# Multiple Peaks and a Long Precursor in the Type IIn Supernova 2021qqp: An
Energetic Explosion in a Complex Circumstellar Environment

Daichi Hiramatsu Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138-1516, USA  The NSF AI Institute for Artificial Intelligence and Fundamental Interactions, USA Daichi Hiramatsu<EMAIL_ADDRESS>Tatsuya Matsumoto Department of Physics and Columbia Astrophysics Laboratory, Columbia University, 538 West 120th Street, New York, NY 10027, USA  Edo Berger Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138-1516, USA  The NSF AI Institute for Artificial Intelligence and Fundamental Interactions, USA  Conor Ransome Department of Astronomy & Astrophysics, The Pennsylvania State University, 525 Davey Laboratory, University Park, PA 16802, USA  V. Ashley Villar Department of Astronomy & Astrophysics, The Pennsylvania State University, 525 Davey Laboratory, University Park, PA 16802, USA  Institute for Computational & Data Sciences, The Pennsylvania State University, University Park, PA 16802, USA  Institute for Gravitation and the Cosmos, The Pennsylvania State University, University Park, PA 16802, USA  Sebastian Gomez Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA  Yvette Cendes Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138-1516, USA  Kishalay De NASA Einstein Fellow  MIT-Kavli Institute for Astrophysics and Space Research, 77 Massachusetts Avenue, Cambridge, MA 02139, USA  K. Azalee Bostroem LSSTC Catalyst Fellow  Steward Observatory, University of Arizona, 933 North Cherry Avenue, Tucson, AZ 85721-0065, USA  Joseph Farah Las Cumbres Observatory, 6740 Cortona Drive, Suite 102, Goleta, CA 93117-5575, USA  Department of Physics, University of California, Santa Barbara, CA 93106-9530, USA  D. Andrew Howell Las Cumbres Observatory, 6740 Cortona Drive, Suite 102, Goleta, CA 93117-5575, USA  Department of Physics, University of California, Santa Barbara, CA 93106-9530, USA  Curtis McCully Las Cumbres Observatory, 6740 Cortona Drive, Suite 102, Goleta, CA 93117-5575, USA  Department of Physics, University of California, Santa Barbara, CA 93106-9530, USA  Megan Newsome Las Cumbres Observatory, 6740 Cortona Drive, Suite 102, Goleta, CA 93117-5575, USA  Department of Physics, University of California, Santa Barbara, CA 93106-9530, USA  Estefania Padilla Gonzalez Las Cumbres Observatory, 6740 Cortona Drive, Suite 102, Goleta, CA 93117-5575, USA  Department of Physics, University of California, Santa Barbara, CA 93106-9530, USA  Craig Pellegrino Las Cumbres Observatory, 6740 Cortona Drive, Suite 102, Goleta, CA 93117-5575, USA  Department of Physics, University of California, Santa Barbara, CA 93106-9530, USA  Akihiro Suzuki Research Center for the Early Universe, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan  Giacomo Terreran Las Cumbres Observatory, 6740 Cortona Drive, Suite 102, Goleta, CA 93117-5575, USA  Department of Physics, University of California, Santa Barbara, CA 93106-9530, USA

###### Abstract

We present optical photometry and spectroscopy of the Type IIn supernova (SN)
2021qqp. Its unusual light curve is marked by a long precursor for $\approx
300$ days, a rapid increase in brightness for $\approx 60$ days, and then a
sharp increase of $\approx 1.6$ mag in only a few days to a first peak of
$M_{r}\approx-19.5$ mag. The light curve then declines rapidly until it re-
brightens to a second distinct peak of $M_{r}\approx-17.3$ mag centered at
$\approx 335$ days after the first peak. The spectra are dominated by Balmer
lines with a complex morphology, including a narrow component with a width of
$\approx 1300\,{\rm km\,s}^{-1}$ (first peak) and $\approx 2500\,{\rm
km\,s}^{-1}$ (second peak) that we associate with the circumstellar medium
(CSM) and a P Cygni component with an absorption velocity of $\approx
8500\,{\rm km\,s}^{-1}$ (first peak) and $\approx 5600\,{\rm km\,s}^{-1}$
(second peak) that we associate with the SN–CSM interaction shell. Using the
luminosity and velocity evolution, we construct a flexible analytical model,
finding two significant mass-loss episodes with peak mass loss rates of
$\approx 10$ and $\approx 5\,M_{\odot}\,{\rm yr}^{-1}$ about $0.8$ and $2$ yr
before explosion, respectively, with a total CSM mass of $\approx
2-4\,M_{\odot}$. We show that the most recent mass-loss episode could explain
the precursor for the year preceding the explosion. The SN ejecta mass is
constrained to be $\approx 5-30\,M_{\odot}$ for an explosion energy of
$\approx(3-10)\times 10^{51}\,{\rm erg}$. We discuss eruptive massive stars
(luminous blue variable, pulsational pair instability) and an extreme stellar
merger with a compact object as possible progenitor channels.

Supernovae (1668); Core-collapse supernovae (304); Type II supernovae (1731);
Massive stars (732); Stellar mass loss (1613); Circumstellar matter (241)

††facilities: AAVSO, ADS, ATLAS, DECam, GALEX, IRSA, Keck (LRIS), LCO
(MuSCAT3, Sinistro), Legacy Surveys, Magellan (LDSS-3), MMT (Binospec), NTT
(EFOSC2), NED, PS1, PTF, SDSS, Swift (XRT, UVOT), VLASS, WISE, ZTF††software:
Astropy (Astropy Collaboration 2018), atlas-fp
(https://gist.github.com/thespacedoctor/86777fa5a9567b7939e8d84fd8cf6a76),
BANZAI (McCully et al., 2018), dynesty (Speagle, 2020), emcee (Foreman-Mackey
et al., 2013), FSPS (Conroy et al., 2009; Conroy & Gunn, 2010), lcogtsnpipe
(Valenti et al., 2016), Matplotlib (Hunter, 2007), NumPy (Oliphant, 2006),
photutils (Bradley et al., 2022), PyRAF (Science Software Branch at STScI,
2012), Prospector (Johnson et al., 2021), pwkit (Williams et al., 2017), SciPy
(Virtanen et al., 2020), seaborn (Waskom et al., 2020), sedpy (Johnson, 2021),
SExtractor (Bertin & Arnouts, 1996)

##  1 Introduction

Among hydrogen-rich (H-rich) Type II supernovae (SNe II), Type IIn SNe (SNe
IIn) are classified based on the presence of “narrow” Balmer-series emission
lines in their spectra (Schlegel, 1990; Filippenko, 1997). The main power
source of SNe IIn is thought to be the shock interaction between the SN ejecta
and circumstellar material (CSM; see Smith 2017a for a review), resulting in
the most heterogeneous SN class in terms of their observed properties (e.g.,
light curves and spectra; see Taddia et al. 2013; Nyholm et al. 2020 for
sample studies). The nature of the underlying SNe and their progenitors
remains elusive, as their observational signatures are mostly hidden below the
photosphere formed at the CSM interaction layer.

The direct progenitor identification of SN IIn 2005gl in a pre-explosion image
points a massive ($>50\,M_{\odot}$) luminous blue variable (LBV) as a
potential progenitor for that event (Gal-Yam et al., 2007; Gal-Yam & Leonard,
2009). Given the observed heterogeneous properties of SNe IIn, however,
various other progenitor channels are also possible, for example, super-
asymptotic giant branch stars ($\sim 8$–$10\,M_{\odot}$; e.g., Kankare et al.
2012; Mauerhan et al. 2013a; Smith 2013; Moriya et al. 2014; Hiramatsu et al.
2021), extreme red supergiants ($\sim 17$–$25\,M_{\odot}$; e.g., Fullerton et
al. 2006; Smith et al. 2009; Moriya et al. 2011; Mauerhan & Smith 2012),
interacting massive binaries ($>20\,M_{\odot}$; e.g., Chevalier 2012; Soker &
Kashi 2013; Kashi et al. 2013; Schrøder et al. 2020; Metzger 2022), and even
pulsational pair-instability SNe (PPISNe; $\sim 110-140\,M_{\odot}$; e.g.,
Woosley et al. 2007; Blinnikov 2010; Moriya et al. 2013a; Woosley 2017).

The observed heterogeneity reflects the diversity in pre-explosion mass loss
responsible for the CSM formation. Therefore, SNe IIn with precursor events
provide a unique opportunity to directly connect mass-loss activity to the
resultant SN properties (e.g., Ofek et al. 2013; see Ofek et al. 2014;
Bilinski et al. 2015; Strotjohann et al. 2021 for sample studies). One of the
most well-observed examples is SN 2009ip, which was discovered during its LBV-
like giant eruption (i.e., SN impostor) phase in 2009 (Smith et al., 2010;
Foley et al., 2011), followed by a more luminous SN IIn-like event in 2012
(Prieto et al., 2013; Mauerhan et al., 2013b; Pastorello et al., 2013; Fraser
et al., 2013; Margutti et al., 2014; Levesque et al., 2014; Smith et al.,
2014; Graham et al., 2014; Mauerhan et al., 2014; Martin et al., 2015; Fraser
et al., 2015; Graham et al., 2017; Reilly et al., 2017; Smith et al., 2022).
Multi-peak light curves seen in some precursor-associated SNe IIn (e.g.,
iPTF13z; Nyholm et al. 2017, as well as SN 2009ip) also suggest complex CSM
structures from eruptive, rather than steady, mass loss.

Here, we report detailed optical photometry and spectroscopy of SN IIn
2021qqp, which exhibits clear precursor activity directly up to the SN
explosion and multiple peaks indicative of distinct eruptive mass-loss
episodes. We further construct an analytical model to directly extract the CSM
and SN properties from the combined light-curve and spectral properties. The
paper is structured as follows. In §2 and 3, we summarize the discovery,
classification, archival and follow-up observations, and data reduction; in
§4, we analyze the host galaxy and SN light curves and spectra; we present an
analytical model to extract the CSM and SN properties in §5; and we discuss
possible progenitor channels in §6 and conclude with a future outlook in §7.

##  2 Discovery and Classification

The Zwicky Transient Facility (ZTF; Bellm et al. 2019; Graham et al. 2019)
discovered SN 2021qqp (ZTF21abgjldn) on 2021 May 23.47 (UT dates are used
throughout; ${\rm MJD}=59357.47$) at an $r$-band magnitude of 20.86 at
$\text{R.A.}=22^{\text{h}}32^{\text{m}}40^{\text{s}}.419$ and
$\text{decl.}=+25^{\circ}34^{\prime}34".79$ (De, 2021). Subsequent discoveries
have been reported by the Asteroid Terrestrial-impact Last Alert System
(ATLAS; Tonry et al. 2018; Smith et al. 2020) and Pan-STARRS1 (PS1; Chambers
et al. 2016), with the PS1 detection being the earliest, on 2020 December
24.22 (${\rm MJD}=59207.22$; $150$ days before discovery), with an $i$-band
magnitude of 21.39 at
$\text{R.A.}=22^{\text{h}}32^{\text{m}}40^{\text{s}}.416$ and
$\text{decl.}=+25^{\circ}34^{\prime}34".75$. Given the smallest pixel scale,
we adopt the PS1 coordinates in this work.

Chu et al. (2021) obtained an optical spectrum of SN 2021qqp on 2021 July 6.51
(${\rm MJD}=59401.51$; $44$ days after discovery) with the Low Resolution
Imaging Spectrometer (LRIS; Oke et al. 1995; McCarthy et al. 1998; Rockosi et
al. 2010) mounted on the 10 m Keck I Telescope (Hawaii, USA), classifying it
as an SN IIn at $z=0.041$ that is consistent with the host galaxy redshift of
$z=0.041475\pm 0.000087$ (ALFALFA 4-043; Martin et al. 2009; Haynes et al.
2011, 2018).111Via the NASA/IPAC Extragalactic Database:
http://ned.ipac.caltech.edu/ A subsequent spectrum was obtained on 2021 July
29.24 (${\rm MJD}=59424.24$; $67$ days after discovery) by the Public European
Southern Observatory (ESO) Spectroscopic Survey for Transient Objects (Smartt
et al., 2015) using the ESO Faint Object Spectrograph and Camera (EFOSC2;
Buzzoni et al. 1984) mounted on the $3.58$ m New Technology Telescope (NTT; La
Silla, Chile), confirming the SN IIn classification and redshift (Muñoz et
al., 2021a, b).

In this work, we assume a standard $\Lambda$CDM cosmology with $H_{0}=71.0$ km
s-1 Mpc-1, $\Omega_{\Lambda}=0.7$, and $\Omega_{m}=0.3$ and convert the
redshift to a luminosity distance of $d_{L}=181$ Mpc (distance modulus,
$\mu=36.28$ mag).

##  3 Observation and Data Analysis

###  3.1 Optical and Infrared Photometry

Through the Global Supernova Project (Howell & Global Supernova Project,
2017), we obtained Las Cumbres Observatory (LCO; Brown et al. 2013)
$BgVri$-band imaging data with the Sinistro cameras on the network of 1 m
telescopes at the Cerro Tololo Inter-American Observatory (District IV,
Chile), McDonald Observatory (Texas, USA), South African Astronomical
Observatory (Sutherland, South Africa), and Teide Observatory (Canary Islands,
Spain), as well as $griz$-band imaging data with the Multicolor Simultaneous
Camera for studying Atmospheres of Transiting exoplanets 3 (MuSCAT3; Narita et
al. 2020) on the 2 m Faulkes Telescope North (Hawaii, USA) from 2021 November
17 to 2022 November 25 (${\rm MJD}=59535-59908$). LCO photometry was performed
with point-spread function (PSF) fitting using
lcogtsnpipe222https://github.com/LCOGT/lcogtsnpipe (Valenti et al., 2016), a
PyRAF-based photometric reduction pipeline. $BV$\- and $griz$-band data were
calibrated to Vega and AB magnitudes, respectively, using the 9th Data Release
of the AAVSO Photometric All Sky Survey (Henden et al., 2016) and the 13th
Data Release of the Sloan Digital Sky Survey (SDSS; Albareti et al. 2017).

