11institutetext: Physics Department and Tsinghua Center for Astrophysics
(THCA), Tsinghua University, Beijing, 100084, China 22institutetext: INAF -
Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, 35122 Padova,
Italy 33institutetext: Università degli Studi di Padova, Dipartimento di
Fisica e Astronomia, Vicolo dell’Osservatorio 2, 35122 Padova, Italy
44institutetext: School of Physics, O’Brien Centre for Science North,
University College Dublin, Belfield, Dublin 4, Ireland 55institutetext: INAF-
Osservatorio Astronomico di Capodimonte, Salita Moiariello 16, 80131, Napoli,
Italy 66institutetext: Institute of Space Sciences (ICE, CSIC), Campus UAB,
Carrer de Can Magrans s/n, 08193 Barcelona, Spain 77institutetext: Chinese
Academy of Sciences South America Center for Astronomy, National Astronomical
Observatories, CAS, Beijing 100101, People’s Republic of China
88institutetext: CAS Key Laboratory of Optical Astronomy, National
Astronomical Observatories, Chinese Academy of Sciences, Beijing 100101,
People’s Republic of China 99institutetext: Department of Physics and
Astronomy, University of Turku, FI-20014 Turku, Finland 1010institutetext:
Departamento de Ciencias Fisicas, Universidad Andres Bello, Fernandez Concha
700, Las Condes, Santiago, Chile 1111institutetext: Millennium Institute of
Astrophysics (MAS), Nuncio Monsenor Sòtero Sanz 100, Providencia, Santiago,
Chile 1212institutetext: Astrophysics Research Centre, School of Mathematics
and Physics, Queen’s University Belfast, Belfast BT7 1NN Northern Ireland, UK
1313institutetext: Institute for Astronomy, University of Hawai’i at Manoa,
2680 Woodlawn Dr. Hawai’i, HI 96822, USA 1414institutetext: Institute of
Astrophysics of the Canary Islands, C/ Vía Láctea, s/n, Tenerife, Spain
1515institutetext: The Oskar Klein Centre, Department of Astronomy, Stockholm
University, AlbaNova, SE-10691 Stockholm, Sweden 1616institutetext: Telescopio
Nazionale Galileo, Fundación Galileo Galilei - INAF, Rambla José Ana Fernández
Pérez, 7, 38712 Breña Baja, TF - Spain 1717institutetext: Astrophysics
Research Institute, Liverpool John Moores University, IC2, Liverpool Science
Park, 146 Brownlow Hill, Liverpool L3 5RF, UK 1818institutetext: Max-Planck-
Institut f$\ddot{\mathrm{u}}$r Astrophysik, Karl-Schwarzschild Str. 1, D-85741
Garching, Germany 1919institutetext: Department of Applied Physics, University
of Cádiz, Campus of Puerto Real, E-11510 Cádiz, Spain 2020institutetext:
School of Physics, Trinity College Dublin, The University of Dublin, Dublin 2,
Ireland 2121institutetext: Department of Physics, Anhui Normal University,
Wuhu,Anhui, 241002, China 2222institutetext: Department of Physics and
Astronomy, Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C, Denmark
2323institutetext: Center for Interdisciplinary Exploration and Research in
Astrophysics (CIERA) and Department of Physics and Astronomy,Northwestern
University, Evanston, IL 60208, USA 2424institutetext: Department of Physics
and Astronomy, University of California, 1 Shields Avenue, Davis, CA
95616-5270, USA 2525institutetext: School of Chemistry and Physics, University
of KwaZulu-Natal, Westville Campus, Private Bag X54001, Durban, 4000, South
Africa 2626institutetext: NAOC-UKZN Computational Astrophysics Centre (NUCAC),
University of KwaZulu-Natal, Durban, 4000, South Africa 2727institutetext:
Beijing Planetarium, Beijing Academy of Science and Technology, Beijing,
100044, China 2828institutetext: Department of Astrophysics/IMAPP, Radboud
University, P.O. Box 9010, 6500 GL Nijmegen, Netherlands 2929institutetext:
SRON, Netherlands Institute for Space Research, Sorbonnelaan, 2, NL-3584CA
Utrecht, Netherlands 3030institutetext: Physics Department, Technion, Haifa
32000, Israel 3131institutetext: Departamento de Astronomía, Universidad de
Chile, Camino del Observatorio 1515, Las Condes, Santiago, Chile
3232institutetext: Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer
de Can Magrans, s/n, E-08193 Barcelona, Spain. 3333institutetext: Department
of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot
76100, Israel 3434institutetext: Xinjiang Astronomical Observatory, 150
Science-1 Street, Urumqi 830011, China 3535institutetext: Astronomical
Observatory, University of Warsaw, Al. Ujazdowskie 4, 00-478 Warszawa, Poland
3636institutetext: Department of Astronomy, Shanghai Jiao Tong University,
Shanghai, 200240, China 3737institutetext: School of Physics and Astronomy,
Cardiff University, Queens Buildings, The Parade, Cardiff, CF24 3AA, UK
3838institutetext: Itagaki Astronomical Observatory, Yamagata, Yamagata
990-2492, Japan 3939institutetext: Leiden Observatory, Leiden University,
Niels Bohrweg 2, 2333 CA Leiden, The Netherlands 4040institutetext: Gemini
Observatory/NSF’s NOIRLab, Casilla 603, La Serena, Chile 4141institutetext:
INAF-Osservatorio Astronomico d’Abruzzo, via M. Maggini snc, I-64100 Teramo,
Italy 4242institutetext: The Oskar Klein Centre, Department of Physics,
Stockholm University, AlbaNova, SE-10691 Stockholm, Sweden 4343institutetext:
Xingming Observatory, Mount Nanshan, Xinjiang, China

# Intermediate-luminosity red transients: Spectrophotometric properties and
connection to electron-capture supernova explosions

Y.-Z. Cai Intermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova
explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova
explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova
explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova
explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova explosionsE-mail:
<EMAIL_ADDRESS>red transients:
Spectrophotometric properties and connection to electron-capture supernova
explosionsE-mail<EMAIL_ADDRESS>A. Pastorello Intermediate-
luminosity red transients: Spectrophotometric properties and connection to
electron-capture supernova explosionsE-mail:
<EMAIL_ADDRESS>red transients:
Spectrophotometric properties and connection to electron-capture supernova
explosionsE-mail<EMAIL_ADDRESS>M. Fraser Intermediate-luminosity
red transients: Spectrophotometric properties and connection to electron-
capture supernova explosionsE-mail<EMAIL_ADDRESS>luminosity red transients: Spectrophotometric properties and connection to
electron-capture supernova explosionsE-mail<EMAIL_ADDRESS>M. T.
Botticella Intermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova
explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova explosions N. Elias-
Rosa Intermediate-luminosity red transients: Spectrophotometric properties and
connection to electron-capture supernova explosionsIntermediate-luminosity red
transients: Spectrophotometric properties and connection to electron-capture
supernova explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova
explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova explosions L.-Z. Wang
Intermediate-luminosity red transients: Spectrophotometric properties and
connection to electron-capture supernova explosionsIntermediate-luminosity red
transients: Spectrophotometric properties and connection to electron-capture
supernova explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova
explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova explosions R. Kotak
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connection to electron-capture supernova explosionsIntermediate-luminosity red
transients: Spectrophotometric properties and connection to electron-capture
supernova explosions S. Benetti Intermediate-luminosity red transients:
Spectrophotometric properties and connection to electron-capture supernova
explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova explosions E.
Cappellaro Intermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova
explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova explosions M. Turatto
Intermediate-luminosity red transients: Spectrophotometric properties and
connection to electron-capture supernova explosionsIntermediate-luminosity red
transients: Spectrophotometric properties and connection to electron-capture
supernova explosions A. Reguitti Intermediate-luminosity red transients:
Spectrophotometric properties and connection to electron-capture supernova
explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova
explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova
explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova
explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova
explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova explosions S. Mattila
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connection to electron-capture supernova explosionsIntermediate-luminosity red
transients: Spectrophotometric properties and connection to electron-capture
supernova explosions S. J. Smartt Intermediate-luminosity red transients:
Spectrophotometric properties and connection to electron-capture supernova
explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova explosions C. Ashall
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connection to electron-capture supernova explosionsIntermediate-luminosity red
transients: Spectrophotometric properties and connection to electron-capture
supernova explosions S. Benitez Intermediate-luminosity red transients:
Spectrophotometric properties and connection to electron-capture supernova
explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova explosions T.-W. Chen
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connection to electron-capture supernova explosionsIntermediate-luminosity red
transients: Spectrophotometric properties and connection to electron-capture
supernova explosions A. Harutyunyan Intermediate-luminosity red transients:
Spectrophotometric properties and connection to electron-capture supernova
explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova explosions E. Kankare
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connection to electron-capture supernova explosionsIntermediate-luminosity red
transients: Spectrophotometric properties and connection to electron-capture
supernova explosions P. Lundqvist Intermediate-luminosity red transients:
Spectrophotometric properties and connection to electron-capture supernova
explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova explosions P. A.
Mazzali Intermediate-luminosity red transients: Spectrophotometric properties
and connection to electron-capture supernova explosionsIntermediate-luminosity
red transients: Spectrophotometric properties and connection to electron-
capture supernova explosionsIntermediate-luminosity red transients:
Spectrophotometric properties and connection to electron-capture supernova
explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova explosions A. Morales-
Garoffolo Intermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova
explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova explosions P. Ochner
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supernova explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova
explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova explosions G. Pignata
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connection to electron-capture supernova explosionsIntermediate-luminosity red
transients: Spectrophotometric properties and connection to electron-capture
supernova explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova
explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova explosions S. J.
Prentice Intermediate-luminosity red transients: Spectrophotometric properties
and connection to electron-capture supernova explosionsIntermediate-luminosity
red transients: Spectrophotometric properties and connection to electron-
capture supernova explosions T. M. Reynolds Intermediate-luminosity red
transients: Spectrophotometric properties and connection to electron-capture
supernova explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova explosions X.-W. Shu
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connection to electron-capture supernova explosionsIntermediate-luminosity red
transients: Spectrophotometric properties and connection to electron-capture
supernova explosions M. D. Stritzinger Intermediate-luminosity red transients:
Spectrophotometric properties and connection to electron-capture supernova
explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova explosions L.
Tartaglia Intermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova
explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova explosions G. Terreran
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connection to electron-capture supernova explosionsIntermediate-luminosity red
transients: Spectrophotometric properties and connection to electron-capture
supernova explosions L. Tomasella Intermediate-luminosity red transients:
Spectrophotometric properties and connection to electron-capture supernova
explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova explosions S. Valenti
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connection to electron-capture supernova explosionsIntermediate-luminosity red
transients: Spectrophotometric properties and connection to electron-capture
supernova explosions G. Valerin Intermediate-luminosity red transients:
Spectrophotometric properties and connection to electron-capture supernova
explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova
explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova
explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova explosions G.-J. Wang
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connection to electron-capture supernova explosionsIntermediate-luminosity red
transients: Spectrophotometric properties and connection to electron-capture
supernova explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova
explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova explosions X.-F. Wang
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connection to electron-capture supernova explosionsIntermediate-luminosity red
transients: Spectrophotometric properties and connection to electron-capture
supernova explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova
explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova explosions L. Borsato
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connection to electron-capture supernova explosionsIntermediate-luminosity red
transients: Spectrophotometric properties and connection to electron-capture
supernova explosions E. Callis Intermediate-luminosity red transients:
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explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova explosions G.
Cannizzaro Intermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova
explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova
explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova
explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova explosions S. Chen
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connection to electron-capture supernova explosionsIntermediate-luminosity red
transients: Spectrophotometric properties and connection to electron-capture
supernova explosions E. Congiu Intermediate-luminosity red transients:
Spectrophotometric properties and connection to electron-capture supernova
explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova explosions M. Ergon
Intermediate-luminosity red transients: Spectrophotometric properties and
connection to electron-capture supernova explosionsIntermediate-luminosity red
transients: Spectrophotometric properties and connection to electron-capture
supernova explosions L. Galbany Intermediate-luminosity red transients:
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explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova explosions A. Gal-Yam
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connection to electron-capture supernova explosionsIntermediate-luminosity red
transients: Spectrophotometric properties and connection to electron-capture
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explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova explosions M.
Gromadzki Intermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova
explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova explosions S. Holmbo
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connection to electron-capture supernova explosionsIntermediate-luminosity red
transients: Spectrophotometric properties and connection to electron-capture
supernova explosions F. Huang Intermediate-luminosity red transients:
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explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova explosions C. Inserra
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connection to electron-capture supernova explosionsIntermediate-luminosity red
transients: Spectrophotometric properties and connection to electron-capture
supernova explosions K. Itagaki Intermediate-luminosity red transients:
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explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova explosions Z.
Kostrzewa-Rutkowska Intermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova
explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova
explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova
explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova explosions K. Maguire
Intermediate-luminosity red transients: Spectrophotometric properties and
connection to electron-capture supernova explosionsIntermediate-luminosity red
transients: Spectrophotometric properties and connection to electron-capture
supernova explosions S. Margheim Intermediate-luminosity red transients:
Spectrophotometric properties and connection to electron-capture supernova
explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova explosions S. Moran
Intermediate-luminosity red transients: Spectrophotometric properties and
connection to electron-capture supernova explosionsIntermediate-luminosity red
transients: Spectrophotometric properties and connection to electron-capture
supernova explosions F. Onori Intermediate-luminosity red transients:
Spectrophotometric properties and connection to electron-capture supernova
explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova explosions A. Sagués
Carracedo Intermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova
explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova explosions K. W. Smith
Intermediate-luminosity red transients: Spectrophotometric properties and
connection to electron-capture supernova explosionsIntermediate-luminosity red
transients: Spectrophotometric properties and connection to electron-capture
supernova explosions J. Sollerman Intermediate-luminosity red transients:
Spectrophotometric properties and connection to electron-capture supernova
explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova explosions A. Somero
Intermediate-luminosity red transients: Spectrophotometric properties and
connection to electron-capture supernova explosionsIntermediate-luminosity red
transients: Spectrophotometric properties and connection to electron-capture
supernova explosions B. Wang Intermediate-luminosity red transients:
Spectrophotometric properties and connection to electron-capture supernova
explosionsIntermediate-luminosity red transients: Spectrophotometric
properties and connection to electron-capture supernova explosions D. R. Young
Intermediate-luminosity red transients: Spectrophotometric properties and
connection to electron-capture supernova explosionsIntermediate-luminosity red
transients: Spectrophotometric properties and connection to electron-capture
supernova explosions

(Received Month XX, 2021 / Accepted July 29, 2021 )

We present the spectroscopic and photometric study of five intermediate-
luminosity red transients (ILRTs), namely AT 2010dn, AT 2012jc, AT 2013la, AT
2013lb, and AT 2018aes. They share common observational properties and belong
to a family of objects similar to the prototypical ILRT SN 2008S. These events
have a rise time that is less than 15 days and absolute peak magnitudes of
between $-11.5$ and $-14.5$ mag. Their pseudo-bolometric light curves peak in
the range $0.5$ \- $9.0\times 10^{40}\leavevmode\nobreak\
\mathrm{erg\leavevmode\nobreak\ s}^{-1}$ and their total radiated energies are
on the order of (0.3 - 3) $\times$ 1047 erg. After maximum brightness, the
light curves show a monotonic decline or a plateau, resembling those of faint
supernovae IIL or IIP, respectively. At late phases, the light curves flatten,
roughly following the slope of the 56Co decay. If the late-time power source
is indeed radioactive decay, these transients produce 56Ni masses on the order
of $10^{-4}$ to $10^{-3}$ M⊙ . The spectral energy distribution of our ILRT
sample, extending from the optical to the mid-infrared (MIR) domain, reveals a
clear IR excess soon after explosion and non-negligible MIR emission at very
late phases. The spectra show prominent H lines in emission with a typical
velocity of a few hundred km s-1, along with Ca II features. In particular,
the [Ca ii] $\lambda$7291,7324 doublet is visible at all times, which is a
characteristic feature for this family of transients. The identified
progenitor of SN 2008S, which is luminous in archival Spitzer MIR images,
suggests an intermediate-mass precursor star embedded in a dusty cocoon. We
propose the explosion of a super-asymptotic giant branch star forming an
electron-capture supernova as a plausible explanation for these events.

