | 490.2 | 40.3 | 4000-8900
2021-10-09 | 497.2 | 47.3 | 4000-8900
2021-10-10 | 498.2 | 48.3 | 4000-8900
2021-10-14 | 502.2 | 52.2 | 4000-8900
2021-10-19 | 507.2 | 57.3 | 4000-8900
2021-10-21 | 509.1 | 59.2 | 4000-8900
2021-10-22 | 510.2 | 60.3 | 5300-8900
2021-10-26 | 514.2 | 64.2 | 4000-8900
2021-10-30 | 518.2 | 68.3 | 4000-8900
2021-11-08 | 527.1 | 77.2 | 4000-8900
2021-11-15 | 534.3 | 84.4 | 4000-8900
2021-11-26 | 545.1 | 95.1 | 4000-7700

†Phase given for $t_{exp}=2459449.9$ JD

We began photometry of SN 2021wvw in the optical since +8.4 d past explosion
using the 0.7-m robotic GROWTH-India Telescope (GIT, Kumar et al., 2022) and
the 2.0-m Himalayan Chandra Telescope (HCT), both situated at the Indian
Astronomical Observatory (IAO, Prabhu, 2014), Hanle, India. GIT covered dense
multi-band photometry in SDSS-$g^{\prime}r^{\prime}i^{\prime}z^{\prime}$
filters, and HCT covered photometry in Bessell-$V$ and -$R$ filters. We
supplemented our observations with photometry from the Asteroid Terrestrial-
impact Last Alert System (ATLAS, Tonry et al., 2018; Smith et al., 2020)
forced photometry server (Shingles et al., 2021) in $c$ and $o$ filters. We
also obtained ZTF (Bellm et al., 2019) -$g$ and -$r$ filter apparent
magnitudes from ALeRCE (Förster et al., 2021). The ATLAS photometry, being
noisy, has been binned for 2 d intervals in the late phase using Young (2020)
python script. During the late phase, we took multiple exposures using GIT and
HCT and summed them for a better signal-to-noise ratio in respective filters.
The SN being far away from the host nucleus ($\sim$ 31′′) and at the
periphery, we do not perform any template subtraction. The last detected
photometric points are significantly brighter (1.5-3 mag) than the SDSS
photometry111https://skyserver.sdss.org/dr18/ in the regions around the host
center and near the SN position. Standard photometric data reduction
procedures have been adopted utilizing IRAF and pyraf, the details of which
can be found in Teja et al. (2023a). The photometric data are tabulated in the
Appendix of this work.

We obtained low-resolution ($\rm R\sim 800$) optical spectra with the HFOSC
instrument available on HCT using 167l slit (1.$\arcsec$92 width and
11$\arcmin$ length). The spectra observed with grisms Gr7 and Gr8 were
combined to obtain spectra covering a wavelength range of 4000 to 9000 Å. The
optical spectra were obtained during 5 - 95 d post-explosion. Beyond 95 d, the
SN faded considerably, and spectroscopy with HCT was not feasible. The
observed 2-D spectra were bias corrected using nightly bias frames, and the
1-D spectra were optimally extracted. The wavelength correction was performed
using the dispersion solutions obtained from several arc lamps (FeNe, FeAr)
spectra. The night-sky emission lines (5577, 6300, 6363 Å) in the background
spectra were used to perform the accurate wavelength calibrations, applying
small shifts wherever required. Spectrophotometric standards were observed
periodically to correct the instrumental response and finalize the spectra in
the flux scale. Eventually, a single flux-calibrated spectrum was obtained
after combining spectra from individual grisms. All these steps were performed
using various tasks in IRAF.

The host redshift (z=0.0099, Schneider et al. (1992)) and line of sight
extinction ($E(B-V)=0.24$ mag, Schlafly & Finkbeiner (2011)) are taken from
NED and IRSA, respectively. The redshift corresponds to a distance of
$41.51\pm 2.91$ Mpc or $\mu=33.09\pm 0.15$ mag, assuming the $\Lambda CDM$
cosmology with H$\rm{}_{0}=72.5~{}km~{}s^{-1}~{}Mpc^{-1}$ (Riess et al.,
2022). We used Cardelli et al. (1989) extinction law with $R_{V}=3.1$ to
correct for Galactic reddening. We do not find any discernible Na ID features
at redshift of the host galaxy in SN spectra, and hence assume no extinction
due to the host galaxy.

##  3 Light Curve Evolution

Figure 2: Light curve evolution of SN 2021wvw for various filters from GIT and
HCT is shown. The light curves also include data from ZTF and ATLAS surveys.
The constants added to the individual light curves are for visual clarity.

We present the panchromatic light curve evolution of SN 2021wvw in Figure 2.
The light curve evolution spans roughly 220 d post-explosion. Other than the
bluer bands such as $g$-band, the light curves evolution in different filters
show a very flat evolution up to 70 to 80 d before transitioning sharply into
the tail phase. The plateau and transition phases are very densely sampled in
most filters. In $R$ and $V$ filters, the tail phase is sampled up to 220 d.
We estimate a plateau length of around 75 d (OPTd, Anderson et al., 2014) and
a sharp transition period of about 10 d.

The mid-plateau absolute magnitude is $\rm\approx-16.0\pm 0.1~{}mag$ in
$r$-band. It puts SN 2021wvw in the intermediate luminosity regime for Type
IIP SNe. The duration of the plateau phase is also shorter ($\sim 75$ d),
whereas the typical plateau lengths for Type IIP SNe are $\sim$100 d and even
longer in the case of under-luminous SNe (SN 2005cs, SN 2016bkv, SN 2021gmj).
In Figure 3, SN 2021wvw $r$-band light curve is compared with $r/R$-band light
curves of other intermediate/low luminosity and short plateau SNe,
respectively. We compare with the archetypal SN 2005cs (Pastorello et al.,
2006) and SN 2021gmj (Murai et al., 2024) for low luminosity SNe. Although
short plateaus are very rare in the overall Type II SNe, we compare with other
well-studied short plateau SNe in literature such as SN 2006Y, SN 2006ai, SN
2016egz (Hiramatsu et al., 2021), SN 2018gj (Teja et al., 2023a), SN 2020jfo
(Teja et al., 2022) and SN 2023ixf Teja et al. (2023b); Singh et al. (2024).

Figure 3: SN 2021wvw $r$ band light curve evolution is compared with the $r/R$ band light curves of other short plateau SNe. We also show the archetypal low-luminosity SN 2005cs and an intermediate-luminosity SN 2021gmj. Table 2: Various slopes obtained for different phases of light curves are presented. Slopes and absolute magnitude for other SNe are also compared. The absolute magnitudes ($M_{r/R}$) are reported from the middle of the plateau. SN | $g\ [mag~{}(100~{}d)^{-1}]$ | $r/R\ [mag~{}(100~{}d)^{-1}]$ | $i\ [mag~{}(100~{}d)^{-1}]$ | $M_{r/R}$
---|---|---|---|---
| s1 | s2 | s1 | s2 | s3 | s2 | s3 | [mag]
2021wvw | $2.52\pm 0.53$ | $1.25\pm 0.16$ | $0.34\pm 0.19$ | $0.78\pm 0.17$ | $0.64\pm 0.28$ | $0.10\pm 0.13$ | $1.09\pm 0.25$ | $-16.0$
2005cs | - | - | - | $-0.53\pm 0.01$ | $0.60\pm 0.02$ | - | - | $-15.2$
2006Y | $4.62\pm 0.51$ | $3.28\pm 0.10$ | $4.75\pm 0.13$ | $0.29\pm 0.20$ | - | $1.22\pm 0.10$ | - | $-17.3$
2006ai | $4.44\pm 0.05$ | $2.86\pm 0.06$ | $4.01\pm 0.10$ | $0.96\pm 0.04$ | $1.03\pm 0.13$ | $1.01\pm 0.04$ | $1.53\pm 0.19$ | $-17.5$
2016egz | - | $2.83\pm 0.19$ | - | $0.89\pm 0.13$ | $1.11\pm 0.04$ | $1.51\pm 0.17$ | $1.10\pm 0.10$ | $-17.6$
2021gmj | - | - | - | $0.25\pm 0.01$ | $0.51\pm 0.11$ | $1.28\pm 0.02$ | $1.27\pm 0.03$ | $-15.9$

