11institutetext: Affiliations are listed after the acknowledgements

# A study in scarlet - I. Photometric properties of a sample of Intermediate
Luminosity Red Transients

G. Valerin E–mail<EMAIL_ADDRESS>A. Pastorello 11 A. Reguitti 1122
S. Benetti 11 Y.-Z. Cai 334455 T.-W. Chen 66 D. Eappachen 7788 N. Elias-Rosa
1199 M. Fraser 1010 A. Gangopadhyay 11111212 E. Y. Hsiao 1313 D. A. Howell
14141515 C. Inserra 1616 L. Izzo 17171818 J. Jencson 1919 E. Kankare 2020 R.
Kotak 2020 P. A. Mazzali 21212222 K. Misra 2323 G. Pignata 2424 S. J. Prentice
2525 D. J. Sand 2626 S. J. Smartt 27272828 M. D. Stritzinger 2929 L. Tartaglia
3030 S. Valenti 3131 J. P. Anderson 32323333 J. E. Andrews 2626 R. C. Amaro
2626 S. Brennan 1111 F. Bufano 3434 E. Callis 1111 E. Cappellaro 11 R.
Dastidar 35353333 M. Della Valle 17173636 A. Fiore 1137373838 M. D. Fulton
2828 L. Galbany 993939 T. Heikkilä 2020 D. Hiramatsu 1313141440404141 E.
Karamehmetoglu 11112929 H. Kuncarayakti 20204242 G. Leloudas 4343 M. Lundquist
2626 C. McCully 1414 T. E. Müller-Bravo 993939 M. Nicholl 2828 P. Ochner
114444 E. Padilla Gonzalez 14141515 E. Paraskeva 4545 C. Pellegrino 4646 D. E.
Reichart 4747 T. M. Reynolds 202048484949 R. Roy 5050 I. Salmaso 11 M. Singh
5151 M. Turatto 11 L. Tomasella 11 S. Wyatt 2626 D. R. Young 2828

(Received —-; accepted —-)

###### Abstract

Aims. We investigate the photometric characteristics of a sample of
Intermediate Luminosity Red Transients (ILRTs), a class of elusive objects
with peak luminosity between that of classical novae and standard supernovae.
Our goal is to provide a stepping stone in the path to unveil the physical
origin of such events, thanks to the analysis of the datasets collected.

Methods. We present the multi-wavelength photometric follow-up of four ILRTs,
namely NGC 300 2008OT-1, AT 2019abn, AT 2019ahd and AT 2019udc. Through the
analysis and modelling of their spectral energy distribution and bolometric
light curves we infer the physical parameters associated with these
transients.

Results. All four objects display a single peaked light curve which ends in a
linear decline in magnitudes at late phases. A flux excess with respect to a
single black body emission is detected in the infrared domain for three
objects in our sample, a few months after maximum. This feature, commonly
found in ILRTs, is interpreted as a sign of dust formation. Mid infrared
monitoring of NGC 300 2008OT-1 761 days after maximum allows us to infer the
presence of $\sim$10-3-10-5 M⊙ of dust, depending on the chemical composition
and the grain size adopted. The late time decline of the bolometric light
curves of the considered ILRTs is shallower than expected for 56Ni decay,
hence requiring an additional powering mechanism. James Webb Space Telescope
observations of AT 2019abn prove that the object has faded below its
progenitor luminosity in the mid-infrared domain, five years after its peak.
Together with the disappearance of NGC 300 2008OT-1 in Spitzer images seven
years after its discovery, this supports the terminal explosion scenario for
ILRTs. With a simple semi-analytical model we try to reproduce the observed
bolometric light curves in the context of few M⊙ of material ejected at few
103 km s-1 and enshrouded in an optically thick circumstellar medium.