###### Key Words.:

supernovae: general – supernovae: individual: AT 2010dn, AT 2012jc, AT 2013la,
AT 2013lb, and AT 2018aes – stars: AGB and post-AGB – stars: mass-loss

##  1 Introduction

Modern surveys are discovering new types of stellar transients. Some events
show intermediate luminosities lying between classical novae and core-collapse
(CC) supernovae (SNe), and are collectively named ‘gap transients’ ($-$10 mag
$<$MV$<$ $-$15 mag; e.g. Kulkarni & Kasliwal 2009; Kasliwal 2012; Pastorello &
Fraser 2019) or even intermediate-luminosity optical transients (e.g. Berger
et al. 2009a; Soker & Kashi 2012; Soker 2020; Soker & Kaplan 2021).

A fraction of these transients are called ‘SN impostors’, as they mimic some
observational properties of H-rich interacting SNe, but deep late-time imaging
reveals that the progenitor stars survived (see, e.g. Van Dyk et al. 2000).
Their typical peak absolute magnitudes are between $-13$ and $-15$ mag, and
their spectra show narrow emission lines similar to Type IIn SNe (Schlegel,
1990; Filippenko, 1997). Giant eruptions of luminous blue variables (LBVs) are
considered a plausible interpretation for classical SN impostors. During giant
eruptions, their luminosity increases by over 3 mag with respect to the
quiescent phase, accompanied by severe mass loss, sometimes exceeding 1 M⊙
(Humphreys & Davidson, 1994; Humphreys et al., 1999). Well-studied examples
are the historical giant eruptions of two Galactic LBVs: $\eta$ Carinae (e.g.
Humphreys & Davidson, 1994; Soker, 2001a, b, 2003) and P Cygni (e.g. de Groot,
1969a, b), whose physical parameters (including ejected mass, spatial
geometry, and radiated energy) have been well constrained.

Another class of gap transients has double-peaked light curves and fast-
evolving spectra, showing SN IIn-like spectra at early phases (e.g. blue
continuum and narrow H emission lines) and spectra similar to M-type stars at
late phases (i.e. a much redder continuum and molecular bands). They are
conventionally designated as luminous red novae (LRNe; e.g. see Kochanek et
al., 2014; Pejcha et al., 2016; Smith et al., 2016; Blagorodnova et al., 2017;
Lipunov et al., 2017; MacLeod et al., 2017; Pejcha et al., 2017; Cai et al.,
2019; Pastorello et al., 2019a, b, 2021a, 2021b). The LRN phenomenon is
usually interpreted as a post-common-envelope-ejection phase in a contact
binary system, and may be followed by stellar coalescence (e.g. see Munari et
al., 2002; Soker & Tylenda, 2003, 2006; Tylenda et al., 2011; Soker & Kashi,
2016; Smith et al., 2016; Lipunov et al., 2017; Mauerhan et al., 2018;
Pastorello et al., 2019b; Soker, 2021).

The third group of gap transients are named intermediate-luminosity red
transients (ILRTs; Pastorello & Fraser, 2019, and references therein). These
show a slow rise time ($\approx$ 2 weeks) to maximum ($-$11.5 mag $<$MV$<$
$-$14.5 mag), followed by a linear decline or a plateau lasting about 2-4
months. When late-time light curves are observed, they decline following the
expectation of 56Co decay. Their light curves resemble those of very faint SNe
IIP/L. The spectra are similar to Type IIn SNe with narrow Balmer lines in
emission, but are characterised by prominent Ca ii lines (e.g. Ca H&K, [Ca ii]
doublet, and Ca ii near-infrared triplet); in particular, the [Ca ii]
$\lambda\lambda$ 7291, 7324 doublet is always visible at all phases. ILRTs are
linked to 8-15 M⊙ progenitors and are strong mid-infrared (MIR) emitters,
suggesting their progenitors are embedded in dusty cocoons (see Prieto et al.,
2008; Bond et al., 2009; Botticella et al., 2009; Berger et al., 2009b;
Thompson et al., 2009). However, their origin remains mysterious and different
scenarios are contemplated. These transients have been proposed to be LBV-like
outbursts of moderate-mass stars (e.g. Smith et al., 2009; Andrews et al.,
2020) or stellar mergers (e.g. Kasliwal et al., 2011). A third suggested
scenario is that we are actually observing faint CC SN explosions triggered by
electron captures in the core of super-asymptotic giant branch (S-AGB) stars,
and these are therefore labelled electron-capture (EC) SNe (see, e.g.
Botticella et al., 2009; Pumo et al., 2009). In recent years, a number of
ILRTs have been studied, including SN 2008S (see, e.g. Prieto et al., 2008;
Botticella et al., 2009; Smith et al., 2009; Kochanek, 2011; Szczygieł et al.,
2012; Adams et al., 2016), NGC 300-2008OT1 (NGC 300 OT hereafter) (e.g. Berger
et al., 2009b; Bond et al., 2009; Prieto et al., 2009; Kashi et al., 2010;
Humphreys et al., 2011), M85 OT2006-1 111For M85 OT2006-1 (hereafter M85 OT),
the classification as ILRT or LRN is still controversial (Kulkarni et al.,
2007; Pastorello et al., 2007; Rau et al., 2007). (Kulkarni et al., 2007;
Pastorello et al., 2007; Rau et al., 2007), PTF10fqs (Kasliwal et al., 2011),
AT 2017be (Stephens et al., 2017; Adams et al., 2018; Cai et al., 2018), and
AT 2019abn (Jencson et al., 2019; Williams et al., 2020, Valerin et al. 2021,
in preparation).

In this paper, we analyse a sample of five ILRTs 222International Astronomical
Union (IAU) names for the sampled five ILRTs are used throughout this paper.,
including AT 2010dn, AT 2012jc, AT 2013la, AT 2013lb, and AT 2018aes. In
general, they were initially classified as LBV-like outbursts or, more
generically, SN impostors. Subsequent follow-up campaigns allowed us to
confirm their classifications as ILRTs. In this work, we also compared ILRTs
with other claimed EC SN candidates, such as SN 2018zd (Zhang et al., 2018;
Arcavi et al., 2018; Zhang et al., 2020; Hiramatsu et al., 2021; Kozyreva et
al., 2021, Callis et al. 2021, in preparation), SN 2018hwm (Reguitti et al.,
2021), and SN 2015bf (Lin et al., 2021), as well as underluminous SNe IIP
(i.e. SN 1999br, SN 2005cs; Pastorello et al., 2004, 2006, 2009).

The present paper is organised as follows: general information on the sampled
ILRTs is given in Sect. 2. Photometric and spectroscopic analysis is reported
in Sects. 3 and 4, respectively. The rate of ILRTs is estimated in Sect. 5.
Finally, a discussion on the observational and theoretical properties of ILRTs
is given in Section 6.

##  2 Basic sample information

###  2.1 Host galaxies: distance, reddening and metallicity

AT 2010dn was discovered by the amateur astronomer K. Itagaki in May 2010 at
31.523 UT (hereafter UT will be used throughout this paper) at an unfiltered
magnitude 17.5 mag
(CBAT333http://www.cbat.eps.harvard.edu/iau/cbet/002200/CBET002299.txt). The
object was detected at RA=$10^{h}18^{m}19\aas@@fstack{s}89$, Dec=$+41\degr
26\arcmin 28\arcsec.80$ [J2000], $61\arcsec$ north and $33\arcsec$ east from
the centre of NGC 3184. We adopt $d=14.40\pm 0.33$ Mpc ($\mu=30.79\pm 0.05$
$\mathrm{mag}$) as the distance to the host galaxy, as obtained from Cepheids
(Ferrarese et al., 2000). The Galactic reddening $E(B-V)_{\mathrm{Gal}}=0.017$
$\mathrm{mag}$ is from Schlafly & Finkbeiner (2011). The presence of narrow
interstellar Na I D ($\lambda\lambda$ 5890, 5896) absorption in the transient
spectra at the host galaxy redshift is usually considered as evidence for
additional internal extinction (e.g. Munari & Zwitter, 1997; Turatto et al.,
2003; Pozzo et al., 2006; Sahu et al., 2006; Poznanski et al., 2011). In this
case, the equivalent width (EW) of Na I D varies with time, suggesting that
this dust is likely due to circumstellar material (CSM). For this reason, we
neglect the possible host component of extinction and adopt a total reddening
E($B-V$)Total = E($B-V$)Gal = 0.017 $\mathrm{mag}$, in agreement with Smith et
al. (2011).

AT 2012jc (also known as PSN J14535395+0334049, NGC 5775-2012OT1, SNhunt120
and LSQ12brd) was found by S. Howerton and the Catalina Real-Time Transient
Survey (CRTS444http://crts.caltech.edu/index.html) in March 2012 at 27.460 UT
(Berger et al., 2012; Howerton et al., 2012). Its coordinates are:
RA=$14^{h}53^{m}53\aas@@fstack{s}95$, Dec=$+03\degr 34\arcmin 04\arcsec.90$
[J2000], and it is located at $85\arcsec$ north and $55\arcsec$ west from the
centre of NGC 5775. Based on the weighted average of several estimates using
the Tully-Fisher method (e.g. Tully et al., 2013; Sorce et al., 2014; Tully et
al., 2016) from the NASA/IPAC Extragalactic database (NED555NED;
http://nedwww.ipac.caltech.edu/), a distance of $d=18.62\pm 1.12$ Mpc (hence
$\mu=31.35\pm 0.13$ $\mathrm{mag}$) can be estimated for NGC 5775. A Galactic
reddening E($B-V$)Gal = 0.037 $\mathrm{mag}$ (Schlafly & Finkbeiner, 2011) is
adopted. We measure a constant $EW\simeq 0.9$ Å for the Na i D absorption at
the redshift of NGC 5775 in the early spectra of the transient. Following
Turatto et al. (2003) and assuming RV = 3.1 (Cardelli et al., 1989), we obtain
a host galaxy reddening of $E(B-V)_{\mathrm{Host}}=0.144$ $\mathrm{mag}$.
Hence, the total reddening towards AT 2012jc is $E(B-V)_{\mathrm{Total}}$ =
0.181 $\mathrm{mag}$.

The discovery of AT 2013lb (PSN J15213475-0722183; NGC 5917-2013OT1) was
announced by the CHilean Automatic Supernovas sEarch in January 2013 at 27.340
UT (CHASE666http://www.das.uchile.cl/proyectoCHASE, Pignata et al., 2009;
Margheim et al., 2013). The coordinates are
RA=$15^{h}21^{m}34\aas@@fstack{s}75$, Dec=$-07\degr 22\arcmin 18\arcsec.30$
[J2000], and $19\arcsec$ north and $31\arcsec$ east from the centre of NGC
5917. For this galaxy, we adopt a kinematic distance, assuming a standard
cosmological model with $H_{0}=73$ $\rm{km}\,s^{-1}$$\rm{Mpc}^{-1}$,
$\Omega_{\mathrm{M}}=0.27$, $\Omega_{\mathrm{\Lambda}}=0.73$ (Spergel et al.,
2007), which is used throughout this paper. From the radial velocity corrected
for Local Group infall onto the Virgo Cluster $V_{\mathrm{Vir}}$ = 2024 $\pm$
7 $\rm{km}\,s^{-1}$ (see Sandage & Tammann, 1990; Theureau et al., 1998; Terry
et al., 2002, reported by HyperLeda 777http://leda.univ-lyon1.fr/), we obtain
a luminosity distance $d=27.73\pm 1.90$ Mpc ($\mu=32.21\pm 0.15$
$\mathrm{mag}$). A Galactic reddening $E(B-V)_{\mathrm{Gal}}=0.085$
$\mathrm{mag}$ (Schlafly & Finkbeiner, 2011) is reported for this object.
Additionally, spectroscopy indicates a negligible host galaxy extinction based
on non-detection of the Na i D absorption feature at the redshift of the host
galaxy.

AT 2013la (also named PSN J13100734+3410514; PS1-14ln; UGC 8246-2013OT1) was
discovered by B. Wang and X.
Gao888http://www.cbat.eps.harvard.edu/unconf/followups/J13100734+3410514.html
in December 2013 at 20.932 UT, at RA=$13^{h}10^{m}07\aas@@fstack{s}34$,
Dec=$+34\degr 10\arcmin 51\arcsec 40$ [J2000] (e.g. Tartaglia et al., 2014).
The object is $0.8\arcsec$ south and $32.7\arcsec$ east from the centre of UGC
8246. Averaging several recent Tully-Fisher estimates (e.g. Tully et al.,
2013; Sorce et al., 2014; Tully et al., 2016), we obtain $d=15.21\pm 0.11$ Mpc
(hence, $\mu=30.91\pm 0.02$ $\mathrm{mag}$) for UGC 8246. We adopt the same
line-of-sight reddening as Barsukova et al. (2014), that is,
$E(B-V)_{\mathrm{Total}}=0.009$ $\mathrm{mag}$. We note that, in analogy to AT
2010dn, a variable $EW$ of Na I D suggests the presence of additional
circumstellar dust, which is not accounted for in this reddening estimate. We
hence adopt $E(B-V)_{\mathrm{Total}}=E(B-V)_{\mathrm{Gal}}$.

AT 2018aes (Kait-18M) was discovered by the Lick Observatory Supernova Search
(LOSS999http://w.astro.berkeley.edu/bait/kait.html) in March 2018 at 11.535
(Yunus et al., 2018). It was detected at RA=$13^{h}48^{m}17\aas@@fstack{s}76$,
Dec=$+03\degr 56\arcmin 44\arcsec.20$ [J2000], $18.9\arcsec$ south and
$25.7\arcsec$ east of the nucleus of NGC 5300 (Andrews et al., 2018). We
average a few recent Tully-Fisher distances estimates from NED (e.g. Tully et
al., 2013; Sorce et al., 2014; Tully et al., 2016), obtaining a weighted
average distance $d=18.02\pm 0.61$ Mpc ($\mu=31.28\pm 0.07$ $\mathrm{mag}$).
As there is some persistent spectroscopic signatures of interstellar Na I D at
the host galaxy redshift, following Turatto et al. (2003), we estimate an
internal reddening $E(B-V)_{\mathrm{Host}}=0.160$ $\mathrm{mag}$, while we
adopt a Milky Way contribution $E(B-V)_{\mathrm{Gal}}=0.020$ $\mathrm{mag}$
(Schlafly & Finkbeiner, 2011) for AT 2018aes. Hence, we obtain a total colour
excess $E(B-V)_{\mathrm{Total}}=0.180$ $\mathrm{mag}$.

Although we did not perform precise estimates of metallicity at the locations
of these ILRTs, an estimate of the characteristic oxygen abundance at
$0.4R_{25}$ 101010$R_{25}$, also known as the de Vaucouleurs radius, is
defined as the radius along the semi-major axis where the surface brightness
in B-band is 25 magnitudes per square arcsecond ($\mu_{\rm{B}}=25$
mag/arcsec2) (e.g. de Vaucouleurs et al., 1991; Corwin et al., 1994). can be
done using a statistical approach and the following relation from Pilyugin et
al. (2004):

$12+\mathrm{log}\left(\mathrm{O/H}\right)\leavevmode\nobreak\
$=$\leavevmode\nobreak\ 6.93\leavevmode\nobreak\ \left(\pm\leavevmode\nobreak\
0.37\right)\leavevmode\nobreak\ -\leavevmode\nobreak\
0.079\leavevmode\nobreak\ \left(\pm\leavevmode\nobreak\
0.018\right)\leavevmode\nobreak\ \times\leavevmode\nobreak\ M_{\mathrm{B}},$
(1)

which links the characteristic oxygen abundance to the absolute $B$-band
magnitude ($M_{\mathrm{B}}$) of the galaxy. The oxygen abundances of the ILRT
host galaxies span a very narrow range, from 8.2 to 8.6 $\mathrm{dex}$, which
is nearly solar or marginally subsolar (adopting a solar metallicity of 12 +
log(O/H) = 8.69 dex; see e.g. Asplund et al., 2009; von Steiger & Zurbuchen,
2016; Vagnozzi, 2019). We note that the hosts are all spiral galaxies and the
positions of the ILRTs are towards their outer edges.

A summary of the ILRTs and their host galaxy parameters is listed in Table 1,
while in Figure 1 we show the location of the transients in their host
galaxies.

Table 1: Basic information for the ILRT host galaxies.

