# Volumetric rates of Luminous Red Novae and Intermediate Luminosity Red
Transients with the Zwicky Transient Facility

Viraj R. Karambelkar<EMAIL_ADDRESS>Cahill Center for Astrophysics,
California Institute of Technology, Pasadena, CA 91125, USA  Mansi M. Kasliwal
Cahill Center for Astrophysics, California Institute of Technology, Pasadena,
CA 91125, USA  Nadejda Blagorodnova Department of Astrophysics/IMAPP, Radboud
University, Nijmegen, The Netherlands  Jesper Sollerman The Oskar Klein
Centre, Department of Astronomy, Stockholm University, AlbaNova, SE-10691
Stockholm, Sweden  Robert Aloisi Department of Astronomy, University of
Wisconsin-Madison, 475 North Charter Street, Madison, WI 53706, USA  Shreya G.
Anand Cahill Center for Astrophysics, California Institute of Technology,
Pasadena, CA 91125, USA  Igor Andreoni Joint Space-Science Institute,
University of Maryland, College Park, MD 20742, USA  Department of Astronomy,
University of Maryland, College Park, MD 20742, USA  Astrophysics Science
Division, NASA Goddard Space Flight Center, Mail Code 661, Greenbelt, MD
20771, USA  Thomas G. Brink Department of Astronomy, University of California,
Berkeley, CA 94720-3411, USA  Rachel Bruch  Department of Particle Physics and
Astrophysics, Weizmann Institute of Science, 234 Herzl St, 76100 Rehovot,
Israel  David Cook IPAC, California Institute of Technology, 1200 E.
California Blvd, Pasadena, CA 91125, USA  Kaustav Kashyap Das Cahill Center
for Astrophysics, California Institute of Technology, Pasadena, CA 91125, USA
Kishalay De  MIT-Kavli Institute for Astrophysics and Space Research, 77
Massachusetts Ave., Cambridge, MA 02139, USA  Andrew Drake  Cahill Center for
Astrophysics, California Institute of Technology, Pasadena, CA 91125, USA
Alexei V. Filippenko  Department of Astronomy, University of California,
Berkeley, CA 94720-3411, USA  Christoffer Fremling Cahill Center for
Astrophysics, California Institute of Technology, Pasadena, CA 91125, USA
Caltech Optical Observatories, California Institute of Technology, Pasadena,
CA 91125, USA  George Helou  IPAC, California Institute of Technology, 1200 E.
California Blvd, Pasadena, CA 91125, USA  Anna Ho Department of Astronomy,
Cornell University, Ithaca, NY 14853, USA  Jacob Jencson Department of Physics
and Astronomy, Johns Hopkins University, 3400 North Charles Street, Baltimore,
MD 21218, USA  David Jones Instituto de Astrofísica de Canarias, E-38205 La
Laguna, Tenerife, Spain  Departamento de Astrofísica, Universidad de La
Laguna, E-38206 La Laguna, Tenerife, Spain  Russ R. Laher IPAC, California
Institute of Technology, 1200 E. California Blvd, Pasadena, CA 91125, USA
Frank J. Masci IPAC, California Institute of Technology, 1200 E. California
Blvd, Pasadena, CA 91125, USA  Kishore C. Patra  Nagaraj-Noll-Otellini
Graduate Fellow, Department of Astronomy, University of California, Berkeley,
CA 94720-3411, USA  Josiah Purdum Caltech Optical Observatories, California
Institute of Technology, Pasadena, CA 91125, USA  Alexander Reedy  Cahill
Center for Astrophysics, California Institute of Technology, Pasadena, CA
91125, USA  Tawny Sit Department of Astronomy, The Ohio State University, 140
West 18th Avenue, Columbus, OH 43210, USA  Yashvi Sharma Cahill Center for
Astrophysics, California Institute of Technology, Pasadena, CA 91125, USA
Anastasios Tzanidakis Department of Astronomy, University of Washington,
Seattle, WA 98195, USA  Stéfan J. van der Walt  Berkeley Institute for Data
Science, University of California, Berkeley  Yuhan Yao Cahill Center for
Astrophysics, California Institute of Technology, Pasadena, CA 91125, USA
Chaoran Zhang  Center for Gravitation, Cosmology, and Astrophysics, Department
of Physics, University of Wisconsin, Milwaukee, WI 53201, USA

###### Abstract

Luminous red novae (LRNe) are transients characterized by low luminosities and
expansion velocities, and are associated with mergers or common envelope
ejections in stellar binaries. Intermediate-luminosity red transients (ILRTs)
are an observationally similar class with unknown origins, but generally
believed to either be electron capture supernovae (ECSN) in super-AGB stars,
or outbursts in dusty luminous blue variables (LBVs). In this paper, we
present a systematic sample of 8 LRNe and 8 ILRTs detected as part of the
Census of the Local Universe (CLU) experiment on the Zwicky Transient Facility
(ZTF). The CLU experiment spectroscopically classifies ZTF transients
associated with nearby ($<150$ Mpc) galaxies, achieving 80% completeness for
m${}_{r}<20$ mag. Using the ZTF-CLU sample, we derive the first systematic
LRNe volumetric-rate of 7.8${}^{+6.5}_{-3.7}\times 10^{-5}$ Mpc-3 yr-1 in the
luminosity range $-16\leq$ Mr $\leq-11$ mag. We find that in this luminosity
range, the LRN rate scales as dN/dL $\propto L^{-2.5\pm 0.3}$ – significantly
steeper than the previously derived scaling of $L^{-1.4\pm 0.3}$ for lower
luminosity LRNe (M${}_{V}\geq-10$). The steeper power law for LRNe at high
luminosities is consistent with the massive merger rates predicted by binary
population synthesis models. We find that the rates of the brightest LRNe
(M${}_{r}\leq-13$ mag) are consistent with a significant fraction of them
being progenitors of double compact objects (DCOs) that merge within a Hubble
time. For ILRTs, we derive a volumetric rate of $2.6^{+1.8}_{-1.4}\times
10^{-6}$ Mpc-3yr-1 for M${}_{\rm{r}}\leq-13.5$, that scales as dN/dL $\propto
L^{-2.5\pm 0.5}$. This rate is $\approx 1-5\%$ of the local core-collapse
supernova rate, and is consistent with theoretical ECSN rate estimates.

##  1 Introduction

The advent of time domain surveys in the last decades has led to the discovery
of “gap transients" – a new class of explosions that have $-16\leq
M_{V}\leq-10$ and occupy the luminosity gap between novae and supernovae (SNe)
(Kasliwal et al., 2011; Pastorello & Fraser, 2019). This class includes a
diverse variety of transients such as faint core-collapse SNe (Yang et al.,
2021), .Ia-like SNe (Bildsten et al., 2007), low-luminosity Iax SNe
(Karambelkar et al., 2021), luminous red novae (LRNe, Kulkarni et al. 2007),
intermediate luminosity red transients (ILRTs, Thompson et al. 2009) and
outbursts in luminous blue variable (LBV) stars (Smith et al., 2011). Among
gap transients, there is a sub-class of hydrogen-rich explosions characterized
by low expansion velocities and interaction with surrounding circumstellar
material (CSM). This sub-class comprises of LRNe, ILRTs and LBV outbursts.

LRNe are transients associated with the final stages of common envelope
evolution (CEE) in a stellar binary system (Ivanova et al., 2013a; Tylenda,
2005; Pastorello et al., 2019a). The loss of angular momentum in a binary can
initiate CEE that terminates with the inspiral of the binary on dynamical
timescales. This can either lead to the merger of the two stars or the
ejection of the CE and formation of a stable binary in a tighter orbit. Both
cases are accompanied by energetic outbursts that are powered primarily by
shocks or recombination in the ejected material (Ivanova et al., 2013a;
MacLeod et al., 2017; Pejcha et al., 2017; Matsumoto & Metzger, 2022). The
association of LRNe with CE-related outbursts was supported by the discovery
of V1309Sco – a Galactic LRN with archival photometric data showing a binary
with a rapidly decaying orbital period in the years leading to the transient
(Tylenda et al., 2011). LRNe thus present an opportunity to probe the poorly
understood physics of CEE, see Ivanova et al. (2013b). This is of particular
importance because CEE is a crucial phase in the formation of double compact
objects (DCOs, Vigna-Gómez et al. 2020) that merge to radiate gravitaional
waves, which are being detected regularly by LIGO (The LIGO Scientific
Collaboration et al., 2021a).

LRNe generally have low expansion velocities ($<1000$ km s-1), a wide range of
luminosities ($-3<M_{V}<-16$), long lasting ($\sim 100$ day) multi-peaked
light curves that redden rapidly due to dust formation (Kamiński & Tylenda,
2011; Kamiński et al., 2015). Prior to 2021, only 4 Galactic and 11
extragalactic LRNe were known (Kochanek et al. 2014; Blagorodnova et al. 2021
and references therein). The extragalactic LRNe have $-9\leq
M_{\rm{peak}}\leq-15$, while the Galactic LRNe in general have much lower
luminosities. Progenitor primary stars have been identified for 7 LRNe so far
and have revealed interesting correlations between the masses and peak
luminosities (Blagorodnova et al., 2021; Pastorello et al., 2019a). Despite
these advances, the volumetric rates of LRNe are largely unconstrained. The
best estimate of the rate comes from Kochanek et al. (2014), who used 3
Galactic LRNe that had $-4<M_{V}<-10$ discovered over the last 30 years to
determine their rate in the Milky Way. They find that very low luminosity
events (M${}_{r/V,\rm{peak}}\approx-3$ mag) are fairly common ($\sim 0.5$ yr
-1), but the rate drops as $\approx L^{-1.4}$ with increasing luminosity. The
rate of the more luminous, extragalactic LRNe has not been measured yet; and
extrapolations based on the Galactic rate disagree by orders of magnitude with
the expectations from population synthesis (Howitt et al., 2020). An accurate
measurement of the rate and luminosity function of LRNe is needed to probe
several CEE parameters (see Howitt et al. 2020 for examples).

ILRTs are an observationally related class of transients that are also
characterized by low expansion velocities and reddening photometric evolution,
but have single-peaked lightcurves and a narrower luminosity range
($-11<M_{V}<-15$) compared to LRNe (Cai et al., 2021). The origin of ILRTs
still remains a mystery. They have been proposed to be electron-capture SNe in
super-AGB stars (Botticella et al., 2009; Cai et al., 2021) or outbursts in
dusty LBV stars (Smith et al., 2009; Andrews et al., 2021). Both explanations
are supported by the peculiar progenitors of ILRTs. The ILRTs SN 2008S, NGC
300 OT, AT 2019abn have been associated with extremely dusty, infrared-(IR)
bright progenitors (Botticella et al., 2009; Prieto et al., 2008; Jencson et
al., 2019) consistent with super-AGB stars, while the proposed ILRT AT 2019krl
was associated with a blue supergiant or LBV progenitor (Andrews et al.,
2021). About a dozen ILRTs have been studied extensively in the last decade
(see Cai et al. 2021 and references). Similar to LRNe, the volumetric rate has
not been reliably measured. Based on two ILRTs SN 2008S and NGC 300 OT,
Thompson et al. (2009) estimate the ILRT rate to be $\approx 20\%$ of the CCSN
rate. Cai et al. (2021) use a sample of 5 ILRTs reported by different surveys
over the last decade and estimate a lower limit of $\approx 8\%$ of the CCSN
rate.

Reliable LRNe and ILRTs rate measurements have been hindered by their
heterogeneous sample. The existing rate estimates have used transients
reported by different surveys, and have not accounted for effects of survey
completeness or selection biases (Kochanek et al., 2014; Cai et al., 2021). A
systematic sample of LRNe and ILRTs, preferably from a single survey is
required to accurately constrain their rate. Such studies are now possible
with experiments like the Census of the Local Universe (CLU, De et al., 2020)
on the Zwicky Transient Facility (ZTF, Bellm et al. 2019; Graham et al. 2019;
Dekany et al. 2020). ZTF is an optical time domain survey with a 47 sq. deg
field-of-view that surveys the entire accessible northern sky at a cadence of
$\approx 2-3$ days in the _g_ and _r_ bands down to a depth of 20.5 mag. The
CLU experiment aims to build a spectroscopically complete sample of transients
detected by ZTF that are associated with galaxies in the CLU galaxy catalog
(Cook et al., 2019) to a depth of m${}_{r}\approx 20$ mag. The CLU experiment
is ideal to detect low luminosity (M${}_{r}\leq-16$) transients like LRNe and
ILRTs out to large distances ($\approx 100$ Mpc), consequently building a
large sample of such rare transients.

In this paper, we present a systematic sample of LRNe and ILRTs detected by
the ZTF CLU experiment from June 1, 2018 to February 20, 2022. We utilize this
sample and the actual observation history of ZTF to derive the rates of LRNe
and ILRTs. In Sec. 2.1, we describe the selection criteria used to construct
our LRN and ILRT samples. Sec. 2.1 also describes the photometric and
spectrosocopic properties of LRNe and ILRTs identified in the CLU experiment.
Sec. 3 describes our methods to derive the luminosity function and volumetric
rates of LRNe and ILRTs. Sec. 4 compares our results to previous measurements
and theoretical predictions, and discusses the implications for progenitors of
LRNe and ILRTs. We conclude with a summary of our results in Sec. 5.