To explore possible pre-explosion variability (as indicated by the first PS1
detection being $\approx 5$ months before the ZTF discovery; §2) and to obtain
additional post-explosion photometry of SN 2021qqp, we process and examine
ZTF, ATLAS, PS1, Palomar Transient Facility (PTF; Law et al. 2009), and Wide-
field Infrared Survey Explorer (WISE; Wright et al. 2010; Mainzer et al. 2014)
survey data. ZTF and ATLAS photometry was directly retrieved from,
respectively, the ZTF forced-photometry
service333https://ztfweb.ipac.caltech.edu/cgi-bin/requestForcedPhotometry.cgi
(Masci et al., 2019) in the $g$, $r$, and $i$ bands (date range: 2018 April 26
to 2023 January 12; ${\rm MJD}=58234-59956$), and the ATLAS forced photometry
server444https://fallingstar-data.com/forcedphot/ (Shingles et al., 2021) in
the $c$ and $o$ bands (date range: 2015 August 6 to 2023 January 21; ${\rm
MJD}=57240-59965$).

We retrieved PS1 and PTF single-epoch and co-added reference images from the
PS1 Image Cutout Service555http://ps1images.stsci.edu/cgi-bin/ps1cutouts
(Flewelling et al., 2020) in the $g$, $r$, and $i$ bands (date range: 2010
August 16 to 2014 October 12; ${\rm MJD}=55424-56942$) and PTF NASA/IPAC
Infrared Science Archive
(IRSA)666https://irsa.ipac.caltech.edu/Missions/ptf.html in the $g$ and $R$
bands (date range: 2010 July 26 to 2014 October 30; ${\rm MJD}=55403-56944$),
respectively. The data processing, combining, and scaling processes used are
described by Magnier et al. (2020) and Waters et al. (2020) for PS1 and Ofek
et al. (2012) for PTF. In both cases, during the stacking process, the single-
epoch images have a scaling factor applied such that the stacked image zero-
point magnitudes are 25 for PS1 and 27 for PTF. We used the scaling factor to
scale the single-epoch images to the stacked image and subtract the co-added
image from the single epochs to remove host galaxy light. Forced aperture
photometry was performed using standard photutils (v1.7.0; Bradley et al.,
2022) routines with aperture sizes representative of the typical FWHM of each
survey (2” for PTF and 2$\farcs$5 for PS1).

The SN field has also been observed by the ongoing NEOWISE all-sky mid-IR
survey in the $W1$ ($3.4$ $\mu$m) and $W2$ ($4.5$ $\mu$m) bands (Wright et
al., 2010; Mainzer et al., 2014). We retrieved time-resolved co-added images
of the field created as part of the unWISE project (Lang, 2014; Meisner et
al., 2018). To remove contamination from the host galaxy, we used a custom
code (De et al., 2020) based on the ZOGY algorithm (Zackay et al., 2016) to
perform image subtraction on the NEOWISE images using the full-depth coadds of
the WISE and NEOWISE mission (obtained during 2010–2014) as reference images.
Photometric measurements were obtained by performing forced PSF photometry at
the transient position on the subtracted WISE images until the epoch of the
unWISE data release (data acquired until 2021 December).

The detection significance ($\sigma$) of the ZTF, ATLAS, PS1, PTF, and WISE
forced photometry was determined from the ratio of measured flux ($f$) to its
error ($f_{\rm err}$). For the measurements above and below $3\sigma$, we
report their detections ($-2.5\,{\rm log}_{10}(f)+{\rm ZP}$) and $3\sigma$
upper limits ($-2.5\,{\rm log}_{10}(3\times f_{\rm err})+{\rm ZP}$),
respectively, where “ZP” is the zero-point in the AB magnitude system.

Figure 1: Multi-band light curves (Top) and $g-r$ color evolution (Bottom) of
SN 2021qqp. Filled and open symbols in the left panel are used for detections
and $3\sigma$ upper limits (binned every 30 days), respectively. Error bars
denote $1\sigma$ uncertainties and are sometimes smaller than the marker size.
The data gaps are due to Sun observing constraints. The gray vertical dashed
lines mark the times of spectroscopic observations (Figure 2); dotted and
dashed-dotted lines mark radio and X-ray observations (§ 3.3), respectively.
The light curve transitions from a gradual to a sharper rise at $\approx-65$
days, corresponding to the precursor-to-SN transition (the black vertical
line). The $g-r$ color co-evolves with the light curve, with bluer colors as
the light curve peaks. A few faint $\sim 3\sigma$ detections are apparent up
to $6.5$ yr prior to the SN peak. (The data used to create this figure are
available.)  Figure 2: Spectral time series of SN 2021qqp with the phases
denoted on the right. The Balmer lines and blue continuum are seen in the
first two spectra, while the weaker He i, Na i, Ca i, and Fe ii lines are also
seen in the last four spectra as the continuum drops. The host galaxy [O ii]
and [O iii] emission lines are detected in the final two spectra after the SN
flux faded sufficiently (see also Figure 6). (The data used to create this
figure are available.)

###  3.2 Optical Spectroscopy

Through our FLEET program (Gomez et al., 2020, 2023), we obtained optical
spectra on 2022 July 6 and August 30 (${\rm MJD}=59766$ and $59821$) with
Binospec (Fabricant et al., 2019) mounted on the 6.5 m MMT Observatory
(Arizona, USA) and on 2022 July 27 and August 27 (${\rm MJD}=59787$ and
$59818$) with the Low Dispersion Survey Spectrograph 3 (LDSS-3; Stevenson et
al. 2016) mounted on the 6.5 m Magellan Clay Telescope (Cerro Manqui, Chile).
The combinations of the 270 grating (Binospec) and VPH-All grism (LDSS-3) with
a $1"$-long slit were used for dispersion, resulting in wavelength coverage of
$3820-9210\,\textup{\AA}$ ($R\approx 1500$) and $3700-10060\,\textup{\AA}$
($R\approx 700$), respectively. One-dimensional spectra were extracted,
reduced, and calibrated following standard procedures using PyRAF and flux
calibrated to a standard taken during the same week as the target spectra.
Additionally, we retrieved the public Keck/LRIS and NTT/EFOSC2 classification
spectra (§2) via the Transient Name Server (TNS)777https://www.wis-tns.org/
and include them in the subsequent analysis. Additional flux calibration was
applied to all the spectra using coeval photometry.

All photometry and spectroscopy of SN 2021qqp are presented in Figures 1 and
2, respectively. No Na i D absorption is seen at the host redshift (Figure 2),
indicating low host extinction at the SN position (Figure 3). Thus, we correct
all photometry and spectroscopy only for the Milky Way (MW) extinction of
$A_{V}=0.176$ mag (Schlafly & Finkbeiner, 2011),888Via the NASA/IPAC IRSA:
https://irsa.ipac.caltech.edu/applications/DUST/ assuming the Fitzpatrick
(1999) reddening law with $R_{V}=3.1$ and extended to the WISE bands with the
relative optical-to-infrared extinction values from Wang & Chen (2019). As SN
2021qqp is best sampled in the ZTF $r$ band, we use its epoch at maximum light
(${\rm MJD}_{r,{\rm max}}=59438.33$) as the zero-point reference for all
phases unless otherwise specified.

###  3.3 X-Ray and Radio

We obtained Neil G. Gehrels Swift X-Ray Telscope (XRT) observations on 2022
August 9 (${\rm MJD}=59800$; phase of $+348$ days) with a total on-source
exposure time of 3185 s.999UVOT observations were also obtained
contemporaneously. As the SN signal is not detected in the UVOT images, we use
them for the host-galaxy analysis in § 4.1. A $3\sigma$ upper limit of
$4.4\times 10^{-3}$ counts s-1 ($0.3-10$ keV) was estimated using the Swift-
XRT web tool101010https://www.swift.ac.uk/user_objects/index.php (Evans et
al., 2007, 2009). With a MW H i column density of $4.6\times 10^{20}$ cm-2
(HI4PI Collaboration et al., 2016)111111Via the NASA HEASARC NH Tool:
https://heasarc.gsfc.nasa.gov/cgi-bin/Tools/w3nh/w3nh.pl and assuming a power-
law spectrum with a photon index of 2, the count rate is converted121212Via
the NASA HEASARC WebPIMMS: https://heasarc.gsfc.nasa.gov/cgi-
bin/Tools/w3pimms/w3pimms.pl to an unabsorbed flux limit of $F_{\rm X}\lesssim
1.8\times 10^{-13}$ erg s-1 cm-2, corresponding to $L_{\rm X}\lesssim
6.8\times 10^{41}$ erg s-1.

We further obtained images at the location of the SN from the Very Large Array
Sky Survey (VLASS; Lacy et al., 2020) and measured the flux density with the
imtool fitsrc command within pwkit (Williams et al., 2017). Two VLASS images
exist, where the first was taken on 2019 May 26 (${\rm MJD}=58629$; phase of
$-777$ days) and the second on 2021 September 29 (${\rm MJD}=59486$; phase of
$+46$ days). In both cases, we place a $3\sigma$ upper limit of $\lesssim 0.3$
mJy ($2-4$ GHz), corresponding to $L_{\rm radio}\lesssim 3.4\times 10^{37}$
erg s-1.

The luminosity and temporal ranges probed by the X-ray and radio observations
are not particularly constraining as compared to previous SN IIn detections:
$L_{\rm X}\sim 10^{41}$ and $L_{\rm radio}\sim 10^{37}$ erg s-1 at $\sim 1000$
days after explosion (e.g., Chandra 2018).

##  4 Analysis

###  4.1 Host Galaxy

Figure 3: The location of SN 2021qqp (red circle) relative to its host galaxy,
indicating an association with a spiral arm. The dashed circles indicate
$r_{50}=7\farcs 9=6.9$ kpc and $r_{80}=13\farcs 3=11.7$ kpc ($50\%$ and $80\%$
light radii), respectively. The image is in the $g$ band from the DESI Legacy
Imaging Surveys (Dey et al., 2019) Data Release 9.  Figure 4: Observed UV
(GALEX+Swift) and optical (Swift+SDSS+PS1) fluxes for the host galaxy along
with Prospector model fits (blue line and squares). The inferred parameters
from the model are listed in §4.1.

The host galaxy of SN 2021qqp is a face-on spiral
galaxy,131313https://ned.ipac.caltech.edu/byname?objname=ALFALFA+4-043&hconst=67.8&omegam=0.308&omegav=0.692&wmap=4&corr_z=1
as shown in Figure 3. SN 2021qqp is offset from the center of its host by
$\approx 12\farcs 2$, or $10.7$ kpc with the assumed standard $\Lambda$CDM
cosmology. As can be seen in Figure 3, SN 2021qqp coincides with a spiral arm
and is located just within the $r_{80}\approx 13\farcs 3$ light radius. The
location of SN 2021qqp is not particularly unusual for SNe IIn (e.g. Galbany
et al., 2014, 2016, 2018; Schulze et al., 2021; Ransome et al., 2022). We note
that there exists a cataloged PSF-like (i.e., stellar-like) object spatially
coincident with the SN location (within $\approx 0\farcs 03$, smaller than a
typical PSF width of $1\farcs 2$, or $1.1$ kpc) in the DESI Legacy Imaging
Surveys (from 2014 February to 2019 March; ${\rm MJD}\approx 56689-58573$; Dey
et al. 2019) Data Release
9141414https://datalab.noirlab.edu/query.php?name=ls_dr9.tractor with the
following AB magnitudes: $m_{g}=22.8$ ($M_{g}=-13.4$), $m_{r}=22.5$
($M_{r}=-14.0$), and $m_{z}=23.1$ ($M_{z}=-13.3$). Given the luminosity, the
cataloged object is unlikely to be a single quiescent star, but we cannot
distinguish between a precursor activity (Figure 1) and an unresolved star-
forming region.

To estimate global host parameters such as stellar mass ($M_{\star}$),
metallicity ($Z$), age ($t_{\rm age}$), and star formation rate (SFR), we use
Prospector, a stellar population Bayesian inference package (Johnson et al.,
2021) that has been extensively used to fit the spectral energy distributions
(SEDs) of field galaxies and transient host galaxies (e.g., Leja et al. 2017;
Blanchard et al. 2017; Nicholl et al. 2017; Schulze et al. 2021). Prospector
fits photometry and/or spectra and creates an SED model. We fit photometry
from the Galaxy Evolution Explore (GALEX; Martin et al. 2005) in the far-UV
($155$ nm) and near-UV ($230$ nm) bands; Swift UV/Optical Telescope
(UVOT)151515The host-galaxy photometry was extracted with an aperture size of
$r_{80}$. in the $UVW2,UVM2,UVW1,U,B$, and $V$ bands; SDSS in the $u,g,r,i$,
and $z$ bands; and PS1 in the $g,r,i$, and $z$ bands using appropriate prior
distributions ($M_{\star}$, $Z$, and $\tau$, a characteristic $e$-folding
timescale of the delayed-$\tau$ star-formation history, ${\rm SFH}\propto
t\times e^{-t/\tau}$; see Carnall et al., 2019, and references therein for
details) and nested sampling using dynesty (v2.1.1; Speagle, 2020).

The fitting results are shown in Figure 4, from which we find
$M_{\star}=1.74^{+0.64}_{-0.63}\times 10^{10}\,M_{\odot}$, ${\rm
log}_{10}(Z/Z_{\odot})=-0.29^{+0.28}_{-0.34}$, $t_{\rm
age}=8.98^{+3.24}_{-3.33}$ Gyr, $\tau=1.86^{+0.83}_{-0.76}$ Gyr, and a current
SFR (=SFH($t_{\rm age}$)) of $0.59\,\pm\,0.22\,M_{\odot}\,{\rm yr}^{-1}$.
Moreover, using the GALEX UV photometry, we estimate an SFR of
$0.62\,\pm\,0.05\,M_{\odot}\,{\rm yr}^{-1}$ with the Salim et al. (2007)
calibration, which is consistent with the value from the SED fitting. The
inferred $M_{\star}$ and current SFR are a few times smaller than those of the
MW (e.g., Licquia & Newman 2015), but these global host properties are typical
among SN IIn hosts (e.g., Schulze et al. 2021).