The photospheric phase light curve evolution of SN 2021wvw, particularly for
$r$\- and $i$\- bands, is gradual, which is atypical for short plateau SNe,
for which the decline is generally rapid (Hiramatsu et al., 2021). Although
the early ($s1$) phase after maximum is not evident in the multi-band light
curves, upon closer inspection, the $g$\- and $r$\- bands show a gradual
decline in the post-peak evolution. We find this to be $\rm
2.52^{+0.52}_{-0.53}~{}mag~{}100~{}d^{-1}$ and $\rm
0.34^{+0.19}_{-0.19}~{}mag~{}100~{}d^{-1}$ in $g$\- and $r$\- band,
respectively, whereas the decline is much steeper in other objects: for
example, SN 2006Y and SN 2006ai have $\rm
4.62^{+0.51}_{-0.52}~{}mag~{}100~{}d^{-1}$ and $\rm
4.44^{+0.05}_{-0.05}~{}mag~{}100~{}d^{-1}$ respectively in $g$-band. We also
estimated the decline rates of the plateau phase (s2) and tail phase (s3). The
estimated values of various slopes and the mid-plateau absolute magnitudes are
shown in Table 2. Interestingly, the plateau phase in the $i-$ band for SN
2021wvw is almost non-declining with $\rm s2=0.10\pm
0.13~{}mag~{}100~{}d^{-1}$, whereas for other SNe, both with lower luminosity
and shorter-plateau SNe, it is around an order of magnitude higher. Evidently,
the tail phase decline ($\rm s3=0.64\pm 0.28mag~{}100~{}d^{-1}$) of SN 2021wvw
in the $r$-band is close to the values obtained for other lower luminosity SNe
(SN 2021gmj, SN 2005cs). At a similar phase, slope s3 in the $i$-band is non-
differentiable for both low-luminosity and short-plateau SNe with values
ranging from 1.1 to 1.5 mag$\rm~{}100~{}d^{-1}$.

Comparing the mid-plateau luminosity ($\rm M_{tp1/2}$) in $r/R$-band with
other SNe, we find that SN 2021wvw has a similar magnitude as of SN 2021gmj
($\rm-15.9~{}mag$), and about $\rm 1~{}mag$ higher than the $\rm M_{tp1/2}$ of
SN 2005cs ($\rm-15.2~{}mag$). $\rm M_{tp1/2}$ of a majority of other short-
plateau SNe is higher than $\rm-17~{}mag$ except for SN 2018gj
($\rm-16.7~{}mag$) as shown in Figure 3.

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

The late-time evolution is primarily powered by the radioactive decay of
$\rm{}^{56}Ni$ formed during explosive nucleosynthesis. It is the ultimate
powering source in the Type II SNe during the nebular phase. Hence, the late-
time bolometric light curve can provide tight constraints on estimating the
$\rm{}^{56}Ni$ mass. We use SuperBol (Nicholl, 2018) to estimate the pseudo-
bolometric light curve and a complete bolometric light curve evolution from
extrapolated blackbody estimates. The extinction-corrected multi-band light
curves were used as input, taking well-sampled $r$-band as the reference light
curve. The filters utilized for the pseudo-bolometric curves were $groiz$.

We estimate the $\rm{}^{56}Ni$ using the following equation given in Yuan et
al. (2016) which also takes into account the $\gamma-$ray leakage in case of
an stripped envelope:

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

where, $\Delta t=t-t_{exp}$, $\rm L_{0}$, $\rm t_{Co}$, and $\rm t_{Ni}$ are
$\rm 1.41\times 10^{43}\ erg~{}s^{-1}$, $\rm 111.4~{}d$ and $\rm 8.8~{}d$,
respectively. Here, $t_{c}$ is the characteristic time when the optical depth
for $\gamma-$rays approaches unity (Yuan et al., 2016). We use scipy and emcee
packages to fit and estimate errors in the values. Using the pseudo-bolometric
light curve, we estimate $\rm{}^{56}Ni$ mass as $\rm 0.011\pm
0.001~{}M_{\odot}$. This provides a lower limit on the $\rm{}^{56}Ni$ mass. In
addition, considering the blackbody fitted luminosity as bolometric
luminosity, we obtain $\rm M_{{}^{56}Ni}=\rm 0.023\pm 0.003~{}M_{\odot}$,
which we consider as an upper limit for the estimated values. The latter value
is more than twice what was obtained using the pseudo-bolometric light curve,
but, synonymous with a $\sim$ 50% NIR contribution seen in the nebular phase
of SN 2023ixf (Singh et al., 2024). We lack NIR data to provide more
information about the accuracy of the contribution in the late phase.
Nevertheless, the 56Ni mass estimated implies a significant NIR flux
contribution at late phases. Hence, NIR observations for such objects in the
nebular phase are crucial for a better understanding. In subsequent sections,
we perform light curve modeling to constrain the nickel mass and other
parameters more robustly.

##  4 Spectra

We present a complete spectral evolution of SN 2021wvw covering the plateau
and transition phases in Figure 4. The spectra have been calibrated with the
corresponding multi-band fluxes, corrected for the host redshift, and de-
reddened with the estimated extinction. The phases mentioned are with respect
to the estimated explosion epoch. All the well-identified lines are marked for
clarity in the figure.

Figure 4: Spectral sequence for SN 2021wvw. The spectra have been corrected
for absolute flux using corresponding photometry and also de-reddened using MW
LOS extinction.

Figure 5: SYNAPPS model fitting to the observed spectra around the mid and end
plateau phases. The lower small panels show the model spectra of individual
species when the contribution from rest of the species is turned off.

###  4.1 Evolution and comparisons

The first spectrum was obtained at $\rm+5.5~{}d$. The spectrum comprises a
blue continuum with broad Balmer features and He I $\lambda~{}5876$ superposed
on it. After that, there is a gap of around 15 d; the following spectrum is on
+21 d. Thereafter, the spectral evolution is densely sampled until the
supernova enters the nebular phase. Qualitatively, absorption features appear
relatively narrow at first glance compared to typical IIP SNe, indicating
relatively low velocities, and they become narrower with time. Although there
are some hints of Fe II in the bluer region at $\rm+21~{}d$, these features do
not evolve much till $\rm+37~{}d$, after which we start to see Fe II lines
conspicuously. Around $\rm+21~{}d$, we also observe the appearance of Ca NIR
triplet feature in the red-ward region, strengthening as the SN ejecta evolves
further in the photospheric phase. Interestingly, the region between Fe II
lines and H$\alpha$ is devoid of any lines except a weak appearance of Na ID
from $\rm+37~{}d$ onward. Similarly, the region between H$\alpha$ and Ca
triplet lacks any discernible features until the end of the observed
evolution. We observe a band of emission lines between H$\beta$ and H$\gamma$,
usually attributed to Fe lines.