###### Key Words.:

supernovae: general – supernovae: individual: NGC 300 2008OT-1, AT 2019abn, AT
2019ahd, AT 2019udc – galaxies: individual: NGC300, M51 – stars: Massive
stars, Mass Loss

##  1 Introduction

It is well established that single stars with an initial mass below $\sim$8 M⊙
will end their lives as white dwarfs, cooling down while supported by the
electron degeneracy pressure in their cores. In contrast, stars with initial
masses between $\sim$10 M⊙ and 40 M⊙ will complete all the nuclear burning
cycles and will undergo a violent explosion as their core collapses (Woosley
et al., 2002). This apparently simple distinction raises a complicated
question: what is the exact initial mass limit that separates the two opposite
fates? Stars with a zero-age-main-sequence mass between 8 M⊙ and 10 M⊙ are
expected to form a degenerate O-Ne-Mg core during their lifetime (Nomoto,
1984). Such stars are labelled Super-Asymptotic Giant Branch stars (SAGB), and
the outcome of their evolution is uncertain. In fact, if the O-Ne-Mg core
accretes enough material to approach the Chandrasekhar limit, the star will
explode as an Electron Capture Supernova (ECSN), but if the core fails to
reach this critical mass the star will end its evolution as an O-Ne-Mg white
dwarf (e.g. Miyaji et al. 1980; Nomoto 1984; Jones et al. 2013; Moriya et al.
2014; Doherty et al. 2015; Limongi et al. 2024). Whether such critical mass
can be reached depends on the competing effects of mixing, convective
overshooting and mass loss rates, which make the modelling of the core and its
evolution a challenging endeavor (Poelarends et al., 2008). An additional
complication, as pointed out by Kozyreva et al. (2021), is that even small
changes in the initial mass and metallicity of the progenitor star may give
rise to a Fe core-collapse supernova (SN) instead of an ECSN, overall showing
similar observables.

While stellar evolution theory predicts the existence of ECSNe, finding their
observational counterparts is still an open issue. Proving that a transient
originates from the core-collapse of an O-Ne-Mg core, rather than from a
classical Fe core collapse, is not trivial. However, there has been no
shortage of attempts: Low Luminosity Supernovae Type IIP (LL SNe IIP) (e.g.
Spiro et al. 2014; Reguitti et al. 2021; Valerin et al. 2022) and also some
interacting transients (e.g. Smith 2013; Hiramatsu et al. 2021) have been
proposed as ECSN candidates. In order to be a reasonable ECSN candidate, an
object should fulfill the key expectations for the explosion following the
collapse of an O-Ne-Mg core. First of all, the energy released by an ECSN
should be significantly lower ($\sim$ 1050 erg) compared to classical SN
explosions, therefore directing the investigation towards faint targets with
low velocity ejecta (Janka et al., 2008). Secondly, the nucleosynthesis
following the collapse of an O-Ne-Mg core yields limited amounts of 56Ni (few
10-3 M⊙), placing constraints on the luminosity of the late time decline of
the candidate (Wanajo et al., 2009). Finally, the progenitor star of a
candidate should be compatible with a luminous ($\sim$105 L⊙) SAGB star, since
that is the only kind of star able to produce a degenerate O-Ne-Mg core
massive enough to trigger an ECSN explosion (Poelarends et al., 2008).

Intermediate Luminosity Red Transients (ILRTs) are a class of objects,
populating the luminosity gap between classical novae and standard SNe
(Pastorello & Fraser, 2019), which are appealing ECSN candidates. Their
physical origin is still debated, with some studies associating ILRTs to
non–terminal eruptions of post–main sequence stars (e.g. Humphreys et al.
2011). However, there are several indicators that favour the ECSN
interpretation to explain the observed properties of these transients. The low
luminosity characterizing ILRTs, which show peak absolute magnitudes ranging
between Mr $\sim$ –12 mag and –15 mag, is consistent with the expected weak
explosion originating from the collapse of an O-Ne-Mg core (Pumo et al.,
2009). Likewise, the late time decline in luminosity points towards small 56Ni
masses synthesized, fulfilling the condition presented by Wanajo et al. (2009)
(see also Cai et al. 2021). Furthermore, all of the progenitor stars
associated with ILRTs have been consistent with a SAGB star, corroborating the
ECSN scenario (Thompson et al., 2009; Jencson et al., 2019). Recent estimates
have shown that the rate of ILRTs is a few percent of all the local CC SNe
events ($\approx$8% according to Cai et al. 2021, or $\approx$1–5%, according
to Karambelkar et al. 2023), compatible with the theoretical expectations for
ECSNe (Poelarends et al., 2008; Thompson et al., 2009; Doherty et al., 2015).
Finally, an important step towards understanding the nature of ILRTs was
performed by Adams et al. (2016), who showed that a few years after their
maximum luminosity the remnants of the two ILRTs SN 2008S (Botticella et al.,
2009) and NGC 300 2008OT-1 (Bond et al., 2009; Berger et al., 2009; Humphreys
et al., 2011) had become fainter in the mid-infrared (MIR) than their
progenitor stars. Extreme dust extinctions would be needed to obscure a
surviving star, therefore favouring a genuine terminal explosion over a non-
terminal outburst.