Table 1: Properties of the 34 ZTF transients of interest

ZTF | AT | Mabs | multi-peak/ | Archival | Gal typea | H$\alpha$-FWHMb | [Ca II] | Mol. | Classification
---|---|---|---|---|---|---|---|---|---
Name | Name | at peak | plateau | (PTF/ATLAS) |  | (km s-1) |  | feats. |
ZTF18acbwfza* | 18hso | $-13.82\pm 0.15$ | mp | –/no | SB(r)a pec | 500 | em? | yesc | LRN-gold
ZTF19adakuot | 19zhd | $-9.60\pm 0.15$ | pl | no/yes | SA(s)b |  |  | yesc | LRN-gold
ZTF20aawdwch* | 20hat | $-11.43\pm 0.15$ | pl | no/no | SAB(rs)cd | 130 | no | yes | LRN-gold
ZTF21aancgbm* | 21biy | $-13.86\pm 0.15$ | mp | yes/no | SB(s)d. | 500 | em? | yes | LRN-gold
ZTF21aagppzg* | 21blu | $-13.50\pm 0.15$ | mp | no/no | starforming | 500 | no | yes | LRN-gold
ZTF21acpkzcc* | 21aess | $-15.12\pm 0.15$ | mp | –/no | SB(s)m? | 500 | no | – | LRN-gold
ZTF18abwxrhi* | 18gzz | $-14.50\pm 0.16$ | mp | no/no | (R’)SB(rs)ab | 300 | no | no | LRN-silver
ZTF21aaekeqd* | 21afy | $-13.95\pm 0.16$ | pl | –/no | starforming | 700 | no | no | LRN-silver
ZTF18aajgqmr | 20ifb | $-15.36\pm 0.17$ | mp | –/no | starforming |  |  |  | LRN-bronze
ZTF20abjgdec | 20afdb | $-14.37\pm 0.16$ | mp | –/no | starforming |  |  |  | LRN-bronze
ZTF21aabfwwl | 21iy | $-15.72\pm 0.16$ | mp | –/no | starforming |  |  |  | LRN-bronze
ZTF18acdyopn | 18hcj | $-14.33\pm 0.19$ | no | –/no | SAdm. | 300 | em | no | ILRT-gold
ZTF19aadyppr* | 19abn | $-14.73\pm 0.15$ | no | yes/no. | Sa | 700 | em | no | ILRT-gold
ZTF19acoaiub* | 19udc | $-14.62\pm 0.15$ | no | –/no | SAB(s)a | 1250 | em | no | ILRT-gold
ZTF19acdrkbh | 19sfo | $-14.62\pm 0.20$ | – | –/no | starforming | 600 | em | no | ILRT-gold
ZTF19aagqkrq* | 19ahd | $-13.72\pm 0.15$ | no | –/no. | SA(s)cd | 700 | em | no | ILRT-gold
ZTF21aclzzex* | 21adlx | $-15.68\pm 0.16$ | no | yes/no | Sb | 700 | em | no | ILRT-silver
ZTF21abtduah* | 21vdr | $<-14.96$ | – | no/no | SB(s)d: | 1300 | no | no | ILRT-silver
ZTF21abfxjld | 21prj | $<-14.21$ | – | no/no. | starforming | $<300$ | no | no | ILRT-silver
ZTF18acrygkg | 18lqq | $<-14.14$ | no | –/no | SA(s)bc |  |  |  | ILRT-bronze
ZTF19aavwbxs | 19fxy | $-14.44\pm 0.17$ | no | –/no | starforming |  |  |  | ILRT-bronze
ZTF19acpmbvd | 19wbg | $-14.66\pm 0.15$ | mp | yes/yes | SAB(r)a | 1700 |  |  | LBV?
ZTF20abwilhb | 20swt | $-13.87\pm 0.16$ | no. | no/no | Scd | 3300 | no | no | LBV/Type II?
ZTF21aagydmn | 21bug | $-14.36\pm 0.15$ | no | yes/no | SAd | 2600 | no | no | LBV?
ZTF21aantupk | 21efb | $-14.71\pm 0.15$ | no | –/yes | - |  |  |  | LBV/AGN?
ZTF21aclyyfm | 21adlw | $-16.03\pm 0.15$ | no | –/yes | SA(rs)b |  | no | no | LBV?
ZTF21aaitlhy | 21afm | $-15.44\pm 0.15$ | mp | yes/yes | SBb |  |  |  | LBV?
ZTF18aawoeho | 21ahuh | $-15.51\pm 0.15$ | no | no/no | starburst |  |  |  | ?
ZTF20ablmyzj | 20afdc | $-15.95\pm 0.30$ | no | –/no | S |  |  |  | ?
ZTF20acfxnmv | 20afdd | $-14.67\pm 0.15$ | – | –/no | SB(s)cd |  |  |  | ?
ZTF20acivtfy | 20afde | $-13.72\pm 0.16$ | – | –/no | starforming |  |  |  | ?
ZTF21aapngrj | 21gcg | $-12.75\pm 0.15$ | no | –/no |  |  |  |  | ?
ZTF21aakbdzz | 21czz | $-14.83\pm 0.10$ | no | –/no | S |  |  |  | ?
ZTF21aamwyxf | 21dtz | $-15.98\pm 0.15$ | no | no/no | E |  |  |  | ?

  * •

– or unfilled entries indicate instances for which data is not available.

  * •

* : Events used for rate calculation, in Sec. 3; $a$ : Galaxy morphologies are taken from NED; $b$: Where multiple spectra are available, the maximum FWHM is reported; $c$: The molecular features are visible in spectra from the literature (see Sec. 2.2.2).

##  2 Sample selection

###  2.1 Candidate filtering

We focus our search on transients discovered as part of the ZTF CLU experiment
(De et al., 2020). Briefly, CLU aims to build a spectroscopically complete
sample of transients associated with galaxies in the local universe ($<$200
Mpc). The CLU experiment uses alerts generated from all three (public,
collaboration and Caltech) components of the ZTF survey (see De et al. 2020
for details). CLU uses the platform skyportal to save and coordinate followup
of sources (van der Walt et al., 2019). During ZTF Phase I (2018 June 01 –
2020 October 30), the experiment was limited to all transients that 1) were
within $100\arcsec$ of known galaxies in the CLU galaxy catalog (Cook et al.,
2019), 2) had more than two detections in ZTF-_g_ or _r_ filters, and 3) were
brighter than $m_{r}=20$ mag. Starting 2020 October 30 (ZTF Phase II), the
filtering criteria were updated to select transients that were 1) within 100
kpc of CLU galaxies closer than 140 Mpc, 2) brighter than m${}_{r}=20.5$ mag,
and 3) less luminous than M${}_{r}=-17$ mag. A total of 3442 transients were
saved by the CLU experiment since start of the ZTF survey. The experiment
achieved a spectroscopic completeness of 88.5% in ZTF Phase I and 79% in ZTF
phase II for sources brighter than 20 mag.

Candidate LRNe and ILRTs were selected from their real-time ZTF alert
photometry using the following selection criteria –

  * •

the transient must pass the CLU selection criteria,

  * •

the transient must be less luminous than M${}_{r}=-16$ mag,

  * •

the transient must have two ZTF alerts (i.e. two $>5\sigma$ detections)
brighter than 20 mag in either _g_ or _r_ bands.

The sample presented in this paper is restricted to events saved before 2022
February 20.

523 transients satisfied the selection criteria listed above. 109 of these
were found to lie on top of faint underlying galaxies that are not present in
the CLU catalog. These transients were excluded as they are likely supernovae
in distant host galaxies. 55 additional candidates were excluded as they were
flagged as image processing artifacts on visual inspection of the difference
images. 73 candidates were eliminated as they showed small, long-term ($>1$
year) variations in brightness without significant colour changes, and were
coincident with stars in the Milky Way or nearby galaxies (M31 or M33).

To further filter our candidates, we used follow-up spectroscopic observations
(either from our followup campaigns or on TNS). In addition to the CLU
experiment, some of our spectra were collected as part of the ZTF Bright
Transient Survey (BTS, Fremling et al. 2020; Perley et al. 2020). The BTS
classifications are already public, while all CLU classifications will be
presented in separate papers focusing on different sub-samples (e.g. De et al.
2020, Tzanidakis et al. in prep., Sit et al. submitted). Of the CLU transients
that pass our criteria, seven sources were spectroscopically classified as
active galactic nucleii (AGN), 65 as hydrogen-poor SNe (Ia, Iax, Ca-rich, Ib
and Ic SNe), 11 as classical novae, 128 as Type II SNe – based on broad
($v\geq 5000$ km s-1) H emission lines. 2 additional candidates were studied
low-luminosity Type II SNe (Reguitti et al., 2021; Yang et al., 2021) showing
low velocity hydrogen lines. We were now left with 73 sources that did not
match any of the above categories.

We ran forced point-spread function (PSF) photometry at the location of these
73 sources on all ZTF difference images (Masci et al., 2019). This provides
more accurate photometry than the real-time ZTF alerts, and also enables the
recovery of sub-threshold ($>3\sigma$) detections. From this set, 14
candidates were ruled out as their forced photometry revealed them to have
absolute magnitudes brighter than $-16$ mag. 18 additional sources were ruled
out because their forced photometry lightcurves revealed slow, small amplitude
long term ($>500$ day) variations. These slowly varying sources are likely
foreground variable stars, but some could also be long duration giant
outbursts in LBV stars such as $\eta-$Car or UGC 2773-OT (Humphreys et al.,
1999; Smith et al., 2016). One additional source at redshift z=0.002 showed
fast erratic variations in ZTF data. Finally, five sources had
M${}_{r}\geq-10$ and fast fading lightcurves ($<10$ d), suggesting that they
are classical novae. Of the remaining, one source showed a declining
lightcurve with $g-r<0$ mag, similar to late-time SN lightcurves, unlike LRNe
or ILRTs. The remaining 34 sources are promising LRNe and ILRT candidates, and
are listed in Table 1.

###  2.2 Classification

The shortlist of 34 transients in Table 1 consists of LRNe, ILRTs, LBV
outbursts and possibly some supernovae observed at late phases. Here, we
discuss the classifications of these transients using their ZTF lightcurves,
spectroscopic data and archival photometry.

LRNe typically show multi-peaked lightcurves (Pejcha et al., 2017; Matsumoto &
Metzger, 2022) which allows to photometrically differentiate them from ILRTs
(Cai et al., 2021). Table 1 indicates the transients that show multiple peaks
in their ZTF lightcurves.

Searching for previous outbursts in archival data can help distinguish LBV
eruptions from LRNe/ILRTs, as LBV outbursts can be recurring. While LRNe are
also known to show precursor emission in the years leading up to the merger,
the precursors usually have much lower luminosities than the actual merger.
The detection of historic outbursts comparable in brightness to the latest
outburst is thus suggestive of an LBV eruption. We checked for historical
activity at the locations of these sources using data from the ATLAS (Tonry et
al. 2018; Smith et al. 2020, depth $\approx$ 19.5 mag, dating back to
$\sim$2014) and PTF (Law et al. 2009; Rau et al. 2009, depth $\approx$ 21.5
mag, dating back to $\sim$2009) surveys. All 34 sources have ATLAS data while
15 have PTF data. Table 1 indicates which transients were detected in the
archival ATLAS or PTF data. The full forced photometry lightcurves will be
available online (see Sec. 7)

Spectroscopic data is available for 19 of the 34 transients. 11 of these
sources only have medium resolution optical spectra, while the remaining 8
also have medium resolution NIR spectra. The optical spectra were taken with
the Low-Resolution Imaging Spectrograph (LRIS, Oke et al. 1995, R$\approx$750)
on the Keck I Telescope, the Double Beam Spectrograph (DBSP, Oke & Gunn 1982,
R$\approx$1000) on the 200-inch Hale telescope (P200) on Mount Palomar, the
Alhambra Faint Object Spectrograph and Camera (ALFOSC,R$\approx$360) on the
2.56m Nordic Optical Telescope (NOT), the Kast Double Spectrograph on the
Shane 3-m telescope at the Lick Observatory (R$\approx 1000$) and the
Spectrograph for Rapid Acquisition of Transients (SPRAT, R$\approx$350) on the
Liverpool Telescope. For ZTF 21acpkzcc, we obtained a high resolution
(R$\approx$15000) spectrum with the South African Large Telescope High
Resolution Spectrograph (HRS, Bramall et al. 2010). The NIR spectra were taken
with the Near-Infrared Echelle Spectrograph (NIRES, Wilson et al. 2004,
R$\approx$2700) on the Keck II telescope and the Triplespec spectrograph
(Herter et al. 2008, R$\approx$2500) on P200. The log of the spectroscopic
observations is listed in Table 2. In addition to these, we also obtained
several low-resolution (R$\approx$100) spectra of these transients with the
Spectral Energy Distribution Machine (SEDM; Blagorodnova et al. 2018; Rigault
et al. 2019; Kim et al. 2022) spectrograph on the 60-inch telescope at Palomar
Observatory. These spectra are not discussed here as their resolutions are too
low for a useful analysis. All our spectra (including the low-resolution ones)
will be made available online (Sec. 7).

LRNe, ILRTs and LBV outbursts can have similar spectroscopic properties
especially at early times. However, some LBV eruptions have expansion
velocities exceeding $\approx 2000$ km s-1, while LRNe and ILRTs have lower
expansion velocities (typically $\sim 1000$ km s-1). The FWHM velocities of
the H$\alpha$ emission line in the transients with spectroscopic coverage are
listed in Table 1. For transients with multiple spectra, the maximum velocity
is listed. Early time spectra of both LRNe and ILRTs are characterized by
narrow H$\alpha$ ($v_{\rm{FWHM}}\leq 1000$ km s-1) emission. [Ca II] emission
was thought to be a defining feature of ILRTs, however it was recently
discovered that some LRNe can show [Ca II] emission (Cai et al., 2019), while
some ILRTs do not show [Ca II] at certain phases (Andrews et al., 2021). Late-
time spectroscopic observations can help confidently distinguish between LRNe
and ILRTs. In LRNe, H$\alpha$ emission grows narrower and weaker with time
since peak, and eventually reemerges. Late-time spectra of LRNe also exhibit
molecular absorption features. On the contrary, ILRTs show persistent narrow H
emission throughout their evolution. Their late time spectra do not show
molecular features, but have strong H$\alpha$ and Ca II emission lines.

Table 2: Observation log of spectra presented in this paper Name | Tel./ Inst. | Date | Resolution | Name | Tel./ Inst. | Date | Resolution
---|---|---|---|---|---|---|---
ZTF18abwxrhi | P200/DBSP | 2018-09-18 | 1500 | ZTF21aancgbm | Keck/NIRES | 2021-04-18 | 1000
ZTF18abwxrhi | P200/DBSP | 2018-10-10 | 1000 | ZTF21aagppzg | Keck/NIRES | 2021-04-18 | 1000
ZTF18acbwfza | Gemini/GMOS | 2018-11-02 | 2000 | ZTF21aaekeqd | Keck/LRIS | 2021-05-09 | 750
ZTF18acbwfza | P200/DBSP | 2018-11-02 | 1000 | ZTF21abfxjld | Keck/LRIS | 2021-07-06 | 750
ZTF18acbwfza | Keck/LRIS | 2018-11-10 | 750 | ZTF21abfxjld | Keck/LRIS | 2021-08-14 | 750
ZTF18acdyopn | Keck/LRIS | 2018-11-10 | 750 | ZTF21abfxjld | Keck/NIRES | 2021-09-25 | 1000
ZTF19aadyppr | P200/DBSP | 2019-01-26 | 1000 | ZTF21abtduah | P200/DBSP | 2021-11-06 | 1000
ZTF19aagqkrq | NOT/ALFOSC | 2019-02-11 | 350 | ZTF21aclyyfm | P200/DBSP | 2021-11-06 | 1000
ZTF19aagqkrq | P200/DBSP | 2019-02-12 | 1000 | ZTF21aclzzex | Shane/KAST | 2021-11-12 | 1000
ZTF19aadyppr | NOT/ALFOSC | 2019-02-23 | 350 | ZTF21acpkzcc | Keck/NIRES | 2021-11-17 | 1000
ZTF19aadyppr | Keck/LRIS | 2019-03-07 | 750 | ZTF21acpkzcc | SALT/HRS | 2021-11-29 | 15000
ZTF19aadyppr | P200/DBSP | 2019-03-16 | 1000 | ZTF21acpkzcc | P200/DBSP | 2021-12-01 | 1000
ZTF19aadyppr | P200/DBSP | 2019-04-13 | 1000 | ZTF21abtduah | P200/DBSP | 2021-12-01 | 1000
ZTF19aadyppr | P200/DBSP | 2019-05-13 | 1000 | ZTF21aclzzex | P200/DBSP | 2021-12-01 | 1000
ZTF19acdrkbh | Keck/LRIS | 2019-10-27 | 750 | ZTF21aagppzg | P200/TSpec | 2021-12-12 | 1000
ZTF19acoaiub | P200/DBSP | 2019-11-05 | 1000 | ZTF21acpkzcc | P200/DBSP | 2022-01-12 | 1000
ZTF19acoaiub | Keck/NIRES | 2019-12-04 | 1000 | ZTF21acpkzcc | P200/TSpec | 2022-01-20 | 1000
ZTF19acpmbvd | LT/SPRAT | 2019-12-23 | 350 | ZTF21aclzzex | Keck/LRIS | 2022-01-26 | 750
ZTF20aawdwch | NOT/ALFOSC | 2020-05-15 | 300 | ZTF21aclyyfm | P200/DBSP | 2022-02-02 | 1000
ZTF20abwilhb | Keck/LRIS | 2020-10-20 | 750 | ZTF21aancgbm | Keck/LRIS | 2022-02-03 | 750
ZTF21aagppzg | P200/DBSP | 2021-02-08 | 1000 | ZTF21acpkzcc | Keck/LRIS | 2022-02-03 | 750
ZTF21aaekeqd | Keck/LRIS | 2021-02-17 | 750 | ZTF21abtduah | Keck/LRIS | 2022-02-03 | 750
ZTF21aagppzg | P200/DBSP | 2021-02-20 | 1000 | ZTF21aclzzex | Keck/LRIS | 2022-03-01 | 750
ZTF21aagydmn | P200/DBSP | 2021-02-20 | 1000 | ZTF21abtduah | Keck/LRIS | 2022-03-03 | 750
ZTF21aagppzg | LT/SPRAT | 2021-03-19 | 350 | ZTF21aclzzex | Keck/LRIS | 2022-03-03 | 750
ZTF21aancgbm | P200/DBSP | 2021-04-09 | 1000 | ZTF21aagppzg | Keck/NIRES | 2022-03-16 | 1000
ZTF21aagppzg | P200/DBSP | 2021-04-09 | 1000 | ZTF21aancgbm | Keck/NIRES | 2022-03-17 | 1000
ZTF21aaekeqd | Keck/LRIS | 2021-04-14 | 750 | ZTF21aclzzex | Keck/NIRES | 2022-03-17 | 1000
ZTF21aaekeqd | Keck/NIRES | 2021-04-18 | 1000 | ZTF21aclzzex | Keck/NIRES | 2022-04-15 | 1000