The mid-plateau and end-plateau spectra are modeled using SYNAPPS/Syn++
(Thomas et al., 2011) to better ascertain the minimum number of species
required to explain the observed spectra. SYNAPPS/Syn++ is a direct
implementation of parameterized spectral synthesis code SYNOW (Parrent et al.,
2010). It assumes a spherical symmetry with homologous expansion of the
ejecta. The emission of photons is from a sharp photosphere, with the optical
depth taken as an exponential function of velocity.

$\tau_{ref}(v)=\tau_{ref}(v_{ref})\exp{\left(\frac{v_{ref}-v}{v_{e}}\right)}$

where $v_{ref}$ is reference velocity for parameterization and $v_{e}$ is the
maximum velocity allowed at the outer edge of the line-forming region (Thomas
et al., 2011). For a particular optical depth, the reference line profile is
estimated for a given ion with the remaining lines following Boltzmann
statistics (Parrent et al., 2010). SYNAPPS iteratively generates synthetic
spectra based on a provided input file with parameters such as ions list,
blackbody temperature, expansion velocities, and opacities. The synthetic
spectra thus obtained are compared with the observed spectra for each
iteration. The procedure is automated and requires only initial input
parameters with user-defined ranges for each parameter to constrain the
parameter space physically. SYNAPPS has been predominantly used to model
stripped-envelope and thermonuclear SNe spectra but has been successfully
utilized in a number of hydrogen-rich SNe cases as well (Takáts & Vinkó, 2012;
Sahu et al., 2013; Bostroem et al., 2019; Dastidar et al., 2021).

Figure 6: Spectral comparisons at the early and late plateau phase with short-
plateau SNe and with other sub-luminous SNe.

For the first setup to model the $\rm+37~{}d$ spectrum, we include only five
species namely H I, Ca II, Na I, Sc II and Fe II. The overall best-fit spectra
and various species contributions are shown in Figure 5. The individual
species contributions are obtained by utilizing the best-fit output as input
in syn++ by turning on one species at a time in the input file. No warping
function is applied, i.e., a1=a2=0. Only a0 is varied, which signifies the
flux level. Photospheric velocity obtained on the day $\rm+37~{}d$ is
3830$\rm~{}km~{}s^{-1}$.

For end-plateau spectra at $\rm+77~{}d$, in addition to the previously
included species, we add three more metal species, namely Ba II, Fe I, and O
I. Further, we find that the broad emission band around 4800 Å is a blend of
multiple metal lines originating from neutral Fe, Sc II, and Ba II. The
photospheric velocity obtained from these fits around $\rm+77~{}d$ is
2170$\rm~{}km~{}s^{-1}$.

In Figure 6, we compare the SN 2021wvw spectra with a few other short-plateau
SNe along with the low-luminosity SN 2005cs and intermediate luminosity SN
2021gmj. Firstly, in the top panel of Figure 6, we compare the spectra around
20 d when the metal features are well developed. We clearly observe that there
are similarities as well as dissimilarities in the spectral features. At first
glance, the features appear similar to SN 2005cs and SN 2021gmj, i.e., narrow
and strong absorption. The H$\alpha$ absorption appears shallow, which seems
to be the general trend for the short-plateau SNe and is completely
indiscernible in some of the brighter and fast-declining short-plateau SNe,
for example, SN 2006Y, SN 2006ai, and SN 2016egz. At similar epochs, other SNe
have well-developed metal features such as Fe II lines toward the blue end,
whereas we only see a hint of these lines in SN 2021wvw. In the bottom panel
of the same figure, we compare SN 2021wvw spectra during the end plateau
phase, where we find the appearance of the strongest metallic features.
Comparison spectra for other SNe are taken at similar epochs. The SN 2021wvw
spectra show similar features to other sub-luminous SNe, but the absorption
depths are shallow. However, SN 2021wvw has well-developed P-Cygni (more
representative of a typical Type IIP) profiles compared to much shallower
absorption depths in short-plateau SNe SN 2006Y, SN 2006ai, and SN 2016egz.

###  4.2 Velocities

Figure 7: Expansion velocity evolution estimated from several prominent
metallic features (including Balmer lines) observed in the spectra. The
velocities have been compared with a large sample taken from Gutiérrez et al.
(2017). The shaded region gives the corresponding 1-$\sigma$ scatter around
the sample mean.

We utilize some of the well-resolved absorption features to estimate expansion
velocities of the ejecta. We iteratively measure the absorption minimum of
these lines using IRAF by fitting an inverted Gaussian assuming a multitude of
continuum points. The absorption minima are corrected for redshift and
eventually converted to the expansion velocities using the central rest
wavelengths of the corresponding features. We have estimated these velocities
for six lines as shown in Figure 7. The errors in velocity estimates are much
smaller than the instrumental resolution; hence, the latter has been quoted as
the errors in the velocities.

For the first epoch ($\rm+5.5~{}d$), we could identify the absorption dips
blueward of H$\alpha$ and H$\beta$ rest wavelengths corresponding to $\rm\sim
9,100~{}km~{}s^{-1}$ and $\rm\sim 10,600~{}km~{}s^{-1}$ line velocity
respectively. At $\rm+21~{}d$, apart from Balmer features, we could measure
the velocity from Fe II 5169 Å. Up to $\rm+85~{}d$, the velocities are
measured, and their time evolution is shown in Figure 7. Around $\rm+40~{}d$,
which is proximal to the mid-plateau mark, we measure the H$\alpha$ and Fe II
5169 Å velocities as $\rm\sim 5,700~{}km~{}s^{-1}$ and $\rm\sim
2,800~{}km~{}s^{-1}$, respectively. The SYNAPPS modeling around similar phase
gives a value which is between these two values ($\rm\sim
3830~{}km~{}s^{-1}$). As the ejecta evolves, the expansion velocities keep
decreasing until we can confidently resolve the absorption minimum. Towards
the end of the plateau phase, around +75 d, we find the expansion velocities
to be $\rm\sim 2,000~{}km~{}s^{-1}$ from Fe lines and $\rm\sim
5,100~{}km~{}s^{-1}$ from H$\alpha$. The model spectrum around a similar phase
gives $\rm\sim 2,170~{}km~{}s^{-1}$ as the photospheric velocity, which is
much closer to the values obtained from the metallic features.

We further compare these velocities with the mean expansion velocities
obtained from a larger sample of Type II SNe (Gutiérrez et al., 2017). The
mean velocities and 1-$\sigma$ scatter in these are overplotted in Figure 7.
We see that the SN 2021wvw velocities lie at the lower 1-$\sigma$ end of the
sample, implying that this is a slowly evolving ejecta. For metal lines, the
velocities are even smaller than the lower 1-$\sigma$ edge from the sample.
Around mid-plateau, the difference between the mean velocities of the sample
and SN 2021wvw observed velocities is $\rm\sim 1,500~{}km~{}s^{-1}$.

##  5 Plausible Progenitor

###  5.1 Semi-analytical models

Figure 8: Semi-analytical fit for fixed radii of 500 R⊙. The values provided
in the inset are for the best-matching models.