While the considerations presented so far are certainly encouraging, the
discussion on ILRTs as ECSN candidates is still ongoing. This is, after all, a
relatively young class of transients, only established around a fifteen years
ago. Their rates are not particularly low but their faintness makes their
discovery occasional and their follow-up challenging. Since only a handful of
ILRTs have been accurately characterized so far, additional data is key to
improve our understanding of this poorly studied class of objects. In this
paper we present and analyse original photometric data of four ILRTs: NGC 300
2008OT-1, AT 2019abn, AT 2019ahd and AT 2019udc. This work is the first part
of a series of two papers: in the second installment (“A study in scarlet II.
Spectroscopic properties of a sample of Intermediate Luminosity Red
Transients”, Valerin et al. 2024, hereafter “Paper II”) we will present and
discuss the spectroscopic data collected for the same targets analysed here.
This paper is organized as follows: in Section 2 we discuss the methodology
used to obtain and reduce the data, while in Section 3 the photometric data
and the host properties are presented. In Section 4 we discuss the reddening
estimate, while in Section 5 we discuss the physical parameters obtained
through modelling of the spectral energy distribution fits. In Section 6 we
study the late time behaviour of NGC 300 2008OT-1 and in Section 8 we present
a simple model to reproduce the light curves of ILRTs. Finally, in Section 9
we summarise the results obtained.

Transient Host Galaxy Type Redshift Distance [Mpc] $\mu$ [mag] Galactic AV
[mag] Local AV [mag] AT 2019abn M51 Sa 1.54 (-) x10-3 8.6 (0.1) 29.67 (0.02)
0.096 (0.006) 2.34 (0.06) AT 2019ahd NGC 3423 SA(s)cd 3.35 (0.01) x10-3 11.1
(0.7) 30.22 (0.14) 0.079 (0.003) 0.37 (0.03) AT 2019udc NGC 0718 SAB(s)a 5.78
(0.03) x10-3 19.9 (1.4) 31.49 (0.15) 0.100 (0.001) 0.00 (0.00) NGC 300 OT NGC
300 SA(s)d 4.80 (0.03) x10-4 1.92 (0.14) 26.43 (0.09) 0.034 (0.001) 0.78
(0.06)

Table 1: Basic information on the galaxies hosting the transients in the
sample. Morphological classifications are from Karachentsev et al. (1985) for
M51 and from de Vaucouleurs et al. (1991) for the other galaxies.

##  2 Data reduction

The objects presented in this paper were followed with several instruments at
different facilities reported in Table [5]. In particular, the majority of the
private data was collected with the Nordic Optical Telescope (NOT) within the
NOT Unbiased Transient Survey 2 (NUTS2) collaboration (Holmbo et al., 2019),
with the Liverpool Telescope (Steele et al., 2004), with the GROND imager
(Greiner et al., 2008), within the ePESSTO+ collaboration (Smartt et al.,
2015) as well as the Global Supernova Project (GSP, Howell 2019). Images
obtained were reduced through standard iraf tasks (Tody, 1986), removing the
overscan, correcting them for bias and flat field. When multiple exposures
were taken the same night, we combined them to improve the signal to noise
ratio (S/N). To measure the magnitudes of the transients observed, we used a
dedicated, python-based pipeline called ecsnoopy (Cappellaro, 2014). ecnoopy
is a collection of python scripts that call iraf standard tasks like daophot
through pyraf, and it was designed for Point Spread Function (PSF) fitting of
multi-wavelenght data acquired from different instruments and telescopes. The
PSF model was built from the profiles of isolated, unsaturated stars in the
field. The instrumental magnitude of the transient was then retrieved by
fitting this PSF model and accounting for the background contribution around
the target position through a low-order polynomial fit. The error on this
procedure was obtained through artificially placed stars close to the target,
with magnitudes similar to that inferred for the object. The dispersion of the
artificial stars instrumental magnitudes was combined in quadrature with the
PSF fitting error given by daophot to obtain the total error associated with
that measure. Zero Point (ZP) and Colour Terms (CT) corrections were computed
for each instrument by observing standard fields: SDSS (York et al., 2000) was
used as reference for Sloan filters, the Landolt (1992) catalogue was used for
Johnson filters and the 2MASS (Skrutskie et al., 2006) catalogue was used for
Near Infrared (NIR) filters.