Object | Host Galaxya |  $m_{\mathrm{B}}$b | Redshift | Distance | Distance Modulus | Radial Distancec | Metallicity | $E(B-V)_{\mathrm{Gal}}$ | $E(B-V)_{\mathrm{Host}}$
---|---|---|---|---|---|---|---|---|---
|  | ($\mathrm{mag}$) |  | ($\mathrm{Mpc}$) | ($\mathrm{mag}$) | ($\mathrm{kpc}$) | ($\mathrm{dex}$) | ($\mathrm{mag}$) | ($\mathrm{mag}$)
AT 2010dn | NGC 3184 [SABc] | 10.3 | 0.00198 | 14.40 (0.33) | 30.79 (0.05) | 4.8 (0.1) | 8.55 (0.74) | 0.017 | 0
AT 2012jc | NGC 5775 [SBc] | 12.2 | 0.00561 | 18.62 (1.12) | 31.35 (0.13) | 9.1 (0.5) | 8.44 (0.71) | 0.037 | 0.144 (0.080)
AT 2013lb | NGC 5917 [Sb] | 13.7 | 0.00635 | 27.73 (1.90) | 32.21 (0.15) | 2.7 (0.1) | 8.39 (0.70) | 0.085 | 0
AT 2013la | UGC 8246 [SBc] | 14.6 | 0.00271 | 15.21 (0.11) | 30.91 (0.02) | 4.0 (0.3) | 8.22 (0.66) | 0.009 | 0
AT 2018aes | NGC 5300 [SABc] | 12.1 | 0.00391 | 18.02 (0.61) | 31.28 (0.07) | 2.8 (0.1) | 8.45 (0.72) | 0.020 | 0.160 (0.085)
SN 2008S | NGC 6946 [SABc] | 8.2 | 0.00013 | 5.70 (0.21) | 28.78 (0.08) | 5.6 (0.2) | 8.56 (0.74) | 0.360 | 0.320 (0.031)
NGC300 OT | NGC 0300 [Scd] | 8.8 | 0.00048 | 1.88 (0.12) | 26.37 (0.14) | 2.5 (0.2) | 8.32 (0.69) | 0.011 | 0.250 (0.148)
PTF10fqs | NGC 4254 [Sc] | 10.2 | 0.00803 | 14.26 (3.41) | 30.77 (0.52) | 6.9 (1.7) | 8.56 (0.74) | 0.040 | 0
AT 2017be | NGC 2537 [SBm] | 13.1 | 0.00144 | 7.82 (0.54) | 29.47 (0.15) | - | 8.22 (0.66) | 0.048 | 0.040 (0.02)
M85 OT | NGC 4382 [S0-a] | 10.1 | 0.00243 | 15.85 (0.88) | 31.00 (0.12) | 2.5 ( 0.1) | 8.58 (0.75) | 0.027 | 0.113 (0.108)

$Notes:$ Our sample is reported in the top half of the table and other
published objects are in the lower half. The uncertainties on distance,
distance modulus, radial distance, and metallicity are obtained from error
propagations, while host galaxy extinction is computed from the standard
deviation of measurements.

a Galaxy type from HyperLeda.

b $B$-band apparent magnitude of the host galaxy, from NED.

c Projected distance of the ILRT location from the host galaxy nucleus.

###  2.2 Data reduction

Routine follow-up campaigns were triggered soon after the announcement of the
ILRT discoveries, using the instruments available to our collaboration.
Information on the instrumental configurations is reported in Table 6
(Appendix A). For some transients, additional early-time unfiltered data were
collected from amateur astronomers. We also collected historical data
available in public archives.

The raw images were first pre-reduced, applying overscan, bias and flat-field
corrections through standard iraf111111http://iraf.noao.edu/ tasks (Tody,
1986, 1993). When necessary, multiple-exposure frames were median-combined to
increase the signal-to-noise ratio (S/N). Photometric measurements were
performed through a dedicated pipeline, ecsnoopy121212ecsnoopy is a package
for SN photometry using PSF fitting and/or template subtraction developed by
E. Cappellaro. A package description can be found at
http://sngroup.oapd.inaf.it/snoopy.html.. ecsnoopy is a python-based script,
which makes use of a series of packages for photometry and template
subtraction (e.g. sextractor131313www.astromatic.net/software/sextractor/,
daophot141414http://www.star.bris.ac.uk/~mbt/daophot/,
hotpants151515http://www.astro.washington.edu/users/becker/v2.0/hotpants.html/;
Bertin & Arnouts, 1996; Stetson, 1987; Becker, 2015). Individual instrumental
magnitudes were measured with the point-spread function (PSF) fitting
technique. We first subtracted the background contaminating the object using a
low-order polynomial fit. A standard PSF template was constructed by fitting
the profiles of several isolated stars (usually from 5 to 10 stars) in the SN
frames. The PSF model was then fitted to the target source, and the goodness
of the fit was evaluated by inspecting the residuals at the SN location. When
the object was faint or had a complex background, we used the template-
subtraction technique to remove the background contamination from our
measurements. Specifically, we applied it to measurements of AT 2010dn, AT
2013la, and AT 2018aes. The errors were estimated via artificial star tests,
in which several fake stars were placed close to the SN location. The fake
stars were fitted with the PSF method, and the standard deviation of these
measurements provided us the instrumental errors. These were combined in
quadrature with the PSF-fit error, finally providing the total photometry
error.

We applied the instrumental zero points (ZPs) and colour terms (CTs) to the
instrumental magnitudes obtained through observations of standard fields
obtained in photometric nights. Specifically, the Johnson-Cousins magnitudes
were determined with reference to the Landolt (1992) catalogue, and Sloan-
filter data were calibrated via the SDSS DR 13 catalogue (Albareti et al.,
2017). In order to obtain an accurate calibration, a sequence of reference
stars in the field of each ILRT was used to correct the ZPs in non-photometric
nights. When available, the Sloan magnitudes of the reference stars in the
ILRT field were directly taken from SDSS, while the Johnson-Cousins magnitudes
were obtained from the SDSS data using the conversion relations of Chonis &
Gaskell (2008).

Near-infrared (NIR) data reduction includes flat fielding, distortion
correction and sky subtraction. We performed pre-reduction on NOT/NOTCam and
NTT/SOFI raw images using dedicated pipelines for NOTCam (version 2.5) and
SOFI (PESSTO pipeline, version 2.2.10; Smartt et al., 2015) respectively.
Standard iraf tasks were used to reduce LT/SupIRCam and TNG/NICS images.
Instrumental magnitudes were measured via ecsnoopy, and then calibrated using
the Two Micron All Sky Survey
(2MASS161616http://irsa.ipac.caltech.edu/Missions/2mass.html/, Skrutskie et
al., 2006) catalogue (assuming negligible colour corrections).

The Spitzer Space Telescope was equipped with the InfraRed Array Camera (IRAC;
two channels: CH1=3.6 $\mu$m and CH2=4.5 $\mu$m). We used the Level 2 post-BCD
(Basic Calibrated Data) images, which were reduced with the Spitzer
pipeline171717The IRAC Instrument Handbook is available on the website:
https://irsa.ipac.caltech.edu/data/SPITZER/docs/irac/iracinstrumenthandbook/.
These pBCD images are composed of a mosaic image, after rejection of most
instrumental artefacts, an uncertainty image, and an associated coverage image
which is the map of how many frames per position are available to generate the
mosaic image. We note that AT 2010dn was targeted at 14 epochs by the Spitzer
Space Telescope during 2010 – 2015 and the data are available from Spitzer
Heritage Archive
(SHA)181818http://irsa.ipac.caltech.edu/applications/Spitzer/SHA/. We took the
Spitzer images from 2019 September 14 as templates191919Note that there were
some images taken before AT 2010dn exploded, but as these were taken during
the cryogenic phase of the Spitzer mission they would be less suitable for our
data., which were matched and transformed to each epoch of the observed images
and then subtracted using hotpants (Becker, 2015). We performed aperture
photometry on the subtracted images using a small (4$\times$$0.6\arcsec$ pBCD
pixel) aperture, and then applied an aperture correction and a conversion from
MJy/sr to mJy/pix to get the fluxes. With this approach, we obtained ten
detections for the CH1 and CH2 channels over a time-span of five years (from
2010 to 2015). For a few other epochs we have non-detections down to
3$\sigma$. The resulting magnitudes are reported in Table 10 (Appendix C).

Figure 1: Top-left: AT 2010dn in one of the spiral arms of the host galaxy.
Sloan $r$-band image taken in June 2010 at 19 with the 2m robotic Faulkes
Telescope North (FTN) operated by Las Cumbres Observatory (LCO; Brown et al.,
2013). Top-middle: AT 2012jc at the north edge of its host galaxy. Johnson-
Cousins $R$-band image obtained in April 2012 at 06 with the 0.41m PROMPT5
telescope. Top-right: AT 2013lb in the outskirts of its host galaxy. Johnson-
Cousins $R$-band image obtained in February 2013 at 20 with the 2m fully
robotic Liverpool Telescope (LT) with RATCam. Bottom-left: AT 2013la at the
east edge of its galaxy. A zoom-in of the transient position is shown in the
lower-left corner. Sloan $r$-band image obtained in February 2014 at 12 with
the LT equipped with IO:O. Bottom-right: AT 2018aes and its host galaxy.
LT/IO:O Sloan $r$-band image obtained in May 2018 at 17 with a blow-up of the
transient site in the lower-left inset.

##  3 Photometry

Our follow-up campaigns for each of the five transients started soon after
their discovery, and lasted several months. The photometric measurements of
the transients are reported in Tables 8 \- 17 (Appendix C), while individual
light curves are shown in Figure 2. As a reference epoch, we selected the
$R/r$-band maximum, obtained using a third-order polynomial fit to the
observed light curves between about $-$20 and $+$20 days from maximum (see
below).

###  3.1 Apparent light curves

Figure 2: Multi-band light curves of AT 2010dn (top-left), AT 2012jc (top-
right), AT 2013lb (middle-left), AT 2013la (middle-right), and AT 2018aes
(bottom). The dashed vertical lines indicate the $R/r$-band maximum time.
Upper limits are marked by empty symbols with arrows. The light curves are
shifted with some constants for clarity and the shift amount is reported at
the top. The errors of most magnitudes are smaller than the plotted symbol
sizes. Table 2: Decline rates of the light curves of individual ILRTs
(mag/100d), along with their uncertainties.

Filter | Phase i ($\gamma$1) | Phase ii ($\gamma$2) | Phase iii ($\gamma$3)
---|---|---|---
AT 2010dn
$u$ | 6.32 (0.54) | 4.25 (0.56) | –
$B$ | 6.23 (0.92) | 4.02 (0.38) | –
$V$ | 6.36 (1.24) | 2.14 (0.36) | 0.08 (0.05)
$r$ | 5.17 (0.96) | 1.50 (0.38) | 0.08 (0.05)
$i$ | 6.16 (0.43) | 1.03 (0.51) | 0.29 (0.15)
$z$ | 0.89 (0.06) | 0.89 (0.06) | –
$J$ | 1.45 (0.11) | 1.45 (0.11) | 1.41 (0.00)
$H$ | 0.72 (0.05) | 0.72 (0.05) | 0.80 (0.00)
$K$ | – | – | 1.75 (0.00)
AT 2012jc
$U$ | 5.78 (0.79) | 5.78 (0.79) | –
$B$ | 4.16 (0.29) | 2.77 (0.19) | 2.77 (0.19)
$V$ | 3.17 (0.37) | 2.20 (0.10) | 2.20 (0.10)
$R$ | 4.98 (0.44) | -0.11 (0.35) | 2.68 (0.27)
$I$ | 4.14 (0.44) | 0.09 (0.20) | 2.24 (0.08)
AT 2013lb
$B$ | – | 3.41 (0.09) | 3.41 (0.09)
$V$ | 1.90 (0.12) | 1.90 (0.12) | 4.94 (0.52)
$R$ | 1.10 (0.11) | 1.10 (0.11) | 5.13 (0.18)
$I$ | 0.59 (0.10) | 0.59 (0.10) | 5.12 (1.35)
$J$ | 0.56 (0.10) | 0.56 (0.10) | 0.56 (0.10)
$H$ | 0.74 (0.10) | 0.74 (0.10) | 0.74 (0.10)
$K$ | 0.91 (0.12) | 0.91 (0.12) | 0.91 (0.12)
AT 2013la
$u$ | 2.22 (0.04) | 2.22 (0.04) | –
$B$ | 2.08 (0.07) | 0.71 (0.11) | –
$V$ | 1.79 (0.03) | 0.59 (0.27) | –
$r$ | 1.70 (0.05) | 0.62 (0.04) | 1.17 (0.12)
$i$ | 1.72 (0.07) | 0.37 (0.11) | 1.14 (0.09)
AT 2018aes
$B$ | 2.21 (0.21) | 3.78 (0.13) | 5.02 (1.99)
$g$ | 1.85 (0.22) | 4.02 (0.23) | 4.97 (0.90)
$V$ | 2.25 (0.25) | 4.33 (0.27) | 5.01 (2.05)
$r$ | 2.55 (0.34) | 3.75 (0.13) | 6.51 (0.04)
$i$ | 2.17 (0.68) | 4.03 (0.21) | 4.48 (0.39)
$z$ | 2.52 (0.89) | 3.72 (0.30) | 5.02 (0.14)
$J$ | 2.32 (0.28) | 2.32 (0.28) | 2.32 (0.28)
$H$ | 2.01 (0.26) | 2.01 (0.26) | 2.01 (0.26)
$K$ | 1.57 (0.21) | 1.57 (0.21) | 1.57 (0.21)

In Figure 2 we show the apparent light curves of the five events, which are
similar to those of other ILRTs in the literature. Most of the objects have a
rise time of about two weeks, but AT 2018aes has a longer rise of about 24.1
d. After maximum, the light curve evolution of the sample resembles that of
SNe IIP/IIL. We divide the light curve evolution into three different phases:
Phase i ($\gamma$1), Phase ii ($\gamma$2), and Phase iii ($\gamma$3), each
with a different decline rate. The values obtained through linear fits are
reported in Table 2. In general, ILRTs decline quite rapidly in all bands
during Phase i, with the blue bands usually fading faster than the red bands.
After Phase i, a sort of plateau (see AT 2012jc and AT 2013la) or a linear
decline (see AT 2013lb and AT 2018aes) is observed in ILRTs. When late-time
observations are available (i.e. AT 2013la, SN 2008S, and NGC 300 OT), a slow
evolution is observed, consistent with that expected from the 56Co decay. We
discuss the implications of this in Sect. 3.4.

###  3.2 Colour evolution

The colour evolution of the five transients is shown in Figure
LABEL:pic:colour, along with those of other ILRTs and comparison objects from
the literature. For the ILRTs, the $B-V$ colour evolves steadily from $\sim$
0.2 - 0.4 mag at early phases to $\sim 0.7$ \- 1.0 mag at around 100 days past
maximum, suggesting that the temperature decreases with time (see panel a in
Figure LABEL:pic:colour). At the later phases ($>$100 days), $B-V$ becomes
bluer again, from 0.8 to 0.5 mag. At similar epochs, the $R-I$/$r-i$ colours
increase from $\sim$ 0.1 - 0.3 mag to 0.5 - 1.0 mag (Figure LABEL:pic:colour,
panel b). Very late-time colours show a large dispersion. AT 2013la is
somewhat discrepant, with the $r-i$ colour becoming bluer (reaching $\sim-0.2$
mag) than at early epochs. The $J-K$ colour usually shows a minimum at 30-70
days. The best-sampled NIR dataset is that of NGC 300 OT, which allows us to
estimate a minimum value of $\sim$ 1.1 mag. Later, $J-K$ rises to 3.0 mag at
$\sim$ 230 days (Figure LABEL:pic:colour, panel c). As shown in Figure
LABEL:pic:colour, the comparison objects are bluer (e.g. SN 2018zd and SN
2005cs: $B-V$ $\approx$ $-$0.2 mag) at early phase and become redder (e.g. SN
2005cs: $B-V$ $\approx$ 2.0 mag at tail phase) over time.

Figure 4: Comparison of the $R/r$-band absolute light curves of ILRTs and SN
2018zd, SN 2018hwm, SN 1999br, and SN 2005cs. Reddenings and distance moduli
of the comparison objects are taken from their respective papers (also see
Table 7 in Appendix B). The dashed vertical line indicates the time of
$r$-band maximum light. Upper limits are marked by empty symbols with down
arrows.

###  3.3 Absolute light curves

The $R/r$-band absolute light curves of our ILRT sample, calibrated in the
Vega system, are shown in Figure 4. We used third-order polynomial fits to
estimate the $R/r$-band peak absolute magnitudes202020These fits were
performed on the absolute light curves about $-$20 to $+$20 days from
maximum., and the resulting values are listed in Table 3. All transients have
rise times to their maximum $\lesssim$ 2 weeks, apart from AT 2018aes, which
reaches the light curve peak in $\sim$ 3 weeks. The peak absolute magnitudes
span a range from $\sim-11\leavevmode\nobreak\ (\pm\leavevmode\nobreak\ 0.5)$
to $-15\leavevmode\nobreak\ (\pm\leavevmode\nobreak\ 0.5)$ mag, still within
the range expected for gap transients ($-10<M<-15$ mag; Pastorello & Fraser,
2019). If we consider all objects in this study, we obtain an averaged
absolute peak magnitude of $M_{\rm R}=-13.04\pm 0.91$ mag. As shown in Figure
4, we compared the $R/r$-band absolute light curves of ILRTs with three
proposed EC SN candidates: SN 2018zd, SN 2018hwm, and SN 2015bf; and two
subluminous Type IIP SNe: SN 1999br and SN 2005cs. They show a wide range of
peak magnitudes, with the faint SN 1999br ($\sim$ $-$ 13.8 mag), the
relatively luminous SN 2018zd and SN 2015bf ($\sim$ $-$ 18.0 mag), and
intermediate-luminosity SN 2018hwm and SN 2005cs ($\sim$ $-$ 15.5 mag). SN
1999br, SN 2018hwm, and SN 2005cs are characterised by long-lasting plateaus
of above 100 days. At the end of the plateau, these comparison objects show a
sudden drop in luminosity of 2.5-4.0 mag. Finally, they all settle onto the
radioactive tails.