We attempt to model the bolometric light curve of SN 2021wvw using a two-
component progenitor model (Nagy & Vinkó, 2016) to roughly constrain a few
parameters and motivate detailed modeling. This formulation comprises of a
dense ‘core’ and an extended ‘envelope,’ representing the bulk of the ejecta
and the near-surface layers, respectively. Arnett & Fu (1989) form the basis
of this semi-analytical formulation with subsequent additions by Blinnikov &
Popov (1993); Nagy et al. (2014) to obtain approximate ejecta mass ($\rm
M_{ej}$), progenitor radius ($\rm R_{0}$), energy ($\rm E_{tot}$), and
$\rm{}^{56}Ni$ mass ($\rm M_{Ni}$) estimates. The total energy $\rm E_{tot}$
comprises ejecta kinetic energy ($\rm E_{k}$) and initial thermal energy ($\rm
E_{th}$) deposited by the shock ($\mathrm{E_{tot}=E_{k}+E_{sh}}$). In this
analytical formulation, the SN ejecta, which is spherically symmetric, is
divided into two components: a) an interior core with a constant (or flat)
density; b) an outer less dense shell with an exponential (n=2) density
profile (Nagy & Vinkó, 2016). These components have independent sets of
physical parameters, with the origin of the radius being the same. The
contribution from each component to the light curve is estimated
independently.

There is a degeneracy among various parameters (Nagy & Vinkó, 2016). In a
similar analysis for two other short plateau SNe, SN 2018gj and SN 2020jfo,
the progenitor radii did not match well with the results obtained using
detailed hydrodynamical modeling (Teja et al., 2023a, 2022). So, in this work,
we do not attempt to constrain the radius of the progenitor; instead, we fix
the radius to multiple values beforehand. We take three cases: a fairly
compact progenitor (300 $\rm R_{\odot}$), a typical RSG radius (700 $\rm
R_{\odot}$), and a radius in between (500 $\rm R_{\odot}$). We vary other
parameters to get a light curve matching the observed light curve. Another
caveat to consider is the lack of early UV and $U$-band data, which, in
models, is usually governed by the shell part. This outer envelope could also
act as proximal CSM around the RSG progenitor (Nagy & Vinkó, 2016). Due to
lack of data, no attempts were made to estimate CSM. Instead, we fixed the
shell values (to a negligible contribution) so that they do not affect the
early light curve. Since the models are analytical, the errors are estimated
by first obtaining a match to the observed light curve data, followed by
varying the parameters to fit the upper and lower error bars associated with
the observed light curve. The best parameters obtained for the fixed radii
values are presented in Table 3. We could find that the model fits equally
well with very similar parameters within error bars for each radii value. The
case for 500 $\rm R_{\odot}$ is shown in Figure 8.

The best-fit values of the parameters $\rm M_{ej}$ and $\rm M_{Ni}$ do not
vary much for the different radii considered here. The only considerable
changes are in the energy values. From these models, we find the $\rm M_{ej}$
to be $\rm\sim 6.5~{}M_{\odot}$, $\rm M_{Ni}=0.020\pm 0.005~{}M_{\odot}$, and
a total energy between 1.1 to 1.3 foe. The $\rm M_{ej}$ values for SN 2021wvw
are similar to those obtained in other short plateau cases (for example, SN
2018gj, SN 2020jfo) but with lower explosion energy. The lower energy values
are expected for SN 2021wvw, considering its sub-luminous nature. The total
energy contribution from the core in the case of low-luminosity SN 2005cs is
$\rm\sim 0.5~{}foe$ (Nagy & Vinkó, 2016) with $\rm M_{ej}=8.0~{}M_{\odot}$.
Considering the intermediate brightness of SN 2021wvw and a shorter plateau
length, the estimated parameters are reasonably well constrained with tight
bounds on the $\rm{}^{56}Ni$ mass. Using these values as our reference point,
we delve into more details about the progenitor and its origins using complete
hydrodynamical modeling.

Table 3: Core parameters for best matching semi-analytical models

Parameters∗ | R=300 $\rm M_{\odot}$ | R=500 $\rm M_{\odot}$ | R=700 $\rm M_{\odot}$
---|---|---|---
$\rm M_{ej}$ ($\rm M_{\odot}$) | $6.50^{+0.20}_{-0.20}$ | $6.20^{+0.20}_{-0.05}$ | $6.60^{+0.10}_{-0.10}$
$\rm E_{th}$ ($\rm 10^{51}~{}erg$) | $0.27^{+0.13}_{-0.05}$ | $0.17^{+0.04}_{-0.04}$ | $0.12^{+0.03}_{-0.02}$
$\rm E_{kin}$ ($\rm 10^{51}~{}erg$) | $1.00^{+0.20}_{-0.12}$ | $0.93^{+0.03}_{-0.02}$ | $1.05^{+0.01}_{-0.01}$
$\rm M_{Ni}$ ($\rm M_{\odot}$) | $0.020^{+0.004}_{-0.006}$ | $0.020^{+0.004}_{-0.005}$ | $0.020^{+0.004}_{-0.005}$

∗ $\rm T_{rec}\approx 6000~{}K$, $\rm A_{g}=6.5\times 10^{10}~{}d^{2}$

###  5.2 Hydrodynamical Modeling

In the previous section, we obtained rough estimates of the progenitor
parameters. Unfortunately, we lack the nebular phase spectra, which could also
be utilized to constrain the progenitor’s C/O core mass. Initially, we looked
for models representative of SN 2021wvw evolution in other previous studies.
However, none of the grids of model light curves or individual models
available in the literature could provide a short plateau length with low
luminosity (Dessart et al., 2010; Eldridge et al., 2018; Moriya et al., 2023).
For the case of short-plateau SNe, it has been noticed that a wide range of
plausible RSG masses could give rise to these SNe ranging from $\rm
8-12~{}M_{\odot}$ (Sollerman et al., 2021; Teja et al., 2022; Utrobin &
Chugai, 2024) and reaching up to $20-30$ $\rm M_{\odot}$ (Dessart et al.,
2010; Hiramatsu et al., 2021). Therefore, to ascertain the properties of the
plausible progenitor of SN 2021wvw, its evolutionary scenario, mass loss
before the explosion, explosion energy, and ejecta mass, we perform the
hydrodynamical modeling by evolving progenitors for both the lower and higher
end of RSGs, allowing arbitrarily enhanced winds to mimic the impact of prior
mass loss (due to binary interaction Laplace et al. 2021, e.g.; Ercolino et
al. 2024, e.g. or eruptive mass loss during the star’s life Cheng et al. 2024,
e.g.) on the mass of the H-rich ejecta.