For the ”Asteroid Terrestrial–impact Last Alert System” (ATLAS) data (Tonry et
al., 2018), we combined the flux values obtained through forced photometry
released from their archive111https://fallingstar–data.com/forcedphot/, and
converted the result into magnitudes as prescribed in the ATLAS webpage. While
reducing WISE (Wright et al., 2010) and Spitzer (Lacy et al., 2005) data we
adopted the ZP provided on their respective
websites222https://wise2.ipac.caltech.edu/docs/release/prelim/expsup/sec4_3g.html,
https://irsa.ipac.caltech.edu/data/SPITZER/docs/irac/iracinstrumenthand
book/14/. We also performed PSF fitting measurements on publicly available
images taken with the James Webb Space Telescope (JWST, Gardner et al. 2006).
The pipeline-reduced JWST+NIRCam/MIRI ‘i2d’ images (and Level-3 mosaics when
available) were retrieved from the MAST
archive333https://mast.stsci.edu/portal/Mashup/Clients/Mast/Portal.html. It is
worth noticing that in the NIR and Mid Infrared (MIR) we assumed negligible
CT, so we only computed the ZP correction. Images from the $Swift$ UV/Optical
Telescope Roming et al. (2005) were reduced using standard heasoft tasks, and
the magnitudes were retrieved through aperture photometry, applying the
aperture correction reported in the $Swift$
website444https://swift.gsfc.nasa.gov/analysis/uvot_digest/apercor.html when
needed. In order to account for non-photometric nights, we selected a series
of stars in the field of each observed transient: measuring the average
magnitude variation of the reference stars, we computed the ZP correction for
each night in each band. Applying ZP and CT corrections to the instrumental
magnitudes of our targets, we obtained the apparent magnitudes which are
reported in this paper. We adopted the AB magnitudes system for $u$, $g$, $r$,
$i$, $z$, $cyan$, $orange$ bands and Vega magnitudes for $UVW2$, $UVM2$,
$UVW1$, $U$, $B$, $V$, $R$, $I$, $J$, $H$, $K$, $W1$, $W2$, $[3.6]$ $\mu m$,
$[4.5]$ $\mu m$ bands. We resorted to template subtraction at late epochs,
when the transients were too faint to be detected otherwise. The template
subtraction procedure was performed on late time observations, again with
ecsnoopy, with template images taken from SDSS (York et al., 2000),
Pan–STARRS1 (Chambers et al., 2016) and Liverpool Telescope (Steele et al.,
2004). The photometric measurements we obtained are reported in Appendix B.

Figure 1: Optical, NIR and MIR light curves of AT 2019abn. Filled circles
represent unpublished data, while empty circles represent data points from the
literature. Empty triangles represent upper limits. Figure 2: Optical and NIR
light curves of AT 2019ahd. Filled circles represent unpublished data, while
empty circles represent ZTF data points. Empty triangles represent upper
magnitude limits. Magnitude shifts on $i$ and $z$ bands have been applied for
clarity.