Table 3: Light-curve parameters for ILRTs.

Object | MJDnon.d. | MJDexp. | MJDfirst.d. | MJDR/r,peak | $M_{\rm{R/r,peak}}$ | $L_{\rm{peak}}$ | $E_{\rm{rad.}}$ |  56Ni Mass |
---|---|---|---|---|---|---|---|---|---
|  |  |  |  | ($\mathrm{mag}$) | ($\rm{10^{40}\leavevmode\nobreak\ erg\leavevmode\nobreak\ s^{-1}}$) | ($\rm{10^{47}\leavevmode\nobreak\ erg}$) | (M⊙ ) |
AT 2010dn | 55338.00 | 55343 (5) | 55348.04 | 55354.9 (3.1) |  $-$13.51 (0.27) | 3.65 (0.09) | - |  $2.5\times 10^{-3}$ \- 2.7 $\times 10^{-3}$ |
AT 2012jc | 56003.39 | 56008 (5) | 56013.49 | 56024.5 (2.0) |  $-$14.50 (0.13) | 9.97 (1.16) | 2.94 (0.38) | - |
AT 2013lb | 56112.03 | – | 56319.34 | 56324.5 (3.0) |  $-$13.73 (0.11) | 4.12 (0.52) | 1.61 (0.24) | - |
AT 2013la | 56463.22 | – | 56646.93 | 56652.0 (2.1) |  $-$12.97 (0.39) | 1.95 (0.05) | 1.10 (0.04) | $>4.8\times 10^{-3}$ |
AT 2018aes | 58184.61 | 58187 (2) | 58188.54 | 58211.1 (7.6) |  $-$12.88 (0.04) | 2.16 (0.07) | 1.02 (0.07) | - |
SN 2008S | 54481.50 | 54486 (4) | 54489.50 | 54502.5 (2.0) |  $-$14.24 (0.03) | 5.36 (0.22) | 2.93 (0.47) |  $3.2\times 10^{-3}$ \- 3.5$\times 10^{-3}$ |
NGC 300 OT | 54504.00 | – | 54580.15 | 54600.0 (2.0) |  $-$12.77 (0.06) | 1.76 (0.53) | 0.69 (0.36) | $>1.4\times 10^{-3}$ |
PTF10fqs | 55295.20 | 55299 (4) | 55302.39 | 55315.3 (4.0) |  $-$11.55 (0.35) | 0.59 (0.30) | 0.30 (0.15) | - |
AT 2017be | 57751.48 | 57755 (4) | 57759.51 | 57767.8 (2.0) |  $-$12.01 (0.14) | 0.93 (0.08) | 0.43 (0.06) |  $6.7\times 10^{-4}$ \- 7.2$\times 10^{-4}$ |
M85 OT | 52672.00 | – | 53742.00 | 53753.6 (2.0) |  $-$12.21 (0.90) | 0.70 (0.13) | 0.30 (0.13) | $<1.0\times 10^{-3}$ |

$Notes:$ Object name (column 1), last non-detection MJD (column 2), explosion
MJD (column 3), first detection MJD (column 4), maximum MJD (column 5), peak
magnitude (column 6), peak bolometric ($B$ to $I$) luminosity (column 7),
radiated energy (column 8), 56Ni mass (column 9; We note that for some objects
we do not report the 56Ni mass because of a lack of observed light curve
tails). Uncertainties are reported in parentheses.

###  3.4 Pseudo-bolometric light curves

Figure 5: Pseudo-bolometric $B$ to $I/i$ light curves of ILRTs and comparison
objects. The dashed vertical line indicates the time of $R/r$-band maximum
light.

The bolometric light curve is computed by integrating the spectral energy
distribution (SED) over the whole electromagnetic spectrum. However, in most
cases, observations at wavelengths shorter than the $u$ band, and longer than
$I/i$-band are not available. For this reason, to achieve meaningful
comparisons among ILRTs, we computed pseudo-bolometric light curves including
only the contribution from the $B$ to the $I/i$ band. We first converted the
extinction-corrected magnitudes to flux densities, and finally integrated the
SEDs at their effective wavelengths, assuming a negligible flux contribution
outside of the integration region. The resulting pseudo-bolometric light
curves are presented in Figure 5, while peak luminosities are reported in
Table 3. They show faint peak luminosities ranging from $0.5\times 10^{40}$
erg s-1 to $9.0\times 10^{40}$ erg s-1. For comparison, the claimed EC SNe SN
2018zd and SN 2015bf have peak luminosities of $\sim$ $3.7\times 10^{42}$ erg
s-1 and the faint Type IIP SN 1999br is about $4.7\times 10^{40}$ erg s-1 (see
Figure 5). The pseudo-bolometric light curve shapes of ILRTs are broadly
similar to Type IIP (in particular, PTF10fqs and AT 2017be) and/or Type IIL
(SN 2008S and AT 2012jc) SNe, as demonstrated in Figure 5. In analogy to Type
IIP SNe, the light curves for ILRTs are influenced by a number of factors,
such as the presence of a CSM, the H recombination timescale, and 56Ni
distribution. Finally, we perform a non-parametric fit using the
ReFANN212121ReFANN is a nonlinear interpolating tool based on Artificial
Neural Networks that can reconstruct functions from data (see
https://github.com/Guo-Jian-Wang/refann). code (Wang et al., 2020, 2021) to
reconstruct the pseudo-bolometric light curve, and integrate it over the
covered photometric evolution. The resulting radiated energies are in the
range of (0.30 - 2.94) $\times$ 1047 erg, with values reported in Table 3.
These values should be regarded as lower limits due to our incomplete
wavelength coverage and limited temporal coverage. These observed ILRTs
radiated energies are fractions of about 10-4 \- 10-3 of the theoretical
predictions for the explosion energy of EC SNe (about 1050 erg, Kitaura et
al., 2006; Wanajo et al., 2009; Tominaga et al., 2013). Stritzinger et al.
(2020b) pointed out that theoretical EC SN simulations may overpredict the
explosion energy. Therefore, this discrepancy should be considered in future
observations and modelling efforts.

In order to provide reliable estimates for the ejected 56Ni masses, we need to
compute the bolometric light curves. Unfortunately, most objects do not have
MIR observations, and optical and/or NIR light-curve information is sometimes
incomplete at late times. SN 2008S and NGC 300 OT are exceptions, as they were
followed until late phases, and also have MIR coverage. Observations of these
two objects revealed that the SEDs of ILRTs shift from the optical to the MIR
domain, with the MIR being dominant at late phases (e.g. Botticella et al.,
2009; Kochanek, 2011). To mitigate the limited observational information
available for other objects, we adopted SN 2008S as a template for other
ILRTs, and assumed that all others share the same SED evolution. Hence, we
used SN 2008S to determine the bolometric corrections for all ILRTs that had
incomplete wavelength coverage. We estimated the optical and NIR luminosity
contribution of SN 2008S, using the bolometric light curve model
($L_{\rm{bol}}=L_{0}\times\exp(-t/t_{0})$ \+ $L_{1}$, with $L_{0}\simeq
10^{7.3}L_{\odot}$, $L_{1}\simeq 10^{5.8}L_{\odot}$ and $t_{0}\simeq 48$ days)
from Kochanek (2011). We first computed the
$\frac{L_{\rm{opt}}}{L_{\rm{bol}}}$, $\frac{L_{\rm{NIR}}}{L_{\rm{bol}}}$, and
$\frac{L_{\rm{opt}}+L_{\rm{NIR}}}{L_{\rm{bol}}}$ ratios at late phases for SN
2008S. The $L_{\rm{opt}}$, $L_{\rm{NIR}}$, and $L_{\rm{opt}}+L_{\rm{NIR}}$
contributions for other ILRTs at the same phases were then calculated,
assuming the same ratios as for SN 2008S. Specifically, $L_{\rm{bol}}$ was
computed starting from the measured $L_{\rm{opt}}+L_{\rm{NIR}}$ for AT 2010dn,
from $L_{\rm{opt}}$ for AT 2013la, and $L_{\rm{NIR}}$ for AT 2017be, and then
by applying the adopted bolometric corrections.

Assuming that the late-time evolution of ILRTs are powered by the radioactive
decay chain 56Ni $\to$ 56Co $\to$ 56Fe, the late-time luminosity of ILRTs can
be used to constrain the synthesised 56Ni mass. We use the well-observed Type
II SN 1987A as a reference (Catchpole et al., 1988; Whitelock et al., 1988;
Catchpole et al., 1989) and estimate the ejected 56Ni mass of ILRTs using
Equation 2:

$M\left({}^{56}\mathrm{Ni}\right)_{\mathrm{ILRT}}\leavevmode\nobreak\
$=$M\left({}^{56}\mathrm{Ni}\right)_{\mathrm{SN\leavevmode\nobreak\
1987A}}\times\left(L_{\mathrm{ILRT}}\left(t\right)\over
L_{\mathrm{SN\leavevmode\nobreak\ 1987A}}\left(t\right)\right),$ (2)

where $M(^{56}\mathrm{Ni})_{\mathrm{SN\leavevmode\nobreak\ 1987A}}\sim
0.073\leavevmode\nobreak\ \mathrm{M_{\odot}}$222222This value is computed
through a weighted mean of values reported in Arnett & Fu (1989) and Bouchet
et al. (1991). is the 56Ni mass synthesised by SN 1987A, and
$L_{\mathrm{ILRT}}$ and $L_{\mathrm{SN\leavevmode\nobreak\ 1987A}}$ are late-
time luminosities of an individual ILRT and SN 1987A, respectively. Hereafter,
we only consider five ILRTs that have observations in the nebular phase.
Because of the poor constraints on the explosion epoch of ILRTs, we use the
last non-detection and the first detection to fix the earliest and the latest
possible extremes for the explosion epochs. Hence, we obtain upper and lower
limits of 56Ni masses for the ILRTs, reported in Table 3. SN 2008S ejected the
largest amount of 56Ni ($3.2$ \- $3.5\times 10^{-3}$ M⊙ ), while AT 2017be has
the lowest 56Ni mass ($6.7$ \- $7.2\times 10^{-4}$ M⊙ ). All inferred 56Ni
masses are of the order of $10^{-4}$ to $10^{-3}$ M⊙ , which, as discussed in
Sect. 6, is in agreement with the predictions for EC SNe.

###  3.5 Evolution of the SED of ILRTs: the test case of AT 2010dn

It is well known that SN 2008S, NGC 300 OT, and AT 2012jc already showed an IR
excess soon after their discovery (Botticella et al., 2009; Humphreys et al.,
2011; Stritzinger et al., 2020b). If we assume their progenitors to be
embedded in complex and extended dusty environments, we should expect such IR
excesses to be frequently observed for ILRTs. This can be verified in the case
of AT 2010dn, for which MIR observations are available. Using the light curves
presented in Table 8, 9, and 10, we constructed the SEDs of AT 2010dn at
different epochs using photometry from the optical to the MIR. The first
optical to MIR SED is obtained at $t\sim$30.6 days after maximum, which
clearly reveals an IR excess over a single black body (BB) model (see the top
panel of Figure 6). Hence, the SED was fitted with two-component (hot+warm
components) BB functions instead of a single one. The hot component has a
temperature $T_{\mathrm{hot}}$=5390 $\pm$ 70 K and a radius
$R_{\mathrm{hot}}\approx 2.87\times 10^{14}$ cm, while the warm component has
$T_{\mathrm{warm}}$ $\approx$ 970 K and $R_{\mathrm{warm}}\approx 4.63\times
10^{15}$ cm. In comparison, SN 2008S had $T_{\mathrm{hot}}$= 8076 $\pm$ 150 K,
$R_{\mathrm{hot}}=(2.1\pm 0.1)\times 10^{14}$ cm, $T_{\mathrm{warm}}$
$\approx$ 585 K, $R_{\mathrm{warm}}\approx 9.9\times 10^{15}$ cm at maximum
(Botticella et al., 2009), while AT 2012jc had a BB temperature of
$T_{\mathrm{hot}}$ $\approx$ 6430 K and $T_{\mathrm{warm}}$ $\approx$ 800 K at
+ 26.8 days (Stritzinger et al., 2020b). The hot-component estimates are
consistent with emission from the photosphere, while the warm component
peaking in the MIR domain is likely due to circumstellar dust. For AT 2010dn,
additional epochs of SEDs along with the corresponding best-fit BB functions
are shown in Figure 17 (Appendix C), while the first BB parameters are
reported in Table 11. The $T_{\mathrm{hot}}$ increases to $\sim$ 6490 K and,
when the luminosity fades, $T_{\mathrm{hot}}$ also declines to $\sim$ 3540 K
at $+$199.2 d. The $R_{\mathrm{hot}}$ shows a slow evolution (from 2.4 to 2.9
$\times 10^{14}$ cm) until $+$21.5 d, and declines to 1.6 $\times 10^{14}$ cm
at $+$199.2 d. Three epochs with K band data reveal a possible second warm
component with an almost constant temperature of 1100-1200 K (see Figure 17).

We also measured the residual flux at the location of AT 2010dn in Spitzer MIR
images taken more than 3 years (+1333 days) after the outburst, and
constructed a very late-time SED. This SED can be reproduced by a single BB
function with a characteristic temperature of 440 K (see the bottom panel of
Figure 6). We caution that this temperature should be regarded as an
indicative value because of the limited coverage of MIR data. Similarly, AT
2012jc has very late-phase (+1155 days) Spitzer MIR photometric fluxes
suggesting a BB temperature of about $600\,\rm{K}$. Based on the similarity of
these three cases, we suggest that this SED evolution seems to be typical of
ILRTs. A plausible explanation is that a dusty environment has formed through
mass-loss events prior to the ILRT outbursts, in analogy to what is frequently
observed in a few CC SNe (e.g. SN 1995N, SN 1998S, SN 2010jl, SN 2014ab, SN
2015da; see Gerardy et al., 2002; Andrews et al., 2011; Fransson et al., 2014;
Tartaglia et al., 2020; Moriya et al., 2020). The slowly declining IR flux
lasting around 4 years suggests that the outer dust shell was not destroyed by
the radiation field emitted by the luminous outburst (regardless of the
physical mechanism that produced the ILRTs; Botticella et al., 2009).

Figure 6: Top panel: Two-component black body fits to the SED of AT 2010dn
obtained from optical to MIR at the epoch of +30.6 days. Bottom panel: Single
black body fit for AT 2010dn in the MIR domain at very late phase of +1332.5
days. Although this fit could reproduce the late MIR data, the fitted
temperature should be considered as an indicative value. The MIR measurements
were obtained from the Spitzer Space Telescope + IRAC images at 3.6 $\mu$m and
4.5 $\mu$m.  Table 4: Log of spectroscopic observations of ILRTs.