We use the 1-D stellar evolution code MESA (Paxton et al., 2011, 2013, 2015,
2018, 2019; Jermyn et al., 2023) revision 15140 to evolve the progenitor and
hydrodynamical explosion and STELLA (Blinnikov & Sorokina, 2004; Baklanov et
al., 2005; Blinnikov et al., 2006) to obtain synthetic observables,
specifically light curves and expansion velocity. Most of the parameters in
MESA were kept the same as provided in the inlists make_pre_ccsn_IIp and
ccsn_IIp and described in detail in Farmer et al. (2016) and Paxton et al.
(2018); additional detailed descriptions of the setup and key parameters are
mentioned in (Teja et al., 2022, 2023a). We use the binding-energy fallback
scheme introduced in Paxton et al. (2019); Goldberg et al. (2019) to quantify
late-time fallback during the shock propagation phase. In this work, we mainly
focus on the following parameters: zero-age main-sequence (ZAMS) mass,
metallicity (z), wind scaling factor ($\alpha_{wsf}$), mixing length
($\alpha_{MLT}$), explosion energy, nickel mass, and explosive mixing via the
Duffell Rayleigh Taylor Instability (RTI) (Duffell, 2016) 1D implementation by
varying the ratio of RTI parameter $\eta_{R,e}$ and diffusion parameter
$\eta_{R}$ (Paxton et al., 2018). The progenitor models are exploded in MESA
via a thermal energy injection to a specified total explosion energy, and the
ejecta evolution is followed to just before shock breakout following Paxton et
al. (2018) as discussed in Teja et al. (2022, 2023a) making use of the Duffell
(2016) implementation for mixing via the Rayleigh-Taylor Instability. The
models are then handed off to STELLA when the shock reaches an overhead mass
coordinate of 0.05 $\rm M_{\odot}$. Before evolving a new set of progenitors,
we first try the short-plateau models from previous works, namely SN 2020jfo
(Teja et al., 2022) and SN 2018gj (Teja et al., 2023a). Exploding these with
lower energies to match the plateau luminosities makes the plateau length
longer, leaving these models infructuous. We then proceed to evolve additional
models.

Figure 9: Observed and modeled bolometric evolution of SN 2021wvw for $\rm
13~{}M_{\odot}$ ZAMS models with different sets of parameters. The inset in
the left bottom shows the corresponding modeled and observed Fe II 5169
velocities.

Figure 10: Observed and modeled bolometric evolution of SN 2021wvw for $\rm
18~{}M_{\odot}$ ZAMS models with different sets of parameters. The solid red
curve gives the best description of the model. The inset in the bottom left
shows the corresponding modeled and observed Fe II 5169 velocities.

Firstly, we evolve 13 $\rm M_{\odot}$ ZAMS mass models with solar metallicity
for the lower mass end. We change the wind scaling ($\alpha_{wsf}$) in steps
and explode each progenitor with various explosion energies until we match the
plateau luminosity and its duration. Some of the resulting bolometric light
curves and corresponding Fe II 5169 velocities are presented in Figure 9,
which are compared with the observed values. As stated earlier, we do not
attempt to match the initial 10-20 days of observations exactly with models
due to lack of relevant observations. We find that the velocities, plateau
luminosity, and nickel tail match reasonably well for low-mass RSG models.
However, these models could not reproduce the observed slow decline during the
plateau phase and the sharp transition from the plateau to the tail phase. A
sharp decline for SN 2005cs was obtained by increasing the strength of RTI
mixing, as shown in (Paxton et al., 2018). As a more thoroughly mixed ejecta
is expected to cause a steeper plateau drop due to a more even distribution of
H throughout the entire ejecta, we also attempt to vary the RTI mixing via
$\eta_{R,e}/\eta_{R}$, which directly changes the density structure as well as
the abundance structure of the progenitor and the varied degree of mixing of
species. Even for a value as high as $\eta_{R,e}/\eta_{R}=20$, we only observe
slight changes in the model light curves, but not significant enough to
satisfy the observed transition (refer Figure 9).

We proceed further to explore and explode the higher ZAMS mass models in the
range 18-20 $\rm M_{\odot}$ which plausibly lie on the upper mass limit for
the directly detected progenitors of Type II SNe (Smartt et al., 2009; Davies
& Beasor, 2020). The resulting models are shown in Figure 10 with colored
lines representing the best match to the observations (other models are in
gray color). Owing to their large progenitor radii ($\rm\sim
1000~{}R_{\odot}$) at the mixing length $\alpha_{\rm MLT}=2$, the initial
models were too bright to fit the plateau luminosities even with very low
explosion energies. Hence, we evolved slightly compact progenitors to match
the plateau decline and luminosities by varying the $\alpha_{MLT}$ and
metallicity $z$. For $\rm\alpha_{MLT}=4.0\ \&\ z=0.6Z_{\odot}$, we could
obtain a considerable match with the observed light curves for explosion
energies of $\approx$0.22 to 0.25 foe with $\rm M_{ej}=4.7~{}M_{\odot}$. This
value of $\alpha_{\rm MLT}$ is on the higher end of typically-considered
values (see, e.g. Goldberg & Bildsten, 2020), and is consistent with 3D
simulations of convective RSG envelopes (Goldberg et al., 2022). The
transition to the end of the plateau obtained for these models is inherently
sharp, which is further matched well by varying the RTI parameter. We could
replicate the observed transition profile for $\eta_{R,e}/\eta_{R}=8$. The
mass of $\rm{}^{56}Ni$ required to fit the observed light curve is similar to
the earlier estimates with $\rm M_{Ni}\approx 0.020~{}M_{\odot}$. The ejecta
mass and explosion energies obtained through hydrodynamical modeling are lower
than that obtained from the semi-analytical approach. However, such
discrepancies between semi-analytic and detailed modeling are fairly common in
the literature (see for example, Szalai et al. (2019); Teja et al. (2023a)).
This could be due to various simplified approximations in the semi-analytical
work, including the assumed density and velocity profile of the ejecta, as
well as the assumption of a simple two-zone ejecta with a grey opacity
treatment independent of metallicity (Nagy & Vinkó, 2016).

Figure 11: MESA+STELLA structures for different cases of $\rm 18~{}M_{\odot}$
ZAMS models with different RTI parameter. A few species out of the 22 species
network used in the modeling are shown here. Solid lines present the mass
fraction just after we inject the explosion energy. The other two dashed lines
show the final ejecta structure before the shock breakout (SB) for different
$\eta_{R,e}/\eta_{R}$ values. The final ejecta profiles suffer from
significant fallback during the shock-propagation phase, which we discuss in
Section 6.2.

We show the structural differences in the various models considering the
effect of the RTI parameter in Figure 11 using a few species out of the 22
species network used in the modeling. Solid lines represent the mass fraction
just after we inject the explosion energy. The other two dashed lines show the
final ejecta structure before the shock breakout (SB) for different
$\eta_{R,e}/\eta_{R}$ values. The figure shows that the higher $\eta$ ratio
weakens the RTI mixing with increasing species concentration towards the inner
layers. At the boundary interface, the gradient is steeper for a higher $\eta$
ratio. Due to the small explosion energies, the models experience significant
fallback during the shock-propagation phase as reverse shocks off the steep
density gradients at various compositional boundaries sweep marginally-unbound
material back onto the inner boundary. This is also evident in Figure 11,
where the inner boundary of the final pre-SB structure is at a significantly
higher mass co-ordinate ($\rm\approx 4.5~{}M_{\odot}$) than what was initially
excised as a core remnant mass ($\rm\approx 1.7~{}M_{\odot}$). The detailed
fallback treatment in MESA is described in Goldberg et al. (2019). Due to the
relatively low core binding energy in the suite of 13$\rm M_{\odot}$
progenitors, we find only 0.2 to 0.4 $\rm M_{\odot}$ of material is falling
onto the core in 13 $\rm M_{\odot}$ progenitor case, whereas it is much larger
for high mass scenarios reaching up to 2-3 $\rm M_{\odot}$ (owing to the
larger core binding energy of the high-mass progenitors). Approximately 1 $\rm
M_{\odot}$ of fallback was also present in the SN 2005cs models (Paxton et
al., 2018) even for an initial low mass progenitor (13 $\rm M_{\odot}$).