We also estimate a local SFR and metallicity from the host [O ii] and [O iii]
emission lines detected in our final SN spectrum, when the SN flux faded
sufficiently (Figures 2 and 6). We fit a double Gaussian profile to [O ii]
$\lambda 3727$ and [O ii] $\lambda 3729$ and a single Gaussian profile each to
[O iii] $\lambda 4959$ and [O iii] $\lambda 5007$. These fits yield
luminosities of $L_{\rm[O~{}{\sc II}]\lambda 3727}=(1.8\pm 0.4)\times
10^{38}$, $L_{\rm[O~{}{\sc II}]\lambda 3729}=(1.9\pm 0.3)\times 10^{38}$,
$L_{\rm[O~{}{\sc III}]\lambda 4959}=(1.5\pm 0.3)\times 10^{38}$, and
$L_{\rm[O~{}{\sc III}]\lambda 5007}=(3.6\pm 0.4)\times 10^{38}$ erg s-1. Using
the Kennicutt (1998) SFR calibration with [O ii] $\lambda 3727$ and the
Maiolino et al. (2008) metallicity calibration with [O iii] $\lambda 5007$/[O
ii] $\lambda 3727$, we estimate ${\rm SFR}_{\rm loc}=(2.5\pm 0.9)\times
10^{-3}\,M_{\odot}\,{\rm yr}^{-1}$ and ${\rm log}_{10}(Z_{\rm
loc}/Z_{\odot})=-0.33\pm 0.09$, respectively. The local SFR and metallicity
are on the low end of the distributions for SN IIn local environements
($\lesssim 10\%$ and $\lesssim 20\%$ for SFR and metallicity, respectively;
Galbany et al. 2014, 2016, 2018).

###  4.2 Light-curve Evolution

As shown in Figure 1, the multi-band light curve of SN 2021qqp shows a gradual
rise ($\approx-4$ mmag day-1) from $-14.5$ mag in the $r$ band at $-370$ days
(or possibly even $-2400$ days, although other transient events in the
unresolved star-forming region (§4.1) cannot be ruled out without a clear
rising trend) with possible bumps around $-240$ and $\lesssim-120$ days
(during the Sun constraint). This “precursor” is similar in brightness to the
Great Eruption of Eta Carinae and some SN impostors (e.g., Humphreys &
Davidson 1994; Davidson & Humphreys 1997; Van Dyk & Matheson 2012; Smith
2017b) and likely caused by a pre-explosion mass-loss event(s). The precursor
absolute magnitude and duration of SN 2021qqp ($-15.8\,{\rm mag}\lesssim
M_{g,r,i}\lesssim-14.5\,{\rm mag}$ and $\approx 300$ days) are on the luminous
and long-lasting ends of the SN IIn precursor distributions, respectively
(Ofek et al., 2014; Strotjohann et al., 2021). By comparing with the estimated
rates of precursor luminosity and duration from Strotjohann et al. (2021)
using 18 SNe IIn discovered by ZTF with observed precursors brighter than
$-12$ mag, these correspond to $\lesssim 1\%$ of SNe IIn, which may suggest a
more extreme mass-loss event(s) for SN 2021qqp. By integrating the $r$-band
specific luminosity (Figure 5), the radiated energy during the precursor phase
can be roughly estimated to be $8.0\times 10^{48}$ erg.

After the gradual rise, the light curve transitions to a sharp rise
($\approx-30$ mmag day-1 in the $g$ and $r$ bands) after $\approx-70$ days. We
consider this transition to be the first light of the SN. With a criterion
that the light curve exhibits a monotonic rise above the precursor levels in
all bands, we determine the time of SN first light to be $\approx-65\pm 5$
days. Following the SN first light, the sharp rise continues to $\approx-13$
days and then transitions to a much sharper rise ($\approx-200$ mmag day-1 in
the $g$ and $r$ bands) until reaching a maximum of $M_{g}=-19.4$ and
$M_{r}=-19.5$ mag. The resulting concave-up curvature of the light curve is
atypical of diffusion-dominated light curves (e.g., Arnett 1980, 1982). The
decline from the maximum light is also characterized by a concave-up
curvature, albeit with changes in the slope, i.e., a short ($\approx 6$ day)
plateau during $\approx 6-12$ days after maximum (see also Figure 5 for an
enlarged view around the peak), and roughly a three times longer timescale
than the rapidly rising part.

No photometric measurements are available around $150-220$ days after maximum
due to the Sun constraint. At $\approx 335$ days, the light curve shows
another luminous sharp peak, with $M_{g}=-16.7$ and $M_{r}=-17.3$ mag, with
possible bumps preceding at $\approx 240$ days and following at $\gtrsim 450$
days (during the current Sun constraint). Unlike the first maximum, this
second peak is characterized by a concave-down curvature. The rise starts at
$\approx 315$ days from $M_{g}=-15.5$ and $M_{r}=-16.1$ mag, and the decline
lasts until $\approx 380$ days to $M_{g}=-13.7$ and $M_{r}=-15.0$ mag before
transitioning to yet another potential rise. The photometric monitoring is
planned to be continued after the current Sun constraint (until 2023 mid-May)
to capture further evolution, if any.

Throughout the evolution, the $g-r$ color follows the light curve in that it
reaches local minima at the the light-curve peaks. During $-65$ to $-13$ days,
the $g-r$ color stays roughly constant at $0.32$ mag, albeit with the large
scatters. It reaches $-0.07$ mag at the first light-curve maximum, then
becomes redder during the light-curve decline to $0.71$ mag until $\approx 60$
days and stays roughly constant thereafter. During the second light-curve
peak, it becomes bluer again to $0.47$ mag, then redder to $0.91$ mag until
$\approx 380$ days and stays roughly constant thereafter. Assuming a blackbody
SED, the $g-r$ color evolution corresponds to effective temperature evolution
of $7000\rightarrow 10700\rightarrow 5300\,{\rm K}$ and $5300\rightarrow
6300\rightarrow 4700\,{\rm K}$ during the first and second peaks,
respectively. The actual effective temperatures are likely higher given the
H$\alpha$ line contribution in the $r$-band photometry.

To extract SN and CSM properties from the light-curve modeling in §5, we
construct a bolometric light curve of SN 2021qqp (Figure 8) by fitting and
integrating a blackbody SED to every epoch of photometry containing at least
three filters obtained within 2 days of each other. We note that due to the
strong H$\alpha$ emission feature (Figure 2), the fitted blackbody
temperatures may be underestimated by up to $1500$ K compared to fits of the
spectra (excluding the H$\alpha$ region) at similar epochs; however, the radii
are also overestimated such that the resultant bolometric luminosities agree
within their error bars. By integrating the bolometric light curve, the total
radiated energy is estimated to be $9.5\times 10^{49}$ erg, requiring a
radiative efficiency of $\sim 10\%$ for a typical SN explosion energy of
$10^{51}$ erg. This is divided to $7.2\times 10^{49}$ and $2.3\times 10^{49}$
erg at the first and second peaks, respectively.

####  4.2.1 Comparison to Other Transients

Figure 5: Comparison of the $r$/$R$-band light curve of SN 2021qqp with SNe
IIn 2019zrk and 2009ip, Ibn 2022pda, Icn 2021csp, and ZTF SN IIn sample, as
well as LRN V1309 Scorpii (in the $V$/$I$ band shifted by $-12.5$ mag). SN
2021qqp is characterized by the sharp first peak (half-maximum rise time of
$t_{1/2,{\rm rise}}\approx 4$ days) and distinct luminous second peak
($\approx-17.3$ mag at $335$ days). The precursor and peak magnitudes are
similar to SNe 2019zrk and 2022pda and brighter than SN 2009ip and LRN V1309
Scorpii, while the decline rate in the $30$ days after maximum is higher than
SNe 2019zrk and 2022pda and lower than SN 2021csp. The objects with precursor
events show changes in the slope, i.e., a short ($\approx 5-10$ days)
plateau/peak, within $30$ days of the maximum. Data sources: SNe 2019zrk ($r$
band from Fransson et al. 2022), 2009ip ($R$ band from Prieto et al. 2013;
Mauerhan et al. 2013b; Pastorello et al. 2013; Fraser et al. 2013; Margutti et
al. 2014; Graham et al. 2014, and $r$ band from Graham et al. 2014, 2017),
2022pda ($r$ band retrieved via ZTF forced-photometry server in this work),
and 2021csp ($r$ band from Perley et al. 2022; Pellegrino et al. 2022), LRN
V1309 Scorpii ($I$ band from Tylenda et al. 2011 and $V$ band from Pojmanski
2002 retrieved via AAVSO International Database), and ZTF SN IIn sample ($r$
band retrieved via the ALeRCE ZTF Explorer; Förster et al. 2021).

In Figure 5, we compare the $r$-band light curve of SN 2021qqp with several
other well-observed interaction-dominated transients: precursor-associated SNe
IIn 2009ip (Smith et al., 2010; Foley et al., 2011; Prieto et al., 2013;
Mauerhan et al., 2013b; Pastorello et al., 2013; Fraser et al., 2013; Margutti
et al., 2014; Levesque et al., 2014; Smith et al., 2014; Graham et al., 2014;
Mauerhan et al., 2014; Martin et al., 2015; Fraser et al., 2015; Graham et
al., 2017; Reilly et al., 2017; Smith et al., 2022) and Ibn 2022pda161616Pre-
explosion activity is first noted by Fulton et al. (2022). and fast-evolving
SN Icn 2021csp (Fraser et al., 2021; Perley et al., 2022; Pellegrino et al.,
2022), as well as the luminous red nova (LRN) V1309 Scorpii, argued to arise
from a stellar merger (Mason et al., 2010; Tylenda et al., 2011).

The average precursor and peak magnitudes of SN 2021qqp are more luminous than
SN IIn 2009ip (by $-2.8$ and $-1.6$ mag, respectively) and LRN V1309 Scorpii
(by $-12.4$ and $-12.5$ mag, respectively), and comparable to SNe IIn 2019zrk
and Ibn 2022pda. The characteristic sharp concave-up curvature around maximum
is similar to LRN V1309 Scorpii, albeit with a longer timescale. The peak
magnitudes and half-maximum rise time (the duration above the half-maximum on
the rising phase) of $t_{1/2,{\rm rise}}\approx 4$ days (similar in the $g$
band as well) are within the fast blue optical transient (FBOT) regime, mainly
composed of SNe Ibn/Icn and AT 2018cow-like transients (e.g., Drout et al.
2014; Ho et al. 2019, 2023; Perley et al. 2022; Pellegrino et al. 2022), while
the decline rate in the $30$ days after the maximum is slower than SN Icn
2021csp and faster than SNe IIn 2019zrk and Ibn 2022pda. Interestingly, the
events with precursors show a short ($\sim 5-10$ day) plateau/peak within $30$
days of the maximum (see also Reguitti et al. 2022 for a similar plateau seen
in precursor-associated SN IIn/Ibn 2021foa). These overall light-curve
similarities among different types of transients may suggest a similar
progenitor scenario with differing CSM H/He abundance and explosion energy
(see further §6).

We also collect the $r$-band light curves of ZTF objects classified as “SN
IIn”, “SN IIn-pec”, or “SLSN-II” on TNS and/or the Weizmann Interactive
Supernova Data Repository171717https://wiserep.weizmann.ac.il (WISeREP; Yaron
& Gal-Yam 2012) using the ALeRCE ZTF Explorer181818https://alerce.online/
(Förster et al., 2021) and show them in Figure 5. Initial visual inspections
of the light curves suggest there may be a few more objects with a concave-up
curvature like SN 2021qqp, making up only a few percent of the SN IIn sample.
Given their luminous sharp peaks, they may appear as FBOTs in magnitude-
limited surveys if they happen at a large distance with only near-peak
coverage ($\lesssim-18$ mag). Among the SN IIn sample, SN 2021qqp is unique in
its distinct sharp second peak. A more quantitative sample analysis of the
light-curve curvatures will be presented in a future work (D. Hiramatsu et al.
in preparation).

###  4.3 Spectral Evolution

As seen in Figure 2, the spectra of SN 2021qqp are initially dominated by
Balmer lines on top of a blue continuum ($\leq-13.5$ days), with weaker He i,
Na i, Ca i, and Fe ii lines appearing later as the continuum drops ($\geq
314.9$ days). These spectral behaviors are typically seen in SNe IIn (e.g.,
Gal-Yam 2017). The H$\alpha$ and H$\beta$ lines track the light-curve
evolution (Figure 1) in that their luminosities increase at the light-curve
peaks, likely indicating interaction with a denser CSM (e.g., Chugai 1991;
Salamanca et al. 1998).

Figure 6: Line profile evolution of H$\alpha$ (Left) and H$\beta$ (Right) of
SN 2021qqp. Multi-component (absorption, core, and broad) Gaussian fits are
shown where the absorption minima and core FWHMs are used to estimate the
SN–CSM shell and CSM velocites, respectively. The H$\alpha$ and H$\beta$ lines
co-evolve with the light curve (Figure 1) in that the more luminous line
emission is seen at the light-curve peaks.

In order to decompose the H$\alpha$ and H$\beta$ line profiles, we fit multi-
component Gaussians (absorption, core, and broad; Figure 6) when a certain
component is visible in a spectrum. In the first two spectra taken during the
rise to the light-curve maximum ($-35.4$ to $-13.5$ days), the H$\alpha$ and
H$\beta$ line profiles can be fit well with all three components,191919Except
for the broad H$\beta$ component in the second spectrum due to its low signal-
to-noise ratio, which may result in an overestimation of the core component.
with the resulting absorption minima at $\approx 7000-8900$ km s-1 and core
FWHMs of $\approx 1300-1900$ km s-1. In the fourth spectrum taken at the
light-curve second peak ($335.1$ days),202020We exclude the third spectrum due
to its low signal-to-noise ratio. all three components are still visible in
H$\alpha$ with the broad component peak redshifted, while no broad component
is visible in H$\beta$ due to the presence of strong Fe ii emission. In the
final two spectra taken during the decline from the second peak ($364.7$ to
$367.6$ days), absorption component is still visible in H$\beta$, but not
clearly in H$\alpha$. During the second peak ($314.9$ to $367.6$ days), the
H$\alpha$ and H$\beta$ absorption minima and core FWHMs correspond to $\approx
4200-5600$ and $\approx 2100-2680$ km s-1, respectively.