Date | MJD | Phasea | Telescope+Instrument | Grism | Spectral range | Resolution | Exp. time
---|---|---|---|---|---|---|---
|  | (d) |  |  | ($\AA$) | ($\AA$) | (s)
AT 2010dn
20100602 | 55349.9 | -5.0 | TNG+LRS | LR-R | 5090 - 8340 | 10.5 | 2100
20100603 | 55350.9 | -4.0 | TNG+LRS | LR-B | 3300 - 7990 | 13.5 | 3000
20100604 | 55351.9 | -3.0 | TNG+LRS | VHR-R | 6170 - 7780 | 3.2 | 2700
20100605 | 55352.9 | -2.0 | TNG+LRS | VHR-I | 7290 - 8870 | 3.5 | 2700
20100607 | 55354.9 | +0.0 | WHT+ISIS | R300B/R158R | 3160 - 10300 | 4.1/6.8 | 1800/1800
20100609 | 55356.9 | +2.0 | NOT+ALFOSC | gm4 | 3630 - 8960 | 18 | 3600
20100611 | 55358.9 | +4.0 | TNG+LRS | LR-B | 3520 - 7990 | 11 | 2700
20100616 | 55363.9 | +9.0 | TNG+LRS | VHR-R | 6190 - 7820 | 3.2 | 3000
20100617 | 55364.9 | +10.0 | TNG+LRS | VHR-R | 6190 - 7820 | 3.2 | 3000
20100707 | 55384.9 | +30.0 | WHT+ISIS | R300B/R316R | 3160 - 8860 | 4.1/3.1 | 1200/1200
AT 2012jc
20120329 | 56015.1 | $-8.4$ | Ekar1.82 + AFOSC | gm4 | 3500 - 8060 | 24 | 3600
20120331 | 56017.3 | $-6.2$ | Ir$\rm{\acute{e}}$n$\rm{\acute{e}}$e du Pont + WFCCD | blue (400/mm) | 3600 - 9120 | 5.3 | 1500
20120414 | 56031.2 | $+7.7$ | NTT + EFOSC2 | Gr$\\#$11/Gr$\\#$16 | 3340 - 9920 | 21.3/21 | 1800
20120501 | 56048.3 | $+24.8$ | NTT + EFOSC2 | Gr$\\#$11/Gr$\\#$16 | 3340 - 9920 | 14/13 | 1800
20120623 | 56101.2 | $+77.7$ | Magellan II + LDSS | VPH-All | 3940 - 10300 | 6.5 | 900
AT 2013lb
20130207 | 56330.1 | $+5.6$ | Ekar1.82 + AFOSC | gm4 | 3900 - 8200 | 14 | 2700
20130207 | 56330.4 | $+5.9$ | NTT + EFOSC2 | Gr$\\#$13 | 3650 - 9090 | 17 | 1213
20130207 | 56330.4 | $+5.9$ | Gemini-S + GMOS-S | R400 | 4210 - 8440 | 10 | 900
20130209 | 56332.3 | $+7.8$ | NTT + EFOSC2 | Gr$\\#$11 | 3340 - 7460 | 22 | 1394
20130220 | 56343.3 | $+18.8$ | NTT + EFOSC2 | Gr$\\#$11 | 3340 - 7460 | 22 | 2700
20130305 | 56356.3 | $+31.8$ | NTT + EFOSC2 | Gr$\\#$11/Gr$\\#$16 | 3340 - 9990 | 14/13 | 2700
20130422 | 56404.3 | $+79.8$ | Gemini-S + GMOS-S | R400 | 4210 - 8440 | 10 | 450
AT 2013la
20140108 | 56665.2 | $+13.2$ | Ekar1.82 + AFOSC | gm4 | 3400 - 8200 | 14 | 1800
20140115 | 56672.2 | $+20.2$ | Pennar1.22 + B&C | 300tr | 3350 - 7930 | 10 | 1800
20140203 | 56692.2 | $+40.2$ | TNG+LRS | LR-B | 3430 - 8050 | 10.5 | 3600
20140205 | 56694.2 | $+42.2$ | GTC + OSIRIS | R500R | 5150 - 9990 | 15.5 | 2700
20140228 | 56717.2 | $+65.2$ | GTC + OSIRIS | R1000B | 3650 - 7850 | 7 | 900
20140322 | 56739.1 | $+87.1$ | TNG+LRS | LR-B | 3430 - 8050 | 10.5 | 2700
20140716 | 56854.9 | $+202.9$ | GTC + OSIRIS | R1000B | 3650 - 7850 | 7 | 1500
20140814 | 56883.9 | $+231.9$ | GTC + OSIRIS | R1000B | 3650 - 7850 | 7 | 1900
20141220 | 57012.3 | $+360.3$ | GTC + OSIRIS | R1000B | 3650 - 7850 | 7 | 1800
AT 2018aes
20180331 | 58208.1 | $-3.0$ | GTC + OSIRIS | R1000B/R | 3630 - 10080 | 7.5 | 600/600
20180426 | 58234.1 | $+23.0$ | GTC + OSIRIS | R1000B/R | 3630 -10340 | 7.5 | 600/600

a Phases are relative to the $R/r$-band peak.

##  4 Spectroscopy

Our spectral sequences for AT 2010dn, AT 2012jc, AT 2013lb, AT 2013la and AT
2018aes were obtained using multiple instrumental configurations, which are
listed in Appendix A (Table 6). Basic parameters for the spectra are reported
in Table 4.

The spectra were processed with the standard procedures in iraf. The
preliminary reduction steps included bias, overscan and flat-field
corrections. We then extracted 1D spectra from the 2D frames using the task
apall. Wavelength calibration of the 1D spectra was performed with arc lamp
spectra obtained with the same instrumental configuration as the science ones.
The spectra of spectro-photometric standard stars were used to estimate a
sensitivity function curve necessary to flux-calibrate the spectra of the
transients. The accuracy of the flux calibration was then checked against
coeval broadband photometry, and correction factors were applied in case of
discrepancy. The spectra of the standard stars were also used to correct for
the telluric absorption bands (e.g. O2 and H2O) from the ILRTs spectra. The
resulting ILRT spectra are shown in Figure 7.

Figure 7: Spectral evolution of AT 2010dn (top-left), AT 2012jc (top-right),
AT 2013lb (middle-left), AT 2013la (middle-right), and AT 2018aes (bottom).
The epochs marked to the right of each spectrum are relative to the $R/r$-band
maximum. The $\bigoplus$ symbols mark the position of the strongest telluric
absorption bands. The spectra are only corrected for redshift. Table 5:
Physical parameters inferred from the optical spectra of the ILRTs sample.

Date | MJD | Phasea |  $v$ (H$\alpha$) b |  $L$ (H$\alpha$) c |  $L_{\rm{H_{\alpha}}}$/$L_{\rm{[{\mathrm{Ca\,\mathsc{\leavevmode\nobreak\ }}}II]}}$ c | $T_{\mathrm{BB}}$
---|---|---|---|---|---|---
|  | (d) | (km s-1) | (1038erg s-1) |  | (K)
AT 2010dn |
20100602 | 55349.9 | $-5.0$ | 695 | 2.12 | 2.9 | 7095 $\pm$ 355
20100603 | 55350.9 | $-4.0$ | 671 | 1.85 | 2.6 | 6890 $\pm$ 240
20100604 | 55351.9 | $-3.0$ | 588 | 3.47 | 2.5 | 6540 $\pm$ 330
20100605 | 55352.9 | $-2.0$ | – | – | – | 6435 $\pm$ 320
20100607 | 55354.9 | $+0.0$ | 577 | 2.29 | 2.6 | 6760 $\pm$ 340
20100609 | 55356.9 | $+2.0$ |  $<$823 | 2.63 | 2.5 | 6830 $\pm$ 340
20100611 | 55358.9 | $+4.0$ | 563 | 1.86 | 2.3 | 6690 $\pm$ 195
20100616 | 55363.9 | $+9.0$ | 442 | 2.12 | 2.2 | 6820 $\pm$ 320
20100617 | 55364.9 | $+10.0$ | 438 | 1.81 | 2.1 | 6710 $\pm$ 280
20100707 | 55384.9 | $+30.0$ |  $<$142 | 0.58 | 1.8 | 5020 $\pm$ 250
AT 2012jc |
20120329 | 56015.1 | $-8.4$ |  $<$1097 | 5.30 | – | 8380 $\pm$ 420
20120331 | 56017.3 | $-6.2$ | 614 | 5.30 | 15.4 | 7385 $\pm$ 740
20120414 | 56031.2 | $+7.7$ |  $<$960 | 5.27 | 10.2 | 7995 $\pm$ 205
20120501 | 56048.3 | $+24.8$ |  $<$617 | 2.97 | 5.5 | 6780 $\pm$ 340
20120623 | 56101.2 | $+77.7$ | 842 | 2.36 | – | 5445 $\pm$ 525
AT 2013lb |
20130207 | 56330.1 | $+5.6$ |  $<$640 | 3.33 | – | 6865 $\pm$ 685
20130207 | 56330.4 | $+5.9$ |  $<$777 | 3.36 | 13.4 | 6450 $\pm$ 645
20130207 | 56330.4 | $+5.9$ |  $<$460 | 3.29 | – | 6250 $\pm$ 315
20130209 | 56332.3 | $+7.8$ |  $<$1006 | – | – | 5850 $\pm$ 585
20130219 | 56343.3 | $+18.8$ |  $<$1006 | 2.29 | 8.2 | 6390 $\pm$ 640
20130304 | 56356.3 | $+31.8$ |  $<$617 | 1.87 | 4.8 | 6450 $\pm$ 325
20130422 | 56404.3 | $+79.8$ | 680 | 2.33 | – | 4375 $\pm$ 220
AT 2013la d |
20140108 | 56665.2 | $+13.2$ |  $<$640 | 6.31 | – | 5880 $\pm$ 295
20140115 | 56672.2 | $+20.2$ |  $<$457 | 5.92 | – | 7110 $\pm$ 1420
20140203 | 56692.2 | $+40.2$ | 778 | – | – | 6050 $\pm$ 1210
20140205 | 56694.2 | $+42.2$ |  $<$709 | 5.33 | – | 5345 $\pm$ 270
20140228 | 56717.2 | $+65.2$ | 400 | 4.99 | – | 5290 $\pm$ 265
20140322 | 56739.1 | $+87.1$ |  $<$480 | 5.04 | – | 6005 $\pm$ 1200
20140716 | 56854.9 | $+202.9$ | 446 | 3.98 | – | 5055 $\pm$ 255
20140814 | 56883.9 | $+231.9$ | 503 | 3.87 | – | 4285 $\pm$ 225
20141220 | 57012.3 | $+360.3$ | 499 | 2.68 | – | 4485 $\pm$ 180
AT 2018aes |
20180331 | 58208.1 | $-3.0$ | 708 | 0.85 | 2.7 | 6620 $\pm$ 330
20180426 | 58234.1 | $+23.0$ | 609 | 0.77 | 2.2 | 5675 $\pm$ 285

a Phases are relative to the $R/r$-band light curve peaks.
$b$ Most of our measurements are limited by the instrumental resolution
constraints, hence the FWHM velocities may have large error bars, and in many
cases they should be regarded as upper limits.
$c$ We adopt conservative errors of $\sim$20% for the H$\alpha$ luminosity and
the $L_{\rm{H_{\alpha}}}$/$L_{\rm{[{\mathrm{Ca\,\mathsc{\leavevmode\nobreak\
}}}II]}}$ ratio because of the uncertainty in the flux calibration of the
spectra.
$d$ H$\alpha$ has a complex profile in AT 2013la, and was therefore fitted
with multiple components. The narrowest Gaussian emission and absorption
components are usually below the instrumental resolution limit. For this
reason, only the FWHM velocities of the broader Lorentzian components are
reported here.

###  4.1 Spectroscopic evolution and line identification

The five objects of our sample have spectra showing little evolution over the
period of their spectral monitoring (from $\sim-8$ days to 1 year after
maximum). At all epochs, the spectra have an almost featureless continuum,
which is relatively blue at early phases, becoming redder with time. Narrow
emission lines of the Balmer series are superposed on the continuum, with
H$\alpha$ and H$\beta$ being the most prominent spectral features. Weak Fe ii
lines are also observed, along with Na I D and Ca H&K in absorption. Apart
from the H lines, the most prominent spectral emissions are the [Ca ii]
doublet ($\lambda\lambda$ 7291, 7324) and the Ca NIR triplet ($\lambda\lambda$
8498, 8542, 8662). In addition, O i, Fe ii, Sc ii and Ba ii lines are also
tentatively identified in some spectra with decent S/N and resolution (e.g.
see a GTC/OSIRIS spectrum at + 41.9 d of AT 2013la). Detailed line
identification performed on the best-quality spectra of the five transients is
given in Figure 8. We note that the lines of the [Ca ii] doublet are visible
in all spectra with good S/N shown in this paper and are therefore considered
a characteristic feature of ILRTs. In Figure 9, all ILRTs share almost the
same spectral features, supporting a remarkable overall homogeneity in their
observables. However, as shown in Figure 9, the spectra of the comparison
objects show much bluer continuum than ILRTs. In addition, H$\alpha$ has a
classical broad P-Cygni profile and there is no obvious [Ca ii] doublet
feature.

During the follow-up campaign of AT 2013la, we collected spectra covering all
the evolutionary phases. Hence, we take AT 2013la as a representative object
to describe the spectral evolution of ILRTs. The spectral continuum evolves
quite slowly, from initially blue (e.g. at phase $\sim$ +13.2 d) to much
redder at late phases (+360.0 d). AT 2013la resembles other ILRT spectra in
its continuum evolution and characteristic lines. However, we see additional
strong He I (5876 $\AA$) absorption feature in all GTC/OSIRIS spectra, most
clearly at +42.2, +65.2, +202.9, +231.9, and +360.3 days (see middle right
panel in Figure 7). We note that narrow P-Cygni absorptions imposed on
H$\alpha$ lines are also detected in the highest resolution spectra (see e.g.
the GTC/OSIRIS spectra of AT 2013la in Figures 7 and 25). Such spectra allow
us to infer the wind velocity via measurement of the position of the deep
minimum of the P-Cygni profiles. This blueshifted absorption component on top
of the H$\alpha$ emission (see Figure 25) has velocities of $\sim$ 360 - 410
$\rm{km}\,s^{-1}$, and may originate from a dense, slow-moving wind. This is
discussed more widely in Sect. 4.2.

We assume that the SEDs of ILRTs in the optical domain covered by our spectra
are approximated by black bodies. Therefore, we estimate the temperature
through a black body fit to the spectral continuum. The inferred continuum
temperatures are reported in Table 5, while the temperature evolution is shown
in the top panel of Figure 10. For all objects in our sample, the temperature
rapidly declines from $\sim$ 7000 - 8500 K near maximum, to nearly 5000 K at
$\sim$ 100 days. At late phases, the temperature decreases more slowly to
$\sim$ 4200 - 4500 K at about 1 year after maximum. Overall, all our ILRTs
show a similar temperature evolution. We note that the comparison objects show
much higher temperatures than ILRTs at early phases, and this is consistent
with their early-time bluer colours.

Figure 8: Line identification in the spectra of the five transients presented
in this paper. The spectra have been corrected for redshift and reddening.
Phases are relative to their $R/r$-band maximum. Figure 9: Spectral comparison
of a sample of ILRTs and SN 2018zd, SN 2018hwm, SN 2015bf, SN 1999br, and SN
2005cs. The spectra of M85 OT, SN 2008S, PTF10fqs, AT 2017be, SN 2018zd, SN
2018hwm, SN 2015bf, SN 1999br, and SN 2005cs are taken from Kulkarni et al.
(2007), Botticella et al. (2009), Kasliwal et al. (2011), Cai et al. (2018),
Zhang et al. (2020), Reguitti et al. (2021), Lin et al. (2021), Pastorello et
al. (2004), and Pastorello et al. (2006, 2009). The right panel shows the
region of [Ca ii], marked with the grey-shaded region in the left panel. All
spectra were obtained at similar epochs from the $R/r$-band maxima, and were
corrected for redshift and reddening.  Figure 10: Evolution of the black body
temperature (top) and the H$\alpha$ luminosity (bottom) for a sample of ILRTs,
and SN 2018zd (Zhang et al., 2020), SN 2018hwm (Reguitti et al., 2021), SN
2015bf (Lin et al., 2021), SN 1999br (Pastorello et al., 2004), and SN 2005cs
(Pastorello et al., 2006, 2009).

###  4.2 H$\alpha$ and Ca ii line evolution

In order to understand the evolution of individual spectral features, we
performed a detailed analysis of the spectra of our ILRT sample at three
critical phases232323These critical phases are fixed on the basis of
relatively large changes in the colour evolution.: around 0, +30, and +70 days
from maximum (see Figure 25). We measure the full width at half maximum (FWHM)
of H$\alpha$ through a single Lorentzian function fit, as in general this type
of fit accurately describes the line profiles of narrow-lined SNe (e.g. SNe
IIn; see Taddia et al., 2013; Smith, 2017; Nyholm et al., 2017). The H$\alpha$
profile is dominated by a narrow component in the spectra of most objects
(e.g. AT 2010dn, AT 2012jc, AT 2013lb, and AT 2018aes). However, AT 2013la
shows H$\alpha$ with a more complex profile, with narrow, blueshifted P-Cygni
absorption lines. For AT 2013la, we therefore fitted the H$\alpha$ emission
lines in our higher resolution spectra (i.e. at phases +65.2d, +202.9, +231.9
and +360.3d) via multiple components: an intermediate-width Lorentzian
profile, a narrow Gaussian emission and a Gaussian absorption. We also fitted
the H$\alpha$ line at phase +42.2d with only a broader Lorentzian component
plus a narrow Gaussian. The narrow component of H$\alpha$ arises from the
unshocked photoionised CSM, while the intermediate-width component likely
originates from the shocked CSM. Finally, the broad component is produced by
the faster ejecta. The FWHM velocities ($v_{\mathrm{FWHM}}$) of H$\alpha$,
after correcting for instrumental resolution ($v_{\mathrm{FWHM}}$ =
$\sqrt{v_{\mathrm{observation}}^{2}-v_{\mathrm{instrument}}^{2}}$), are
reported in Table 5 and plotted in Figure 11. We note that most spectra of our
sample have modest resolution. Hence, in most instances our measurements have
to be considered upper limits for the expansion velocities. We also measured
the H$\alpha$ velocity for the comparison objects in Figure 11, which were
inferred from the minima of the broad P-Cygni absorptions. These show a
remarkably large velocity evolution, ranging from $\sim$ 8000
$\rm{km}\,s^{-1}$ to $\sim$ 1000 $\rm{km}\,s^{-1}$. In contrast, ILRTs show a
slow evolution in H$\alpha$ velocity ($<$ 1000 $\rm{km}\,s^{-1}$) over the
entire monitoring campaigns. In Figure 12, we show the temporal evolution of
H$\alpha$ profiles in the velocity space for AT 2013la, SN 2018zd, and SN
2005cs. AT 2013la shows a modest velocity evolution in H$\alpha$ profile,
while SN 2018zd and SN 2005cs experience significant velocity evolution along
with the gradual emergence of broad P-Cygni features.