##  6 Discussion

###  6.1 Scaling relation degeneracies and model differences for short-plateau
SNe

Figure 12:  Plausible $E_{exp}$ and $M_{ej}$ ranges plotted from the scaling
relations obtained in Goldberg et al. (2019). The scatter points represent the
ejecta masses obtained for various models utilized in this work. The energy
values for all the evolved models are between 0.1 to 0.3 foe. The shaded
regions include the values obtained considering the errors in the observables.

Many works have highlighted the non-uniqueness of hydrodynamical modeling of
SN-IIP lightcurves and plateau velocities (Goldberg et al., 2019; Dessart &
Hillier, 2019; Martinez & Bersten, 2019; Goldberg & Bildsten, 2020). Semi-
analytical scalings between luminosity and plateau duration with progenitor
properties thus entail families of explosions which may produce qualitatively
similar lightcurves, with higher $\rm M_{ej}$ and $\rm E_{exp}$ at lower $R$
being comparable to smaller $\rm M_{ej}$ and $\rm E_{exp}$ at higher $R$
(Popov, 1993; Kasen & Woosley, 2009; Sukhbold et al., 2016; Goldberg et al.,
2019; Goldberg & Bildsten, 2020). We compare a selection of our MESA models
(from Section 5) to the scaling relations obtained by Goldberg et al. (2019)
to estimate a comprehensive set of ejecta mass and explosion energies, shown
in Fig 12. We note that these scaling relations were calibrated to higher Ni
masses and more typical (i.e., less-stripped) events. We do not take these
scaling relations as the absolute truth in this regime, but rather, show them
as representative of the degeneracies characteristic of SNe IIP (Dessart &
Hillier, 2019; Goldberg et al., 2019; Goldberg & Bildsten, 2020), and use them
to motivate and contextualize our hydrodynamical modeling efforts. For radii
between 400-1000 $\rm R_{\odot}$, we find the explosion energy varies from
$\rm\approx 2.5\times 10^{50}~{}erg~{}s^{-1}$ to much lower $\rm 5\times
10^{49}~{}erg~{}s^{-1}$.

For the given radii range, the predicted ejecta masses are less than 3 $\rm
M_{\odot}$. The modeled ejecta masses lie somewhat above the values obtained
utilizing scaling relations for all the progenitors, possibly due to the
smaller ratio of core mass to envelope mass in the sample used to calibrate
the scalings compared to the models presented here. The explosion energy
provides good matching values. These relations tend to give similar values
obtained by semi-analytical modeling for the much more compact radii
($\rm<400~{}R_{\odot}$), also seen in the case of another short plateau SN
2018gj (Teja et al., 2023a).

In both the low and high mass cases for SN 2021wvw, we find apparent
differences in the early phase ($\rm<40~{}d$) modeled and observed velocities.
The differences are significant in the $\rm 13~{}M_{\odot}$ models. This
tension is further increased in low-mass models when we try to match the
observed plateau luminosity by increasing their progenitor radius. In other
modeling works, it has been noted that the MESA+STELLA models provide an
excellent velocity match with typical Type IIP SNe observed velocities from
the early phase until the photospheric phase, which is not the case for the
short plateau events.

###  6.2 Fallback during the shock propagation phase

In a majority of the modeled sub-luminous SNe that are the result of low-
energy explosions, whether they come from low to moderate mass (8-18 $\rm
M_{\odot}$) RSGs (Chugai & Utrobin, 2000; Pumo et al., 2017; Lisakov et al.,
2018; Valerin et al., 2022) or high-mass RSG explosions ($\rm>20~{}M_{\odot}$
Zampieri et al., 2003), there are discussions related to fallback material
onto the core. Namely, when the total explosion energy is positive but only
comparable in magnitude to the total binding energy of the progenitor star,
late-time fallback from reverse shocks during the pre-SBO phase may sweep
marginally unbound material back onto the central remnant (Colgate 1971, see,
e.g.; Perna et al. 2014, see, e.g.. In some cases, the central remnant has
been speculated to turn into a black hole post-accretion, but with no
observational evidence (Zampieri et al., 2003). In other cases, very late-time
enhanced luminosity is associated with the accretion of material to the
central remnant (Gutiérrez et al., 2020). For many of these objects, the
$\rm{}^{56}Ni$ mass obtained is an order of magnitude or even much lesser than
the $\rm{}^{56}Ni$ mass obtained for SN 2021wvw. Further, the velocity
obtained for these cases is much less than the usual Type II expansion
velocities.

Interestingly, the short plateau and a sharp transition to the plateau phase
are remarkable features for SN 2021wvw, which are unusual for low to
intermediate luminosity SNe. Given the low inferred $\rm E_{exp}$, the short
plateau length requires a low H-rich ejecta mass for both low-mass and high-
mass progenitors, which could be the result of a higher mass loss during
evolution. Such high mass loss might be consistent with the notion that the
sharp drop from the plateau is actually excess luminosity during the plateau
drop driven by late-time interaction with previously ejected material. But, as
observed in the spectral evolution (Section 4), there are no discernible CSM
signatures in the spectra. On the other hand, if there is an actual fallback
(as occurs during hydrodynamical modeling in Section 5) of the inner layers
onto the core, the inward receding photosphere may reach earlier to the base
of the H-rich ejecta, giving a short plateau with a sharp transition. This may
manifest in late-time signatures of accretion if such accretion persists (see,
e.g. Dexter & Kasen, 2013; Moriya et al., 2019). However, the lack of late
time light curve (beyond 300 d) and spectral information restricts us from
saying anything about further observational signatures of fallback accretion.

While the short plateau and its sharp transition could be due to fallback,
further discussion of the physical consequences of this fallback and
ascertaining its influence on the sharp transition from plateau requires
further detailed modeling, which is beyond the scope of this work. We
nonetheless encourage follow-up observations searching for any signatures of
continued accretion or very late-time circumstellar interaction from this
unique event.

###  6.3 SN 2021wvw in the Type II domain

Figure 13: Top: Correlation between plateau brightness at 50 d, $\rm
M_{V}^{50}$ and expansion velocities at 50 d after explosion. Bottom: Mid-
plateau brightness, $M_{V}$ versus plateau duration ($\rm t_{p}$) for a large
sample including a wide range of Type II SNe obtained from Fang et al. (2024).

We compare SN 2021wvw with a large sample of normal Type IIP SNe (Hamuy, 2003)
and low-luminosity Type II SNe (Spiro et al., 2014) as shown in Fig 13. SN
2021wvw fits well in the established tight correlation between expansion
velocity and luminosity for Type II SNe at 50 d. Moreover, we find it
bifurcating the two populations in both luminosity and expansion velocities.
In this space, it is a bridging object between the normal Type IIP SNe and
under luminous ones. Apart from this expected behavior, SN 2021wvw is unique
due to its short plateau and low luminosity. Considering existing works (e.g.,
refer Fig 17 in Valenti et al. 2016) showing a correlation between plateau
luminosity and plateau duration, SN 2021wvw clearly is an outlier. Even for a
larger sample for all Type II subclasses (Fang et al., 2024), SN 2021wvw
stands apart, as is evident in the bottom panel of Fig 13. SN 2021wvw has the
shortest plateau among all the intermediate and low-luminosity SNe. In
contrast, it is the faintest SN among all the short plateau subclass of Type
IIP SNe presented in the sample and, presumably, in the literature.