We associate the H$\alpha$ absorption and line core velocities with the SN–CSM
shell and CSM, respectively (the core CSM component and the absorption + broad
P Cygni components from the SN–CSM shell; Figure 8) and reproduce them with
the light-curve modeling in §5. The SN–CSM shell velocity decreases from
$\approx 8500$ to $\approx 5600$ km s-1 from the first to second light-curve
peaks, while the CSM velocity increases from $\approx 1300$ to $\approx
2300-2680$ km s-1 from the first to second light-curve peaks (i.e., earlier
CSM ejection is moving faster). This increasing CSM velocity is on the fast
end of those seen in typical SN precursors (Ofek et al., 2014; Strotjohann et
al., 2021) and comparable to some faster components seen, for example, in the
SN 2009ip precursors (Smith et al., 2010; Foley et al., 2011; Mauerhan et al.,
2013b; Pastorello et al., 2013) and some giant eruptions of Eta Carinae
(Smith, 2008; Smith et al., 2018). Finally, we note that a narrower wind P
Cygni component is not detected on top of the core component, but we cannot
rule out its existence below our spectral resolution ($\lesssim 200$ km s-1).

##  5 Modeling with CSM Interaction

###  5.1 Analytical Model

Given the observed properties of SN 2021qqp (§4), we model the light curve
assuming the emission is produced purely by the shock interaction between the
SN ejecta and CSM. For multi-peak transients like SN 2021qqp, the CSM is
expected to have a more complicated profile than a single power law as adopted
in many previous studies (e.g., Chatzopoulos et al. 2012; Moriya et al.
2013b). While it is still possible to use a more complicated functional form
for the CSM (e.g., a single power law and Gaussian; Gomez et al., 2021;
Hosseinzadeh et al., 2022), here we propose a more flexible approach that does
not require the functional form of the CSM profile. A more detailed
description and application to other interacting transients will be presented
in a forthcoming paper (T. Matsumoto et al. in preparation).

We consider SN ejecta colliding with the CSM, which forms a shell separated
from the un-shocked CSM and SN ejecta by a forward shock (FS) and a reverse
shock (RS), respectively. Assuming the shell is geometrically thin and hence
its location, velocity, and mass are given by $R_{\rm sh}$, $v_{\rm sh}$, and
$M_{\rm sh}$, the time evolution of the shell is described by two equations
(Chevalier, 1982; Moriya et al., 2013b),

$\displaystyle M_{\rm sh}\frac{dv_{\rm sh}}{dt}$ $\displaystyle=4\pi R_{\rm
sh}^{2}\rho_{\rm SN}(v_{\rm SN}-v_{\rm sh})^{2}-4\pi R_{\rm sh}^{2}\rho_{\rm
CSM}(v_{\rm sh}-v_{\rm CSM})^{2},$ (1) $\displaystyle\frac{dM_{\rm sh}}{dt}$
$\displaystyle=4\pi R_{\rm sh}^{2}\rho_{\rm SN}(v_{\rm SN}-v_{\rm sh})+4\pi
R_{\rm sh}^{2}\rho_{\rm CSM}(v_{\rm sh}-v_{\rm CSM})\ ,$ (2)

where $\rho_{\rm SN}$ and $v_{\rm SN}=R_{\rm sh}/t$ are the density and
velocity of the un-shocked SN ejecta at $R_{\rm sh}$, respectively, and
$\rho_{\rm CSM}$ and $v_{\rm CSM}$ are the un-shocked CSM density and
velocity, respectively. We assume that the un-shocked SN ejecta expands
homologously, and its density is approximated by a broken power-law profile
(e.g., Chevalier & Fransson, 1994; Matzner & McKee, 1999),

$\displaystyle\rho_{\rm
SN}(v,t)=A\begin{cases}(v/v_{*})^{-\delta}&\,\,v<v_{*}\ ,\\\
(v/v_{*})^{-n}&\,\,v\geq v_{*}\ ,\end{cases}$ (3)

where

$\displaystyle v_{*}$ $\displaystyle=\sqrt{\frac{2(5-\delta)(n-5)E_{\rm
SN}}{(3-\delta)(n-3)M_{\rm SN}}}$ (4)
$\displaystyle\overset{\begin{subarray}{c}\delta=0\\\
n=12\end{subarray}}{\approx}3600{\,\rm km\,s^{-1}\,}\left(\frac{M_{\rm
SN}}{10\,M_{\odot}}\right)^{-1/2}\left(\frac{E_{\rm SN}}{10^{51}{\,\rm
erg}}\right)^{1/2}\ ,$

where $M_{\rm SN}$ and $E_{\rm SN}$ are the total mass and kinetic energy of
the SN ejecta, respectively. Typically, $\delta=0-1$ and $n\simeq 12$ is
expected for red supergiant progenitors or $n\simeq 10$ for progenitors with
radiative envelopes, e.g., blue supergiants (Matzner & McKee, 1999). The
normalization $A$ is given such that the integration of $\rho_{\rm SN}$ gives
$M_{\rm SN}$.

In contrast to previous works that used a parameterized CSM profile, we
determine it by requiring the shock luminosity to produce the observed
bolometric luminosity,

$\displaystyle L_{\rm obs}\approx\varepsilon_{\rm FS}L_{\rm
kin,FS}+\varepsilon_{\rm RS}L_{\rm kin,RS},$ (5)

where the dissipated kinetic energy luminosities at the FS and RS are given by

$\displaystyle L_{\rm kin,FS}$ $\displaystyle=\frac{9\pi}{8}R_{\rm
sh}^{2}\rho_{\rm CSM}(v_{\rm sh}-v_{\rm CSM})^{3}\ ,$ (6) $\displaystyle
L_{\rm kin,RS}$ $\displaystyle=\frac{9\pi}{8}R_{\rm sh}^{2}\rho_{\rm
SN}(v_{\rm SN}-v_{\rm sh})^{3}\ ,$ (7)

where we assumed an ideal gas (see, e.g., Metzger et al., 2014). The
quantities $\varepsilon_{\rm FS}$ and $\varepsilon_{\rm RS}$ represent the
conversion efficiency from the dissipated energy to optical photons. While the
efficiencies may vary with time (e.g., Tsuna et al., 2019), we simply assume a
constant and identical efficiency for both FS and RS: $\varepsilon_{\rm
FS}=\varepsilon_{\rm RS}=\varepsilon$. With Equations (5) and (6), the CSM
density is estimated by

$\displaystyle\rho_{\rm CSM}=\frac{8(L_{\rm obs}-\varepsilon L_{\rm
kin,RS})}{9\pi\varepsilon R_{\rm sh}^{2}(v_{\rm sh}-v_{\rm CSM})^{3}}\ .$ (8)

We can then rewrite Equations (1) and (2) without the CSM density:

$\displaystyle M_{\rm sh}\frac{dv_{\rm sh}}{dt}$
$\displaystyle=-\frac{32L_{\rm obs}}{9\varepsilon(v_{\rm sh}-v_{\rm
CSM})}+\frac{32(v_{\rm SN}-v_{\rm CSM})L_{\rm kin,RS}}{9(v_{\rm SN}-v_{\rm
sh})(v_{\rm sh}-v_{\rm CSM})}\ ,$ (9) $\displaystyle\frac{dM_{\rm sh}}{dt}$
$\displaystyle=\frac{32L_{\rm obs}}{9\varepsilon(v_{\rm sh}-v_{\rm CSM})^{2}}$
$\displaystyle+$ $\displaystyle\frac{32(v_{\rm SN}-v_{\rm CSM})(2v_{\rm
sh}-v_{\rm SN}-v_{\rm CSM})L_{\rm kin,RS}}{9(v_{\rm SN}-v_{\rm sh})^{2}(v_{\rm
sh}-v_{\rm CSM})^{2}}\ .$ (10)

We note that the kinetic luminosity, $L_{\rm kin,RS}$, can be calculated for a
given $R_{\rm sh}$ and $v_{\rm sh}$ for an assumed SN ejecta profile by using
Equation (7).

Equations (9) and (10), with $dR_{\rm sh}/dt=v_{\rm sh}$, can be solved for a
given observed bolometric light curve ($L_{\rm obs}$) and assumed SN
properties ($E_{\rm SN}$, $M_{\rm SN}$, $\delta$, and $n$), the emission
efficiency $\varepsilon$, and the CSM velocity $v_{\rm CSM}$. As an initial
condition, we assume that the interaction happens at $t_{0}$ since the SN
explosion (at $t_{\rm exp}$) with the initial shell velocity $v_{\rm sh,0}$.
The initial shell mass is dominated by the swept-up SN ejecta, which is given
by $M_{\rm sh,0}=M_{\rm SN}(>v_{\rm sh,0})=\int_{v_{\rm sh,0}}4\pi
r^{2}\rho_{\rm SN}dr$. Once the time evolution of $R_{\rm sh}$ and $v_{\rm
sh}$ are obtained, the density profile is reconstructed using Equation (6). We
assume the shock power completely dominates the light curve and neglect any
radioactive nickel heating. This can be justified for SN 2021qqp given its
sharp concave-up first peak and blueward color evolution (Figure 1),
indicating that shock interaction shapes the light curve.

###  5.2 Application to SN 2021qqp

We apply our analytical model to SN 2021qqp to determine the required SN and
CSM properties. In Figure 8, we show representative solutions for different
assumed SN energies and fixed parameters of $M_{\rm SN}=10\,M_{\odot}$,
$\delta=0$, $n=12$, and $\varepsilon=0.3$. The choice of the values of
$\delta$ and $n$ does not noticeably affect the result. The value of
$\varepsilon$ is motivated by having a mildly optically thick CSM, as well as
the required energetics (see below). We assume that the SN explosion happened
at a phase of $t_{\rm exp}=-65\,\rm days$ (i.e., at the SN first light; §4.2)
and the shock interaction started $0.01\,\rm days$ after the explosion (i.e.,
$t_{0}-t_{\rm exp}=0.01\,\rm day$). The following results do not change
significantly for different values of $t_{\rm exp}$ and $t_{0}$ unless it is
after the first peak (i.e., $t_{0}\gtrsim 0\,\rm day$). Motivated by the
observed H$\alpha$ line profiles (Figure 6), the initial shell velocity is set
to $v_{\rm sh,0}=8500\,\rm km\,s^{-1}$, and we consider a gradually increasing
CSM velocity from $v_{\rm CSM}\simeq 1500$ to $2200\,\rm km\,s^{-1}$. As the
observed bolometric light curve has a gap between 100 and 300 days due to the
Sun constraint, we linearly interpolate the light curve to fill the gap.

The right panel of Figure 8 shows the time evolution of the shell velocity. At
the fist peak, the shell decelerates by colliding with the massive CSM,
producing the first light-curve peak. For large SN energies, the deceleration
is weak, and the shell moves almost at a constant velocity, while for smaller
energies, the deceleration is significant and even stalls the shell. These
evolution for very low and high $E_{\rm SN}$ are inconsistent with the
observed line velocity (black points). A mild deceleration, as required by the
spectroscopic data, is realized only for a moderate SN energy of $E_{\rm
SN}\approx 4\times 10^{51}\,\rm erg$. The left panel of Figure 8 depicts the
resulting RS shock luminosity (dashed curves), as well as the observed
bolometric luminosity (black curve). By construction, the observed luminosity
is automatically reproduced by the sum of the FS and RS luminosities. When the
shell decelerates at the first peak, the SN ejecta catches up with the shell
and powers bright RS emission. In particular, for drastic deceleration, the RS
luminosity exceeds the observed bolometric luminosity, and such a solution
($E_{\rm SN}\lesssim 2\times 10^{51}\,\rm erg$) can be rejected. For this
particular choice of $M_{\rm SN}=10\,M_{\odot}$, the modeled RS luminosity and
velocity evolution for $E_{\rm SN}\approx 4\times 10^{51}\,\rm erg$ are both
consistent with SN 2021qqp.

Figure 7: The bolometric light curve (Left) and time evolution of shell
velocity (Right) for different SN explosion energies, with other parameters
fixed to $M_{\rm SN}=10\,M_{\odot}$, $n=12$, $\delta=0$, $\varepsilon=0.3$,
$v_{\rm sh,0}=8500\,\rm km\,s^{-1}$, and $t_{\rm exp}=-65\,\rm days$ (shown by
the vertical black dashed line). We assume that the shock interaction starts
almost at the same time as the SN explosion ($t_{0}-t_{\rm exp}=0.01\,\rm
day$). The velocities inferred from the absorption and core-emission of the
H$\alpha$ lines (Figure 6) are shown by black and gray points, respectively.
The former and latter likely correspond to the shell and CSM velocities,
respectively. The CSM velocity increases with time (gray dashed-dotted line).
In the left panel, the dashed curves show the RS luminosities. For this
particular set of assumed parameters, we find $E_{\rm SN}\approx 4\times
10^{51}$ erg matches both the velocity evolution and the requirement that
$L_{\rm RS}\lesssim L_{\rm obs}$. In the left panel, the linearly interpolated
gap in the observed light curve for $100$–$300\,\rm days$ is shown by a dotted
line.