Provided that not all of our sources have late-time spectroscopic coverage, we
use the available spectra (from literature wherever necessary) together with
the lightcurves to create a classification scheme for these transients. We
classify the 34 transients into eight categories – Possible LBV outbursts,
LRN-gold, LRN-silver, LRN-bronze, ILRT-gold, ILRT-silver, ILRT-bronze, and
Ambiguous. We describe these categories in detail below. Briefly, for LRNe and
ILRTs, the gold sample comprises transients that we can confidently classify
in either category, the silver sample comprises transients that have
photometry and spectra indicative to their class, but lack smoking gun
signatures associated with the class, and the bronze category comprises
transients that have photometric evolution similar to their class, but do not
have any spectroscopic data. The “Ambiguous" category consists of 7 sources
that have poor quality data, i.e. no spectra _and_ low-quality sparse
photometric coverage owing to bad weather or solar conjunction of the
transient, rendering us unable to place them in any of the other categories.
Table 1 lists the classification of these sources based on this scheme. We
describe the sources in each category below.

####  2.2.1 Possible LBV eruptions

This category includes sources that show broad ($v_{\rm{FWHM}}\geq 2000$ km
s-1) H$\alpha$ emission in their spectra, _or_ have historic outbursts in
archival data. A total of 6 transients in our shortlist satisfy these
criteria. Two of these – ZTF 21aagydmn and ZTF 20abwilhb show broad H$\alpha$
emission with FWHM velocities of 2600 and 3300 km s-1 and are likely LBV
outbursts. The ATLAS and PTF data classifies four additional sources as
potential LBVs – ZTF 19acpmbvd, ZTF 21aantupk, ZTF 21aclyyfm and ZTF
21aaitlhy. We describe these sources in the Appendix A.

Figure 1: Forced photometry lightcurves of the 11 LRNe in our sample. The
transients in gold, silver and bronze samples are marked in parantheses with
g, s and b respectively. The ZTF-g, ZTF-r, ZTF-i, ATLAS-c and ATLAS-o band
datapoints are plotted as green, red, brown, blue and orange points
respectively. The J, H and Ks band magnitudes are plotted as gray, brown and
black crosses respectively. Downward pointing triangles indicate 5-$\sigma$
upper limits. The days are in observer frame. The lightcurves have been
corrected for extinction using the values listed in Table 3. Solid black
vertical lines indicate epochs at which the spectra were obtained. Figure 2:
Optical spectra for LRNe presented in this paper. Figure 3: NIR spectra for
LRNe presented in this paper.

####  2.2.2 LRN-gold

This category includes six spectroscopically confirmed LRNe detected in ZTF
data in the last three years. Three of these have been studied in detail
previously – ZTF 18acbwfza (AT 2018hso, Cai et al. 2019), ZTF 19adakuot (AT
2019zhd, Pastorello et al. 2021a) and ZTF 20aawdwch (AT 2020hat, Pastorello et
al. 2021b). Three other transients – ZTF 21aancgbm (AT 2021biy, Cai et al.
2022), ZTF 21aagppzg (AT 2021blu, Pastorello et al. 2022) and ZTF 21acpkzcc
(AT 2021aess, Davis et al. 2021) were identified as possible LRNe in 2021. We
initiated optical and NIR photometric and spectroscopic followup campaign for
these objects, which confirmed their nature as LRNe.

Our lightcurves of these transients are shown in Fig. 1. For all our
calculations, we use host galaxy redshifts corrected for local velocity flows
from the NASA Extragalactic Database (NED), and assume H${}_{0}=73$ km s-1
Mpc-1. We use Milky Way line-of-sight extinction values from Schlafly et al.
(2012). We calculate the host galaxy extinctions for LRNe using Na I D
equivalent widths in their early time spectra (see discussion of individual
objects below). We calculate the peak magnitudes and epoch of maximum
brightness by fitting polynomials to the near-peak lightcurve. We calculate
the pseudo-bolometric lightcurves by fitting blackbodies to the available
optical data. The derived photometric properties and the adopted distances and
extinctions for the LRNe in our sample are listed in Table 3.

Our spectra of these transients are shown in Fig. 2 and 3. We analyze the
optical spectra and derive the hydrogen Balmer line velocities by fitting
lorentzian profiles (which are better fits than gaussian profiles). We also
measure the Balmer decrement ($\beta$) as the ratio of H$\alpha$ to H$\beta$
line fluxes in the spectra where both lines are detected. The spectroscopic
properties are listed in Table 4. We now briefly describe individual members
of our sample.

1\. ZTF 18acbwfza (AT 2018hso) is located in the starforming galaxy NGC 3729.
Our earliest spectrum (7 days before peak) shows Na I D absorption with an
equivalent width of $1.5\pm 0.4$ Å. Assuming the source of this absorption is
dust in the interstellar medium and the correlation from Turatto et al. (2003)
we derive $E(B-V)_{\rm{host}}=0.23\pm 0.06$ mag. This is consistent with the
value used by Cai et al. (2019). The lightcurve is characteristic of LRNe,
with an early blue peak lasting for $\approx 20$ days, followed by a prolonged
plateau where the transient evolves rapidly to redder colors. We note that the
transient shows signs of evolving back to bluer colors at late times, when the
_r_ -band lightcurve is declining but the _g_ -band lightcurve has plateaued.
However, we caution that the _g_ -band detections at this phase from ZTF have
low significance (3$\sigma$). Our spectra sample only the first blue peak, and
show strong Balmer emission lines with v${}_{\rm{FWHM}}\approx 500$ km s-1.
These spectra also show narrow Ca II NIR triplet lines with a P-cygni profile.
The absorption of the P-cygni profile extends to a maximum velocity
v${}_{m}\approx 400-500$ km s-1. Cai et al. (2019) report weak [Ca II] in this
transient. We find marginal evidence for [Ca II] emission in only one of our
spectra, taken 1 day post peak. Late-time spectra from Cai et al. (2019) show
strong molecular absorption features.

2\. ZTF 19adakuot (AT 2019zhd) is located in M31. Following Pastorello et al.
(2021a), we assume that the total extinction is dominated by the Milky Way.
The transient has the lowest luminosity in our sample (peaking at
M${}_{r}\approx-9.5$ mag). We do not have any spectroscopic data for this
transient, but late-time spectra presented in Pastorello et al. (2021a) show
molecular absorption features.

As noted in Pastorello et al. (2021a), this transient shows precursor activity
for a few months leading up to the explosion. In these months, the field of
ZTF 19adakuot was imaged with the ZTF camera several times per night. We stack
the ZTF forced photometry from images taken on the same night, and recover
several additional detections than the ones reported in Pastorello et al.
(2021a), which are plotted in Fig. 4. We further bin the photometry in bins of
ten days to increase the significance of the detections. The ZTF detections
date back to 160 days before the _r_ -band peak, when the transient was first
detected at m${}_{r}\approx 22.7\pm 0.3$ mag. The binned ZTF lightcurve shows
that the transient went through a gradual, bumpy brightening phase for
$\approx 160$ days before the main explosion. Three bumps can be identified in
the _r-_ band lightcurve, each with a duration of $\approx 50$ days. During
each of these bumps, the transient brightens by an increasing amount
($\approx$ 0.5, 1 and 2.5 mag respectively) before plateauing or declining by
a modest amount ($\approx 0.5$ mag) at the end of each bump. After the third
bump, the transient brightens gradually by $\approx 1$ mag for 25 days before
brightening rapidly by 4 mag as it transitions into the main explosion. This
bumpy rise is reminiscent of the pre-outburst evolution of M31-LRN-2015
(Blagorodnova et al., 2020), V838 Mon (Munari et al., 2002; Tylenda, 2005) and
AT 2020hat (Pastorello et al., 2019b).

At the end of the first bump (MJD 58759), fitting a single blackbody to the
_g_ and _r_ -band detections suggests a source with
T${}_{\rm{eff}}=6600^{+2400}_{-1600}$ K, a radius R $=17^{+14}_{-7}$ R⊙ and a
luminosity of 5.5${}^{+1.3}_{-0.7}\times 10^{2}$ L⊙. This photosphere is most
likely formed by mass outflowing from the outer Lagrangian (L2) point (for
example Pejcha et al. 2017 or MacLeod et al. 2022). On the second bump, the
transient is only detected in _r_ band, with the most constraining _g_ band
upper limit giving $g-r>0.8$ mag, suggesting the optically thick photosphere
has cooled. This likely continues up to the beginning of the third bump on MJD
58837, where the temperature has cooled down to T$=3900^{+700}_{-700}$ K and
the photosphere has expanded to R$=170^{+140}_{-70}$ R⊙ and
L$=6.1^{+3.9}_{-1.7}\times 10^{3}$ L⊙. This would imply a photospheric
expansion speed of $\approx 10-30$ km s-1. After this, the temperature
increases quickly in the next 12 days on the third bump to
5700${}^{+300}_{-300}$ K with L $=7.5^{+0.3}_{-0.3}\times 10^{3}$ L⊙, and
reduced R $=90^{+12}_{-12}$ R⊙ on MJD 58849, suggesting the temperature
increase was accompanied by a drop in opacity. This is followed by a
surprisingly sharp decline in the redder (_r_ , _o_) bands but a slow
brightening in the _g_ -band. During this decline, the temperature increases
to 6900${}^{+1100}_{-1000}$ K but the radius drops to 69${}^{+27}_{-16}$ R⊙
with increased luminosity of 9.5${}^{+0.8}_{-0.6}\times 10^{3}$ L⊙ on MJD
58871. This is followed by an increase in luminosity and photospheric radius
accompanied by a slight decrease in temperature, to L$=1.7^{+0.2}_{-0.1}\times
10^{4}$ L⊙ on MJD 58887. In the next five days, the transient brightens
rapidly to its peak luminosity of $\approx 5.2\times 10^{5}$ L⊙.

A full analysis of this complex precursor photometric evolution is outside the
scope of this paper. A possible explanation for the abrupt temperature
increases in this final phase is shocks due to collisions within the
L2-stream, as suggested in Pejcha et al. (2017). The total energy radiated
during this $\approx 40$ day duration is $\approx 10^{44}$ erg. Assuming an L2
velocity of 30 km s-1, the mass required in the L2 stream is $\geq 10^{-2}$M⊙.

Figure 4: Pre-explosion _g_ , _r_ and _i_ -band detections for ZTF 19adakuot.
For phases $<-75$ days, we bin the ZTF flux measurements taken on the same day
to increase the sensitivity. These points are plotted as faint background
circles. We further bin these measurements in bins of 10 days to increase
their significance. The binned measurements are showed in solid squares. For
phases $>-75$ days, the squares represent ZTF forced photometry from single
visits. The triangles denote 5-$\sigma$ upper limits. The crosses denote
measurements reported previously in Pastorello et al. (2021a). At the epochs
marked by the dotted vertical lines, we indicate the effective temperatures
and photospheric radii to demonstrate the dramatic variations exhibited by the
precursor (see text). The initial pre-explosion behaviour is consistent with a
photosphere L2-mass loss forming an optically thick photosphere detectable by
ZTF at $\approx-150$ days, which expands and cools up to $\approx-70$ days.
Further collisions in the L2 stream, or accretion onto the companion star can
cause sudden increases in temperature over the next 70 days, until the
transient brightens rapidly transitioning to the main explosion (marked by the
red arrow).

3\. ZTF20aawdwch (AT 2020hat) is located in NGC 5068. We follow Pastorello et
al. (2021b) and assume that the extinction is dominated by the Milky Way. The
ZTF lightcurve samples the post-peak decline, starting at mr=17.90$\pm$0.06
mag. Our sole spectrum was taken at a phase of 30 days since peak, which shows
a reddened continuum, extremely weak H$\alpha$ emission, some broad but weak
molecular absorption features and Ca II NIR triplet absorption lines –
characteristic of LRNe on the red plateau phase. Molecular absorption features
are clearly detected in late-time spectra presented in Pastorello et al.
(2021b).

4\. ZTF 21aancgbm (AT 2021biy, Smith et al. 2021a; Cai et al. 2022) is located
in the galaxy NGC 4631. We do not have spectra at early phases, so we adopt
the host extinction derived by Cai et al. (2022) using Na I D absorption. The
lightcurve is characteristic of LRNe, with an initial blue peak lasting for
$\approx$ 50 days, followed by a rebrightening and a prolonged red plateau of
$\approx$ 350 days. The field of ZTF 21aancgbm is not part of the regular
2-day cadence ZTF survey, so the ZTF lightcurve samples only a small portion
of the lightcurve. We combine the ZTF data with ATLAS data, which shows that
the lightcurve lasts for more than 400 days, and is the longest duration LRN
in our sample.

We obtained _JHKs_ NIR imaging with P200/WIRC on several epochs on the
plateau, which shows that the transient was significantly brighter in the NIR
bands (by $>1$ mag) than in the optical (see Fig. 1). The transient shows a
late-time bump once it falls off the plateau, likely the result of collision
with CSM as noted in Cai et al. (2022). Our spectroscopic coverage comprises
two optical spectra at +60 and +360 days since peak, and two NIR spectra at
+69 and +402 days since peak. The +60 day spectrum shows a reddened continuum
with weak, unresolved H$\alpha$ emission (v${}_{\rm{FWHM}}\approx 350$ km s-1)
and Ca II NIR triplet with P-cygni line profiles (with v${}_{m}\approx 400$ km
s-1). We also detect weak [Ca II] lines with P-cygni line profiles. The +69 d
NIR spectrum shows several metallic absorption lines, as well as the CO
absorption bandhead. The very late-time optical spectrum at +360 days shows a
highly reddened continuum with several strong molecular absorption features of
TiO and VO, which confirms the classification as a LRN. This spectrum also
shows strong, narrow H$\alpha$ emission (with increased
v${}_{\rm{FWHM}}\approx 500$ km s-1) and Ca II NIR lines with P-cygni profiles
(v${}_{m}\approx 600$ km s-1).