##  7 Summary

This work provides a comprehensive set of multi-band photometric and optical
spectroscopic observations of an under-luminous, short-plateau supernova SN
2021wvw. We have presented detailed light curves and spectral comparisons with
other short-plateau SNe. The light curves and spectra are modeled to obtain
the physical parameters of the explosion. Some of the key findings are
summarized as follows:

  * •

SN 2021wvw is fainter (at $\rm M_{r}\approx-16~{}mag$) compared with other
short-plateau SNe and shows the shortest plateau ($\rm\approx 75~{}d$) among
the intermediate luminosity SNe, with a sharp transition period of $\sim$ 10 d
from plateau to tail phase.

  * •

The ejecta expansion velocities are slowly evolving and lie below the
1-$\sigma$ lower bound compared to a large sample of Type II SNe.

  * •

Early spectra show fewer metallic features as compared to other short-plateau
and sub-luminous SNe. The lack of metal features is evident till the last
spectrum (+95 d) presented here.

  * •

Detailed MESA+STELLA hydrodynamical modeling disfavors the lower mass RSG
models and is more inclined towards the higher mass end of RSGs. A compact
progenitor with 18 $\rm M_{\odot}$ ZAMS mass, radius of 650-700 $R_{\odot}$
and a final H-rich ejecta mass of $\rm\approx 5~{}M_{\odot}$ is seen to
provide a good fit to the observed properties.

  * •

Modeling also suggests a low explosion energy ($\rm\approx 0.23\times
10^{51}erg$) with an estimated $\rm 0.020~{}M_{\odot}$ of radioactive
$\rm{}^{56}Ni$.

With the increasing number of short-plateau SNe, we find that these events
have varied luminosities, synthesized 56Ni masses, and expansion velocities.
It is evident that these are not restricted to moderate to luminous events, as
seen previously. With the upcoming large surveys such as LSST, this number
would only increase and possibly make the Type IIP class or subclasses more
homogenous in different parameter spaces.

##  8 Software and third party data repository citations

## Acknowledgements

We are grateful to the anonymous referee for thoroughly evaluating the
manuscript, which helped improve it.

RST would like to acknowledge Dr. Takashi J. Moriya for his insights and
helpful discussions on this supernova.

RST and JAG thank Dr. Daichi Hiramatsu for readily providing observational
data for a few short-plateau SNe, as well as for valuable discussions.

DKS acknowledges the support provided by DST-JSPS under grant number
DST/INT/JSPS/P 363/2022.

GCA thanks the Indian National Science Academy for support under the INSA
Senior Scientist Programme.

The Flatiron Institute is supported by the Simons Foundation.

The GROWTH India Telescope (GIT) is a 70-cm telescope with a 0.7-degree field
of view, set up by the Indian Institute of Astrophysics (IIA) and the Indian
Institute of Technology Bombay (IITB) with funding from Indo-US Science and
Technology Forum and the Science and Engineering Research Board, Department of
Science and Technology, Government of India. It is located at the Indian
Astronomical Observatory (IAO, Hanle). We acknowledge funding by the IITB
alumni batch of 1994, which partially supports the operation of the telescope.

We thank the staff of IAO, Hanle, CREST, and Hosakote, who 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) resources
https://www.iiap.res.in/?q=facilities/computing/nova made available by the
Computer Center of the Indian Institute of Astrophysics, Bangalore.

This work has made use of 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 catalogs 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.

This research has made use of the NASA/IPAC Extragalactic Database (NED),
which is funded by the National Aeronautics and Space Administration and
operated by the California Institute of Technology.

This research has made use of the NASA/IPAC Infrared Science Archive, which is
funded by the National Aeronautics and Space Administration and operated by
the California Institute of Technology

##  Appendix A DATA

The following section provides the apparent magnitudes obtained for SN
2021wvw. The magnitudes are given in Table 4.