Figure 8: CSM density at the FS crossing (Left) and time evolution of the
mass-loss rate relative to the time of SN explosion (Right) reconstructed by
using the results in Figure 8. Both CSM density and mass-loss rate have a
double peak as expected from the observed light curve. The SN energies of
$E_{\rm SN}\leq 2\times 10^{51}\,\rm erg$ (shown with light colors) are
rejected because they give a stalling shell or unphysical negative FS
luminosity (i.e., $L_{\rm RS}\gtrsim L_{\rm obs}$). In the left panel, the
black dashed curve shows a rough estimate of the optical depth
($\rho=1/(\kappa R_{\rm sh})$ with $\kappa=0.32\,\rm cm^{2}\,g^{-1}$). The CSM
density should roughly satisfy $\tau\gtrsim 1$ so that we observe thermal
(optical) emission. The dotted segment of each result corresponds to the gap
in the light curve for $100-300\,\rm days$ (see the left panel of Figure 8).

In Figure 8, we show the CSM density when the FS arrives at each radius and
the reconstructed mass-loss rates resulting from the models in Figure 8. It
should be noted that the CSM density does not represent the CSM profile
because the CSM expands at different velocities. For a less energetic SN, the
CSM density is higher to compensate for the lower shell velocity and still
reproduce the observed luminosity. For $\varepsilon=0.3$, the CSM has a
moderate optical depth $\tau\sim 1$, which may be consistent with the observed
optical emission.212121It is not trivial whether the CSM optical depth should
be smaller or larger than unity. On the one hand, the optical depth may be
required to be $\tau>1$ to avoid bright hard X-ray emission. On the other
hand, $\tau<1$ may also be required to explain the observed velocities in the
Balmer lines. These disagreeing requirements likely indicate the limitation of
the assumption of spherical symmetry. We defer a more detailed discussion to a
future work. Corresponding to the double-peaked light curve, we find that the
CSM density has two distinct peaks, indicating that the progenitor experienced
two distinct mass-loss episodes. To explore this structure, we translated the
density to a mass-loss rate in the right panel of Figure 8. We find that the
mass-loss rate is as high as $\sim 1-10\,M_{\odot}\,\rm yr^{-1}$ at $\approx
0.8$ and $\approx 2$ yr before the explosion (for the model with $E_{\rm
SN}\approx 4\times 10^{51}$ erg) over relatively short episodes of $\approx
0.2-0.5\,\rm yr$. The mass-loss episode directly preceding the SN explosion is
more extreme. The total CSM mass is $M_{\rm CSM}\approx 2.7\,M_{\odot}$ (for
$E_{\rm SN}=4\times 10^{51}\,\rm erg$). The bluer $g-r$ color evolution and
more luminous H$\alpha$ and H$\beta$ line emission around the light-curve
peaks can also be explained by the interaction with these denser CSM.

Figure 9: Estimated CSM mass for different SN ejecta masses and energies. The
other parameters are the same as those adopted for Figure 8. The parameters
giving the shell velocity consistent with the observed one ($5640\pm 530\,\rm
km\,s^{-1}$ at $335$ days) are shown by black curves. Along the black dashed
line, the initial velocity is the same as the characteristic ejecta velocity
(Equation 4). The dotted gray vertical and diagonal lines (Equations 12 and
13, respectively) give rough boundaries within which the shell does not stall
during the observation.

The results above were provided for a fixed example value of $M_{\rm
SN}=10\,M_{\odot}$. To explore the parameter space of SN properties more
broadly, we carried out the same analysis for different SN ejecta masses and
energies to find the parameter space consistent with the observed light curve
and velocities. In Figure 9, we show the allowed parameter region. The colored
region denotes the space over which the shell expands continuously without
stalling and gives a finite $M_{\rm CSM}$. We derive the parameter space
satisfying the condition that the shell decelerated mildly and its velocity at
$335$ days is consistent with the observed value of $5640\pm 530\,\rm
km\,s^{-1}$. The allowed region is enclosed by the black thin curves
accounting for the velocity uncertainty, while the black thick curve
corresponds to the velocity being exactly the same as the observed value.
Along the allowed region, the CSM mass is relatively well constrained to
$M_{\rm CSM}\approx 2-4\,M_{\odot}$. The SN ejecta is constrained to have an
energy of $\gtrsim 3\times 10^{51}\,\rm erg$, which is slightly larger than
typical values but still consistent with the stellar explosion scenario,
potentially further enhanced by jets (e.g., Soker 2010; Papish & Soker 2011;
Shishkin & Soker 2023).

The allowed parameter space exhibits two branches, based on the initial shell
velocity $v_{\rm sh,0}$. Too-low initial velocity $v_{\rm sh,0}<v_{*}$ (left
of the black dashed diagonal line in Figure 9) means that most of the SN
ejecta forms a shell instantaneously when the shock interaction starts, which
is not natural, and we therefore disfavor this portion of the parameter space.
More natural solutions appear for the initial shell velocity larger than
$v_{*}$, which means that the shock interaction begins at the high-velocity
tail in the SN ejecta. In this case, the initial shell mass is much smaller
than the whole SN ejecta, and the shell readily decelerates when it collides
with a dense CSM bump.

We can derive critical conditions for which the shell stalls during the
observation. These conditions are obtained by considering the initial
deceleration timescale of the shell,

$\displaystyle t_{\rm dec}$ $\displaystyle=\frac{v_{\rm sh,0}}{dv_{\rm
sh}/dt}\approx\frac{9\varepsilon M_{\rm sh,0}v_{\rm sh,0}^{2}}{32L_{\rm obs}}\
,$ (11)

where we used Equation (9) neglecting the CSM velocity and RS luminosity. When
the initial shell velocity is smaller than the SN characteristic velocity,
$v_{*}$, the deceleration timescale is determined by the SN mass. By equating
$t_{\rm dec}$ with the characteristic emission timescale (e.g., peak
timescale), we have a critical mass below which the shell stalls over the
emission timescale,

$\displaystyle M_{\rm SN,\times}\approx
0.6{\,M_{\odot}\,}\left(\frac{\varepsilon}{0.3}\right)^{-1}\left(\frac{E_{\rm
rad}}{10^{50}\,\rm erg}\right)\left(\frac{v_{\rm sh,0}}{10^{4}\,\rm
km\,s^{-1}}\right)^{-2}\ ,$ (12)

where $E_{\rm rad}$ is the radiated energy over the peak timescale. The gray
dotted vertical line shows this condition.

For the case of higher initial velocity $v_{\rm sh,0}>v_{*}$, the shell’s mass
is smaller than the total SN ejecta mass. In the same way as for Equation
(12), we have a relation between $E_{\rm SN}$ and $M_{\rm SN}$ corresponding
to the gray dotted diagonal line,

$\displaystyle E_{\rm SN,\times}>$ $\displaystyle 2.9\times 10^{51}{\,\rm
erg\,}\left(\frac{\varepsilon}{0.3}\right)^{-2/9}\left(\frac{E_{\rm
rad}}{5\times 10^{48}\,\rm erg}\right)^{2/9}$ $\displaystyle\left(\frac{M_{\rm
SN}}{10\,M_{\odot}}\right)^{7/9}\left(\frac{v_{\rm
sh,0}}{10^{4}{\,\rm\,km\,s^{-1}}}\right)^{14/9}\ ,$ (13)

where we used $n=12$ and $\delta=0$ and the radiated energy up to $-20$ days
because the shell decelerates and stalls roughly before this timescale. This
condition also gives a scaling law for the allowed parameter space,

$\displaystyle E_{\rm SN}\approx 4\times 10^{51}{\,\rm
erg\,}\left(\frac{\varepsilon}{0.3}\right)^{-2/9}\left(\frac{M_{\rm
SN}}{10\,M_{\odot}}\right)^{7/9}\ ,$ (14)

along the black thick curve with $v_{\rm sh,0}>v_{*}$. Within a reasonable
energy range of $E_{\rm SN}\approx(3-10)\times 10^{51}$ erg in the allowed
parameter space, the corresponding allowed mass range is $M_{\rm SN}\approx
5-30\,M_{\odot}$.

##  6 Summary and Discussion

Before addressing the implications of our findings, below we summarize the key
observed and modeled properties of SN 2021qqp (§4 and §5):

  * •

A luminous ($-15.8\,{\rm mag}\lesssim M_{g,r,i}\lesssim-14.5\,{\rm mag}$) and
long-lasting ($\sim 300$ days) precursor leading up to the SN explosion.

  * •

A multi-peaked SN light curve with a first concave-up peak ($M_{g}=-19.4$,
$M_{r}=-19.5$ mag) $\approx 65$ days after explosion and a second concave-down
peak ($M_{g}=-16.7$, $M_{r}=-17.3$ mag) $\approx 335$ days after first peak.

  * •

Bluer $g-r$ colors (i.e., higher temperatures) around the light-curve peaks.

  * •

Spectra dominated by Balmer lines, with weaker He i, Na i, Ca i, and Fe ii
lines.

  * •

More luminous H$\alpha$ and H$\beta$ line emission around the light-curve
peaks.

  * •

A decreasing shell velocity (from $\approx 8500$ km s-1 in the first peak to
$\approx 5600$ km s-1 in the second peak) and increasing CSM velocity (from
$\approx 1300$ km s-1 in the first peak to $\approx 2500$ km s-1 in the second
peak).

  * •

Two distinct CSM density peaks from episodic mass loss ($\dot{M}\approx
10\,M_{\odot}\,{\rm yr}^{-1}$ about $0.8$ yr before explosion and $\approx
5\,M_{\odot}\,{\rm yr}^{-1}$ about $2$ yr before explosion), with a total CSM
mass of $M_{\rm CSM}\approx 2-4\,M_{\odot}$.

  * •

An allowed SN ejecta mass range of $M_{\rm SN}\approx 5-30\,M_{\odot}$ for an
explosion energy range of $E_{\rm SN}\approx(3-10)\times 10^{51}$ erg,
satisfying a consistent RS luminosity limit and the observed velocity
evolution.

These observed and modeled properties suggest eruptive mass-loss episodes
preceding an energetic explosion. The final mass-loss episode is likely
related to the pre-explosion outburst detected starting about a year before
the explosion with a luminosity of $\approx 3\times 10^{41}\,\rm erg\,s^{-1}$
(Figure 5). Such a precursor can be produced by an eruption of a giant star
($\sim 10^{2}\,R_{\odot}$) with an ejection mass of a few $M_{\odot}$ and
velocity of $\sim 10^{3}$ km s-1 (Matsumoto & Metzger, 2022b), which is
consistent with the inferred CSM properties (Figures 8–9). The previous mass-
loss episode with a less violent mass ejection may result in a luminosity
around the detection threshold of $\approx 10^{41}\,\rm erg\,s^{-1}$ with a
shorter duration of $\approx 30$ days. We remark that the ejected material in
this episode $2$ yr before explosion would not affect the observed precursor
because its optical depth is at most $\tau\sim 1$ (see the left panel in Fig.
8).

We now discuss two possible progenitor channels for generating SN
2021qqp:222222The sharp light-curve morphology also resembles gravitational
microlensing events (e.g., Gaudi 2012); however, the chromatic evolution seen
in SN 2021qqp excludes such a possibility. (i) stellar activity preceding an
SN explosion (e.g., Poelarends et al. 2008; Quataert & Shiode 2012; Jones et
al. 2013; Shiode & Quataert 2014; Quataert et al. 2016; Fuller 2017; Doherty
et al. 2017; Fuller & Ro 2018; Wu & Fuller 2021, 2022; Matsumoto & Metzger
2022b) and (ii) common envelope (CE) evolution preceding a stellar merger
(e.g., Chevalier 2012; Pejcha et al. 2016, 2017; MacLeod et al. 2017; Metzger
& Pejcha 2017; MacLeod et al. 2018b, a; Schrøder et al. 2020; MacLeod & Loeb
2020b, a; Metzger 2022; Matsumoto & Metzger 2022a).

As the first scenario, we consider the eruptive mass-loss episodes from pre-
explosion stellar activity. Typical mass-loss rates and velocities from
supergiant stars (e.g., extreme red supergiant and super-asymptotic giant
branch stars; Smith 2014, 2017a) of $\dot{M}\lesssim 10^{-3}\,M_{\odot}\,{\rm
yr}^{-1}$ and $v_{\rm CSM}\leq 100$ km s-1, respectively, are lower than the
inferred CSM values. Enhancements in mass loss may be achieved with thermal
pulses and/or internal gravity waves excited by late-stage nuclear burning
(e.g., He, C, O/Ne, and Si; Poelarends et al. 2008; Shiode & Quataert 2014;
Fuller 2017; Wu & Fuller 2022); however, the expected maximum energy output of
$\lesssim 10^{48}$ erg is lower than the observed radiated energy of $\approx
8\times 10^{48}$ erg during the SN 2021qqp precursor. Instead, LBV giant
eruptions, like those seen in Eta Carinae, P Cygni, and SN impostors
($\dot{M}\sim 10^{-2}-10\,M_{\odot}\,{\rm yr}^{-1}$ and $v_{\rm CSM}\sim
100-1000$ km s-1; e.g., Humphreys & Davidson 1994; Davidson & Humphreys 1997;
Vink 2012; Van Dyk & Matheson 2012; Smith 2014, 2017b), may be responsible for
the precursor, given their comparable luminosities. Although the high initial
mass range of LBVs ($\gtrsim 30\,M_{\odot}$) seems to be at odds with the
estimated SN ejecta mass ($\lesssim 30\,M_{\odot}$ for $E_{\rm SN}\lesssim
10^{52}$ erg; Figure 9), this might be reconciled through significant mass
loss in successive eruptions prior to the explosion (e.g., Vink 2012; Smith et
al. 2019).

A more exotic explanation in the context of eruptive mass loss is a PPISN
(e.g., Woosley et al. 2007; Blinnikov 2010; Moriya et al. 2013a; Woosley
2017). The ejecta mass and explosion energy inferred for SN 2021qqp may be
reproduced with a PPISN model with an initial mass range of $\sim
110-140\,M_{\odot}$ (Woosley, 2017). In this model, the bulk of the mass is
lost during the progenitor’s evolution and pair-instability pulses, followed
by a final collapse to a black hole (BH). The expected pulsational pulse
intervals span a wide range, but if several pulses with H-rich mass ejection
could occur in the last few years before collapse, the CSM configuration might
resemble that of SN 2021qqp.