The lightcurve shape and long duration of ZTF 21aancgbm make it an interesting
member of the LRN family. The 200 day long plateau resembles that seen in SNe
IIP, and it is tempting to posit that it is powered by hydrogen recombination.
Matsumoto & Metzger (2022) provide scaling relations between the plateau
luminosity (Lpl), duration (tpl) and ejected mass (Mej) for a recombination-
powered LRN plateau, given by

$M_{\rm{ej}}\approx 1.6\,\rm{M}_{\odot}\times
f_{\rm{ad,0.3}}^{-1}\times(\frac{t_{\rm{pl}}}{100\rm{d}})\times(\frac{L_{\rm{pl}}}{10^{39}\rm{erg/s}})$
(1)

with f${}_{\rm{ad},0.3}\approx 1$ is a dimensionless factor quantifying
inefficiencies in radiating the recombination energy. We define the plateau as
the duration between the point where the transient begins rebrightening after
the first blue peak to the time when it falls off the plateau to the same
brightness. We calculate an average plateau luminosity L${}_{\rm{pl}}\approx
2.3\times 10^{40}$ erg s-1 and a plateau duration t${}_{\rm{pl}}\approx 274$
days. This suggests a recombining ejecta mass of $\approx$ 100 M⊙ for this
LRN, implying an extremely massive progenitor. This seems unlikely, given that
the correlation between peak luminosity and progenitor mass for LRNe
(Blagorodnova et al., 2021) predicts the primary progenitor mass in the range
$\sim 10-50$ M⊙. Additionally, from archival _HST_ imaging Cai et al. (2019)
suggest a progenitor mass $\sim 17-24$ M⊙. It is therefore very likely that
the plateau luminosity is too high to be explained by hydrogen recombination
alone. A plausible source of additional energy is shock interaction between
the merger ejecta and pre-existing material around the binary that was ejected
during the CE phase. Following Matsumoto & Metzger (2022), assuming that only
the timescale but not the luminosity of the transient is set by hydrogen
recombination, the required recombining ejected mass is

$t_{\rm{pl}}\approx
140\,\rho_{i,-11}^{-1/3}(\frac{M_{\rm{ej}}}{M_{\odot}})^{1/3}(\frac{v_{E}}{300\,\rm{km/s}})^{-1}\,\,\rm{days}$
(2)

where vE is the mean ejecta velocity and $\rho_{i,-11}=\rho_{i}/10^{-11}$g
cm${}^{-3}\approx 1$ where $\rho_{i}$ is the characteristic density at which
the recombination completes. We adopt v${}_{E}\approx 430$ km s-1 from Cai et
al. (2022) which gives M${}_{\rm{ej}}\approx 22$ M⊙. This value is larger than
that derived in Cai et al. (2022) due to the larger plateau duration that we
have assumed. Assuming that this ejected mass runs into pre-existing mass
(M${}_{\rm{pre}}<<M_{\rm{ej}}$) with velocity
v${}_{\rm{pre}}<<\rm{v_{\rm{E}}}$, the generated shock luminosity can be
written as (Matsumoto & Metzger, 2022)

$L_{\rm{pl}}^{\rm{sh}}\approx 7\times
10^{39}\rho_{i,-11}^{-1/3}(\frac{M_{\rm{pre}}}{0.1M_{\rm{ej}}})(\frac{v_{E}}{300\,\rm{km/s}})^{3}(\frac{M_{\rm{ej}}}{M_{\odot}})^{2/3}\,\,\rm{erg/s}$
(3)

The observed plateau luminosity can be explained by shock interactions from
Eq. 2 and 3 if M${}_{\rm{pre}}\approx 0.3\,\rm{M}_{\odot}$. Given the very
late-time bump in the lightcurve of this LRN, it is not unreasonable to expect
significant CSM around the binary, providing a plausible explanation for its
plateau.

5\. ZTF 21aagppzg (AT 2021blu, Smith et al. 2021b; Pastorello et al. 2022) is
located on the outskirts of the galaxy UGC 5829. It was first classified as an
LBV outburst (Uno et al., 2021), however, our late-time NIR spectra show
strong molecular absorption features, indicating that this is a LRN. We adopt
the extinction to be dominated by the Milky Way, as our early optical spectra
do not show any strong Na ID absorption lines.

The lightcurve is characteristic of LRNe and shows two pronounced peaks – an
initial blue peak for $\approx$ 50 days, followed by a second red peak lasting
for $\approx 200$ days. Unlike ZTF 21aancgbm, the second peak does not show a
plateau but has a smooth rise and decline. The P200/WIRC NIR photometry shows
that ZTF 21aagppzg was also significantly brighter in NIR than in the optical.
Particularly, at late times when the transient has faded below ZTF detection
limits in the _r_ -band ($>21$ mag), it continues to be detected at $\approx$
17 mag in the K band (see Fig. 1). We stack the ZTF forced photometry prior to
the outburst in 5-day bins and recover some archival detections. The first
detection in _r_ band is $\approx 1040$ days prior to peak with
m${}_{r}=22.3\pm 0.2$. The transient was detected again at four epochs in the
_r_ and _g_ bands between 400 and 300 days before peak, at roughly constant
magnitudes of m${}_{r}=22.4\pm 0.3$ and m${}_{g}=22.5\pm 0.3$. Finally, it is
detected again 95 days before peak at m${}_{r}=21.8\pm 0.3$, brightens to
m${}_{r}=20.9\pm 0.2$ 65 days before peak and fades back to m${}_{r}=21.9\pm
0.3$ mag at 27 days before peak. It is also detected in the _i_ band during
this time period, with m${}_{i}=21.0\pm 0.3$ mag.

Our spectroscopic coverage comprises four optical spectra at $-5$, +6, +34 and
+54 days since peak and three NIR spectra at +63, +301 and +395 days since
peak. The two early-time optical spectra are characterized by a hot blue
continuum with strong Balmer emission lines. The H$\alpha$ emission line has
$v_{\rm{FWHM}}\approx 500-600$ km s-1. The H$\beta$ line profile appears to be
a superposition of a broad component with a narrow component, however our
spectral resolution is not sufficient to distinguish between the two. These
spectra do not show the Ca II NIR triplet lines. The third optical spectrum
has lower resolution and a lower signal-to-noise ratio (S/N). It shows a
reddened continuum, with H$\alpha$ being the only prominent feature. The final
optical spectrum was obtained two months post peak, and shows a reddened
continuum. The strength and velocity of the Balmer emission decreased, the
H$\alpha$ line developed a double-peaked profile and the H$\beta$ is not
detected. This spectrum also shows weak Ca II NIR triplet absorption lines,
along with a forest of metallic absorption lines. The NIR spectrum at +63 days
shows hydrogen emission lines with some metallic absorption lines. Our two
final late-time NIR spectra show strong molecular absorption features of TiO,
VO and H2O.

Similar to ZTF 21aancgbm, we can use scaling relations to determine the ejecta
masses. We estimate the median luminosity on the red plateau
L${}_{\rm{pl}}\approx 1.6\times 10^{40}$ erg s-1 and a plateau duration
t${}_{\rm{pl}}\approx 180$ days. Using v${}_{E}\approx 500$ km s-1 and Eq. 2
gives the recombining ejecta mass M${}_{\rm{ej}}\approx 10$ M⊙, although the
estimate is very sensitive to the assumed ejecta velocity. Similar to ZTF
21aancgbm, the recombination alone is not sufficient to explain the luminosity
of the plateau, and Eq. 3 implies interaction with pre-existing mass
M${}_{\rm{pre}}\approx 0.2$ M⊙. Pastorello et al. (2022) discuss archival
_HST_ and ground-based imaging of this transient, and the properties of the
putative progenitor. We note that in addition to the data presented in their
paper, this transient also has archival _Spitzer Space Telescope_ /IRAC
imaging from 2007-12-27. We detect a marginal source at the location of the
transient with m${}_{3.6}=20.48\pm 0.16$ mag and m${}_{4.5}=19.79\pm 0.21$ mag
(Vega system). We leave a more detailed analysis of this LRN and its
progenitor properties to a future study.

6\. ZTF 21acpkzcc (AT 2021aess) is the most luminous LRN in our sample, with
peak M${}_{\rm{r}}=-15.12\pm 0.15$. We do not identify strong Na I D in our
early time spectra, although this is possibly due to low S/N. We assume that
the extinction is dominated by the Milky Way, but caution that extinction due
to the host galaxy could increase the peak luminosity estimates for this
transient. Similar to the other LRNe described above, the lightcurve shows two
distinct peaks – a blue initial peak lasting $\approx 40$ days followed by a
reddened plateau. However, our photometric coverage stops at $\approx 50$ days
into the plateau as the transient went into solar conjunction. Similar to the
previous two LRNe, ZTF 21acpkzcc is also brighter in the NIR (by $>1$ mag)
than in the optical bands. Stacking the archival ZTF lightcurve in three day
bins shows some archival detections $\approx 70$ days before peak at
m${}_{g}=21\pm 0.3$ and m${}_{r}=21.1\pm 0.3$. Our spectroscopic coverage
comprises three optical spectra at +4, +46 and +68 days since peak and one NIR
spectrum at +54 days since peak. The early spectra shows narrow H$\alpha$ with
$v_{\rm{FWHM}}\approx 500$ km s-1, which grows weaker and narrower with time
(FWHM $<350$ km s-1 at 46 days). The +68d spectrum also shows a weak P-cygni
profile for H$\alpha$. The early time spectra also show a forest of Fe II
lines and the Ca II NIR triplet lines with P-cygni profiles. The initial blue
lightcurve peak with a red plateau together with weakening H$\alpha$ with time
and NIR excess suggest that ZTF21 acpkzcc is a LRN. The high luminosity of ZTF
21acpkzcc is similar to the LRN AT 2017jfs (Pastorello et al., 2019b),
suggesting a massive binary origin.

We note that two additional LRNe were reported in the last three years – AT
2018bwo (Blagorodnova et al., 2021) and AT 2020kog (Pastorello et al., 2021b).
AT 2020kog was missed by ZTF because it landed in the chip-gaps of the ZTF
detector. AT 2018bwo was discovered on 2018-05-22, when ZTF was in the
reference-building phase. The first ZTF visit to the field of AT 208bwo was
two months later on 2018-07-14. No alerts were generated as this field did not
have a ZTF reference image. We ran post-facto image subtractions and measured
forced PSF photometry and recover two detections of AT 2018bwo in the _r_ band
at $19.76\pm 0.08$ and 20.15$\pm 0.12$ mag on 2018-07-21 and 2018-07-24
respectively.

####  2.2.3 LRN-silver

This category includes two sources that do not show all hallmarks of a LRN,
but resemble LRNe in several aspects. Their lightcurves are plotted in Fig. 1
and their optical and near-infrared spectra are shown in Fig. 2 and 3
respectively.

1\. ZTF 18abwxrhi (AT 2018gzz) has peak M${}_{\rm{r}}=-14.82\pm 0.17$ and
shows two pronounced lightcurve features : a blue first peak followed by a
longer lasting red peak/plateau. Our photometric data is sparse for the red
peak/plateau as the transient did not brighten significantly above the ZTF
sensitivity limits. However, the lightcurve evolution inferred from the
available data is strikingly similar to the LRNe in the gold sample.
Additionally, a spectrum taken during the first blue peak shows narrow,
marginally resolved Balmer emission lines with $v_{\rm{FWHM}}\approx 300$ km
s-1 ruling out a supernova origin, narrow, unresolved Ca II NIR triplet lines
with P-Cygni profiles and narrow Ca II H & K absorption lines. We do not
detect Na I D in this spectrum, and hence assume negligible host extinction.
There is no spectroscopic coverage at late times. Given these similarities
with LRNe, ZTF 18abwxrhi is most likely a LRN, and we include it in the LRN-
silver category.

2\. ZTF 21aaekeqd (AT 2021afy) is located on the outskirts of the galaxy UGC
10043. While Pastorello et al. (2022) classify this transient as a LRN, their
late-time spectra do not show obvious molecular absorption features (e.g. as
those seen in ZTF 21aancgbm). We also do not identify similar molecular
features in any of our spectra. As noted in Pastorello et al. (2022), the
lightcurve differs from other LRNe with similar luminosities. For these
reasons, we include ZTF 21aaekeqd in our LRN-silver sample. It is possible
that obvious molecular features appear at later times, where spectroscopic
coverage does not exist.

The transient has a 100-day long lightcurve with two low contrast peaks and is
detected only in _r_ and _i_ bands by ZTF. In our earliest spectrum, we detect
Na I D absorption with equivalent width $1.8\pm 0.6$ Å , consistent with
Pastorello et al. (2022). This corresponds to E(B–V)${}_{\rm{host}}\approx
0.28\pm 0.10$ mag, assuming that the interstellar medium is alone responsible
for the Na I D absorption. However, we caution that this is unlikely, given
the remote location of the transient in the host. It is possible that the
sodium absorption originates in circumstellar dust around the progenitor of
the explosion, in which case the extinction estimate will be incorrect
(Poznanski et al., 2012). Accounting for the Galactic component, we adopt a
total E(B–V)$=0.33\pm 0.10$ mag. With this, the transient reaches
M${}_{\rm{r,peak}}=-13.95\pm 0.16$, and is one of the brighter members of our
sample. We obtained an epoch of _J-_ band imaging at +60 days since peak with
$J-r\approx 1$ mag, similar to other LRNe.

Our spectroscopic coverage comprises 3 optical spectra at phases of +33 d, +89
d, +114 d and one NIR spectrum at +92 d since first peak. The +33 day spectrum
shows a reddened continuum with narrow H$\alpha$ ($v_{\rm{FWHM}}\approx 650$
km s-1) and Ca II NIR triplet in absorption. Of the three Ca II triplet lines,
we detect only the 8542 and 8662 Å absorption lines. This is likely because
the transition probability for the 8498 Å line is $\approx 10$ times smaller
than for the other two. Notably, the absorption lines are unresolved, with
v${}_{\rm{FWHM}}\leq 200$ km s-1 (instrumental resolution in this wavelength
range is v${}_{\rm{inst}}\approx 250$ km s-1, measured from sky emission
lines). This velocity is much lower than the H$\alpha$ photospheric velocity
at this phase ($\approx 650$ km s-1). These absorption lines likely originate
in a dense, slow-moving shell of circumstellar medium outside the photosphere,
that was likely ejected prior to the explosion possibly during the CE phase.
The +89 day spectrum shows a more reddened continuum with slower, marginally
resolved H$\alpha$ ($v_{\rm{FWHM}}\approx 400$ km s-1) and narrow H$\beta$
($v_{\rm{FWHM}}\approx 300$ km s-1). The Ca II NIR triplet lines are now seen
as a superposition of an emission component with v $\approx 500$ km s-1, and a
central narrow absorption component (see Fig. 5). A possible explanation for
this is that the ejecta have crashed into the CSM at this epoch, and the
resulting shock has swept up only part of the CSM. A photosphere forms at the
shock interface from where the emission lines originate (Ca II predominantly
excited by collisions). The narrow, weak absorption component originates from
the unshocked CSM shell lying outside the photosphere. The +80 day NIR
spectrum shows similar narrow hydrogen emission lines. The spectrum also shows
a weak broad feature in the _H_ band, which is similar to the H2O absorption
seen in ZTF 21aagppzg. The final optical spectrum at +113 d shows a very weak
continuum, but extraordinarily strong H$\alpha$ (v${}_{\rm{FWHM}}\approx 300$
km s-1) and strong, unresolved H$\beta$ (v${}_{\rm{FWHM}}<400$ km s-1). The Ca
II NIR triplet is seen purely in emission. This suggests that the shock has
swept up all the CSM. The Balmer decrement in this spectrum is $\beta\approx
7$, supporting that the emission originates in an interaction-dominated
region. The absorption to emission transition of the Ca II line profiles
suggests that there is a dense, slow-moving shell of CSM around the
progenitor. None of the other LRNe in our sample show such a transition. The
late-time spectrum with very strong emission lines is unlike the late-time
optical spectra of other LRNe in our sample (e.g. ZTF 21aancgbm at 360 days),
that show strong molecular absorption bands.