Table 4: Photometric observations of SN 2021wvw from GIT and HCT. JD (2459000+) | Phase† (d) | g (mag) | V (mag) | r (mag) | R (mag) | i (mag) | z (mag)
---|---|---|---|---|---|---|---
458.3 | 8.4 | 18.07 $\pm$ 0.18 | - | 17.68 $\pm$ 0.09 | - | 17.72 $\pm$ 0.11 | -
459.3 | 9.4 | 18.10 $\pm$ 0.12 | - | 17.68 $\pm$ 0.08 | - | 17.65 $\pm$ 0.11 | 17.45 $\pm$ 0.11
460.2 | 10.3 | 18.11 $\pm$ 0.15 | - | 17.65 $\pm$ 0.10 | - | 17.64 $\pm$ 0.14 | -
462.3 | 12.4 | - | - | 17.66 $\pm$ 0.05 | - | 17.63 $\pm$ 0.06 | -
463.3 | 13.4 | 18.12 $\pm$ 0.10 | - | 17.67 $\pm$ 0.05 | - | - | 17.36 $\pm$ 0.13
465.3 | 15.4 | 18.17 $\pm$ 0.10 | - | - | - | - | -
471.3 | 21.4 | - | - | - | - | - | 17.40 $\pm$ 0.18
474.3 | 24.4 | 18.30 $\pm$ 0.16 | - | 17.69 $\pm$ 0.08 | - | 17.66 $\pm$ 0.07 | 17.44 $\pm$ 0.10
476.3 | 26.4 | 18.40 $\pm$ 0.12 | 18.06 $\pm$ 0.01 | 17.81 $\pm$ 0.05 | 17.56 $\pm$ 0.01 | 17.64 $\pm$ 0.06 | -
477.3 | 27.4 | - | 18.05 $\pm$ 0.01 | 17.79 $\pm$ 0.06 | 17.55 $\pm$ 0.02 | 17.64 $\pm$ 0.07 | 17.49 $\pm$ 0.09
478.2 | 28.3 | - | - | - | - | 17.62 $\pm$ 0.12 | -
479.3 | 29.4 | - | - | 17.80 $\pm$ 0.06 | - | 17.70 $\pm$ 0.08 | -
485.3 | 35.4 | - | - | 17.76 $\pm$ 0.05 | - | 17.66 $\pm$ 0.06 | -
486.3 | 36.4 | 18.49 $\pm$ 0.11 | - | 17.65 $\pm$ 0.05 | - | 17.63 $\pm$ 0.08 | 17.56 $\pm$ 0.12
487.3 | 37.4 | - | - | 17.75 $\pm$ 0.06 | - | 17.69 $\pm$ 0.07 | 17.51 $\pm$ 0.11
488.4 | 38.5 | 18.53 $\pm$ 0.15 | - | 17.75 $\pm$ 0.09 | - | 17.67 $\pm$ 0.08 | -
489.2 | 39.3 | 18.51 $\pm$ 0.14 | - | 17.76 $\pm$ 0.09 | - | 17.61 $\pm$ 0.11 | -
490.2 | 40.3 | 18.55 $\pm$ 0.14 | 18.07 $\pm$ 0.01 | 17.78 $\pm$ 0.06 | 17.56 $\pm$ 0.01 | 17.66 $\pm$ 0.09 | -
491.3 | 41.4 | 18.58 $\pm$ 0.16 | - | 17.79 $\pm$ 0.08 | - | 17.61 $\pm$ 0.09 | 17.52 $\pm$ 0.11
492.2 | 42.3 | 18.62 $\pm$ 0.14 | - | 17.81 $\pm$ 0.11 | - | 17.68 $\pm$ 0.10 | 17.46 $\pm$ 0.11
493.3 | 43.4 | 18.62 $\pm$ 0.15 | - | 17.78 $\pm$ 0.09 | - | 17.72 $\pm$ 0.09 | 17.55 $\pm$ 0.12
494.2 | 44.3 | 18.54 $\pm$ 0.14 | - | 17.78 $\pm$ 0.09 | - | 17.66 $\pm$ 0.14 | -
495.4 | 45.5 | 18.57 $\pm$ 0.15 | - | 17.81 $\pm$ 0.09 | - | 17.64 $\pm$ 0.11 | 17.56 $\pm$ 0.14
497.3 | 47.4 | 18.60 $\pm$ 0.15 | - | 17.83 $\pm$ 0.12 | - | 17.67 $\pm$ 0.13 | 17.53 $\pm$ 0.16
498.2 | 48.3 | 18.58 $\pm$ 0.12 | - | 17.81 $\pm$ 0.12 | - | 17.72 $\pm$ 0.09 | -
501.3 | 51.4 | 18.72 $\pm$ 0.20 | - | 17.77 $\pm$ 0.12 | - | - | 17.61 $\pm$ 0.14
502.2 | 52.3 | 18.60 $\pm$ 0.14 | - | 17.84 $\pm$ 0.07 | - | 17.67 $\pm$ 0.08 | -
503.2 | 53.3 | 18.51 $\pm$ 0.24 | - | - | - | - | -
504.1 | 54.2 | 18.75 $\pm$ 0.13 | - | 17.92 $\pm$ 0.06 | - | 17.66 $\pm$ 0.07 | 17.56 $\pm$ 0.08
507.1 | 57.2 | - | - | 17.89 $\pm$ 0.08 | - | 17.63 $\pm$ 0.10 | 17.60 $\pm$ 0.12
508.3 | 58.4 | - | - | 17.75 $\pm$ 0.08 | - | 17.73 $\pm$ 0.10 | 17.66 $\pm$ 0.15
514.4 | 64.5 | - | - | 17.94 $\pm$ 0.13 | - | - | 17.69 $\pm$ 0.14
515.4 | 65.5 | 18.83 $\pm$ 0.16 | - | 18.05 $\pm$ 0.10 | - | 17.83 $\pm$ 0.11 | -
516.3 | 66.4 | - | - | 17.93 $\pm$ 0.14 | - | - | 17.65 $\pm$ 0.21
517.2 | 67.3 | - | - | 18.04 $\pm$ 0.07 | - | 17.87 $\pm$ 0.08 | -
518.3 | 68.4 | 18.89 $\pm$ 0.23 | - | 18.01 $\pm$ 0.16 | - | - | -
519.1 | 69.2 | - | - | 18.06 $\pm$ 0.08 | - | 17.89 $\pm$ 0.08 | -
521.2 | 71.3 | 18.85 $\pm$ 0.19 | - | 18.13 $\pm$ 0.11 | - | - | -
522.2 | 72.3 | 18.94 $\pm$ 0.20 | - | 18.13 $\pm$ 0.11 | - | 17.98 $\pm$ 0.11 | 17.72 $\pm$ 0.13
523.2 | 73.3 | - | - | 18.21 $\pm$ 0.13 | - | - | -
524.2 | 74.3 | 18.99 $\pm$ 0.16 | - | 18.12 $\pm$ 0.07 | - | 17.99 $\pm$ 0.10 | 17.81 $\pm$ 0.12
525.1 | 75.2 | 19.02 $\pm$ 0.18 | - | 18.13 $\pm$ 0.08 | - | 18.00 $\pm$ 0.09 | -
526.2 | 76.3 | 19.03 $\pm$ 0.22 | - | 18.21 $\pm$ 0.13 | - | - | 17.84 $\pm$ 0.16
527.1 | 77.2 | 19.28 $\pm$ 0.19 | - | 18.29 $\pm$ 0.10 | - | - | -
528.2 | 78.3 | 19.38 $\pm$ 0.24 | - | 18.29 $\pm$ 0.13 | - | 18.12 $\pm$ 0.14 | 17.94 $\pm$ 0.16
529.2 | 79.3 | - | - | 18.45 $\pm$ 0.14 | - | 18.18 $\pm$ 0.14 | 18.33 $\pm$ 0.20
530.1 | 80.2 | 19.70 $\pm$ 0.16 | - | 18.57 $\pm$ 0.09 | - | 18.35 $\pm$ 0.08 | -
531.1 | 81.2 | 19.90 $\pm$ 0.11 | - | 18.79 $\pm$ 0.04 | - | 18.68 $\pm$ 0.06 | -
532.1 | 82.2 | - | - | 19.04 $\pm$ 0.05 | - | - | -
533.1 | 83.2 | - | - | - | - | 18.86 $\pm$ 0.07 | -
534.1 | 84.2 | - | - | 19.38 $\pm$ 0.14 | - | 19.31 $\pm$ 0.11 | -
535.1 | 85.2 | - | - | 19.52 $\pm$ 0.05 | - | 19.42 $\pm$ 0.08 | -
536.1 | 86.2 | - | - | 19.73 $\pm$ 0.06 | - | - | -
541.1 | 91.2 | - | - | 19.69 $\pm$ 0.08 | - | - | -
542.1 | 92.2 | - | - | 19.85 $\pm$ 0.08 | - | - | -
543.1 | 93.2 | - | - | 19.75 $\pm$ 0.07 | - | 19.50 $\pm$ 0.07 | -
544.1 | 94.2 | - | - | 19.77 $\pm$ 0.07 | - | - | -
548.2 | 98.3 | - | - | 19.78 $\pm$ 0.15 | - | - | -
555.1 | 105.2 | - | - | - | - | 19.59 $\pm$ 0.17 | -
563.1 | 113.2 | - | - | - | - | 19.64 $\pm$ 0.12 | -
568.2 | 118.3 | - | - | 19.67 $\pm$ 0.08 | - | - | -
575.0 | 125.1 | - | 20.95 $\pm$ 0.10 | - | 19.81 $\pm$ 0.05 | - | -
580.0 | 130.1 | - | 21.17 $\pm$ 0.28 | - | - | - | -
597.3 | 147.4 | - | - | 19.91 $\pm$ 0.10 | - | - | -
600.2 | 150.3 | - | - | 20.21 $\pm$ 0.19 | - | - | -
605.0 | 155.1 | - | 21.15 $\pm$ 0.26 | - | 20.19 $\pm$ 0.12 | - | -
610.2 | 160.3 | - | - | 20.01 $\pm$ 0.24 | - | - | -
625.0 | 175.1 | - | 21.19 $\pm$ 0.27 | - | 20.08 $\pm$ 0.10 | - | -
626.2 | 176.3 | 20.97 $\pm$ 0.19 | - | - | - | - | -
628.0 | 178.1 | - | 21.09 $\pm$ 0.12 | - | 20.44 $\pm$ 0.06 | - | -
629.2 | 179.3 | - | - | - | - | 20.50 $\pm$ 0.23 | -
636.0 | 186.1 | - | 21.03 $\pm$ 0.15 | - | - | - | -
650.1 | 200.2 | - | - | 20.63 $\pm$ 0.12 | - | - | -
665.0 | 215.1 | - | 21.65 $\pm$ 0.11 | - | 20.91 $\pm$ 0.10 | - | -
†Phase given for $t_{exp}=2459449.9$ JD |  |  |  |

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