##  3 Photometric follow-up

###  3.1 AT 2019abn

AT 2019abn was discovered on 2019 January 22.6 UT by the Zwicky Transient
Facility (ZTF, Graham et al. 2019) on a spiral arm of Messier 51 (M51) at the
coordinates RA$=$ $13^{h}29^{m}42^{s}.41$, Dec $=$ +47°11’ 16”.6. The
discovery and early observations are discussed by Jencson et al. (2019), while
the evolution of the transient up until 200 days from the discovery is covered
by Williams et al. (2020). In this paper we provide additional optical data,
especially at later stages of evolution, while also publishing original NIR
and MIR observations obtained with IO:I and NOTCam, which put constraints on a
critical section of the Spectral Energy Distribution (SED). By measuring the
magnitude of the standard stars used as reference by Williams et al. (2020) we
integrate their dataset with our observations by applying the following
magnitude corrections to their observations (likely due to a different choice
of reference stars): $\Delta B$ = +0.07 mag, $\Delta r$ = +0.04 mag and
$\Delta i$ = +0.05 mag. Discrepancies in $V$, $z$ and NIR bands were within
photometric uncertainty, and no correction was needed. Similarly, we
incorporate the observations performed by Jencson et al. (2019) in our dataset
after applying the following corrections: $\Delta J$ = -0.13 mag, $\Delta H$ =
-0.05 mag and $\Delta K$ = -0.06 mag. We adopt a distance modulus of $\mu$ =
29.67 $\pm$ 0.02 mag to M51, obtained through the method of the tip of the red
giant branch (McQuinn et al., 2016, 2017). The Galactic absorption in the
direction of M51 is AV = 0.096 $\pm$ 0.006 mag, from Schlafly & Finkbeiner
(2011), under the assumption that $R_{V}$=3.1 (Cardelli et al., 1989). The
local absorption is more challenging to estimate and will be discussed, for
all objects, in Section 4.

Figure 3: On the right panel we present optical and NIR light curves of AT
2019udc. Magnitude shifts have been applied for clarity. Filled circles
represent unpublished data, while empty circles represent ZTF data points. On
the left panels, DLT40 monitoring of AT 2019udc. In particular, on the upper
left panel is shown the high cadence follow up of the rise of AT 2019udc:
DLT40 data points are shown as stars and are integrated with observations
obtained through other facilities, represented as circles. On the lower left,
years of upper limits collected by DLT40 are displayed as black triangles,
with the detections of the transient appearing as green symbols on the right
edge of the figure.

The light curves of AT 2019abn are shown in Figure 1. Thanks to the early
discovery, it is possible to follow the evolution of AT 2019abn from very
early stages. The rise in luminosity is observed in multiple bands, and lasts
roughly 20 days before the transient reaches a peak apparent magnitude of mr =
16.73 $\pm$ 0.01 mag on MJD = 58527.3. Thanks to this excellent coverage of
the rise, it is possible to estimate the rising rates ($\gamma_{1}$) for the
observed bands. To do so, we perform a linear regression of the measured
magnitudes in each band between 25 and 11 days before maximum: such rising
(and declining) rates are useful to quantitatively compare the behaviour of
each band at different phases, as well as the differences between each
transient (see Cai et al. 2021 for similar measurements on other ILRTs). For
sake of simplicity, we separate each light curve in multiple linear segments,
and we display their declining (or rising) rates in Table 6 and following
tables. As a reference, here in the text we report the decline rates measured
on the $r$ band in units of [mag/100 days]. At 11 days before maximum, AT
2019abn starts departing from its initial linear increase in magnitude
($\gamma_{1}$=-21$\pm$1), forming a broad peak also described by Williams et
al. (2020). The post maximum luminosity evolution is slow
($\gamma_{2}$=1.37$\pm$0.01) especially in the red bands, while the decline
rate becomes more steep after 110 days ($\gamma_{3}$=2.49$\pm$0.04). Between
180 and 195 days after maximum, there is a sudden drop in luminosity of $\sim$
0.9 magnitudes in all observed optical and NIR bands. After this abrupt
change, the light curves settle on slow decline rates
($\gamma_{4}$=0.80$\pm$0.06). The MIR sampling of AT 2019abn, obtained through
the Spitzer and WISE (survey NEOWISE) space telescopes, is unprecedented for
an ILRT. After the first data point, at 50 days after maximum, the MIR light
curves show at first a decline faster compared to the optical bands, but after
$\sim$100 days the decline becomes more shallow. Interestingly, the luminosity
drop at $\sim$180 days is not as evident in the MIR bands.