Figure 5: Evolution of Ca II line profiles of ZTF 21aaekeqd. In the earliest
spectrum (+32 d, black), the lines are seen purely in absorption, and likely
originate from a shell of slow-moving CSM around the binary. In the second
spectrum, the profile has transitioned to emission superposed with a narrow
absorption component. This is likely because the ejecta have crashed into the
CSM, and swept up only part of the CSM. The shocks in the ejecta produce the
emission, while the absorption comes from the unshocked, dense CSM shell
outside the photosphere. In the final optical spectrum, the line profiles are
pure emission, suggesting that all of the CSM has been swept up by the ejecta.

####  2.2.4 LRN-bronze

This category includes three sources - ZTF 18aajqkmr, ZTF 20abjgdec and ZTF
21aabfwwl that show multiple peaks in their lightcurves but do not have
spectroscopic coverage (see Fig. 1). These transients have peak absolute
magnitudes of $-15.36$, $-14.37$ and $-15.72$, respectively. ZTF 21aabfwwl was
initially classified as a Type II SN (Hinkle, 2021), but the spectrum
available on TNS is noisy and no H lines are clearly visible. We list these
three transients as candidate LRNe.

Table 3: Photometric properties of LRN and ILRTsa

Name | DMb | E(B–V)c | mr,peak | Mr,peak | MJDpeak | Lpeak
---|---|---|---|---|---|---
| (mag) | (mag) | (mag) | (mag) | (d) | (erg s-1)
ZTF18acbwfza | $31.60$ | 0.250 | $18.47\pm 0.02$ | $-13.82\pm 0.15$ | $58430.9\pm 0.2$ | $9.3_{-0.3}^{+0.3}\times 10^{40}$
ZTF19adakuot | $24.45$ | 0.055 | $15.00\pm 0.01$ | $-9.60\pm 0.15$ | $58891.6\pm 0.1$ | $2.0_{-0.1}^{+0.1}\times 10^{39}$
ZTF20aawdwch | $28.97$ | 0.093 | $17.79\pm 0.02$ | $-11.43\pm 0.15$ | $58963.0\pm 1.2$ | $>1.2\times 10^{40}$
ZTF21aagppzg | $29.90$ | 0.020 | $16.45\pm 0.01$ | $-13.50\pm 0.15$ | $59258.9\pm 0.1$ | $7.9_{-0.1}^{+0.1}\times 10^{40}$
ZTF21aancgbm | $29.43$ | 0.261 | $16.28\pm 0.03$ | $-13.86\pm 0.15$ | $59252.9\pm 0.5$ | $>8.9\times 10^{40}$
ZTF21acpkzcc | $32.09$ | 0.032 | $17.05\pm 0.03$ | $-15.12\pm 0.15$ | $59545.5\pm 0.2$ | $3.3_{-0.2}^{+0.2}\times 10^{41}$
ZTF18abwxrhi | $33.70$ | 0.047 | $19.33\pm 0.06$ | $-14.50\pm 0.16$ | $58386.2\pm 0.9$ | $1.9_{-0.3}^{+1.5}\times 10^{41}$
ZTF21aaekeqd | $32.87$ | 0.330 | $19.82\pm 0.06$ | $-13.95\pm 0.16$ | $59229.2\pm 1.6$ | $6.0_{-4.6}^{+6.4}\times 10^{41}$
ZTF18aajgqmr | $35.00$ | 0.018 | $19.69\pm 0.09$ | $-15.36\pm 0.17$ | $58969.7\pm 1.0$ | $3.3_{-0.4}^{+0.7}\times 10^{41}$
ZTF20abjgdec | $33.78$ | 0.141 | $19.80\pm 0.06$ | $-14.37\pm 0.16$ | $59045.6\pm 2.1$ | $2.4_{-1.2}^{+13.3}\times 10^{41}$
ZTF21aabfwwl | $33.99$ | 0.043 | $18.39\pm 0.05$ | $-15.72\pm 0.16$ | $59239.5\pm 1.8$ | $5.2_{-0.7}^{+1.1}\times 10^{42}$
ZTF18acdyopn | $33.92$ | 0.064 | $19.76\pm 0.11$ | $-14.33\pm 0.19$ | $58426.8\pm 2.4$ | $2.2_{-1.0}^{+21.7}\times 10^{41}$
ZTF19aadyppr | $29.45$ | 0.705 | $16.65\pm 0.01$ | $-14.73\pm 0.15$ | $58534.7\pm 0.5$ | $2.3_{-0.1}^{+0.1}\times 10^{41}$
ZTF19acoaiub | $31.83$ | 0.038 | $17.31\pm 0.02$ | $-14.62\pm 0.15$ | $58799.1\pm 0.1$ | $2.0_{-0.2}^{+0.2}\times 10^{41}$
ZTF19acdrkbh | $34.33$ | 0.051 | $19.85\pm 0.12$ | $-14.62\pm 0.20$ | $58764.3\pm 1.9$ | $1.8_{-0.4}^{+0.9}\times 10^{41}$
ZTF19aagqkrq | $30.76$ | 0.200 | $17.58\pm 0.03$ | $-13.72\pm 0.15$ | $58538.3\pm 1.1$ | $8.0_{-0.4}^{+0.5}\times 10^{40}$
ZTF21aclzzex | $33.89$ | 0.019 | $18.26\pm 0.06$ | $-15.68\pm 0.16$ | $59528.6\pm 1.7$ | $5.2_{-1.2}^{+3.7}\times 10^{41}$
ZTF21abtduah | $33.22$ | 0.022 | $<18.31$ | $<-14.96\pm 0.15$ | $<59522.5$ | $>1.3\times 10^{41}$
ZTF21abfxjld | $33.43$ | 0.106 | $<19.51$ | $<-14.21\pm 0.20$ | $<59359.8$ | $>8.0\times 10^{40}$
ZTF19aavwbxs | $33.26$ | 0.038 | $18.92\pm 0.08$ | $-14.44\pm 0.17$ | $58644.7\pm 8.1$ | $2.2_{-0.3}^{+0.6}\times 10^{41}$
ZTF18acrygkg | $33.35$ | 0.036 |  $<19.31$. | $<-14.14\pm 0.16$ | $<58447.5$ |

  * •

$a$ : The two classes LRN and ILRT are separated by a horizontal line.

  * •

$b$ : The distance moduli have uncertainties of 0.15 mag and are taken from
NED.

  * •

$c$ : Galactic extinction values are taken from Schlafly & Finkbeiner (2011);
host extinction is calculated as described in the text.

####  2.2.5 ILRT-gold

This category includes six sources that we spectroscopically classify as
ILRTs. Their lightcurves are shown in Fig. 6. We calculate the distances and
extinction due to the Milky Way as was done for the LRNe (see Sec. 2.2.2). It
is challenging to estimate the host galaxy extinctions because ILRTs have
extremely dusty progenitors, and often exhibit variable Na I D originating in
outflows (Cai et al. 2021; Smith et al. 2009, also see discussion of ZTF
19acoaiub below). Instead, we use the peak optical $g--r$ colors of ILRTs to
estimate the host extinction, similar to Humphreys et al. (2011); Smith et al.
(2009); Jencson et al. (2019). The spectra of ILRTs at peak show F-type
absorption features, suggesting T $\approx 7500$ K. Cai et al. (2021) find
that the ILRTs in their sample have peak B$-$V colors in the range $0.2-0.4$
mag, consistent with this interpretation. We use the peak colors of the ILRTs
in our sample to estimate the value of E(B$-$V)host required to bring the
colors in this range. We estimate a non-negligible extinction for two ILRTs in
our sample – E(B$-$V) $\approx 0.7$ for ZTF 19aadyppr (consistent with Jencson
et al. 2019) and E(B$-$V) $\approx$ 0.2 for ZTF 19aagqkrq. For the other
transients, we assume the extinction to be dominated by the Galactic
component. We calculate pseudo-bolometric luminosities by fitting blackbodies
to the available data. Table 3 lists the derived photometric properties of the
ILRTs. Our optical and NIR spectra for these transients are shown in Figs. 7
and 8. Similar to the LRNe, we derive line velocities by fitting Lorentzian
line profiles and list the derived values in Table 4. We briefly discuss the
properties of the transients here.

Two of these transients – ZTF 19aadyppr and ZTF 21aclzzex have spectroscopic
coverage extending to late times. Of these, ZTF 19aadyppr is in the galaxy M
51 and has been studied in detail by Jencson et al. (2019), who identified its
red, dusty progenitor. The object shows a single-peaked red lightcurve, and
its spectra show narrow H$\alpha$ and [Ca II] emission, characteristic of
ILRTs.

ZTF 21aclzzex is the brightest ILRT in our sample, with peak
M${}_{r}=-15.68\pm 0.16$ mag. Our lightcurve coverage is sparse and noisy, but
the available data shows indications that the transient is red, and possibly
has multiple peaks. However, our spectroscopic coverage extends to 163 days
since peak, and resembles the evolution of ILRTs. An early time spectrum at 9
days since peak shows a blue continuum with narrow H$\alpha$, H$\beta$, Ca II
and [Ca II] emission. The spectrum also shows Ca II H & K absorption. The next
optical spectrum obtained at 84 d since peak shows a reddened continuum with
narrow H$\alpha$, Ca II, [Ca II] emission and Ca II H & K absorption. [O I] is
detected as a weak emission line. The 118 d optical spectrum shows similar
features, except the [O I] has become stronger. Similar [O I] emission was
observed in the ILRT AT 2013la (Cai et al., 2021). The 134 d NIR spectrum
shows strong, narrow hydrogen emission lines, He I and O I emission. Although
the lightcurve is not informative enough to classify the transient, the
spectroscopic evolution is strikingly similar to several ILRTs, especially
with [Ca II] emission seen consistently in all spectra. For this reason, we
classify it as an ILRT.

The other four transients have only early-time spectroscopic coverage.
Analogous to the other ILRTs, they all show narrow H$\alpha$ and [Ca II]
emission in their spectra. We note that while the LRN AT 2018hso also showed
[Ca II] emission in its early spectra, it also had two pronounced peaks in its
lightcurve. None of these four transients show multiple peaks and are not AT
2018hso-like LRNe. We thus classify them as ILRTs based on narrow H$\alpha$,
[Ca II] emission and lack of multi-peaked lightcurves.

Of these four, ZTF 19acoaiub (AT 2019udc) and ZTF 19aagqkrq (AT 2019ahd) have
the best sampled lightcurves. ZTF 19acoaiub is located in NGC 718 and has peak
M${}_{r}=-14.68\pm 0.04$ mag, a relatively fast declining single-peaked
lightcurve. The ZTF lightcurve also samples the pre-peak rise. 7 days before
peak, the transient was extremely red with $g-r\approx 0.8$ mag. As it
brightens, the transient also evolves to bluer colors of $g-r\approx 0.4$ mag
five days before peak and $g-r\approx 0.2$ mag at peak. The transient then
declines at a rate of $\approx$0.03 mag day-1 for the next 60 days as it
evolves back to redder colors. Our only optical spectrum was obtained 7 days
before the peak and shows strong H$\alpha$ emission with
v${}_{\rm{FWHM}}\approx 1300$ km s-1. This spectrum also shows narrow Ca II
and [Ca II] emission features, similar to several other ILRTs. This pre-peak
spectrum shows very strong Na I D absorption with EW $\approx 4.8\pm 0.7$
Åconsistent with its pre-peak red colors. A likely explanation for this
behaviour is that the progenitor of ZTF 19acoaiub was dust enshrouded. This
circumstellar dust was destroyed by the explosion, causing the transient to
evolve to bluer colors as it brightened. This transient demonstrates the issue
with using early-time Na I D features to estimate the host extinction.

ZTF 19aagqkrq (AT 2019ahd) has peak M${}_{r}=-13.72\pm 0.15$ mag and has a
blue color up to a few days before peak but rapidly transitions to red colors.
Out spectroscopic coverage comprises two optical spectra obtained on
successive nights at peak and 1 day post-peak. Both spectra show H$\alpha$
emission with v${}_{\rm{FWHM}}\approx 700$ km s-1 and strong Ca II and [Ca II]
emission lines.

The remaining two – ZTF 18acdyopn and ZTF 19acdrkbh – have relatively sparse
lightcurve sampling. ZTF 18acdyopn has a peak absolute magnitude
M${}_{r}=-14.33\pm 0.19$ mag and declines by 1.5 mag in the _r_ band in 80
days. Although our lightcurve does not sample the peak, the available data
shows that the transient had red colors a few days post-peak. An optical
spectrum taken five days since peak shows narrow hydrogen Balmer emission
lines (v${}_{\rm{FWHM}}\approx 300$ km s-1), [Ca II] , Ca II H & K as well as
Ca II NIR triplet emission lines. Similarly, ZTF 19acdrkbh has peak
M${}_{r}=-14.62\pm 0.15$, and was detected at the threshold of ZTF
sensitivity, and has $g-r\approx 0.6$ mag at peak. An optical spectrum at +19
days since peak shows narrow H$\alpha$ (v${}_{\rm{FWHM}}\approx 600$ km s-1)
and possible Na I D absorption, similar to other ILRTs.