Figure 11:  H$\alpha$ velocity evolution of a sample of ILRTs, SN 2018zd
(Zhang et al., 2020), SN 2018hwm (Reguitti et al., 2021), SN 2015bf (Lin et
al., 2021), SN 1999br (Pastorello et al., 2004), and SN 2005cs (Pastorello et
al., 2006, 2009). The H$\alpha$ velocities were estimated by measuring the
FWHM for ILRTs, while those for SNe II were determined from the position of
the minimum of the absorption component.  Figure 12: Evolution of the
H$\alpha$ profile in selected spectra of the ILRT AT 2013la (left panel), SN
2018zd (Zhang et al., 2020, middle panel), and the underluminous Type IIP SN
2005cs (Pastorello et al., 2006, 2009, right panel). The H$\alpha$ lines are
shown in the velocity space, with zero velocity (rest wavelength) being marked
by a grey dashed line.

The [Ca ii] doublet and Ca ii NIR triplet lines were fitted with Lorentzian
functions. The [Ca ii] doublet is produced by quadrupole transitions from
$4s^{2}S$ to the metastable $3d^{2}D$ level, in which $\lambda_{1}$ at 7291
$\AA$ and $\lambda_{2}$ at 7324 $\AA$ are associated to ${}^{2}S_{1/2}$ \-
${}^{2}D_{5/2}$ and ${}^{2}S_{1/2}$ \- ${}^{2}D_{3/2}$ transitions,
respectively (e.g. Osterbrock, 1951; Lambert et al., 1969; Chevalier &
Fransson, 1994). The [Ca ii] doublet likely originates from extremely low-
density gas, possibly in a slow-moving circumstellar shell. The Ca ii NIR
triplet lines with $\lambda$1,2,3= 8498, 8542, 8662 Å are common features in
many cool transients, and are produced by transitions from $4p^{2}P_{1/2,3/2}$
to $3d^{2}D_{3/2,5/2}$ levels (e.g. Mallik, 1997, 1998; Andretta et al., 2005;
Busà et al., 2007; Martin et al., 2017).

At early phases (see Figure 25, left panel), the H$\alpha$ FWHM velocities of
the transients presented in this paper are 600-700 $\rm{km}\,s^{-1}$ (with
upper limits up to 1000 $\rm{km}\,s^{-1}$ in cases of unresolved features),
which are comparable to those of other ILRTs (e.g. $\sim$750 $\rm{km}\,s^{-1}$
and $\sim$600 $\rm{km}\,s^{-1}$ for SN 2008S and AT 2017be, respectively). We
conclude that in all ILRTs the ejected material expands with similar
velocities of several hundred $\rm{km}\,s^{-1}$. In most cases the FWHM of the
[Ca ii] doublet is below the resolution limits, and we do not have reliable
estimates for the outflow velocity inferred from this feature. The doublet is
resolved only in the spectra of AT 2010dn at $-3.0$ d, providing an FWHM
velocity of 145 $\rm{km}\,s^{-1}$. The feature was also resolved in a spectrum
of AT 2012jc at phase $-$6.2 d, where we measured $v_{\mathrm{FWHM}}$ $\sim$
220 $\rm{km}\,s^{-1}$. For AT 2018aes, a velocity of $v_{\mathrm{FWHM}}$
$\sim$ 310 $\rm{km}\,s^{-1}$ was derived for the [Ca ii] feature at phase -3.0
d. We conclude that the [Ca ii] doublet originates in a slow-moving CSM
($\sim$ 145 - 310 $\rm{km}\,s^{-1}$), while the broader H$\alpha$ component
forms in fast-expanding ejected gas.

At 3-5 weeks after maximum (Figure 25, middle panel), the spectra become
redder. We also see a strengthening of a narrow P-Cygni profile superimposed
on H$\alpha$ in AT 2013la, the minimum of which is blueshifted by about 360 -
410 $\rm{km}\,s^{-1}$. However, we cannot rule out that the non-detection of
this feature in other objects is a mere resolution effect. The FWHM velocities
of H$\alpha$ are in the range 600-850 $\rm{km}\,s^{-1}$ for all objects, with
M85 OT being the only outlier with $v_{\mathrm{FWHM}}$ $\sim$ 350
$\rm{km}\,s^{-1}$. A resolved velocity of 115 $\rm{km}\,s^{-1}$ was reported
at this phase for [Ca ii] in AT 2017be (Cai et al., 2018).

At late phases (+70 to +80 d; Figure 25, right panel), the H$\alpha$ velocity
does not change significantly, still ranging from 400 (in AT 2013la) up to 850
$\rm{km}\,s^{-1}$ (in the other objects). The spectra of AT 2013la also
provide an averaged [Ca ii] $v_{\mathrm{FWHM}}$ $\sim$ 365 $\rm{km}\,s^{-1}$.
In most cases, the low resolution or the low S/N of our spectra prevent us
from probing the Ca ii triplet lines in detail, with an exception being the
Magellan spectrum of AT 2012jc obtained on 2012 June 23 (phase +77.7 d), where
the triplet emission lines show a symmetric profile, with an average
$v_{\mathrm{FWHM}}$ $\simeq$ 905 $\rm{km}\,s^{-1}$. The [Ca ii] profile
appears to show very little evolution in the FWHM until $t\sim$ 70 days, and
this is a further argument in favour of the hypothesis that these lines form
in the circumstellar environment. We also note that none of the typical
nebular lines, such as [O iii] ($\lambda\lambda$= 4959, 5007 Å) and [S ii]
($\lambda\lambda$= 6716, 6731 Å) lines (Lundqvist & Fransson, 1996; Lundqvist
et al., 2015, 2020), were detected in spectra. This implies that the wind
density is high enough for those nebular lines to be collisionally de-excited,
but that [Ca ii] can exist at much higher density (e.g. critical density:
$\rho$${}_{\rm{[S\leavevmode\nobreak\ II]}}$ = 1 $\times$ 104 cm-3,
$\rho_{\rm{[Ca\leavevmode\nobreak\ II]}}$ = 1 $\times$ 109 cm-3; Li & McCray,
1993). In such a dense wind, the [Ca ii] lines could also be broadened by
Thomson scattering, albeit to a lesser extent than the Balmer lines because
these latter are formed further out in the wind/CSM.

We use the few spectra with higher S/N to highlight the evolution of the
H$\alpha$ to [Ca ii] luminosity ratio. The values for the different ILRTs are
reported in Table 5 and shown in Figure 14. The values for AT 2012jc and AT
2013lb show a faster decline (by a factor of three) from maximum (when
H$\alpha$ largely dominates) to one month later. However, for AT 2010dn and AT
2018aes, the above ratio shows a much flatter evolution (ratio from about 3 to
2) over the same temporal window. Interestingly, in these two ILRTs, the [Ca
ii] doublet is very luminous with respect to H$\alpha$. In addition, the
H$\alpha$ luminosity evolution is also shown in the bottom panel of Figure 10.

Figure 13: Evolution of H$\alpha$ and [Ca ii] in ILRTs. The spectra of M85 OT,
SN 2008S, PTF10fqs, and AT 2017be, downloaded from WISeREP archive
252525https://wiserep.weizmann.ac.il/ (Yaron & Gal-Yam, 2012), were published
by Kulkarni et al. (2007), Botticella et al. (2009), Kasliwal et al. (2011),
and Cai et al. (2018). All spectra were corrected for redshift and reddening.
Figure 14: Ratio of H$\alpha$ to [Ca ii] (total profiles at
$\lambda\leavevmode\nobreak\ \approx$ 7300 Å) luminosities until phase $\sim$
30 d.

##  5 Rate estimates for ILRTs

In the past 12 years (2008 - 2019), 12 objects have been confirmed to be ILRT
events262626We note that we only include confirmed ILRTs prior to 2020, as
systematic surveys and monitoring campaigns were almost globally suspended
because of the Covid-19 pandemic in 2020. In addition to the objects listed in
Table 1 (M85 OT was excluded in the rate estimate sample because of its
controversial nature as discussed by Kulkarni et al. (2007), Pastorello et al.
(2007), and Rau et al. (2007)), there are three confirmed ILRTs to be added in
2019: AT 2019abn (De et al., 2019; Nordin et al., 2019; Burke et al., 2019;
Fremling et al., 2019), AT 2019ahd (Jha et al., 2019; Jha, 2019; Tonry et al.,
2019), and AT 2019udc (Malesani et al., 2019b; Siebert et al., 2019; Malesani
et al., 2019a; Valenti et al., 2019). ; the observed rate of discoveries is
1.0 event per year, but this does not account for the luminosity distribution
of ILRTs, or the efficiency or observing strategy of the surveys. The ILRTs in
our sample are distributed in a radius of 30 Mpc, corresponding to a volume of
1.13 $\times$ 105 Mpc3. Hence, we obtain a volumetric rate of ILRTs of 0.09
$\times$ 10-4 Mpc-3yr-1. In the same temporal window and volume, 147 CC SNe
were discovered272727Bright SNe archive: http://www.rochesterastroncamomy.org;
Asiago SN group archive: http://graspa.oapd.inaf.it/asnc.html.  corresponding
to a rate of 1.1 $\times$ 10-4 Mpc-3yr-1. Therefore, assuming that the
discovery of ILRTs suffers the same selection effects as all CC SNe, the rate
of ILRTs is 8% that of CC SNe. We note that Thompson et al. (2009) estimated
an EC SN rate of 2%-10% of CC SNe in 10 years (before 2008), while Poelarends
et al. (2008) obtained an EC SN fraction of CC SNe of only about 6% based on a
standard Salpeter initial mass function (IMF; Salpeter, 1955) and an EC SN
mass range of 9.00 - 9.25 M⊙ . Assuming a narrow mass range $\Delta\approx$
0.2 M⊙ and a metallicity range $Z$ = 0.0001 - 0.02, Doherty et al. (2015,
2017) calculated that 2%-5% of CC SNe are EC SNe. However, theoretical
estimates for EC SN rates are dependent on the uncertainties on the initial
mass range, metallicity, and the details of stellar models. While theoretical
calculations show some variations, they are roughly consistent with our rate
estimate based on the observations. We note that we did not take into account
the fact that ILRTs are on average fainter than CC SNe and surveys are
incomplete up to 30 Mpc. Therefore, the true relative rate is larger than the
current observed rate, and future advanced surveys could increase this
estimate.

##  6 Discussion and conclusions

###  6.1 Observables and parameter correlations

In this paper, we systematically analyse a sample of ILRTs. They show
relatively homogeneous spectrophotometric properties that can be summarised as
follows:

  1. I

They all show single-peaked light curves, resembling those of Type IIP/IIL SNe
but scaled down in luminosity (see Figure 4). The duration of the plateau is
determined by the effective recombination time of the hydrogen envelope (e.g.
see Grassberg et al., 1971; Eastman et al., 1994; Soma et al., 2010).

  2. II

They show a homogeneous colour (hence temperature) evolution. The temperature
evolution shows an initial fast decline (usually lasting $<$30 days), followed
by a much slower decline which is still ongoing at the end of the follow up.
The temperature evolution of ILRTs is similar to what is observed in the
hydrogen recombination of classical Type II SNe (e.g. see the Type IIP SN
2005cs in the top panel of Figure 10). We note that ILRTs are usually redder
than low-luminosity SNe IIP and other Type II events proposed to be EC SN
candidates (see Figure LABEL:pic:colour).

  3. III

Their peak magnitudes range from $-$11 ($\pm$ 0.5) to $-$15 ($\pm$ 0.5) mag.
Their quasi-bolometric ($B$ to $I$) light curve peaks are in the range $\sim
5\times 10^{39}$ to $\sim 9\times 10^{40}$ erg s-1 and the radiated energies
span from 0.30 $\times$ 1047 to 2.94 $\times$ 1047 erg. ILRTs are typically
fainter than most SNe II, although they are comparable in luminosity to the
most subluminous Type IIP SN 1999br (see Figure 4 and 5).

  4. IV

The SED of ILRTs with optical to MIR observations shows evidence of prominent
IR excesses both at early and late phases. This is consistent with the
expectation that the progenitors of ILRTs have dusty local environments.
Furthermore, it corroborates the use of the nomenclature: ‘red’ transients.
Another common feature in the SED evolution of ILRTs is the monotonic decrease
of the photospheric radius, which could be a diagnostic tool to distinguish
ILRTs from LRNe (see Figure 4 of Cai et al., 2019).

  5. V

Their spectra experience relatively slow evolution. Prominent lines include
the Balmer series, along with Ca ii (e.g. Ca H&K, [Ca ii] doublet, and Ca NIR
triplet), Na i D, Fe ii, and possibly O i. The [Ca ii] doublet is normally
visible during the entire monitoring campaign. However, the study of AT
2019abn challenges this paradigm with a barely detectable [Ca ii] doublet at
early phases (Jencson et al., 2019; Williams et al., 2020). In addition, this
feature is never detected in SNe IIP at early phases (see Figure 9), while it
is always visible in the nebular phases.

  6. VI

The ejecta velocities inferred from the H$\alpha$ FWHM lie between about 400
and 800 $\rm{km}\,s^{-1}$. The measurements of the minimum of P-Cygni profiles
indicate a modest wind velocity of about 360 - 410 $\rm{km}\,s^{-1}$. In
addition, the [Ca ii] feature width suggests the existence of slow-moving CSM
with $v_{\mathrm{FWHM}}$ $\sim$ 170 - 300 $\rm{km}\,s^{-1}$. In ILRTs, the
H$\alpha$ velocity is much lower than those inferred for SNe II at all phases
(see Figure 11).

In order to better characterise ILRTs, we looked for possible correlations
among their physical parameters. In Figure 15, we plot peak luminosity
($L_{\rm{peak}}$; reported in Table 3) against different physical parameters
of ILRTs, namely the time ($\Delta\mathrm{t}_{0.5}$) for the luminosity to
decline by a factor of two from maximum, the 56Ni mass, the H$\alpha$
velocity, and the H$\alpha$ luminosity at maximum. Unfortunately, several
factors (e.g. poorly sampled light curve peaks; lack of late-time
observations; low spectral resolution or modest S/N; incomplete wavelength
coverage) limit the information available for the sample. More specifically,
there seems to be no correlation between $L_{\rm{peak}}$ and decline time
$\Delta\mathrm{t}_{0.5}$, which is in the range of 20-50 days (Figure 15, top-
left panel). The lack of a correlation may point to variation in the
progenitor mass loss or the strength of CSM-ejecta interaction. A trend may
exist linking the peak luminosity to the ejected 56Ni mass (Figure 15 top-
right panel), although the lower limit for AT 2013la is somewhat discrepant
with those of other ILRTs. We cannot rule out that the ejecta-CSM interaction
significantly affects the late-time luminosity, therefore biasing the 56Ni
mass estimates of the sampled objects. The limited range of 56Ni masses
($\sim$ 1-5 $\times 10^{-3}$ M⊙ ) may be attributed to their progenitor masses
lying within a narrow mass range ($\sim$ 8-10 M⊙ ). As a comparison, both Type
II and Type Ib/c SNe also show a similar correlation, but they have higher
energies and wider 56Ni mass ranges than ILRTs (Hamuy, 2001, 2003; Pastorello
et al., 2005). SN 2018zd 282828Hiramatsu et al. (2021) estimated a much lower
56Ni mass ($\sim 8.6\times 10^{-3}$ M⊙ ) for SN 2018zd, adopting a very low
distance obtained through the standard candle method (SCM). We note however
that the SCM distance is discrepant with the significantly larger kinematic
estimates (e.g. Zhang et al., 2020, Callis et al., in preparation)., which was
also proposed as a possible EC SN, has a significantly higher 56Ni mass (0.013
- 0.035 M⊙ ; Zhang et al., 2020), exceeding that of ILRTs ($\sim$ 1-5 $\times
10^{-3}$ M⊙ ) by nearly one order of magnitude. In the bottom-left panel, the
H$\alpha$ velocity seems to be uncorrelated with $L_{\rm{peak}}$. The fact
that $v$ (H$\alpha$) $=$ 600 $\pm$ 200 $\rm{km}\,s^{-1}$ for all objects
suggests a common explosive or eruptive mechanism for all ILRTs, and again a
relatively small range of progenitor masses. From this, the LBV giant eruption
scenario appears less likely. The diagram showing bolometric versus H$\alpha$
luminosity at peak reveals a trend, with ILRTs clustered along two different
lines. In particular, we note that ILRTs along the lower line of the diagram
(PTF10fqs, AT 2017be, and AT 2013la) show a clear plateau in their light
curves. A wider sample of well-monitored ILRTs is necessary to confirm or rule
out the putative trends mentioned above. Figure 15 shows how the different
classes of objects discussed in this paper distribute in the $L_{\rm{peak}}$
versus $\Delta\mathrm{t}_{0.5}$ and H$\alpha$ velocity diagrams. The clear
separation of ILRTs from the comparison SNe II suggests that they are a
distinct class of transients.