On the other hand, the similarity of SN 2021qqp’s light curve to that of LRN
V1309 Scorpii (Figure 5) motivates the alternative scenario of a stellar
merger. Although the energetics for LRNe from a typical stellar merger
($\lesssim 10^{41}$ erg s-1; Pejcha et al. 2016, 2017; Metzger & Pejcha 2017;
Matsumoto & Metzger 2022a) are well below what is required for SN 2021qqp, a
merger of a Wolf-Rayet (WR) star and a neutron star (NS) or BH (e.g.,
Chevalier 2012; Schrøder et al. 2020; Metzger 2022) may be able to reproduce
the light curve of SN 2021qqp. In this scenario, a massive star ($\gtrsim
20\,M_{\odot}$) and NS/BH (from an earlier SN) undergo CE evolution, leaving a
tight WR-NS/BH binary. The H-rich CE ejection is manifested as a precursor,
and if a merger-induced explosion ($>10^{51}$ erg) follows promptly ($\lesssim
10$ yr), the system may resemble a precursor-associated SN IIn. The estimated
CSM and SN ejecta masses for SN 2021qqp are within the model expectations if
the merger happens within $\sim 1$ yr of the CE ejection. However, it is
unclear if this model can produce successive mass ejections with $\sim 10^{3}$
km s-1 that can reproduce the multi-peaked CSM density profile of SN 2021qqp
(Figure 8). This may be possible if several eccentric encounters happen prior
to the onset of the CE phase (e.g., Vigna-Gómez et al. 2020; Vick et al.
2021), leading to successive CSM peaks as increasing quasi-periodic mass
ejections are expected toward the merger (see e.g., Soker & Kashi 2013; Kashi
et al. 2013 for an application to SN 2009ip). Continued optical monitoring of
SN 2021qqp may reveal the presence of even earlier CSM peaks that may be
expected in this eccentric encounter scenario.

As proposed in Metzger (2022), depending on the time delay between the CE
ejection and stellar merger, this scenario may be responsible for the light-
curve similarities seen across different interacting SN types (Figure 5), with
the difference attributed to CSM H/He abundances. For example, SNe IIn 2009ip
and 2019zrk may arise similarly to the scenario considered for SN 2021qqp,
where the merger and explosion happen promptly while still embedded in the
H-rich CE. With a longer delay to the merger ($\sim 10^{4}$ yr), an unstable
Roche-lobe overflow from the WR onto the NS/BH creates a H-poor/He-rich CSM,
which may reproduce the precursor and explosion seen in an event like the Type
Ibn SN 2022pda. With an even longer delay ($\sim 10^{5}$ yr), the shock
interaction between the post-merger disk wind and pre-merger CSM may result in
an event such as the Type Icn SN 2021csp. Precursors for SNe Icn are yet to be
seen, but they have the potential to probe this late merger stage.

##  7 Conclusions

We have presented optical photometric and spectroscopic observations of the
unusual SN IIn 2021qqp, covering a year-long precursor preceding the explosion
and a second distinct peak about a year after the explosion. The precursor is
on the luminous ($-15.8\,{\rm mag}<M_{g,r,i}<-14.5\,{\rm mag}$) and long-
lasting ($\sim 300$ days) ends of the distribution for SN IIn, suggesting
extreme mass-loss event(s). The sharp first maximum ($M_{g}=-19.4$,
$M_{r}=-19.5$ mag) is characterized by a concave-up curvature, while the
second peak ($M_{g}=-16.7$, $M_{r}=-17.3$ mag) is characterized by a concave-
down curvature, with possible hints of additional bumps. Throughout the
evolution, the spectra are dominated by Balmer lines, with weaker He i, Na i,
Ca i, and Fe ii lines appearing around the second peak. By decomposing the
multi-component H$\alpha$ and H$\beta$ lines, the CSM and SN–CSM shell
velocities are estimated from the core FWHMs and absorption minima,
respectively, as $\approx 1300$ and $8500$ km s-1 (first peak) and $\approx
2500$ and $5600$ km s-1 (second peak).

Motivate by these observations, we have constructed an analytical model to
extract the CSM and SN properties from the bolometric light curve and velocity
evolution. We infer the presence of two distinct CSM density peaks resulting
from episodic mass loss with $\dot{M}\approx 10\,M_{\odot}\,{\rm yr}^{-1}$
about $0.8$ yr before explosion and $\dot{M}\approx 5\,M_{\odot}\,{\rm
yr}^{-1}$ about $2$ yr before explosion, with a total $M_{\rm CSM}\approx
2-4\,M_{\odot}$. Moreover, the light-curve precursor could be explained by the
most recent mass-loss episode. By imposing a consistent RS luminosity and
velocity evolution with the observations, the SN ejecta mass range is
constrained to be $M_{\rm SN}\approx 5-30\,M_{\odot}$ for an explosion energy
range of $E_{\rm SN}\approx(3-10)\times 10^{51}$ erg.

An eruptive massive star (LBV giant eruption, PPISN) or WR-NS/BH merger may be
possible progenitor channels for producing such an energetic explosion in a
complex CSM environment. Continued monitoring of SN 2021qqp is necessary to
further investigate the progenitor channel. If less luminous light-curve
peak(s), corresponding to less dense CSM peak(s), were seen quasi-
periodically, the stellar merger scenario with eccentric encounters would be
favored. The lack of such light-curve peak(s) or periodicity would instead
favor the eruptive stellar activity scenario.

Finally, we note that given the sharp light-curve morphology, events like SN
2021qqp may appear as FBOTs if only observed near peak, for example, at
$z\gtrsim 0.13$ for current transient surveys, such as ZTF, with a typical
limiting magnitude of $\approx 21$. We therefore speculate that some FBOTs may
have precursor activity and mass-loss episodes similar to those we infer for
SN 2021qqp. Looking forward, the much deeper observations available from the
Vera C. Rubin Observatory’s Legacy Survey of Space and Time ($\approx 25$ mag;
Ivezić et al. 2019) will reveal SN 2021qqp-like precursors ($\lesssim-14.5$
mag) to $z\approx 0.17$, providing a much larger sample size with complete
light-curve coverage (by a factor of $\approx 300$ for volume compared to
ZTF), including for FBOTs. Such a large sample of precursor-associated
transients coupled with our analysis and modeling frameworks presented here
would allow us to systematically explore detailed CSM configurations in a
self-consistent way and potentially map them to their progenitor systems.

##  8 acknowledgments

We are grateful to Morgan MacLeod, Brian Metzger, Noam Soker, Dillon Brout,
and Floor Broekgaarden for useful discussions; Joel Leja for helpful advice on
Prospector; Benjamin Weiner for scheduling the MMT Binospec observations; Yuri
Beletsky for performing the Magellan LDSS-3 observations; and Jamison Burke
for assisting in scheduling LCO observations.

The Berger Time-Domain research group at Harvard is supported by the NSF and
NASA. T.M. is supported in part by JSPS Overseas Research Fellowships. C.R.
and V.A.V. are supported by Charles E. Kaufman Foundation New Investigator
grant KA2022-129525. The LCO group is supported by NSF grants AST-1911151 and
AST-1911225. This publication was made possible through the support of an
LSSTC Catalyst Fellowship to K.A.B., funded through grant 62192 from the John
Templeton Foundation to LSST Corporation. The opinions expressed in this
publication are those of the authors and do not necessarily reflect the views
of LSSTC or the John Templeton Foundation.

Observations reported here were obtained at the MMT Observatory, a joint
facility of the Smithsonian Institution and the University of Arizona. This
paper includes data gathered with the 6.5 meter Magellan Telescopes located at
the Las Campanas Observatory, Chile.

This work makes use of observations from the Las Cumbres Observatory global
telescope network. This paper is based in part on observations made with the
MuSCAT3 instrument, developed by the Astrobiology Center and under financial
support by JSPS KAKENHI (grant No. JP18H05439) and JST PRESTO (grant No.
JPMJPR1775), at Faulkes Telescope North on Maui, HI, operated by the Las
Cumbres Observatory. The authors wish to recognize and acknowledge the very
significant cultural role and reverence that the summit of
Haleakal$\bar{\text{a}}$ has always had within the indigenous Hawaiian
community. We are most fortunate to have the opportunity to conduct
observations from the mountain.

This work has made use of data from the Zwicky Transient Facility (ZTF). ZTF
is supported by NSF grant No. AST-1440341 and a collaboration including
Caltech, IPAC, the Weizmann Institute for Science, the Oskar Klein Center at
Stockholm University, the University of Maryland, the University of
Washington, Deutsches Elektronen-Synchrotron and Humboldt University, Los
Alamos National Laboratories, the TANGO Consortium of Taiwan, the University
of Wisconsin at Milwaukee, and Lawrence Berkeley National Laboratories.
Operations are conducted by COO, IPAC, and UW. The ZTF forced-photometry
service was funded under the Heising-Simons Foundation grant No. 12540303 (PI:
Graham).

ALeRCE is an initiative funded by the Millennium Institute for Astrophysics –
MAS, the Center for Mathematical Modeling - CMM at Universidad de Chile, and
since 2020 the Data Observatory, in collaboration with researchers from
Universidad Adolfo Ibáñez - UAI, Universidad Austral de Chile - UACH
(Informatics), Universidad Catlica de Chile - UC (Astronomy), Universidad de
Chile - UCH (Astronomy - DAS, Electrical Engineering - DIE), Universidad de
Concepción - UdeC (Informatics), Universidad Nacional Andres Bello – UNAB
(Astronomy), Universidad de Santiago de Chile - USACH (Statistics),
Universidad Tecnológica Metropolitana - UTEM (Computer Science), Universidad
de Valparaíso - UV (Astronomy), and REUNA in Chile, and international
researchers from Caltech and Harvard U. and U. of Washington.

This work has made use of data from the Asteroid Terrestrial-impact Last Alert
System (ATLAS) project. ATLAS is primarily funded to search for near-Earth
asteroids through NASA grant Nos. 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 No. J1944/80NSSC19K0112 and
HST grant No. GO-15889, and STFC grant Nos. 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.

The PS1 and the PS1 public science archives have been made possible through
contributions by the Institute for Astronomy, the University of Hawaii, the
Pan-STARRS Project Office, the Max-Planck Society and its participating
institutes, the Max Planck Institute for Astronomy, Heidelberg and the Max
Planck Institute for Extraterrestrial Physics, Garching, The Johns Hopkins
University, Durham University, the University of Edinburgh, the Queen’s
University Belfast, the Harvard-Smithsonian Center for Astrophysics, the Las
Cumbres Observatory Global Telescope Network Incorporated, the National
Central University of Taiwan, the Space Telescope Science Institute, NASA
under grant No. NNX08AR22G issued through the Planetary Science Division of
the NASA Science Mission Directorate, NSF grant No. AST-1238877, the
University of Maryland, Eotvos Lorand University, the Los Alamos National
Laboratory, and the Gordon and Betty Moore Foundation.

This publication makes use of data products from the Wide-field Infrared
Survey Explorer, which is a joint project of the University of California, Los
Angeles, and the Jet Propulsion Laboratory/California Institute of Technology,
funded by the National Aeronautics and Space Administration.

This work made use of data supplied by the UK Swift Science Data Centre at the
University of Leicester.

The National Radio Astronomy Observatory is a facility of the National Science
Foundation operated under cooperative agreement by Associated Universities,
Inc.

The Legacy Surveys consist of three individual and complementary projects: the
Dark Energy Camera Legacy Survey (DECaLS; Proposal ID #2014B-0404; PIs: David
Schlegel and Arjun Dey), the Beijing-Arizona Sky Survey (BASS; NOAO Prop. ID
#2015A-0801; PIs: Zhou Xu and Xiaohui Fan), and the Mayall z-band Legacy
Survey (MzLS; Prop. ID #2016A-0453; PI: Arjun Dey). DECaLS, BASS and MzLS
together include data obtained, respectively, at the Blanco telescope, Cerro
Tololo Inter-American Observatory, NSF’s NOIRLab; the Bok telescope, Steward
Observatory, University of Arizona; and the Mayall telescope, Kitt Peak
National Observatory, NOIRLab. The Legacy Surveys project is honored to be
permitted to conduct astronomical research on Iolkam Du’ag (Kitt Peak), a
mountain with particular significance to the Tohono O’odham Nation.

NOIRLab is operated by the Association of Universities for Research in
Astronomy (AURA) under a cooperative agreement with the National Science
Foundation.

This project used data obtained with the Dark Energy Camera (DECam), which was
constructed by the Dark Energy Survey (DES) collaboration. Funding for the DES
Projects has been provided by the U.S. Department of Energy, the U.S. National
Science Foundation, the Ministry of Science and Education of Spain, the
Science and Technology Facilities Council of the United Kingdom, the Higher
Education Funding Council for England, the National Center for Supercomputing
Applications at the University of Illinois at Urbana-Champaign, the Kavli
Institute of Cosmological Physics at the University of Chicago, Center for
Cosmology and Astro-Particle Physics at the Ohio State University, the
Mitchell Institute for Fundamental Physics and Astronomy at Texas A&M
University, Financiadora de Estudos e Projetos, Fundacao Carlos Chagas Filho
de Amparo, Financiadora de Estudos e Projetos, Fundacao Carlos Chagas Filho de
Amparo a Pesquisa do Estado do Rio de Janeiro, Conselho Nacional de
Desenvolvimento Cientifico e Tecnologico and the Ministerio da Ciencia,
Tecnologia e Inovacao, the Deutsche Forschungsgemeinschaft and the
Collaborating Institutions in the Dark Energy Survey. The Collaborating
Institutions are Argonne National Laboratory, the University of California at
Santa Cruz, the University of Cambridge, Centro de Investigaciones
Energeticas, Medioambientales y Tecnologicas-Madrid, the University of
Chicago, University College London, the DES-Brazil Consortium, the University
of Edinburgh, the Eidgenossische Technische Hochschule (ETH) Zurich, Fermi
National Accelerator Laboratory, the University of Illinois at Urbana-
Champaign, the Institut de Ciencies de l’Espai (IEEC/CSIC), the Institut de
Fisica d’Altes Energies, Lawrence Berkeley National Laboratory, the Ludwig
Maximilians Universitat Munchen and the associated Excellence Cluster
Universe, the University of Michigan, NSF’s NOIRLab, the University of
Nottingham, the Ohio State University, the University of Pennsylvania, the
University of Portsmouth, SLAC National Accelerator Laboratory, Stanford
University, the University of Sussex, and Texas A&M University.