Table 4: Spectroscopic properties of LRN and ILRTs

Name | MJD | Phase | v${}_{\rm{H}\alpha,\rm{FWHM}}^{a}$ | v${}_{\rm{H}\beta,\rm{FWHM}}^{a}$ | $\beta$
---|---|---|---|---|---
| (d) | (d) | (km s-1) | (km s-1) |
|  |  | LRNe |  |
ZTF18acbwfza | 58424 | –7.1 | 510 $\pm$ 60 |  |
ZTF18acbwfza | 58424 | –7.1 | 450 $\pm$ 30 | 750 $\pm$ 60 | 2.1 $\pm$ 0.1
ZTF18acbwfza | 58432 | +0.9 | 350 $\pm$ 40 | 760 $\pm$ 120 | 2.2 $\pm$ 0.2
ZTF18abwxrhi | 58379 | –9.3 | 280 $\pm$ 40 | 250 $\pm$ 120 | 3.8 $\pm$ 0.7
ZTF21aaekeqd | 59262 | +33.4 | 650 $\pm$ 20 |  |
ZTF21aaekeqd | 59318 | +89.3 | 340 $\pm$ 30 | 260 $\pm$ 70 | 2.1 $\pm$ 0.2
ZTF21aaekeqd | 59343 | +113.8 | 300 $\pm$ 20 |  $<$ 370 | 7.6 $\pm$ 0.6
ZTF21aagppzg | 59253 | –5.9 | 490 $\pm$ 60 | 760 $\pm$ 100 | 2.5 $\pm$ 0.2
ZTF21aagppzg | 59265 | +6.1 | 420 $\pm$ 40 | 700 $\pm$ 80 | 2.7 $\pm$ 0.2
ZTF21aagppzg | 59313 | +54.1 | 500 $\pm$ 60 |  |
ZTF21aancgbm | 59313 | +60.1 | $<350$ |  |
ZTF21aancgbm | 59613 | +360.1 | 460 $\pm$ 40 |  |
ZTF21acpkzcc | 59549 | +4.6 | 470 $\pm$ 50 | 540 $\pm$ 70 | 3.7 $\pm$ 0.3
ZTF21acpkzcc | 59591 | +46.6 |  $<$ 340 |  |
ZTF21acpkzcc | 59613 | +68.6 |  $<$ 300 |  |
|  |  | ILRTs |  |
ZTF18acdyopn | 58432 | +5.1 | 300 $\pm$ 40 | 630 $\pm$ 120 | 3.3 $\pm$ 0.4
ZTF19aadyppr | 58509 | –25.7 | 330 $\pm$ 50 |  $<$ 250 | 2.5 $\pm$ 0.3
ZTF19aadyppr | 58526 | –8.7 | 640 $\pm$ 80 | 680 $\pm$ 180 | 2.4 $\pm$ 0.4
ZTF19aadyppr | 58537 | +2.2 | 470 $\pm$ 170 | 2400 $\pm$ 850 | 0.9 $\pm$ 0.3
ZTF19aadyppr | 58549 | +14.3 | 530 $\pm$ 120 |  |
ZTF19aadyppr | 58558 | +23.2 | 710 $\pm$ 180 |  |
ZTF19aadyppr | 58586 | +51.3 | 400 $\pm$ 70 |  |
ZTF19aadyppr | 58616 | +81.3 | 330 $\pm$ 40 |  |
ZTF19acoaiub | 58792 | –7.1 | 1250$\pm$ 300 | 2000 $\pm$ 850 | 3.4 $\pm$ 1.1
ZTF19acdrkbh | 58783 | +18.7 | 590 $\pm$ 80 |  |
ZTF19aagqkrq | 58525 | –13.4 | $<850$ | 1000 $\pm$ 200 | 2.3 $\pm$ 0.3
ZTF19aagqkrq | 58526 | –12.4 | 670 $\pm$ 50 | 2000 $\pm$ 500 | 1.6 $\pm$ 0.2
ZTF21aclzzex | 59530 | +1.9 | 670 $\pm$ 60 | 1200 $\pm$ 180 | 3.5 $\pm$ 0.5
ZTF21aclzzex | 59605 | +76.9 | 500 $\pm$ 60 | 380 $\pm$ 110 | 5.5 $\pm$ 1.9
ZTF21aclzzex | 59639 | +110.3 | 550 $\pm$ 40 | 300 $\pm$ 70 | 7.9 $\pm$ 0.9
ZTF21abtduah | 59524 | +1.5 | 1170 $\pm$ 100 |  |
ZTF21abtduah | 59549 | +26.5 | 1290 $\pm$ 100 |  |
ZTF21abtduah | 59613 | +90.5 | 870 $\pm$ 30 | 690 $\pm$ 70 | 8.4 $\pm$ 0.6
ZTF21abtduah | 59641 | +118.5 | 770 $\pm$ 30 | 780 $\pm$ 60 | 10.6 $\pm$ 0.6
ZTF21abfxjld | 59401 | +41.7 |  $<$ 290 |  $<$ 250 | 3.6 $\pm$ 0.5
ZTF21abfxjld | 59440 | +80.2 |  $<$ 270 |  $<$ 260 | 4.6 $\pm$ 0.4

  * •

The velocities have been corrected for instrumental resolutions listed in
Table 2. Upper limits are reported for unresolved lines.

####  2.2.6 ILRT-silver

This category includes two sources – ZTF 21abtduah and ZTF 21abfxjld – that
show luminosities and spectral evolution broadly similar to ILRTs, but do not
have [Ca II] emission. Although [Ca II] emission in ILRTs is a sign of
interaction with the surrounding circumstellar material (CSM), its strength is
sensitive to the CSM density (Humphreys et al., 2011). For example, the
proposed ILRT AT 2019krl did not show Ca II emission in several of its spectra
(Andrews et al., 2021).

For both transients, our lightcurve coverage does not sample the peak, and it
is not clear whether they have multiple peaks. For ZTF 21abtduah, our
lightcurve samples the brightening and fading of the transient (see Fig. 6).
We estimate a fiducial peak time by fitting a polynomial to these points. For
ZTF 21abfxjld, the ZTF lightcurve samples the fading of the lightcurve.
However, the ATLAS _o-_ band lightcurve shows two measurements separated by 5
days that do not show significant evolution, suggesting that the transient
peaked around then. We determine the peak time by fitting a polynomial to the
ATLAS _o-_ band lightcurve. We have late-time spectroscopic coverage for both
these transients. In a spectrum taken 24 days since the (fiducial) peak, ZTF
21abtduah shows H$\alpha$ with v${}_{\rm{FWHM}}\approx 1200$ km s-1. A second
spectrum obtained at 48 days since peak shows a double-peaked H$\alpha$
profile, suggesting interaction with slow moving CSM, or absorption in an
external shell. This spectrum also shows narrow Ca II NIR triplet in emission.
The final spectrum taken at 140 days since peak shows strong H$\alpha$,
H$\beta$, Ca II NIR and O I emission lines, similar to ZTF 21aclzzex and AT
2013la (however [Ca II] lines are not seen). The H$\alpha$ line profile in
this spectrum is also double-peaked. ZTF 21abfxjld has spectra at +44d and 83
days since peak, both of which show H$\alpha$ emission with
v${}_{\rm{FWHM}}\leq 300$ km s-1, and narrow [Ca II] emission. We also have
two NIR spectra taken at +26 d and +125 d since peak. The 26 day NIR spectrum
shows narrow H emission lines. However, the 125 day spectrum shows strong but
narrow H and He absorption in the _J_ band. Such features are not seen in any
other ILRTs.

The low expansion velocities of these transients argue against a core-collapse
SN origin for them. The lack of any molecular features at late times rules out
LRNe. None of them show any significant outbursts in archival data. The nature
of these transients is not completely clear. Their spectral features point
towards CSM interaction. The lack of Ca II emission suggests that the CSM is
denser than in typical ILRTs. These transients could represent a peculiar
variety of ILRTs. For these reasons, we classify these as ILRT-silver sources.

####  2.2.7 ILRT-bronze

This category includes two sources ZTF 19aavwxbs and ZTF 18acrygkg. ZTF
19aavwxbs shows a single peak lasting 20 days in the ZTF and ATLAS lightcurve
before it went into solar conjunction. A low resolution (R$\sim 100$) spectrum
of ZTF 19aavwxbs taken with the Spectral Energy Distribution Machine (SEDM;
Blagorodnova et al. 2018; Rigault et al. 2019) spectrograph on the 60-inch
telescope at Palomar Observatory shows H$\alpha$ emission with
v${}_{\rm{FWHM}}\leq 3000$ km s-1. No other features are discernible in the
spectrum. ZTF 18acrygkg has a lightcurve lasting for 40 days in the ZTF data.
There is no spectroscopic data for ZTF 18acrygkg. It is possible that both
these transients are low-luminosity Type II SNe so we only list them as ILRT
candidates.

####  2.2.8 Ambiguous sources

Finally, we have seven sources that do not have spectroscopic coverage and the
photometric data is not enough to determine a tentative classifications. Most
of these sources are likely supernovae where the ZTF data samples the late-
time phases. The 5-$\sigma$ alert lightcurves of these transients have
durations shorter than 25 days.

Figure 6: Forced photometry lightcurves of the 10 ILRTs in our sample. The
transients in gold, silver and bronze samples are marked in parantheses with
g, s and b respectively. The ZTF-g, ZTF-r, ZTF-i, ATLAS-c and ATLAS-o band
datapoints are plotted in green, red, brown, blue and orange circles
respectively. Downward pointing triangles indicate 5-$\sigma$ upper limits.
The days are in observer frame. The lightcurves have been corrected for
extinction using the values listed in Table 3. Solid black vertical lines
indicate epochs at which the spectra were obtained. Figure 7: Optical spectra
for ILRTs presented in this paper. Figure 8: NIR spectra for ILRTs presented
in this paper.

##  3 Volumetric Rate

To estimate the volumetric rates, we simulate the ZTF survey from 2018-06-01
to 2022-02-20 with the python package simsurvey (Feindt et al., 2019) using
the ZTF pointing history and actual ZTF difference images to estimate the
limiting magnitudes of each pointing. Using template lightcurves, we then
inject LRNe and ILRTs for a range of possible rates and identify the number of
transients that would be detected by the selection criteria of our experiment.
Comparing simulations to the observed LRN/ILRT sample gives a first estimate
of the rate. This estimate is then corrected for selection effects such as the
spectroscopic completeness of the CLU experiment and the CLU galaxy catalog.

###  3.1 Template lightcurves

LRNe exhibit a dichotomy in their lightcurves. The brighter LRNe
(M${}_{r}\geq-11$) are characterized by a double peaked lightcurve, while the
lower luminosity events have a single peak and much shorter durations
(Blagorodnova et al., 2021; Pastorello et al., 2019a). All except one of the
ZTF events are brighter than $-11$ mag, and have double-peaked lightcurves
lasting for $\sim 150$ days. ZTF 19adakuot with M${}_{\rm{r,peak}}\approx-9.5$
is the least luminous event in our sample and fades quicker than any of the
other events. Owing to the different lightcurve shapes and durations of the
brighter LRNe and the fact that most of the ZTF LRNe belong to this category,
we restrict our rate analysis to events with Mr brighter than $-11$ mag.

We created an empirical LRN lightcurve template using the three well-sampled
LRNe in our sample with M${}_{\rm{r,peak}}\leq-11$ and two double-peaked LRNe
from the literature AT 2017jfs (Pastorello et al., 2019b) and AT 2020kog
(Pastorello et al., 2021b). We first normalized the _g_ and _r_ -band
lightcurves by their peak magnitude in the respective filter. We then fit a
Gaussian Process model with a radial basis function (RBF) kernel to the
normalized lightcurve. The _g_ and _r_ -template lightcurves of the LRNe are
shown in the top row of Fig. 9, and provided online.

The lightcurves of ILRTs are more homogeneous than LRNe. We construct
lightcurve templates using _g_ lightcurves of 4 ILRTs (AT 2018aes, AT 2019abn,
AT 2019udc and AT 2019ahd) and _r-_ band lightcurves of these and 4 additional
ILRTs (AT 2010dn, AT 2012jc, AT 2013la and AT 2013lb). The ILRT templates are
shown in the bottom row of Fig. 9. Both LRN and ILRT template lightcurves are
available online (Sec. 7).

Figure 9: _g_ and _r_ band lightcurve templates (green and red colors
respectively) for LRNe (top row) and ILRTs (bottom row). The solid points
depict lightcurves of transients that were used to build the templates. The
line and shaded regions show the templates and 68% uncertainties derived from
Gaussian Process fits to the transients. The templates capture the essence of
the photometric evolution of LRNe (initial blue peak + long lived second
peak/plateau) and ILRTs (single peak, red lightcurve). These templates are
available online (see Sec. 7).

###  3.2 Luminosity Function

In this paper, we have presented the first controlled sample of LRNe and ILRTs
from a systematic survey. We use this sample to calculate the luminosity
function of LRNe and ILRTs.

We restrict ourselves to all gold and silver LRNe that have peak absolute
magnitudes brighter than $-11$. Fig. 10 shows a histogram of the peak absolute
magnitudes of the events in the ZTF sample. As the events are detectable out
to different volumes (all smaller than the CLU volume limit of 200 Mpc), the
histogram needs to be volume corrected to determine an accurate luminosity
function. The volume corrected distribution of peak absolute magnitudes of
LRNe in our sample is plotted in Fig. 10 with a different color. Each event
has been weighted by $\frac{1}{\rm{V}_{\rm{max}}}$ where Vmax is the maximum
volume out to which that event can be detected ($V_{\rm{max}}\propto
10^{\frac{3}{5}(20-\rm{M_{r,\rm{peak}}})}$). The volume corrected distribution
shows a steep decline of the event rate with increasing peak luminosity. Fig.
10 also shows the distribution of the ZTF events combined with events from
literature (taken from Blagorodnova et al. 2021). The distribution of the ZTF
events is broadly consistent with that of the ZTF+literature events (although
there are significant biases associated with the literature sample). The peak-
luminosity distribution of ZTF events is well-fit by a straight line (in log-
space) with a slope $0.6\pm 0.1$. This corresponds to $\frac{dN}{dL}\propto
L^{-2.5\pm 0.3}$. This is significantly steeper than the luminosity function
derived for low luminosity (MV $>-10$) LRNe (Kochanek et al., 2014). The
implications of these differences are discussed in Sec. 4.1.

Figure 10: Distribution of the peak absolute magnitudes of LRNe (_left_) and
ILRTs (_right_) in our sample. The volume corrected ZTF sample with Poisson
errorbars is shown in red, and the volume corrected ZTF+literature sample is
shown in blue. The black line shows a linear fit to this data (in log-space).
We derive a luminosity scaling dN/dL $\propto L^{-2.5\pm 0.3}$ for LRNe and
dN/dL $\propto L^{-2.5\pm 0.5}$ for ILRTs.

Similarly, we calculate the ILRT luminosity function using the 8 gold and
silver events from our sample. Fig. 10 (right panel) shows the volume-
corrected distribution of the peak absolute magnitudes of ZTF ILRTs. We fit a
straight line with slope $0.6\pm 0.2$ to the distribution (in log-space), for
M${}_{r}<-13.5$. This corresponds to a luminosity function of
$\frac{dN}{dL}\propto L^{-2.5\pm 0.5}$. This scaling only samples the brighter
end of the ILRT luminosity function. Fig. 10 also shows the distribution of
previously known events from literature together with the ZTF sample, which
extends to lower luminosities than the ZTF sample (M${}_{r}\approx-12$). We
note that for both LRNe and ILRTs, including the bronze or excluding the
silver sample does not significantly change the derived luminosity function.

###  3.3 Sub-sample for rate estimates

We build a sub-sample from the candidates listed in Table 1 to use for rate
calculations. All sources listed as potential LBVs are naturally excluded. To
exclude the “ambiguous" transients, we introduce an additional selection
criterion – a minimum threshold of 25 days on the duration of the ZTF
lightcurve (i.e. the 5-$\sigma$ detections in _g_ or _r_ bands should span at
least 25 days). Of the remaining sources, we only include those transients
that have spectroscopic coverage (i.e. the gold and silver categories) to
obtain an estimate of the rate, as this estimate is subsequently corrected for
spectroscopic completeness. The sub-sample used for rate calculations is
marked with an asterisk in Table 1.

The LRN sub-sample used for rate estimates comprises seven out of the eight
gold and silver LRNe from Table 1. ZTF 19adakuot is excluded because of its
low luminosity (Sec. 3.2). As noted in Sec. 2.2.2, the LRNe AT 2018bwo and AT
2020kog were not detected in the ZTF alert stream. Two detections of AT
2018bwo were recovered post-facto, but it is excluded by the lightcurve-
duration criterion. AT 2020kog is excluded because it was in the chip-gaps of
the ZTF camera, an effect that is accounted for by our survey simulations. The
ILRT sub-sample comprises five out of the eight gold and silver ILRTs. The
remaining three do not satisfy the lightcurve duration criterion.

###  3.4 Volumetric Rates

The luminosity functions and template lightcurves were used to simulate LRNe
and ILRTs, and the simsurvey simulations of the ZTF survey were used to count
how many of them would be detected by our experiment. We apply the selection
criteria described in Sec. 2.1 and the lightcurve-duration criterion from Sec.
3.3 to the simulated transients. We conduct 100 iterations of simulations for
each rate to estimate the median and 1-$\sigma$ errors on the number of
transients recovered for each rate.