###  3.2 AT 2019ahd

The discovery of AT 2019ahd was reported by the ATLAS survey (Tonry et al.,
2019; Smith et al., 2020) on 2019 January 29.0 UT. The coordinate of the
transient are RA = $10^{h}51^{m}11^{s}.737$ Dec = +05°50’ 31”.03, which is
2”.6 north and 6”.9 south of the centre of its host, the spiral galaxy NGC
3423. As the distance modulus of the host galaxy, we chose to adopt an average
of the different independent values reported on the NASA/IPAC Extra-galactic
Database (NED) obtaining a distance modulus $\mu$ = 30.22 $\pm$ 0.14 mag,
where the error comes from the standard deviation of the measurements (Tully &
Fisher, 1988; Tully et al., 1992, 2009; Nasonova et al., 2011). We assumed a
cosmology where $H_{0}$ = 73 km s-1 Mpc-1, $\Omega_{\Lambda}$ = 0.73 and
$\Omega_{M}$ = 0.27 (Spergel et al., 2007), which will be used throughout this
whole work. The Galactic absorption in the direction of NGC 3423 is AV = 0.079
$\pm$ 0.003 mag (Schlafly & Finkbeiner, 2011). The object was initially
classified as a Luminous Blue Variable (LBV, Jha 2019) due to its narrow
hydrogen features and relatively red spectrum. The following photometric and
spectroscopic evolution of the transient, in particular the prevalence of
calcium features (Ca II H&K, [Ca II] and Ca NIR triplet; see Paper II), proved
that it is an ILRT instead. The majority of the follow-up performed for this
object is obtained through the GROND telescope, which yielded a remarkably
homogeneous data set (Figure 2). The brightest magnitude is well constrained
at mr = 17.57 $\pm$ 0.07 mag, reached on MJD = 58525.0. Similar to AT 2019abn,
AT 2019ahd displays a slow decline just after peak luminosity
($\gamma_{1}$=1.12$\pm$0.09), but this ”pseudo-plateau” only lasts for 45
days, followed by a steeper decline ($\gamma_{2}$=2.31$\pm$0.10) that ends 105
days after maximum. The subsequent decline rate is again slower
($\gamma_{3}$=1.05$\pm$0.03), in particular in the NIR bands (Table 7).

Figure 4: UV, optical and NIR light curves of NGC 300 OT. Empty triangles
represent upper limits. Filled circles represent unpublished data, while empty
circles represent publicly available SWIFT data.

###  3.3 AT 2019udc

The discovery of AT 2019udc was reported by the survey DLT40 (Tartaglia et
al., 2018) on 2019 November 4.1 UT. The transient lies on a spiral arm of the
galaxy NGC 0718, at RA = $01^{h}53^{m}11^{s}.190$ Dec = +04°11’ 46”.96. We
adopt a kinematic measure of distance for NGC 0718, that provides $\mu$ =
31.49 $\pm$ 0.15 mag, obtained through the redshift of the galaxy with respect
to 3K CMB (Fixsen et al., 1996). The Galactic absorption towards NGC 0718 is
AV = 0.100 $\pm$ 0.001 mag. Similar to AT 2019ahd, also AT 2019udc was
originally classified as an LBV due to its spectral features (Siebert et al.,
2019) but its evolution proves that it is actually an ILRT. AT 2019udc is the
most distant object studied in this sample. The follow-up campaign was stopped
120 days after maximum, due to solar conjunction. The GSP multi-band
monitoring yielded a high cadence follow up of the rise and peak of AT
2019udc, crucially contributing to the collection of a high quality data set
for this object (Figure 3, left panel). During the first two days after
discovery (-10 to -8 days from maximum), the rise in magnitudes can be
approximated as linear, with an increase rate up to three time faster than the
rise of AT 2019abn, with bluer bands showing a systematically faster evolution
($\gamma_{1}$=-47.5$\pm$4.8). After this phase the rise quickly slows down,
departing from a linear behaviour and reaching peak luminosity in about 10
days (mr=17.40 $\pm$ 0.06, MJD = 58801.28). Immediately after maximum, AT
2019udc displays a fast linear decline ($\gamma_{2}$=3.93$\pm$0.09), again
around three times faster than the decline of AT 2019abn just after maximum.
The luminosity drop settles on a gentler slope in all bands at around 35 days
after maximum ($\gamma_{3}$=2.22$\pm$0.12). The resulting light curve is
notably fast evolving for an ILRT: although peculiar compared to the other
objects in the sample, these features are not unique among ILRTs, as shown in
Section 7.