In Figure 16, we also investigated the evolution of luminosity ($L$) against
effective temperature ($T_{\mathrm{eff}}$) of ILRTs, and compared with giant
eruptions of LBVs, claimed EC SNe, and some representative SNe II. The ILRTs
tend to show a homogeneous evolution, and lie in a narrow strip in which the
luminosity declines monotonically with temperature. SNe II lie in a region
that is distinct from that where ILRTs and LBVs are found, and span a wide
range of luminosities and temperatures. The physical homogeneity in this L-T
diagram is suggestive of a common mechanism triggering the ILRTs and seems to
exclude the LBV origin for ILRTs and enable us to distinguish ILRTs from
traditional Type II SNe.

Figure 15: Peak luminosity ($L_{\mathrm{peak}}$) vs. decline time ($\Delta
t_{0.5}$) from $L_{\mathrm{peak}}$ to 0.5$L_{\mathrm{peak}}$ (top-left);
$L_{\mathrm{peak}}$ vs. 56Ni mass (top-right); $L_{\mathrm{peak}}$ vs.
$v_{\mathrm{H\alpha}}$ at peak (bottom-left); and $L_{\mathrm{peak}}$ vs.
H$\alpha$ peak luminosity (bottom-right).  Figure 16: Luminosity ($L$) vs.
effective temperature ($T_{\mathrm{eff}}$). ILRTs are marked as solid lines
with different colours, while the area where LBVs lie is marked in grey.
Comparison SNe II lie in the upper part of the diagram and are labelled with
dashed lines.

###  6.2 Plausible scenarios for ILRTs and conclusions

Although several plausible scenarios have been proposed to explain ILRTs,
their nature is still debated. Possible scenarios include LBV-like eruptions,
LRN-like events (stellar mergers), and EC-induced SN explosions.

Luminous blue variables originate from massive star ($>$ 20 M⊙ ) eruptions,
and show irregular light curves and SN IIn-like spectra292929Although the [Ca
ii] doublet is sometimes visible in LBV spectra, no persistent signature of
this feature has been observed in these events.. A luminous progenitor is
expected to be detected both in pre-outburst and post-outburst optical and NIR
images. No 56Ni is expected to be produced. In addition, LBVs and ILRTs are
distributed in two separate regions in the $L$-$T_{\rm{eff}}$ diagram (see
Figure 16). Our observational arguments disfavour a LBV-like eruption scenario
for ILRTs. However, we note that Andrews et al. (2020) proposed that a recent
gap transient, AT 2019krl, was an unobscured ILRT eruption from a relatively
massive star.

Luminous red novae are another subclass of gap transients, and show double-
peaked (or triple-peaked) light curves and a remarkable spectral evolution.
Specifically, the major drop in continuum temperature, the appearance of
narrow metal lines in absorption, the dramatic change in the H$\alpha$
strength and profile, and the emergence of molecular bands are typical
spectral features of LRNe. In addition, the typical H$\alpha$ FWHM velocities
of LRNe are lower than 500 $\rm{km}\,s^{-1}$ (Pastorello et al., 2019b). Their
colours become progressively redder; for example, the intrinsic $B-V$ colour
of an LRN can even reach 1.8 mag at late phases (see Figure 4 of Pastorello et
al., 2019b). The evolution of the SED and the radius of LRNe is markedly
different from that of ILRTs (Cai et al., 2019; Stritzinger et al., 2020a).
LRNe are likely produced by the coalescence of two stars, however we disfavour
such a merging scenario for ILRTs.

Theory predicts that some stars with initial mass 8-10 M⊙ form a S-AGB star
with a strongly degenerate oxygen–neon–magnesium (O-Ne-Mg) core surrounded by
thin He and H envelopes (e.g. Nomoto, 1984, 1987; Pumo et al., 2009; Takahashi
et al., 2013; Moriya et al., 2014; Doherty et al., 2017; Nomoto & Leung, 2017;
Leung & Nomoto, 2019; Leung et al., 2020). The final O-Ne-Mg core mass is
determined by the competition between core increase from the He and H shell
burning and mass loss through thermal pulses (Siess, 2007; Langer, 2012; Leung
et al., 2020). Once the core reaches the Chandrasekhar mass (1.37 M⊙ ; Nomoto,
1984), electron capture reactions on 20Ne and 24Mg take place, and eventually
ignite an O-Ne deflagration that propagates outward. This type of CC explosion
is referred to as an EC SN (Nomoto, 1984; Zha et al., 2019; Leung et al.,
2020). According to models, EC SNe are expected to explode with low energy,
low ejected 56Ni mass, and typically in a dense and dusty CSM (e.g. Poelarends
et al., 2008; Woosley & Heger, 2015; Moriya & Eldridge, 2016). Although Fe-
core progenitors at the low-mass end of the CC SNe also explode with low
energy ($\sim\leavevmode\nobreak\ 0.5-1.0\times$ 1050 erg) and small 56Ni mass
(4-6 $\times$ 10-3 M⊙ ) (Stockinger et al., 2020), some of them (e.g. low-
lominosity Type IIP SNe 2003gd, 2005cs, and 2008bk; Eldridge et al., 2007;
Maund et al., 2014a, b) can be distinguished from EC SNe through the explosion
mechanism, chemical composition, and nucleosynthesis (Jerkstrand et al.,
2018). The possible correlations among physical parameters, the homogenous
observational properties and the L-T evolution suggest that all ILRTs are
regulated by the same mechanism, and the EC SN explosion is a plausible
scenario. In particular, this scenario for ILRTs is supported by the following
arguments:

  * •

The late-time light curves of SN 2008S and NGC 300 OT2008-1 decline
approximately following the 56Co decay rate (i.e. $\sim$ 0.98 mag/100d). The
56Ni masses inferred from the bolometric light curve are of the order of 10-4
to 10-3 M⊙ , consistent with the expected EC SN yields.

  * •

Investigation of archival optical and IR images of the transient locations
obtained years before the explosion suggests that the ILRT progenitors are
moderately massive, in the range between 8 and 15 M⊙ . Their progenitors
appear to be embedded in dusty cocoons (i.e. SN 2008S; Botticella et al.,
2009; Prieto et al., 2009).

  * •

Inspection of the transient sites a few years after the explosion suggests
that the objects are at least 15 times fainter than the quiescent progenitors
(i.e. SN 2008S and NGC 300 OT; Adams et al., 2016). This supports the terminal
SN explosion nature.

  * •

The estimated ILRT event rate is in fair agreement with EC SN theoretical
predictions.

The observational properties described in this paper agree well with
theoretical expectations, and we favour terminal EC SN explosions as the
possible origin of ILRTs. Future facilities, such as the Vera C. Rubin
Observatory303030https://www.lsst.org/ and the Nancy Grace Roman Space
Telescope313131https://www.nasa.gov/content/goddard/nancy-grace-roman-space-
telescope, will be essential for expanding the sample of ILRTs, and will be
crucial in fine-tuning existing theoretical models.

## Acknowledgments

We thank the reviewer for his/her insightful comments that have improved the
paper. Y.-Z. Cai thanks AP/AR/EC/MT/NER/SB for their training in the
photometric and spectral reduction techniques. We are grateful to Han Lin
(THU-THCA) and JuJia Zhang (CAS-YNAO) for providing the data of SN 2015bf and
SN 2018zd, respectively. We thank F. Taddia and D. E. Wright for their few
images taken with NOT/ALFOSC. We also thank M. Sullivan for his contribution
in a spectrum observed with WHT/GB-GR. This work is funded by China
Postdoctoral Science Foundation (grant no. 2021M691821). This work is
supported by National Natural Science Foundation of China (NSFC grants
12033003, 11633002, 11325313, and 11761141001), National Program on Key
Research and Development Project (grant no. 2016YFA0400803). DAH is supported
by NSF grant AST-1911225. F. H. is supported by NSFC grant 11803021 and the
Startup Fund for Youngman Research at SJTU. KM and SJP are supported by H2020
ERC grant no. 758638. MF is supported by a Royal Society - Science Foundation
Ireland University Research Fellowship. SB, PO, and MT are partially supported
by PRIN-INAF 2017 of Toward the SKA and CTA era: discovery, localization, and
physics of transient sources. EC, NER, LT, FO acknowledges support from MIUR,
PRIN 2017 (grant 20179ZF5KS) ”The new frontier of the Multi-Messenger
Astrophysics: follow-up of electromagnetic transient counterparts of
gravitational wave sources”. LBo acknowledges the funding support from Italian
Space Agency (ASI) regulated by “Accordo ASI-INAF n. 2013-016-R.0 del 9 luglio
2013 e integrazione del 9 luglio 2015 CHEOPS Fasi A/B/C”. L.G. acknowledges
financial support from the Spanish Ministry of Science, Innovation and
Universities (MICIU) under the 2019 Ramón y Cajal program RYC2019-027683 and
from the Spanish MICIU project PID2020-115253GA-I00. T.R. acknowledges the
financial support of the Jenny and Antti Wihuri and the Vilho, Yrjö and Kalle
Väisälä foundations. AR acknowledges support from ANID BECAS/DOCTORADO
NACIONAL 21202412. MG is supported by the Polish NCN MAESTRO grant
2014/14/A/ST9/00121. MS is supported by generous grants from Villum FONDEN
(13261,28021) and by a project grant (8021-00170B) from the Independent
Research Fund Denmark. L.W. is sponsored (in part) by the Chinese Academy of
Sciences (CAS) through a grant to the CAS South America Center for Astronomy
(CASSACA) in Santiago, Chile. AMG acknowledges financial support from the
2014-2020 ERDF Operational Programme and by the Department of Economy,
Knowledge, Business and University of the Regional Government of Andalusia
through the FEDER-UCA18-107404 grant. E.Co. acknowledges support from ANID
project Basal AFB-170002. S.Mo. acknowledges the financial support of the
Magnus Ehrnrooth Foundation. Research by S.V. is supported by NSF grants
AST–1813176 and AST-2008108.

This paper is partially based on observations obtained under the European
supernova collaboration involved in ESO-NTT large programme 184.D-1140 led by
Stefano Benetti and the ESO-NTT Large Program 188.D-3003 (the Public ESO
Spectroscopic Survey for Transient Objects - PESSTO). Based on observations
made with the Nordic Optical Telescope, operated by the Nordic Optical
Telescope Scientific Association at the Observatorio del Roque de los
Muchachos, La Palma, Spain, of the Instituto de Astrofisica de Canarias.
Observations from the NOT were obtained through the NUTS and NUTS2
collaboration which are supported in part by the Instrument Centre for Danish
Astrophysics (IDA). The data presented here were obtained in part with ALFOSC,
which is provided by the Instituto de Astrofisica de Andalucia (IAA) under a
joint agreement with the University of Copenhagen and NOTSA. The Liverpool
Telescope is operated on the island of La Palma by Liverpool John Moores
University in the Spanish Observatorio del Roque de los Muchachos of the
Instituto de Astrofisica de Canarias with financial support from the UK
Science and Technology Facilities Council. The Italian Telescopio Nazionale
Galileo (TNG) operated on the island of La Palma by the Fundación Galileo
Galilei of the INAF (Istituto Nazionale di Astrofisica) at the Spanish
Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de
Canarias. Based on observations obtained with the Gran Telescopio Canarias
(GTC), installed in the Spanish Observatorio del Roque de los Muchachos of the
Instituto de Astrofisica de Canarias, in the island of La Palma. Based on
observations collected at Copernico and Schmidt telescope (Asiago, Italy) of
the INAF - Osservatorio Astronomico di Padova; and the Galilei Telescope of
the Padova University in Asiago. Based on observations obtained at the
international Gemini Observatory, a program of NSF’s NOIRLab, which is managed
by the Association of Universities for Research in Astronomy (AURA) under a
cooperative agreement with the National Science Foundation. on behalf of the
Gemini Observatory partnership: the National Science Foundation (United
States), National Research Council (Canada), Agencia Nacional de Investigación
y Desarrollo (Chile), Ministerio de Ciencia, Tecnología e Innovación
(Argentina), Ministério da Ciência, Tecnologia, Inovações e Comunicações
(Brazil), and Korea Astronomy and Space Science Institute (Republic of Korea).
This work makes use of data from the Las Cumbres Observatory Network and the
Global Supernova Project. This work is based on observations collected at the
William Herschel Telescope (WHT), operated on the island of La Palma by the
Isaac Newton Group of Telescope. This paper includes data gathered with the
6.5 meter Magellan Telescopes located at Las Campanas Observatory, Chile. Data
for this study were gathered with the du Pont telescope at Las Campanas
Observatory, Chile. This publication makes use of data products from the Two
Micron All Sky Survey, which is a joint project of the University of
Massachusetts and the Infrared Processing and Analysis Center/California
Institute of Technology, funded by the National Aeronautics and Space
Administration and the National Science Foundation. This work has made use of
data from the Asteroid Terrestrial-impact Last Alert System (ATLAS) project.
The Asteroid Terrestrial-impact Last Alert System (ATLAS) project is primarily
funded to search for near earth asteroids through NASA grants NN12AR55G,
80NSSC18K0284, and 80NSSC18K1575; byproducts of the NEO search include images
and catalogs from the survey area. This work was partially funded by Kepler/K2
grant J1944/80NSSC19K0112 and HST GO-15889, and STFC grants ST/T000198/1 and
ST/S006109/1. The ATLAS science products have been made possible through the
contributions of the University of Hawaii Institute for Astronomy, the Queen’s
University Belfast, the Space Telescope Science Institute, the South African
Astronomical Observatory, and The Millennium Institute of Astrophysics (MAS),
Chile. The Pan-STARRS1 Surveys (PS1) and the PS1 public science archive 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, the National Aeronautics and Space Administration under
Grant No. NNX08AR22G issued through the Planetary Science Division of the NASA
Science Mission Directorate, the National Science Foundation Grant No.
AST-1238877, the University of Maryland, Eotvos Lorand University (ELTE), the
Los Alamos National Laboratory, and the Gordon and Betty Moore Foundation. The
operation of Xingming Observatory was made possible by the generous support
from the Xinjiang Astronomical Observatory of the Chinese Academy of Sciences.

iraf was distributed by the National Optical Astronomy Observatory, which was
managed by the Association of Universities for Research in Astronomy (AURA)
under a cooperative agreement with the National Science Foundation. This
research has made use of the NASA/IPAC Extragalactic Database (NED), which is
operated by the Jet Propulsion Laboratory, California Institute of Technology,
under contract with the National Aeronautics and Space Administration.