The top-left panel of Fig. 11 shows the number of LRNe that would be detected
by our selection criteria as a function of their volumetric rate. The top-
right panel of Fig. 11 shows a histogram of the fraction of simulations where
the number of detected simulated transients equals the observed number of
seven LRN-gold and LRN-silver events. We fit the distribution with a skewed
gaussian function to estimate the median and 68 percentile confidence limits.
Accounting for an additional poisson uncertainty associated with the seven
observed events we derive a volumetric rate of
$r_{\rm{LRN},u}=5.7^{+4.4}_{-2.7}\times 10^{-5}$ Mpc-3 yr-1.

This estimate does not account for four factors which may result in
underestimation compared to the true LRN rate – 1) the CLU experiment is
limited to 100″or 30 kpc from nucleii of galaxies and will miss farther
transients, 2) the CLU experiment is not 100% spectroscopically complete, 3)
the CLU experiment relies on the CLU galaxy catalog and is affected by its
completeness, and 4) some LRNe will be missed due to inefficiencies of the ZTF
image subtractions pipeline. First, we note that all literature events have
been discovered within 100″or 140 kpc of their respective hosts. We searched
through transients classified as part of the ZTF BTS – an all-sky, magnitude
limited survey with ZTF and did not find any additional LRNe. For this reason,
we believe that the CLU offset criterion does not have a significant effect on
the rate estimate. Second, the CLU experiment is $\approx 80\%$
spectroscopically complete for m${}_{r}<20$ mag transients. This suggests that
the completeness corrected rate is $7.1^{+5.9}_{-3.4}\times 10^{-5}$ Mpc-3
yr-1. However, the CLU completeness is a function of apparent magnitude, and
varies from 100% for m${}_{r}<18$ mag, 95% for m${}_{r}<19$ mag. To account
for this, we calculate the completeness as a function of apparent magnitude in
bins of 1 mag. For each simulation of each of our rates, we bin the simulated
transients by peak apparent magnitude, and count only the fraction of events
that would be classified based on the CLU criteria. This exercise gives a
value consistent with the simplified approach described above. This is because
a majority of the events have faint apparent magnitudes, and the (large)
uncertainties on this estimate are dominated by low number statistics.

Third, to correct for the incompleteness of the galaxy catalog, we used the
redshift completeness factor (RCF) derived from the BTS. As all events in our
sample come from starforming galaxies, we calculate the RCF for starforming
galaxies in the BTS sample as a function of redshift (z) and WISE 3.36
$\upmu$m absolute magnitude (MW1) as described in Fremling et al. (2020). We
then use the redshifts and MW1 magnitudes of the host galaxies of LRNe in our
sample and weight each event by $\frac{1}{RCF(z,M_{W1})}$ to estimate the
effect of galaxy catalog incompleteness. We find that this leads to an
underestimation of the rate by $\approx 10\%$.

Finally, the ZTF image subtraction pipeline has two possible sources of
inefficiency that are relevant for this calculation. In each science image,
the pipeline actively masks pixels that are affected by quality cuts (e.g.
saturation due to high brightness, cosmic rays, bad pixels). This introduces a
time-dependent source of incompleteness. This dynamic masking does not have a
significant effect as LRNe and ILRTs have long durations and are picked up by
the pipeline eventually. A more serious issue pertains to the reduced
efficiency of the image subtraction algorithm on bright galaxy backgrounds, as
are common for the LRNe and ILRTs in our sample. The ZTF pipeline efficiency
as a function of background brightness has not been studied to date, and this
analysis is outside the scope of this paper. We therefore caution that our
rates are possibly lower limits. Applying the corrections described above
(except pipeline efficiency), we derive a corrected rate of
$r_{\rm{LRNe}}=7.8^{+6.5}_{-3.7}\times 10^{-4}$ Mpc-3 yr-1 for LRNe.

Similarly, using the ILRT luminosity function and simsurvey simulations, we
derive an uncorrected rate $r_{\rm{ILRT,u}}=1.9^{+1.3}_{-1.0}\times 10^{-6}$
Mpc-3 yr-1 (see bottom panel of Fig. 11). Correcting for the incompleteness
effects described above gives $r_{\rm{ILRT}}=2.6^{+1.8}_{-1.4}\times 10^{-6}$
Mpc-3 yr-1.

Figure 11: _Left_ : The number of simulated LRNe (_top_) and ILRTs (_bottom_)
that pass our filtering criteria as a function of their volumetric rate.
_Right_ : The fraction of simulations where the number of simulated transients
that pass the filtering criteria LRNe equals the observed number of LRNe
(_top_) or ILRTs (_bottom_). The distributions are fit by a skewed gaussian
function, indicated as black solid curves. The vertical dashed and dotted
lines show the median and 68 percentile confidence limits of the distribution
respectively.

##  4 Discussion

###  4.1 LRNe

Kochanek et al. (2014) used three Galactic mergers to estimate the rate of low
luminosity stellar mergers with M${}_{V}\geq-10$ mag. They find that the
luminosity function of these mergers is roughly $\frac{dN}{dL}\propto
L^{-1.4\pm 0.3}$ and the rates of events brighter than
M${}_{V,\rm{peak}}=-3(-10)$ is $\sim 0.5$ (0.03) yr-1. Our ZTF sample shows
that their scaling does not extend to higher luminosities. For transients
brighter than M${}_{r,\rm{peak}}=-11$, the luminosity function drops at a much
steeper rate ($\frac{dN}{dL}\propto L^{-2.5}$), suggesting a broken power-law
luminosity function for LRNe. Fig. 12 shows the LRNe rate as a function of
peak absolute magnitude derived from our ZTF sample and the Kochanek et al.
(2014) scaling. To convert the Galactic rate measurements from Kochanek et al.
(2014) to volumetric rates, we follow Howitt et al. (2020) and assume that the
LRN rate scales with star-formation. We use a star-formation rate of 2 M⊙ yr-1
for the Milky Way (Licquia & Newman, 2015) and an average cosmic star-
formation rate of 0.015 M⊙ yr-1 (Madau & Dickinson, 2014). The ZTF and
Kochanek et al. (2014) rate estimates diverge at high luminosities. The
volumetric rate of LRNe with brighter than M${}_{r}=-11$ ($-13$) derived from
the ZTF sample is lower by a factor of $\approx 5$ (100) than that
extrapolated from the Kochanek et al. (2014) scaling.

Figure 12: The rate of LRNe brighter than a given absolute magnitude as
determined from our ZTF sample (blue), the Galactic sample of Kochanek et al.
(2014) sample (green) and binary population synthesis models of Howitt et al.
(2020) (black line). The Kochanek et al. (2014) sample was restricted to
$-10\leq$M${}_{V}\leq-4$, while the ZTF sample is restricted to
$-16\leq$M${}_{r}\leq-11$. The green dashed-line indicates the Galactic rate
extrapolation to brighter luminosities. It is evident that the Galactic
scaling overpredicts the observed ZTF rate by several orders of magnitude. The
steeper drop of the LRN rate at higher luminosities is also seen in the BPS
models. The BPS models underpredict the brightest (M${}_{r}\leq-13$) rate of
LRNe, which could be attributed to specific assumptions about CE physics in
the models. The pink shaded regions indicate the constraints on the rates of
BNS, NSBH and BBH mergers as measured by LIGO (The LIGO Scientific
Collaboration et al., 2021a). The rates of the brightest LRNe are consistent
with a significant fraction of them being progenitors of these compact merging
systems.

A steeper luminosity function at the brighter end has also been predicted by
binary population synthesis models (Howitt et al., 2020). They follow the
binary evolution of a population of binary systems with masses drawn from a
Kroupa IMF and a binary fraction of unity, and find that 45% of the simulated
binaries undergo some form of unstable mass transfer. 38% of these binaries
result in stellar mergers while the remaining 62% result in CE ejections.
Qualitatively similar results were also obtained by the population synthesis
study of Politano et al. (2010), although they focused on the remnants of CEE
rather than the associated transients. Howitt et al. (2020) used analytical
expressions to approximate lightcurves associated with their simulated mergers
and CE ejections, and determined the Galactic rate of LRNe as a function of
their peak luminosity. Fig. 12 also shows the volumetric LRN rate from these
BPS simulations as a function of peak magnitude. We derive the volumetric rate
using the Galactic and average cosmic star-formation rates as described above.
As noted by Howitt et al. (2020), the BPS rate agrees with the Kochanek et al.
(2014) value for low luminosities, but diverges for M${}_{\rm{bol}}\leq-10$.
The steep decline in the LRN rate seen in the BPS simulations is consistent
with the rates derived from our ZTF sample. However, we note that the BPS
simulations underpredict the rates for LRNe with M${}_{r}<-13$. This could be
a result of several assumptions about the LRN lightcurves, binary populations
or CE physics used in the BPS simulations. Most importantly, Howitt et al.
(2020) assumed that the LRN lightcurve is powered solely by hydrogen
recombination and used analytical scaling relations from Ivanova et al.
(2013b) to estimate a LRN lightcurve. However, as noted in their analysis,
this model is unable to reach the luminosities of the highest luminosity LRNe.
Similar lightcurve modeling by Matsumoto & Metzger (2022) also shows that
hydrogen recombination alone cannot explain the lightcurves of the highest
luminosity LRNe. Additionally, hydrogen recombination is believed to power the
plateau in LRNe, and not the initial blue peak (which is used for our and
Kochanek et al. 2014 rate calculation). Using the recombination-powered
lightcurve model thus underpredicts the LRN rate at the high luminosity end.
More accurate models of LRN lightcurves are required to reconcile the
predicted rate with the observed rate. Several other parameters about binary
populations and CE physics can also contribute to the observed discrepancy.
For example, a uniform binary fraction was assumed in the simulations, but the
binary fraction increases with stellar mass (Moe & Di Stefano, 2017). This
would mean the number of massive binaries is higher, which would produce
additional LRNe at the bright end.

The broken power-law shape has interesting implications for our sample of
LRNe. Observations as well as theoretical models of LRNe predict that the peak
luminosities and durations of LRNe directly correlate with their progenitor
masses (Kochanek et al., 2014; Blagorodnova et al., 2021; Ivanova et al.,
2013a; Matsumoto & Metzger, 2022; Cai et al., 2022). Using the relation
$L\propto M^{-2.2\pm 0.3}$ from Cai et al. (2022), our luminosity scaling
implies a mass function of $\frac{dN}{dM}\propto M^{-4.3\pm 1.1}$, different
from standard IMF models. Kochanek et al. (2014) found that the lower
luminosity Galactic LRNe have progenitors consistent with the stellar IMF. An
interesting possibility to explain this difference is to postulate that the
low luminosity Galactic events are mergers while the more luminous
extragalactic events are CE ejections. For a binary system with a given
primary mass, the associated LRN is brighter and longer lived if it undergoes
complete CE ejection rather than a merger where only a small fraction of the
envelope is ejected. From their simulations, Howitt et al. (2020) find that
the bright LRNe (M${}_{\rm{bol}}\leq-10$) result almost exclusively from
envelope ejections, while mergers result in lower luminosity transients. The
broken power law would then suggest that the luminous CE ejections are much
rarer than the less luminous stellar mergers. The range of peak luminosities
and durations of the ZTF sample events presented here is consistent with the
CE ejections in Howitt et al. (2020). Thus in this picture, most if not all of
the events in the ZTF sample analyzed here could be CE ejections. In this
case, our derived rate would represent the rate of CE ejections in massive
binaries – an important step in the formation of double compact objects (DCOs,
Vigna-Gómez et al. 2020). It is interesting to compare our rate to the rate of
DCO mergers detected by LIGO. The LIGO Scientific Collaboration et al. (2021b)
determined the volumetric rate of binary neutron star (BNS), neutron star-
black hole (NSBH) and binary black hole (BBH) mergers as $10-1700$ Gpc-3 yr-1,
$7.8-140$ Gpc-3 yr-1 and $17-44$ Gpc-3 yr-1 respectively. The shaded pink
regions in Fig. 12 indicate these DCO merger rates. The plot shows that the
brightest LRNe are consistent with a significant fraction of them being
progenitors of DCO mergers.

Finally, we note another possible source of bias that could affect the LRN
rate determined here. Pejcha et al. (2017) predict a population of LRNe
originating in mergers involving giant primaries that should be completely
dust enshrouded, and emit most of their radiation at IR wavelengths. MacLeod
et al. (2022) also show that dust formation in pre-merger outflows could
obscure the binary system, causing the resulting LRNe to be observable only at
IR wavelengths. Some of the IR-only transients, dubbed SPRITES, that were
discovered by the _Spitzer Space Telescope_ and had no optical counterparts
are potential examples of such dust-enshrouded LRNe (Kasliwal et al., 2017).
Searches for LRNe at infrared wavelengths are required to probe this dust-
enshrouded population of LRNe. Upcoming NIR time-domain surveys such as the
Wide-field Infrared Transient Explorer (WINTER, Lourie et al. 2020) at the
Palomar Observatory and Dynamic REd All-sky Monitoring Survey (DREAMS, Soon et
al. 2020) at the Siding Springs Observatory that are slated to commence
operations in the second half of 2022 will help achieve this. Targeted surveys
of nearby galaxies with these NIR telescopes will help discover and study IR-
only LRNe, and shed light on the complete LRN landscape. Additionally, as all
LRNe are brighter and longer lived at NIR wavelengths than the optical, the
NIR surveys will also increase the population of optically-selected LRNe
similar to those presented in this paper. Of particular importance will be
additional discoveries of lower luminosity LRNe
($-9.5>\rm{M}_{\rm{r,peak}}>-11$) – a luminosity range that has not been
probed by our sample as they have much shorter optical lightcurves and can
lack the early blue optical peak seen in their brighter counterparts
(Blagorodnova et al., 2021). The upcoming NIR surveys will thus provide an
unbiased and more precise measurement of the LRN luminosity function and
volumetric rate.

###  4.2 ILRTs

We derive an ILRT rate of $\rm{R}_{<-13.5}\approx 2.6\times 10^{-6}$ Mpc-3
yr-1 for ILRTs that are more luminous than M${}_{r}=-13.5$ mag. This rate is
smaller than the LRN rate by two orders of magnitude, but we note that the
luminosity threshold of our ILRT sample is brighter than that of our LRN
sample. We cannot constrain the luminosity function of ILRTs with luminosities
lower than M${}_{r}=-13.5$, as none of our events lie in this luminosity
range. In the literature, there are four ILRTs with
$-12\geq\rm{M}_{r}\geq-13.5$, all discovered long before the start of ZTF (Cai
et al., 2021). Assuming our luminosity function extends to
M${}_{r}\approx-12$, the total rate of ILRTs is $\rm{R}_{<-12}\approx 2\times
10^{-5}$ Mpc-3 yr-1. Additional discoveries of ILRTs in this low luminosity
range are required to map out the lower end of the ILRT luminosity function.

Cai et al. (2021) derived a lower limit on the ILRT rate of $9\times 10^{-6}$
Mpc-3 yr-1. They used a sample of 12 ILRTs discovered in the last 12 years
within 30 Mpc to estimate the ILRT rate, but their analysis did not include a
luminosity function or completeness of the surveys. Additionally, their sample
included two events with lower luminosities than our threshold, and their
lower limit is consistent with the rough estimate $\rm{R}_{<-12}$ above.
Comparing to the core-collapse supernova rate of $\approx 1.01\times 10^{-4}$
Mpc-3 yr-1 (Perley et al., 2020), we find that the rate of ILRTs
($\rm{R}_{<-13.5}$) is $\approx 3^{+1.5}_{-1.5}\%$ of the CCSN rate. It
remains to be seen how much the lower luminosity events contribute to this
rate.