Thanks to the prompt discovery and high cadence monitoring of the DLT40
survey, the luminosity rise of AT 2019udc is exceptionally well sampled, as
presented in the upper right panel of Figure 3 (DLT40 data are unfiltered
observations scaled to sloan $r$ band observations). The rise immediately
after the discovery is remarkably fast, 0.8 magnitudes in less than one day,
followed by a more gentle brightening of 0.6 mag in 2.5 days. At this point, 3
days after the first DLT40 detection, AT 2019udc is already close to maximum
luminosity, and its magnitude will only marginally change (within $\pm$0.15
mag) in the following two weeks. We try to fit the rise to maximum of AT
2019udc with a simple fireball model, where the flux increases as $t^{2}$ (as
detailed by e.g. Nugent et al. 2011). However, as shown by the black solid
line in the upper right panel of Figure 3, the observed light curve quickly
departs from the fireball model extrapolated from steep rise of the first two
days. One possible explanation for this discrepancy is that the early light
curves of ILRTs are not dominated by 56Ni decay, unlike the light curves of
SNe Ia (for which the fireball model is a reasonable approximation). DLT40
also provided several years of upper limits to the optical luminosity of the
progenitor of AT 2019udc, which are displayed in the lower right panel of
Figure 3. The absence of outbursts and the overall non-detection in the
optical domain of the progenitor of AT 2019udc is well in line with the
expectations for ILRTs, whose precursors have been identified as dust
enshrouded stars, heavily extincted in the optical wavelengths but luminous in
the MIR Thompson et al. (2009).

###  3.4 NGC 300 2008 OT-1

NGC 300 2008 OT-1 (hereafter NGC 300 OT) was discovered on 2008 May 14 during
the SN search program at the Bronberg Observatory (Monard, 2008). The event,
located in the nearby NGC 300 at RA = $00^{h}54^{m}34^{s}.51$ Dec = -37°38’
31”.4, was extensively studied in the subsequent years (Bond et al., 2009;
Berger et al., 2009; Humphreys et al., 2011; Adams et al., 2016) and became a
prototype for the class of ILRTs together with SN 2008S (Botticella et al.,
2009). Here we present additional optical, NIR and MIR data, adding this
object to our sample of ILRTs. For the distance of NGC 300, we adopt the
results published by Gogarten et al. (2010), where a distance modulus $\mu$ =
26.43 ± 0.09 mag is obtained through the Red Clump method. The Galactic
absorption towards NGC 300 is AV = 0.034 $\pm$ 0.001 mag (Schlafly &
Finkbeiner, 2011). NGC 300 OT is the closest ILRT ever observed, making it an
extremely valuable which was monitored in detail for an extended period of
time. In Figure 4 we present the original optical and NIR photometric data we
collected for this transient. The object was behind the sun during its rise
and peak luminosity, so we lack the first part of its evolution. Our observed
maximum is mr = 14.38$\pm$0.02 mag on MJD = 54602.38. We note that there is a
serendipitous optical detection of NGC 300 OT on MJD = 54580.65 when the
transient is rising (mR=16.30$\pm$0.04 mag, Humphreys et al. 2011), providing
a rough estimate for the onset epoch of the event. The first 35 days display a
slow decline ($\gamma_{1}$=1.11$\pm$0.05), especially in the red bands. From
35 to 75 days, the transient falls from this ”pseudo-plateau”, and its
luminosity starts to fade faster ($\gamma_{2}$=3.32$\pm$0.08). Between 75 and
120 days the decline in luminosity is particularly rapid
($\gamma_{3}$=5.24$\pm$0.06, calculated on the $R$ band due to lack of $r$
band coverage in this phase), comparable to the fast declining phase of AT
2019udc. From 120 and 255 days the fast decline stops, and a slow evolution
ensues ($\gamma_{4}$=0.69$\pm$0.07) before the final phase
($\gamma_{5}$=1.56$\pm$0.05) that encompasses from 255 days onwards. As done
for AT 2019abn, we integrate the dataset provided by Humphreys et al. (2011)
with our observations by applying magnitude corrections to their observations,
calculated by measuring the magnitude of the reference star chosen in their
work: $\Delta B$ = +0.07 mag, $\Delta R$ = +0.05 mag. No correction was needed
for $V$ band, $I$ band and NIR data, since they were perfectly matching. We
also performed aperture photometry on the public images of NGC 300 OT taken
with $Swift$ UVOT which were analysed by Berger et al. (2009). We find a
remarkable agreement in the $U,B,V$ magnitudes reported there, while we
measure overall fainter $UVW2$ and $UVW1$ magnitudes, possibly due to a
different background selection: in particular, we restricted the aperture down
to 3” to limit possible background contamination. The resulting UV fluxes from
our measurements are in line with the behaviour expected from a black body
emission, as shown in the top left panel of Figure 7.