## References

  * Adams et al. (2018) Adams, S. M., Blagorodnova, N., Kasliwal, M. M., et al. 2018, PASP, 130, 034202
  * Adams et al. (2016) Adams, S. M., Kochanek, C. S., Prieto, J. L., et al. 2016, MNRAS, 460, 1645
  * Albareti et al. (2017) Albareti, F. D., Allende Prieto, C., Almeida, A., et al. 2017, ApJS, 233, 25
  * Andretta et al. (2005) Andretta, V., Busà, I., Gomez, M. T., & Terranegra, L. 2005, A&A, 430, 669
  * Andrews et al. (2018) Andrews, J., Smith, N., & Van Dyk, S. D. 2018, The Astronomer’s Telegram, 11441, 1
  * Andrews et al. (2011) Andrews, J. E., Clayton, G. C., Wesson, R., et al. 2011, AJ, 142, 45
  * Andrews et al. (2020) Andrews, J. E., Jencson, J. E., Van Dyk, S. D., et al. 2020, arXiv e-prints, arXiv:2009.13541
  * Arcavi et al. (2018) Arcavi, I., Hosseinzadeh, G., Hiramatsu, D., et al. 2018, Transient Name Server Classification Report, 2018-2082, 1
  * Arnett & Fu (1989) Arnett, W. D. & Fu, A. 1989, ApJ, 340, 396
  * Asplund et al. (2009) Asplund, M., Grevesse, N., Sauval, A. J., & Scott, P. 2009, ARA&A, 47, 481
  * Barsukova et al. (2014) Barsukova, E. A., Goranskij, V. P., Valeev, A. F., & Kaisin, S. S. 2014, Variable Stars
  * Becker (2015) Becker, A. 2015, HOTPANTS: High Order Transform of PSF ANd Template Subtraction
  * Berger (2010) Berger, E. 2010, The Astronomer’s Telegram, 2655
  * Berger et al. (2012) Berger, E., Marion, G. H., Hsiao, E., Foley, R., & Chornock, R. 2012, The Astronomer’s Telegram, 4009
  * Berger et al. (2009a) Berger, E., Roth, K., Stubbs, C., et al. 2009a, Exotic Explosions and Eruptions: Exploring a New Transient Phase-Space with Pan-STARRS, NOAO Proposal
  * Berger et al. (2009b) Berger, E., Soderberg, A. M., Chevalier, R. A., et al. 2009b, ApJ, 699, 1850
  * Bertin & Arnouts (1996) Bertin, E. & Arnouts, S. 1996, A&AS, 117, 393
  * Blagorodnova et al. (2017) Blagorodnova, N., Kotak, R., Polshaw, J., et al. 2017, ApJ, 834, 107
  * Bond et al. (2009) Bond, H. E., Bedin, L. R., Bonanos, A. Z., et al. 2009, ApJ, 695, L154
  * Botticella et al. (2009) Botticella, M. T., Pastorello, A., Smartt, S. J., et al. 2009, MNRAS, 398, 1041
  * Bouchet et al. (1991) Bouchet, P., Danziger, I. J., & Lucy, L. B. 1991, AJ, 102, 1135
  * Brown et al. (2013) Brown, T. M., Baliber, N., Bianco, F. B., et al. 2013, PASP, 125, 1031
  * Burke et al. (2019) Burke, J., Howell, D. A., Arcavi, I., et al. 2019, Transient Name Server Classification Report, 2019-328, 1
  * Busà et al. (2007) Busà, I., Aznar Cuadrado, R., Terranegra, L., Andretta, V., & Gomez, M. T. 2007, A&A, 466, 1089
  * Cai et al. (2018) Cai, Y.-Z., Pastorello, A., Fraser, M., et al. 2018, MNRAS, 480, 3424
  * Cai et al. (2019) Cai, Y. Z., Pastorello, A., Fraser, M., et al. 2019, A&A, 632, L6
  * Cardelli et al. (1989) Cardelli, J. A., Clayton, G. C., & Mathis, J. S. 1989, ApJ, 345, 245
  * Catchpole et al. (1988) Catchpole, R. M., Whitelock, P. A., Feast, M. W., et al. 1988, MNRAS, 231, 75p
  * Catchpole et al. (1989) Catchpole, R. M., Whitelock, P. A., Menzies, J. W., et al. 1989, MNRAS, 237, 55P
  * Chevalier & Fransson (1994) Chevalier, R. A. & Fransson, C. 1994, ApJ, 420, 268
  * Chonis & Gaskell (2008) Chonis, T. S. & Gaskell, C. M. 2008, AJ, 135, 264
  * Corwin et al. (1994) Corwin, Harold G., J., Buta, R. J., & de Vaucouleurs, G. 1994, AJ, 108, 2128
  * De et al. (2019) De, K., Tartaglia, L., Andreoni, I., et al. 2019, The Astronomer’s Telegram, 12433, 1
  * de Groot (1969a) de Groot, M. 1969a, Bull. Astron. Inst. Netherlands, 20, 225
  * de Groot (1969b) de Groot, M. 1969b, Commmunications of the Konkoly Observatory Hungary, 65, 203
  * de Vaucouleurs et al. (1991) de Vaucouleurs, G., de Vaucouleurs, A., Corwin, Herold G., J., et al. 1991, Third Reference Catalogue of Bright Galaxies
  * Doherty et al. (2017) Doherty, C. L., Gil-Pons, P., Siess, L., & Lattanzio, J. C. 2017, PASA, 34, e056
  * Doherty et al. (2015) Doherty, C. L., Gil-Pons, P., Siess, L., Lattanzio, J. C., & Lau, H. H. B. 2015, MNRAS, 446, 2599
  * Eastman et al. (1994) Eastman, R. G., Woosley, S. E., Weaver, T. A., & Pinto, P. A. 1994, ApJ, 430, 300
  * Eldridge et al. (2007) Eldridge, J. J., Mattila, S., & Smartt, S. J. 2007, MNRAS, 376, L52
  * Ferrarese et al. (2000) Ferrarese, L., Mould, J. R., Kennicutt, Jr., R. C., et al. 2000, ApJ, 529, 745
  * Filippenko (1997) Filippenko, A. V. 1997, ARA&A, 35, 309
  * Fransson et al. (2014) Fransson, C., Ergon, M., Challis, P. J., et al. 2014, ApJ, 797, 118
  * Fremling et al. (2019) Fremling, C., Dugas, A., & Sharma, Y. 2019, Transient Name Server Classification Report, 2019-2789, 1
  * Gerardy et al. (2002) Gerardy, C. L., Fesen, R. A., Nomoto, K., et al. 2002, ApJ, 575, 1007
  * Grassberg et al. (1971) Grassberg, E. K., Imshennik, V. S., & Nadyozhin, D. K. 1971, Ap&SS, 10, 28
  * Hamuy (2003) Hamuy, M. 2003, ApJ, 582, 905
  * Hamuy (2001) Hamuy, M. A. 2001, PhD thesis, The University of Arizona
  * Heinze et al. (2018) Heinze, A. N., Tonry, J. L., Denneau, L., et al. 2018, AJ, 156, 241
  * Hiramatsu et al. (2021) Hiramatsu, D., Howell, D. A., Van Dyk, S. D., et al. 2021, Nature Astronomy
  * Howerton et al. (2012) Howerton, S., Prieto, J., Drake, A. J., et al. 2012, The Astronomer’s Telegram, 4004
  * Humphreys et al. (2011) Humphreys, R. M., Bond, H. E., Bedin, L. R., et al. 2011, ApJ, 743, 118
  * Humphreys & Davidson (1994) Humphreys, R. M. & Davidson, K. 1994, PASP, 106, 1025
  * Humphreys et al. (1999) Humphreys, R. M., Davidson, K., & Smith, N. 1999, PASP, 111, 1124
  * Jencson et al. (2019) Jencson, J. E., Adams, S. M., Bond, H. E., et al. 2019, ApJ, 880, L20
  * Jerkstrand et al. (2018) Jerkstrand, A., Ertl, T., Janka, H. T., et al. 2018, MNRAS, 475, 277
  * Jha (2019) Jha, S. 2019, Transient Name Server Classification Report, 2019-1237, 1
  * Jha et al. (2019) Jha, S. W., Eweis, Y., Camacho-Neves, Y., et al. 2019, The Astronomer’s Telegram, 12454, 1
  * Jordi et al. (2006) Jordi, K., Grebel, E. K., & Ammon, K. 2006, A&A, 460, 339
  * Kashi et al. (2010) Kashi, A., Frankowski, A., & Soker, N. 2010, ApJ, 709, L11
  * Kasliwal (2012) Kasliwal, M. M. 2012, PASA, 29, 482
  * Kasliwal et al. (2011) Kasliwal, M. M., Kulkarni, S. R., Arcavi, I., et al. 2011, ApJ, 730, 134
  * Kitaura et al. (2006) Kitaura, F. S., Janka, H. T., & Hillebrandt, W. 2006, A&A, 450, 345
  * Kochanek (2011) Kochanek, C. S. 2011, ApJ, 741, 37
  * Kochanek et al. (2014) Kochanek, C. S., Adams, S. M., & Belczynski, K. 2014, MNRAS, 443, 1319
  * Kozyreva et al. (2021) Kozyreva, A., Baklanov, P., Jones, S., Stockinger, G., & Janka, H.-T. 2021, MNRAS, 503, 797
  * Kulkarni & Kasliwal (2009) Kulkarni, S. & Kasliwal, M. M. 2009, in Astrophysics with All-Sky X-Ray Observations, ed. N. Kawai, T. Mihara, M. Kohama, & M. Suzuki, 312
  * Kulkarni et al. (2007) Kulkarni, S. R., Ofek, E. O., Rau, A., et al. 2007, Nature, 447, 458
  * Lambert et al. (1969) Lambert, D. L., Mallia, E. A., & Warner, B. 1969, Sol. Phys., 7, 11
  * Landolt (1992) Landolt, A. U. 1992, AJ, 104, 340
  * Langer (2012) Langer, N. 2012, ARA&A, 50, 107
  * Leung & Nomoto (2019) Leung, S.-C. & Nomoto, K. 2019, PASA, 36, e006
  * Leung et al. (2020) Leung, S.-C., Nomoto, K., & Suzuki, T. 2020, ApJ, 889, 34
  * Li & McCray (1993) Li, H. & McCray, R. 1993, ApJ, 405, 730
  * Lin et al. (2021) Lin, H., Wang, X., Zhang, J., et al. 2021, MNRAS, 505, 4890
  * Lipunov et al. (2017) Lipunov, V. M., Blinnikov, S., Gorbovskoy, E., et al. 2017, MNRAS, 470, 2339
  * Lundqvist & Fransson (1996) Lundqvist, P. & Fransson, C. 1996, ApJ, 464, 924
  * Lundqvist et al. (2020) Lundqvist, P., Lundqvist, N., Vlahakis, C., et al. 2020, MNRAS, 496, 1834
  * Lundqvist et al. (2015) Lundqvist, P., Nyholm, A., Taddia, F., et al. 2015, A&A, 577, A39
  * MacLeod et al. (2017) MacLeod, M., Macias, P., Ramirez-Ruiz, E., et al. 2017, ApJ, 835, 282
  * Malesani et al. (2019a) Malesani, D. B., Charalampopoulos, P., Angus, C., Izzo, L., & Yaron, O. 2019a, Transient Name Server Classification Report, 2019-2881, 1
  * Malesani et al. (2019b) Malesani, D. B., Charalampopoulos, P., Angus, C. R., et al. 2019b, Transient Name Server AstroNote, 123, 1
  * Mallik (1997) Mallik, S. V. 1997, A&AS, 124, 359
  * Mallik (1998) Mallik, S. V. 1998, Bulletin of the Astronomical Society of India, 26, 479
  * Margheim et al. (2013) Margheim, S. J., Rest, A., & Smartt, S. J. 2013, The Astronomer’s Telegram, 4798
  * Martin et al. (2017) Martin, J., Fuhrmeister, B., Mittag, M., et al. 2017, A&A, 605, A113
  * Mauerhan et al. (2018) Mauerhan, J. C., Van Dyk, S. D., Johansson, J., et al. 2018, MNRAS, 473, 3765
  * Maund et al. (2014a) Maund, J. R., Mattila, S., Ramirez-Ruiz, E., & Eldridge, J. J. 2014a, MNRAS, 438, 1577
  * Maund et al. (2014b) Maund, J. R., Reilly, E., & Mattila, S. 2014b, MNRAS, 438, 938
  * Moriya & Eldridge (2016) Moriya, T. J. & Eldridge, J. J. 2016, MNRAS, 461, 2155
  * Moriya et al. (2020) Moriya, T. J., Stritzinger, M. D., Taddia, F., et al. 2020, A&A, 641, A148
  * Moriya et al. (2014) Moriya, T. J., Tominaga, N., Langer, N., et al. 2014, A&A, 569, A57
  * Munari et al. (2002) Munari, U., Henden, A., Kiyota, S., et al. 2002, A&A, 389, L51
  * Munari & Zwitter (1997) Munari, U. & Zwitter, T. 1997, A&A, 318, 269
  * Nomoto (1984) Nomoto, K. 1984, ApJ, 277, 791
  * Nomoto (1987) Nomoto, K. 1987, ApJ, 322, 206
  * Nomoto & Leung (2017) Nomoto, K. & Leung, S.-C. 2017, Electron Capture Supernovae from Super Asymptotic Giant Branch Stars, ed. A. W. Alsabti & P. Murdin, 483
  * Nordin et al. (2019) Nordin, J., Brinnel, V., Giomi, M., et al. 2019, Transient Name Server Discovery Report, 2019-141, 1
  * Nyholm et al. (2017) Nyholm, A., Sollerman, J., Taddia, F., et al. 2017, A&A, 605, A6
  * Osterbrock (1951) Osterbrock, D. E. 1951, ApJ, 114, 469
  * Pastorello et al. (2019a) Pastorello, A., Chen, T. W., Cai, Y. Z., et al. 2019a, A&A, 625, L8
  * Pastorello et al. (2007) Pastorello, A., Della Valle, M., Smartt, S. J., et al. 2007, Nature, 449, 1
  * Pastorello & Fraser (2019) Pastorello, A. & Fraser, M. 2019, Nature Astronomy, 3, 676
  * Pastorello et al. (2021a) Pastorello, A., Fraser, M., Valerin, G., et al. 2021a, A&A, 646, A119
  * Pastorello et al. (2019b) Pastorello, A., Mason, E., Taubenberger, S., et al. 2019b, A&A, 630, A75
  * Pastorello et al. (2005) Pastorello, A., Ramina, M., Zampieri, L., et al. 2005, in IAU Colloq. 192: Cosmic Explosions, On the 10th Anniversary of SN1993J, ed. J.-M. Marcaide & K. W. Weiler, Vol. 99, 195
  * Pastorello et al. (2006) Pastorello, A., Sauer, D., Taubenberger, S., et al. 2006, MNRAS, 370, 1752
  * Pastorello et al. (2009) Pastorello, A., Valenti, S., Zampieri, L., et al. 2009, MNRAS, 394, 2266
  * Pastorello et al. (2021b) Pastorello, A., Valerin, G., Fraser, M., et al. 2021b, A&A, 647, A93
  * Pastorello et al. (2004) Pastorello, A., Zampieri, L., Turatto, M., et al. 2004, MNRAS, 347, 74
  * Pejcha et al. (2016) Pejcha, O., Metzger, B. D., & Tomida, K. 2016, MNRAS, 461, 2527
  * Pejcha et al. (2017) Pejcha, O., Metzger, B. D., Tyles, J. G., & Tomida, K. 2017, ApJ, 850, 59
  * Pignata et al. (2009) Pignata, G., Maza, J., Antezana, R., et al. 2009, in American Institute of Physics Conference Series, Vol. 1111, Probing Stellar Populations Out to the Distant Universe: Cefalu 2008, Proceedings of the International Conference, ed. G. Giobbi, A. Tornambe, G. Raimondo, M. Limongi, L. A. Antonelli, N. Menci, & E. Brocato, 551–554
  * Pilyugin et al. (2004) Pilyugin, L. S., Vílchez, J. M., & Contini, T. 2004, A&A, 425, 849
  * Poelarends et al. (2008) Poelarends, A. J. T., Herwig, F., Langer, N., & Heger, A. 2008, ApJ, 675, 614
  * Poznanski et al. (2011) Poznanski, D., Ganeshalingam, M., Silverman, J. M., & Filippenko, A. V. 2011, MNRAS, 415, L81
  * Pozzo et al. (2006) Pozzo, M., Meikle, W. P. S., Rayner, J. T., et al. 2006, MNRAS, 368, 1169
  * Prieto et al. (2008) Prieto, J. L., Kistler, M. D., Thompson, T. A., et al. 2008, ApJ, 681, L9
  * Prieto et al. (2009) Prieto, J. L., Sellgren, K., Thompson, T. A., & Kochanek, C. S. 2009, ApJ, 705, 1425
  * Pumo et al. (2009) Pumo, M. L., Turatto, M., Botticella, M. T., et al. 2009, ApJ, 705, L138
  * Rau et al. (2007) Rau, A., Kulkarni, S. R., Ofek, E. O., & Yan, L. 2007, ApJ, 659, 1536
  * Reguitti et al. (2021) Reguitti, A., Pumo, M. L., Mazzali, P. A., et al. 2021, MNRAS, 501, 1059
  * Sahu et al. (2006) Sahu, D. K., Anupama, G. C., Srividya, S., & Muneer, S. 2006, MNRAS, 372, 1315
  * Salpeter (1955) Salpeter, E. E. 1955, ApJ, 121, 161
  * Sandage & Tammann (1990) Sandage, A. & Tammann, G. A. 1990, ApJ, 365, 1
  * Schlafly & Finkbeiner (2011) Schlafly, E. F. & Finkbeiner, D. P. 2011, ApJ, 737, 103
  * Schlegel (1990) Schlegel, E. M. 1990, MNRAS, 244, 269
  * Siebert et al. (2019) Siebert, M. R., Dimitriadis, G., Kilpatrick, C. D., et al. 2019, Transient Name Server Classification Report, 2019-2287, 1
  * Siess (2007) Siess, L. 2007, A&A, 476, 893
  * Skrutskie et al. (2006) Skrutskie, M. F., Cutri, R. M., Stiening, R., et al. 2006, AJ, 131, 1163
  * 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 (2017) Smith, N. 2017, Interacting Supernovae: Types IIn and Ibn, 403
  * Smith et al. (2016) Smith, N., Andrews, J. E., Van Dyk, S. D., et al. 2016, MNRAS, 458, 950