Our rate is also lower than the estimate from Thompson et al. (2009) who
estimated the ILRT rate is $\sim 20\%$ of the CCSN rate based on the two ILRTs
SN 2008S and NGC 300OT. We note that NGC 300OT is below the luminosity
threshold of our sample, and the rough estimate $\rm{R}_{<-12}$ is consistent
with their result.

Given the possible association of ILRT with ECSNe, it is worth comparing our
rate to theoretical predictions. Poelarends et al. (2008a) determine the range
of stellar masses expected to undergo ECSN for different mass-loss and
convective dredge-up prescriptions, and determine their rate to be $\approx
4\%-24\%$ of the CCSN rate. The rate also depends sensitively on the
metallicity, e.g Poelarends (2007) find that for Z = 0.02, the ECSN rate is
$\approx 3\%$ of the CCSN rate but for Z = $10^{-4}$ the rate is $\approx
25\%$. On the contrary, Doherty et al. (2015) use a different metallicity
dependence on the mass-loss rate and find that the ECSN rate is $\approx
2-5\%$ of the CCSN rate for all metallicities in the range Z $=$ [$10^{-5}$,
0.02]. Our measured ILRT rate ($\rm{R}_{<-13.5}$) is on the lower side, but
still consistent with the wide range of theoretical calculations, and it is in
line with the interpretation that several ILRTs could be ECSNe.

We note however that we cannot rule out that some of the ILRTs presented here
are LBV outbursts. Dusty LBV outbursts can also result in red, low luminosity
transients with spectra showing narrow H with Ca II and [Ca II] features,
similar to ILRTs (Andrews et al., 2021). While the transients in our sample do
not show any archival activity for the last $\approx 10$ years, it is possible
that they experienced previous outbursts. Nevertheless,the connection of IRLTs
to ECSNe is supported by strong evidence related to their dust-enshrouded
progenitors with masses between 8–15 M⊙ (Thompson et al., 2009; Botticella et
al., 2009; Jencson et al., 2019) and the fact that their remnants faded below
their progenitor luminosities (Adams et al., 2016). Progenitors are not
detectable for most of the ILRTs in our sample. As this will also be the case
for a large number of ILRTs that will be detected by future large-scale deep
surveys such as the Vera Rubin Observatory (VRO, Ivezić et al. 2019), it is
important to identify additional ways of distinguishing ILRTs from LBV
outbursts to confirm their nature as ECSNe. Possible ways to achieve this are
extensive nebular-phase observations of ILRTs. On the one hand, late-time
photometric observations would allow us to detect the presence, and estimate
the amount of Ni generated in the explosion (see Cai et al. 2021). On the
other hand, nebular spectroscopic observations would allow us to determine the
composition of the ILRT ejecta where the presence of stronger Ni than Fe
lines, weak O, Mg, C, Fe lines and a low [O I]/[Ca II] ratios would be
evidence for the ECSN scenario (similar to AT 2018zd, Hiramatsu et al. 2021).

Figure 13: Host galaxies of the ILRTs in our sample. The positions of the
ILRTs are indicated with a yellow cross, on top of color-coded PS1 images
obtained from here. Similar to LRNe, all ILRTs in our sample are located in
star-forming galaxies.

###  4.3 Host galaxies of LRNe and ILRTs

Fig. 13 shows thumbnails of the host galaxies of the ZTF ILRTs presented in
this paper. The ZTF ILRTs belong to starforming galaxies, similar to all ILRTs
discovered to date (see Cai et al. 2021). As neither ZTF nor the CLU galaxy
catalog are biased towards star-forming galaxies (Cook et al., 2019), the
sample confirms that ILRTs occur in predominantly young environments –
consistent with their ECSN or LBV interpretations.

Fig. 14 shows thumbnails of the host galaxies of the ZTF LRNe presented in
this paper. All ZTF LRNe also belong to late-type starforming galaxies (see
Table 1 for host galaxy morphologies), similar to all LRNe discovered in the
last decade (see Pastorello et al. 2019a; Blagorodnova et al. 2021). This
confirms that the luminous (M${}_{r}\leq-11$) LRNe occur more commonly in
star-forming environments. This is consistent with the expectation that LRNe
in this luminosity range have massive ($\geq 10$M ⊙) progenitors (Blagorodnova
et al., 2021). Early-type galaxies are expected to have LRNe with lower mass
progenitors and hence lower luminosities, making time-domain surveys less
sensitive towards detecting them.

Only three LRNe have been discovered in old environments – OGLE 2002-BLG-360
in the Galactic bulge (Tylenda et al., 2013), M31RV in the bulge of M31 (Rich
et al., 1989) and M85 OT in the S0-type galaxy M85 (Kulkarni et al., 2007). Of
these, M85 OT does not follow the LRN peak luminosity-progenitor mass
correlation (Kochanek et al., 2014; Blagorodnova et al., 2021). The progenitor
mass of M85 OT has been constrained to $<7$M ⊙ (Ofek et al., 2008). This is
expected to produce a LRN with M${}_{r,\rm{peak}}\geq-10$ – much fainter than
its actual peak M${}_{r}\approx-12$. As it is not a canonical LRN, M85 OT has
been suggested to be an ILRT. However, ILRTs have starforming hosts unlike M85
OT. Its progenitor mass is also incompatible with the ECSN or LBV scenario for
ILRTs, suggesting that it is not a canonical ILRT either. An intriguing
possibility is that M85OT is the merger of a WD with a companion evolved star.
Such “CV mergers" are believed to produce transients with observational
characteristics similar to LRNe (Metzger et al., 2021). A WD progenitor would
be consistent with the old environment of M85OT. As this is not a canonical
merger of two stars, we would not expect the transient to follow the
correlations observed in other LRNe. The Galactic slow nova CK Vul has been
proposed to be a merger involving a white dwarf progenitor (Eyres et al.,
2018; Metzger et al., 2021). M85OT could be an extragalactic member of this
class of outbursts. Discoveries of additional LRNe in early-type galaxies will
shed further light on the origin of this population.

Figure 14: Host galaxies of the LRNe in our sample. The positions of the LRNe
are indicated with a yellow cross. ZTF 19adakuot is located in M31. All LRNe
in our sample (including LRN-bronze events) are located in star-forming
galaxies.

##  5 Summary and way forward

Despite the discovery of a dozen LRNe and ILRTs in the last decade, their rate
remained uncertain. In this paper, we compiled a systematic sample of LRNe and
ILRTs using the Census of the Local Universe experiment on the Zwicky
Transient Facility to address this issue. We present a sample of eight LRNe
and eight ILRTs identified by the CLU experiment. We discuss the properties of
these transients, and present new data for the precursor emission in AT
2019zhd and line profile evolution in ZTF 21aaekeqd (AT 2021afy). We conduct
simulations of the ZTF survey using actual ZTF observation history and correct
for the completeness of CLU to derive a rate of $7.8^{+6.5}_{-3.7}\times
10^{-5}$ Mpc-3 yr-1 for LRNe with absolute magnitudes Mr in the range
[$-11$,$-16$]; and $2.6^{+1.8}_{-1.4}\times 10^{-6}$ Mpc-3 yr-1 for ILRTs with
M${}_{r}<-13.5$.

The rates of LRNe in this luminosity range are much lower than those
extrapolated from Galactic measurements of low luminosity Galactic LRNe by
Kochanek et al. (2014). Specifically, we find that the luminosity function of
LRNe scales as $\propto L^{-2.5}$ in the range $-11<M_{r}<-16$, as opposed to
L-1.4 derived by Kochanek et al. (2014) for $-4<M_{V}<-10$. This steeper
decline at higher luminosities is broadly consistent with binary population
synthesis models of Howitt et al. (2020), however the BPS models underpredict
the rates for M${}_{r}<-13$ by as much as two orders of magnitude. This
discrepancy is likely due to assumptions about the lightcurve models used in
the BPS simulation. The rates of the brightest LRNe in our sample are
consistent with a significant fraction of them being progenitors of double
compact object systems. We note that all LRNe in our sample, and those
discovered in the last decade belong to star-forming host galaxies. There have
been no analogs of M85 OT that was discovered in a S0-type galaxy.

The ILRT rate corresponds to $2.6^{+1.8}_{-1.4}$% of the local core-collapse
SN rate. However, our sample only probes the high luminosity end of the ILRT
luminosity function. Assuming our scaling extrapolates to lower luminosities,
our measurement is consistent with previously measured constraints on the ILRT
rate by Thompson et al. (2009) and Cai et al. (2021). The ILRT rate is also
consistent with the wide range of theoretical predictions of rates of
electron-capture SNe by Poelarends et al. (2008b) and Doherty et al. (2015).
Additional nebular phase observations of ILRTs and observations of their
progenitors are required to confidently establish them as electron-capture
SNe.

The future holds exciting prospects for studies of LRNe and ILRTs. Upcoming
NIR time domain surveys such as WINTER and DREAMS will enable substantial
progress in the next few years. These surveys will provide the first unbiased
sample of the dusty, red transients and will be instrumental in uncovering
hidden populations that could be missed by optical surveys. These results will
set the stage for the VRO. Based on our rate estimates, we calculate that VRO
will discover between 300 to 1500 LRNe and 200-700 ILRTs (with
M${}_{r,\rm{peak}}<-13.5$) per year (assuming a sensitivity of m${}_{r}\approx
24.2$ mag). While most of these will be too faint for spectroscopic
classifications, these transients can be identified based on their low
luminosities, long duration lightcurves and red photometric colors. An
experiment similar to the Census of the Local Universe that keeps track of VRO
transients in catalogued galaxies will be instrumental in the study of LRNe
and ILRTs.

##  6 Acknowledgements

Based on observations obtained with the Samuel Oschin Telescope 48-inch and
the 60-inch Telescope at the Palomar Observatory as part of the Zwicky
Transient Facility project. ZTF is supported by the National Science
Foundation under Grants No. AST-1440341 and AST-2034437 and a collaboration
including current partners Caltech, IPAC, the Weizmann Institute of Science,
the Oskar Klein Center at Stockholm University, the University of Maryland,
Deutsches Elektronen-Synchrotron and Humboldt University, the TANGO Consortium
of Taiwan, the University of Wisconsin at Milwaukee, Trinity College Dublin,
Lawrence Livermore National Laboratories, IN2P3, University of Warwick, Ruhr
University Bochum, Northwestern University and former partners the University
of Washington, Los Alamos National Laboratories, and Lawrence Berkeley
National Laboratories. Operations are conducted by COO, IPAC, and UW. The ZTF
forced photometry service was funded under the Heising-Simons Foundation grant
12540303 (PI: Graham). SED Machine is based upon work supported by the
National Science Foundation under Grant No. 1106171. This work is also based
on observations made with the Nordic Optical Telescope, owned in collaboration
by the University of Turku and Aarhus University, and operated jointly by
Aarhus University, the University of Turku and the University of Oslo,
representing Denmark, Finland and Norway, the University of Iceland and
Stockholm University at the Observatorio del Roque de los Muchachos, La Palma,
Spain, of the Instituto de Astrofisica de Canarias. SED Machine is based upon
work supported by the National Science Foundation under Grant No. 1106171. 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 Astrofísica de Canarias with financial support from the UK
Science and Technology Facilities Council. This work is part of the research
program VENI, with project number 016.192.277, which is partly financed by the
Netherlands Organisation for Scientific Research (NWO). A.V.F.’s group
acknowledges generous support from the Christopher R. Redlich Fund, the U.C.
Berkeley Miller Institute for Basic Research in Science, Sunil Nagaraj, Landon
Noll, Sandy Otellini, and many additional donors. A major upgrade of the Kast
spectrograph on the Shane 3 m telescope at Lick Observatory, led by Brad
Holden, was made possible through generous gifts from the Heising-Simons
Foundation, William and Marina Kast, and the University of California
Observatories. Research at Lick Observatory is partially supported by a
generous gift from Google.

##  7 Data Availability

Lightcurves and spectra of the LRNe, ILRTs and possible LBVs presented in this
paper, and template LRN and ILRT lightcurves will be made available online
after publication. The spectra will also be posted to WISeREP. The ZTF
pointing history logs will be made available upon request to the corresponding
author.

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##  Appendix A Properties of sources classified as possible LBV outbursts

The lightcurves of the six sources we classify as potential LBV outbursts are
shown in Fig. 15 and their spectra are shown in Fig. 16. We discuss the
individual objects below.

Figure 15: Lightcurves of transients that are possible LBV outbursts Figure
16: Optical spectra of transients that are possible LBV outbursts

  * •

ZTF 19acpmbvd (AT 2019wbg) is located in the galaxy NGC 4045, and shows a
bumpy, red lightcurve with at least three peaks. The transient was detected in
2016 in iPTF data with m${}_{g}\approx 22$ mag. It was redetected in ZTF in
2022 at m${}_{r}\approx 19.5$ mag. A spectrum taken during this outburst shows
H$\alpha$ with v${}_{\rm{FWHM}}\approx 1700$ km s-1.

  * •

ZTF 20abwilhb (AT 2020swt) is located in the galaxy UGC 03820. The lightcurve
does not show multiple peaks, but shows signs of a $\approx 40$day long
plateau, after which the transient declines. The optical spectrum shows
H$\alpha$ with v${}_{\rm{FWHM}}\approx 3300$ km s-1, suggesting that this
transient could be an LBV outburst or a low luminosity Type II SN.

  * •

ZTF 21aagydmn (AT 2021bug) is located in the galaxy NGC 4533 and shows an
unusual lightcurve that peaks at M${}_{r}\approx-14.4$ and declines quickly.
Once off the first decline, the lightcurve plateaus for $\approx 10$ days, and
then continues to decline. The spectrum shows H$\alpha$ with
v${}_{\rm{FWHM}}\approx 2600$ km s-1, however the lightcurve does not show a
long-duration plateau as seen in low luminosity Type II SNe. The true nature
of this source is unclear, but an outburst in a massive star is a possibility.

  * •

ZTF 21aantupk (AT 2021efb) is located at the nucleus of the galaxy CGC
003-005. The lightcurve shows erratic activity in the ATLAS and the ZTF data
prior for several hundred days prior to the main explosion in 2021. We suggest
that this source is either an LBV outburst or AGN activity.

  * •

ZTF 21aclyyfm (AT 2021adlw) is located in the galaxy NGC 3813, and reached a
peak absolute magnitude of M${}_{r}\approx-16$ in the 2021 outburst. Archival
ATLAS data shows that it underwent a similar outburst (M${}_{o}\approx-15$)
$\approx 1800$ days prior to this outburst. An optical spectrum taken at an
early phase during the 2021 outburst shows narrow H$\alpha$ with
v${}_{\rm{FWHM}}\approx 1000$ km s-1, however late time spectra show ejecta
with much larger velocities. This source is likely an LBV outburst or a “weak"
Type IIn supernova.

  * •

ZTF 21aaitlhy (AT 2021afm) is located close to the center of the galaxy NGC
5657. It shows several detections in ATLAS and ZTF data in the $\approx$1000
days leading up to the 2021 explosion. We also detect the transient in the _g_
-band in PTF data taken during July 2011 and April 2016 at m${}_{g}\approx 20$
mag. Owing to the extensive archival activity, we categorize this source as a
possible LBV outburst.