BASS is a key project of the Telescope Access Program (TAP), which has been
funded by the National Astronomical Observatories of China, the Chinese
Academy of Sciences (the Strategic Priority Research Program “The Emergence of
Cosmological Structures” Grant # XDB09000000), and the Special Fund for
Astronomy from the Ministry of Finance. The BASS is also supported by the
External Cooperation Program of Chinese Academy of Sciences (Grant #
114A11KYSB20160057), and Chinese National Natural Science Foundation (Grant #
11433005).

The Legacy Survey team makes use of data products from the Near-Earth Object
Wide-field Infrared Survey Explorer (NEOWISE), which is a project of the Jet
Propulsion Laboratory/California Institute of Technology. NEOWISE is funded by
the National Aeronautics and Space Administration.

The Legacy Surveys imaging of the DESI footprint is supported by the Director,
Office of Science, Office of High Energy Physics of the U.S. Department of
Energy under Contract No. DE-AC02-05CH1123, by the National Energy Research
Scientific Computing Center, a DOE Office of Science User Facility under the
same contract; and by the U.S. National Science Foundation, Division of
Astronomical Sciences under Contract No. AST-0950945 to NOAO.

This research has made use of the NASA Astrophysics Data System (ADS), the
NASA/IPAC Extragalactic Database (NED), and NASA/IPAC Infrared Science Archive
(IRSA, which is funded by NASA and operated by the California Institute of
Technology), and IRAF (which is distributed by the National Optical Astronomy
Observatory, NOAO, operated by the Association of Universities for Research in
Astronomy, AURA, Inc., under cooperative agreement with the NSF).

TNS is supported by funding from the Weizmann Institute of Science, as well as
grants from the Israeli Institute for Advanced Studies and the European Union
via ERC grant No. 725161.

We acknowledge with thanks the variable star observations from the AAVSO
International Database contributed by observers worldwide and used in this
research.

.

.

## References

  * Albareti et al. (2017) Albareti, F. D., Allende Prieto, C., Almeida, A., et al. 2017, ApJS, 233, 25
  * Arnett (1980) Arnett, W. D. 1980, ApJ, 237, 541
  * Arnett (1982) Arnett, W. D. 1982, ApJ, 253, 785
  * Astropy Collaboration et al. (2018) Astropy Collaboration, Price-Whelan, A. M., Sipőcz, B. M., et al. 2018, AJ, 156, 123
  * Bellm et al. (2019) Bellm, E. C., Kulkarni, S. R., Graham, M. J., et al. 2019, PASP, 131, 018002
  * Bertin & Arnouts (1996) Bertin, E., & Arnouts, S. 1996, A&AS, 117, 393
  * Bilinski et al. (2015) Bilinski, C., Smith, N., Li, W., et al. 2015, MNRAS, 450, 246
  * Blanchard et al. (2017) Blanchard, P. K., Berger, E., Fong, W., et al. 2017, ApJ, 848, L22
  * Blinnikov (2010) Blinnikov, S. I. 2010, Physics of Atomic Nuclei, 73, 604
  * Bradley et al. (2022) Bradley, L., Sipőcz, B., Robitaille, T., et al. 2022, astropy/photutils: 1.5.0, 1.5.0, Zenodo, doi:10.5281/zenodo.6825092
  * Brown et al. (2013) Brown, T. M., Baliber, N., Bianco, F. B., et al. 2013, PASP, 125, 1031
  * Buzzoni et al. (1984) Buzzoni, B., Delabre, B., Dekker, H., et al. 1984, The Messenger, 38, 9
  * Carnall et al. (2019) Carnall, A. C., Leja, J., Johnson, B. D., et al. 2019, ApJ, 873, 44
  * Chambers et al. (2016) Chambers, K. C., Magnier, E. A., Metcalfe, N., et al. 2016, arXiv e-prints, arXiv:1612.05560
  * Chandra (2018) Chandra, P. 2018, Space Sci. Rev., 214, 27
  * Chatzopoulos et al. (2012) Chatzopoulos, E., Wheeler, J. C., & Vinko, J. 2012, ApJ, 746, 121
  * Chevalier (1982) Chevalier, R. A. 1982, ApJ, 259, 302
  * Chevalier (2012) Chevalier, R. A. 2012, ApJ, 752, L2
  * Chevalier & Fransson (1994) Chevalier, R. A., & Fransson, C. 1994, ApJ, 420, 268
  * Chu et al. (2021) Chu, M., Dahiwale, A., & Fremling, C. 2021, Transient Name Server Classification Report, 2021-2605, 1
  * Chugai (1991) Chugai, N. N. 1991, MNRAS, 250, 513
  * Conroy & Gunn (2010) Conroy, C., & Gunn, J. E. 2010, ApJ, 712, 833
  * Conroy et al. (2009) Conroy, C., Gunn, J. E., & White, M. 2009, ApJ, 699, 486
  * Davidson & Humphreys (1997) Davidson, K., & Humphreys, R. M. 1997, ARA&A, 35, 1
  * De (2021) De, K. 2021, Transient Name Server Discovery Report, 2021-2150, 1
  * De et al. (2020) De, K., Hankins, M. J., Kasliwal, M. M., et al. 2020, PASP, 132, 025001
  * Dey et al. (2019) Dey, A., Schlegel, D. J., Lang, D., et al. 2019, AJ, 157, 168
  * Doherty et al. (2017) Doherty, C. L., Gil-Pons, P., Siess, L., & Lattanzio, J. C. 2017, PASA, 34, e056
  * Drout et al. (2014) Drout, M. R., Chornock, R., Soderberg, A. M., et al. 2014, ApJ, 794, 23
  * Evans et al. (2007) Evans, P. A., Beardmore, A. P., Page, K. L., et al. 2007, A&A, 469, 379
  * Evans et al. (2009) Evans, P. A., Beardmore, A. P., Page, K. L., et al. 2009, MNRAS, 397, 1177
  * Fabricant et al. (2019) Fabricant, D., Fata, R., Epps, H., et al. 2019, PASP, 131, 075004
  * Filippenko (1997) Filippenko, A. V. 1997, ARA&A, 35, 309
  * Fitzpatrick (1999) Fitzpatrick, E. L. 1999, PASP, 111, 63
  * Flewelling et al. (2020) Flewelling, H. A., Magnier, E. A., Chambers, K. C., et al. 2020, ApJS, 251, 7
  * Foley et al. (2011) Foley, R. J., Berger, E., Fox, O., et al. 2011, ApJ, 732, 32
  * Foreman-Mackey et al. (2013) Foreman-Mackey, D., Hogg, D. W., Lang, D., & Goodman, J. 2013, PASP, 125, 306
  * Förster et al. (2021) Förster, F., Cabrera-Vives, G., Castillo-Navarrete, E., et al. 2021, AJ, 161, 242
  * Fransson et al. (2022) Fransson, C., Sollerman, J., Strotjohann, N. L., et al. 2022, A&A, 666, A79
  * Fraser et al. (2013) Fraser, M., Inserra, C., Jerkstrand, A., et al. 2013, MNRAS, 433, 1312
  * Fraser et al. (2015) Fraser, M., Kotak, R., Pastorello, A., et al. 2015, MNRAS, 453, 3886
  * Fraser et al. (2021) Fraser, M., Stritzinger, M. D., Brennan, S. J., et al. 2021, arXiv e-prints, arXiv:2108.07278
  * Fuller (2017) Fuller, J. 2017, MNRAS, 470, 1642
  * Fuller & Ro (2018) Fuller, J., & Ro, S. 2018, MNRAS, 476, 1853
  * Fullerton et al. (2006) Fullerton, A. W., Massa, D. L., & Prinja, R. K. 2006, ApJ, 637, 1025
  * Fulton et al. (2022) Fulton, M., Bulger, J., Huber, M. E., et al. 2022, Transient Name Server AstroNote, 198, 1
  * Gal-Yam (2017) Gal-Yam, A. 2017, in Handbook of Supernovae, ed. A. W. Alsabti & P. Murdin
  * Gal-Yam & Leonard (2009) Gal-Yam, A., & Leonard, D. C. 2009, Nature, 458, 865
  * Gal-Yam et al. (2007) Gal-Yam, A., Leonard, D. C., Fox, D. B., et al. 2007, ApJ, 656, 372
  * Galbany et al. (2014) Galbany, L., Stanishev, V., Mourão, A. M., et al. 2014, A&A, 572, A38
  * Galbany et al. (2016) Galbany, L., Stanishev, V., Mourão, A. M., et al. 2016, A&A, 591, A48
  * Galbany et al. (2018) Galbany, L., Anderson, J. P., Sánchez, S. F., et al. 2018, ApJ, 855, 107
  * Gaudi (2012) Gaudi, B. S. 2012, ARA&A, 50, 411
  * Gomez et al. (2023) Gomez, S., Berger, E., Blanchard, P. K., et al. 2023, ApJ, 949, 114
  * Gomez et al. (2020) Gomez, S., Berger, E., Blanchard, P. K., et al. 2020, ApJ, 904, 74
  * Gomez et al. (2021) Gomez, S., Berger, E., Hosseinzadeh, G., et al. 2021, ApJ, 913, 143
  * Graham et al. (2019) Graham, M. J., Kulkarni, S. R., Bellm, E. C., et al. 2019, PASP, 131, 078001
  * Graham et al. (2014) Graham, M. L., Sand, D. J., Valenti, S., et al. 2014, ApJ, 787, 163
  * Graham et al. (2017) Graham, M. L., Bigley, A., Mauerhan, J. C., et al. 2017, MNRAS, 469, 1559
  * Haynes et al. (2011) Haynes, M. P., Giovanelli, R., Martin, A. M., et al. 2011, AJ, 142, 170
  * Haynes et al. (2018) Haynes, M. P., Giovanelli, R., Kent, B. R., et al. 2018, ApJ, 861, 49
  * Henden et al. (2016) Henden, A. A., Templeton, M., Terrell, D., et al. 2016, VizieR Online Data Catalog
  * HI4PI Collaboration et al. (2016) HI4PI Collaboration, Ben Bekhti, N., Flöer, L., et al. 2016, A&A, 594, A116
  * Hiramatsu et al. (2021) Hiramatsu, D., Howell, D. A., Van Dyk, S. D., et al. 2021, Nature Astronomy, 5, 903
  * Ho et al. (2019) Ho, A. Y. Q., Goldstein, D. A., Schulze, S., et al. 2019, ApJ, 887, 169
  * Ho et al. (2023) Ho, A. Y. Q., Perley, D. A., Gal-Yam, A., et al. 2023, ApJ, 949, 120
  * Hosseinzadeh et al. (2022) Hosseinzadeh, G., Berger, E., Metzger, B. D., et al. 2022, ApJ, 933, 14
  * Howell & Global Supernova Project (2017) Howell, D. A., & Global Supernova Project. 2017, in American Astronomical Society Meeting Abstracts, Vol. 230, American Astronomical Society Meeting Abstracts #230, 318.03
  * Humphreys & Davidson (1994) Humphreys, R. M., & Davidson, K. 1994, PASP, 106, 1025
  * Hunter (2007) Hunter, J. D. 2007, Computing in Science and Engineering, 9, 90
  * Ivezić et al. (2019) Ivezić, Ž., Kahn, S. M., Tyson, J. A., et al. 2019, ApJ, 873, 111
  * Johnson (2021) Johnson, B. D. 2021, bd-j/sedpy: sedpy v0.2.0, v0.2.0, Zenodo, doi:10.5281/zenodo.4582723
  * Johnson et al. (2021) Johnson, B. D., Leja, J., Conroy, C., & Speagle, J. S. 2021, ApJS, 254, 22
  * Jones et al. (2013) Jones, S., Hirschi, R., Nomoto, K., et al. 2013, ApJ, 772, 150
  * Kankare et al. (2012) Kankare, E., Ergon, M., Bufano, F., et al. 2012, MNRAS, 424, 855
  * Kashi et al. (2013) Kashi, A., Soker, N., & Moskovitz, N. 2013, MNRAS, 436, 2484
  * Kennicutt (1998) Kennicutt, Robert C., J. 1998, ARA&A, 36, 189
  * Lacy et al. (2020) Lacy, M., Baum, S. A., Chandler, C. J., et al. 2020, PASP, 132, 035001
  * Lang (2014) Lang, D. 2014, AJ, 147, 108
  * Law et al. (2009) Law, N. M., Kulkarni, S. R., Dekany, R. G., et al. 2009, PASP, 121, 1395
  * Leja et al. (2017) Leja, J., Johnson, B. D., Conroy, C., van Dokkum, P. G., & Byler, N. 2017, ApJ, 837, 170
  * Levesque et al. (2014) Levesque, E. M., Stringfellow, G. S., Ginsburg, A. G., Bally, J., & Keeney, B. A. 2014, AJ, 147, 23
  * Licquia & Newman (2015) Licquia, T. C., & Newman, J. A. 2015, ApJ, 806, 96
  * MacLeod & Loeb (2020a) MacLeod, M., & Loeb, A. 2020a, ApJ, 895, 29
  * MacLeod & Loeb (2020b) MacLeod, M., & Loeb, A. 2020b, ApJ, 893, 106
  * MacLeod et al. (2017) MacLeod, M., Macias, P., Ramirez-Ruiz, E., et al. 2017, ApJ, 835, 282
  * MacLeod et al. (2018a) MacLeod, M., Ostriker, E. C., & Stone, J. M. 2018a, ApJ, 868, 136
  * MacLeod et al. (2018b) MacLeod, M., Ostriker, E. C., & Stone, J. M. 2018b, ApJ, 863, 5
  * Magnier et al. (2020) Magnier, E. A., Chambers, K. C., Flewelling, H. A., et al. 2020, ApJS, 251, 3
  * Mainzer et al. (2014) Mainzer, A., Bauer, J., Cutri, R. M., et al. 2014, ApJ, 792, 30
  * Maiolino et al. (2008) Maiolino, R., Nagao, T., Grazian, A., et al. 2008, A&A, 488, 463
  * Margutti et al. (2014) Margutti, R., Milisavljevic, D., Soderberg, A. M., et al. 2014, ApJ, 780, 21
  * Martin et al. (2009) Martin, A. M., Giovanelli, R., Haynes, M. P., et al. 2009, ApJS, 183, 214
  * Martin et al. (2005) Martin, D. C., Fanson, J., Schiminovich, D., et al. 2005, ApJ, 619, L1
  * Martin et al. (2015) Martin, J. C., Hambsch, F. J., Margutti, R., et al. 2015, AJ, 149, 9
  * Masci et al. (2019) Masci, F. J., Laher, R. R., Rusholme, B., et al. 2019, PASP, 131, 018003
  * Mason et al. (2010) Mason, E., Diaz, M., Williams, R. E., Preston, G., & Bensby, T. 2010, A&A, 516, A108
  * Matsumoto & Metzger (2022a) Matsumoto, T., & Metzger, B. D. 2022a, ApJ, 938, 5
  * Matsumoto & Metzger (2022b) Matsumoto, T., & Metzger, B. D. 2022b, ApJ, 936, 114
  * Matzner & McKee (1999) Matzner, C. D., & McKee, C. F. 1999, ApJ, 510, 379
  * Mauerhan & Smith (2012) Mauerhan, J., & Smith, N. 2012, MNRAS, 424, 2659
  * Mauerhan et al. (2014) Mauerhan, J., Williams, G. G., Smith, N., et al. 2014, MNRAS, 442, 1166
  * Mauerhan et al. (2013a) Mauerhan, J. C., Smith, N., Silverman, J. M., et al. 2013a, MNRAS, 431, 2599
  * Mauerhan et al. (2013b) Mauerhan, J. C., Smith, N., Filippenko, A. V., et al. 2013b, MNRAS, 430, 1801
  * McCarthy et al. (1998) McCarthy, J. K., Cohen, J. G., Butcher, B., et al. 1998, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 3355, Optical Astronomical Instrumentation, ed. S. D’Odorico, 81–92
  * McCully et al. (2018) McCully, C., Turner, M., Volgenau, N., et al. 2018, LCOGT/banzai: Initial Release, 0.9.4, Zenodo, doi:10.5281/zenodo.1257560
  * Meisner et al. (2018) Meisner, A. M., Lang, D., & Schlegel, D. J. 2018, AJ, 156, 69
  * Metzger (2022) Metzger, B. D. 2022, ApJ, 932, 84
  * Metzger et al. (2014) Metzger, B. D., Hascoët, R., Vurm, I., et al. 2014, MNRAS, 442, 713
  * Metzger & Pejcha (2017) Metzger, B. D., & Pejcha, O. 2017, MNRAS, 471, 3200
  * Moriya et al. (2011) Moriya, T., Tominaga, N., Blinnikov, S. I., Baklanov, P. V., & Sorokina, E. I. 2011, MNRAS, 415, 199
  * Moriya et al. (2013a) Moriya, T. J., Blinnikov, S. I., Tominaga, N., et al. 2013a, MNRAS, 428, 1020
  * Moriya et al. (2013b) Moriya, T. J., Maeda, K., Taddia, F., et al. 2013b, MNRAS, 435, 1520
  * Moriya et al. (2014) Moriya, T. J., Tominaga, N., Langer, N., et al. 2014, A&A, 569, A57
  * Muñoz et al. (2021a) Muñoz, S., Delgado, M., González, R., et al. 2021a, Transient Name Server Classification Report, 2021-2620, 1
  * Muñoz et al. (2021b) Muñoz, S., Delgado, M., González, R., et al. 2021b, Transient Name Server AstroNote, 204, 1
  * Narita et al. (2020) Narita, N., Fukui, A., Yamamuro, T., et al. 2020, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 11447, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, 114475K
  * Nicholl et al. (2017) Nicholl, M., Berger, E., Margutti, R., et al. 2017, ApJ, 845, L8
  * Nyholm et al. (2017) Nyholm, A., Sollerman, J., Taddia, F., et al. 2017, A&A, 605, A6
  * Nyholm et al. (2020) Nyholm, A., Sollerman, J., Tartaglia, L., et al. 2020, A&A, 637, A73
  * Ofek et al. (2012) Ofek, E. O., Laher, R., Law, N., et al. 2012, PASP, 124, 62
  * Ofek et al. (2013) Ofek, E. O., Sullivan, M., Cenko, S. B., et al. 2013, Nature, 494, 65
  * Ofek et al. (2014) Ofek, E. O., Sullivan, M., Shaviv, N. J., et al. 2014, ApJ, 789, 104
  * Oke et al. (1995) Oke, J. B., Cohen, J. G., Carr, M., et al. 1995, PASP, 107, 375
  * Oliphant (2006) Oliphant, T. E. 2006, A Guide to NumPy (USA: Trelgol Publishing)
  * Papish & Soker (2011) Papish, O., & Soker, N. 2011, MNRAS, 416, 1697
  * Pastorello et al. (2013) Pastorello, A., Cappellaro, E., Inserra, C., et al. 2013, ApJ, 767, 1
  * Pejcha et al. (2016) Pejcha, O., Metzger, B. D., & Tomida, K. 2016, MNRAS, 455, 4351
  * Pejcha et al. (2017) Pejcha, O., Metzger, B. D., Tyles, J. G., & Tomida, K. 2017, ApJ, 850, 59
  * Pellegrino et al. (2022) Pellegrino, C., Howell, D. A., Terreran, G., et al. 2022, ApJ, 938, 73
  * Perley et al. (2022) Perley, D. A., Sollerman, J., Schulze, S., et al. 2022, ApJ, 927, 180
  * Poelarends et al. (2008) Poelarends, A. J. T., Herwig, F., Langer, N., & Heger, A. 2008, ApJ, 675, 614
  * Pojmanski (2002) Pojmanski, G. 2002, Acta Astron., 52, 397
  * Prieto et al. (2013) Prieto, J. L., Brimacombe, J., Drake, A. J., & Howerton, S. 2013, ApJ, 763, L27
  * Quataert et al. (2016) Quataert, E., Fernández, R., Kasen, D., Klion, H., & Paxton, B. 2016, MNRAS, 458, 1214
  * Quataert & Shiode (2012) Quataert, E., & Shiode, J. 2012, MNRAS, 423, L92
  * Ransome et al. (2022) Ransome, C. L., Habergham-Mawson, S. M., Darnley, M. J., James, P. A., & Percival, S. M. 2022, MNRAS, 513, 3564
  * Reguitti et al. (2022) Reguitti, A., Pastorello, A., Pignata, G., et al. 2022, A&A, 662, L10
  * Reilly et al. (2017) Reilly, E., Maund, J. R., Baade, D., et al. 2017, MNRAS, 470, 1491
  * Rockosi et al. (2010) Rockosi, C., Stover, R., Kibrick, R., et al. 2010, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 7735, Ground-based and Airborne Instrumentation for Astronomy III, ed. I. S. McLean, S. K. Ramsay, & H. Takami, 77350R
  * Salamanca et al. (1998) Salamanca, I., Cid-Fernandes, R., Tenorio-Tagle, G., et al. 1998, MNRAS, 300, L17
  * Salim et al. (2007) Salim, S., Rich, R. M., Charlot, S., et al. 2007, ApJS, 173, 267
  * Schlafly & Finkbeiner (2011) Schlafly, E. F., & Finkbeiner, D. P. 2011, ApJ, 737, 103
  * Schlegel (1990) Schlegel, E. M. 1990, MNRAS, 244, 269
  * Schrøder et al. (2020) Schrøder, S. L., MacLeod, M., Loeb, A., Vigna-Gómez, A., & Mandel, I. 2020, ApJ, 892, 13
  * Schulze et al. (2021) Schulze, S., Yaron, O., Sollerman, J., et al. 2021, ApJS, 255, 29
  * Science Software Branch at STScI (2012) Science Software Branch at STScI. 2012, PyRAF: Python alternative for IRAF, Astrophysics Source Code Library, record ascl:1207.011, ascl:1207.011
  * Shingles et al. (2021) Shingles, L., Smith, K. W., Young, D. R., et al. 2021, Transient Name Server AstroNote, 7, 1
  * Shiode & Quataert (2014) Shiode, J. H., & Quataert, E. 2014, ApJ, 780, 96
  * Shishkin & Soker (2023) Shishkin, D., & Soker, N. 2023, MNRAS, 522, 438
  * Smartt et al. (2015) Smartt, S. J., Valenti, S., Fraser, M., et al. 2015, A&A, 579, A40
  * Smith et al. (2020) Smith, K. W., Smartt, S. J., Young, D. R., et al. 2020, PASP, 132, 085002
  * Smith (2008) Smith, N. 2008, Nature, 455, 201
  * Smith (2013) Smith, N. 2013, MNRAS, 434, 102
  * Smith (2014) Smith, N. 2014, ARA&A, 52, 487
  * Smith (2017a) Smith, N. 2017a, in Handbook of Supernovae, ed. A. W. Alsabti & P. Murdin
  * Smith (2017b) Smith, N. 2017b, Philosophical Transactions of the Royal Society of London Series A, 375, 20160268
  * Smith et al. (2019) Smith, N., Aghakhanloo, M., Murphy, J. W., et al. 2019, MNRAS, 488, 1760
  * Smith et al. (2022) Smith, N., Andrews, J. E., Filippenko, A. V., et al. 2022, MNRAS, 515, 71
  * Smith et al. (2009) Smith, N., Hinkle, K. H., & Ryde, N. 2009, AJ, 137, 3558
  * Smith et al. (2014) Smith, N., Mauerhan, J. C., & Prieto, J. L. 2014, MNRAS, 438, 1191
  * Smith et al. (2010) Smith, N., Miller, A., Li, W., et al. 2010, AJ, 139, 1451
  * Smith et al. (2018) Smith, N., Rest, A., Andrews, J. E., et al. 2018, MNRAS, 480, 1457
  * Soker (2010) Soker, N. 2010, MNRAS, 401, 2793
  * Soker & Kashi (2013) Soker, N., & Kashi, A. 2013, ApJ, 764, L6
  * Speagle (2020) Speagle, J. S. 2020, MNRAS, 493, 3132
  * Stevenson et al. (2016) Stevenson, K. B., Bean, J. L., Seifahrt, A., et al. 2016, ApJ, 817, 141
  * Strotjohann et al. (2021) Strotjohann, N. L., Ofek, E. O., Gal-Yam, A., et al. 2021, ApJ, 907, 99
  * Taddia et al. (2013) Taddia, F., Stritzinger, M. D., Sollerman, J., et al. 2013, A&A, 555, A10
  * Tonry et al. (2018) Tonry, J. L., Denneau, L., Heinze, A. N., et al. 2018, PASP, 130, 064505
  * Tsuna et al. (2019) Tsuna, D., Kashiyama, K., & Shigeyama, T. 2019, ApJ, 884, 87
  * Tylenda et al. (2011) Tylenda, R., Hajduk, M., Kamiński, T., et al. 2011, A&A, 528, A114
  * Valenti et al. (2016) Valenti, S., Howell, D. A., Stritzinger, M. D., et al. 2016, MNRAS, 459, 3939
  * Van Dyk & Matheson (2012) Van Dyk, S. D., & Matheson, T. 2012, in Astrophysics and Space Science Library, Vol. 384, Eta Carinae and the Supernova Impostors, ed. K. Davidson & R. M. Humphreys, 249
  * Vick et al. (2021) Vick, M., MacLeod, M., Lai, D., & Loeb, A. 2021, MNRAS, 503, 5569
  * Vigna-Gómez et al. (2020) Vigna-Gómez, A., MacLeod, M., Neijssel, C. J., et al. 2020, PASA, 37, e038
  * Vink (2012) Vink, J. S. 2012, in Astrophysics and Space Science Library, Vol. 384, Eta Carinae and the Supernova Impostors, ed. K. Davidson & R. M. Humphreys, 221
  * Virtanen et al. (2020) Virtanen, P., Gommers, R., Oliphant, T. E., et al. 2020, Nature Methods, 17, 261
  * Wang & Chen (2019) Wang, S., & Chen, X. 2019, ApJ, 877, 116
  * Waskom et al. (2020) Waskom, M., Botvinnik, O., Ostblom, J., et al. 2020, mwaskom/seaborn: v0.10.0 (January 2020), v0.10.0, Zenodo, Zenodo, doi:10.5281/zenodo.3629446
  * Waters et al. (2020) Waters, C. Z., Magnier, E. A., Price, P. A., et al. 2020, ApJS, 251, 4
  * Williams et al. (2017) Williams, P. K. G., Gizis, J. E., & Berger, E. 2017, ApJ, 834, 117
  * Woosley (2017) Woosley, S. E. 2017, ApJ, 836, 244
  * Woosley et al. (2007) Woosley, S. E., Blinnikov, S., & Heger, A. 2007, Nature, 450, 390
  * Wright et al. (2010) Wright, E. L., Eisenhardt, P. R. M., Mainzer, A. K., et al. 2010, AJ, 140, 1868
  * Wu & Fuller (2021) Wu, S., & Fuller, J. 2021, ApJ, 906, 3
  * Wu & Fuller (2022) Wu, S. C., & Fuller, J. 2022, ApJ, 930, 119
  * Yaron & Gal-Yam (2012) Yaron, O., & Gal-Yam, A. 2012, PASP, 124, 668
  * Zackay et al. (2016) Zackay, B., Ofek, E. O., & Gal-Yam, A. 2016, ApJ, 830, 27