Figure 5: Absolute $r$ band (upper panel) and $H$ band (lower panel) light
curve comparison between the ILRTs in our sample and other low-luminosity
transients. In particular ILRTs are marked with circles, LRNe with plus signs
and the SN IIP with diamonds.

###  3.5 Comparison with other transients

In Figure 5, we compare the absolute $r$ and $H$ band evolution of our sample
of ILRTs along with that of other transients of similar luminosity. The first
considerations can be made observing the sample of ILRTs, with the addition of
the well studied SN 2008S (Botticella et al., 2009) and AT 2017be (Cai et al.,
2018). We remark the large spread in the optical peak magnitudes, which span
from –12 mag for AT 2017be to –15 mag for AT 2019abn. We note that AT 2019abn
(Mr = –15.00$\pm$0.08 at maximum) is, to date, the brightest ILRT ever
observed, with AT 2019udc (Mr = –14.17$\pm$0.16 at maximum) also falling on
the brighter end of the ILRTs luminosity distribution. AT 2019ahd and NGC 300
OT, instead, display fainter peak magnitudes, –13.17$\pm$0.16 mag and
–12.69$\pm$0.11 mag respectively. Among the least luminous ILRT we find AT
2017be, which is barely brighter than Mr = –12 mag. There are also significant
differences in light curve shapes within the class. AT 2019abn and AT 2019udc
represent the two extreme cases, with the former being characterised by a long
phase of slow decline after peak, almost a pseudo-plateau in the $r$ band
(1.37 $\pm$ 0.01 mag/100 days), while AT 2019udc undergoes a decline that is
three times faster (3.93 $\pm$ 0.09 mag/100 days), after peak luminosity. This
variability is less pronounced in the NIR domain, where both the decline rates
and the peak magnitudes span a smaller range of values. Regardless of their
differences, ILRTs tend to settle on a linear decline at late times, which is
compatible with the expected luminosity decline sustained by
$\textsuperscript{56}Ni$ radioactive decay. This can be visually evaluated by
comparing the late time behaviour of ILRTs with that of SN 2005cs, one of the
prototypes of low-luminosity SNe IIP (Pastorello et al., 2009), whose late
decline is known to be powered by $\textsuperscript{56}Ni$ decay. We also
remark that SN 2005cs is fainter than AT 2019abn at peak luminosity, revealing
an overlap between the brightest ILRTs and the faintest core collapse SNe. To
summarize the features described above, ILRTs are characterized by their
single-peaked, monotonically declining light curves which terminate in a
linear decline at late phases. A clearly different light curve shape is
instead associated to Luminous Red Novae (LRNe, Pastorello et al. 2019b),
another class of transients populating the luminosity ”Gap” which separates
classical novae from standard SNe. LRNe are non-degenerate stellar mergers,
and typically display double peaked light curves, as shown for by AT 2017jfs
(Pastorello et al., 2019a) and to a lesser degree M31-LRN-2015 (Williams et
al., 2015), both reported in Figure 5. With its peak absolute magnitude
fainter than –10 mag, M31-LRN-2015 appears detached from the other transients
shown: indeed, LRNe can be much dimmer, with peak absolute magnitude even
below $\sim$–4 mag (e.g. V1309Sco Tylenda et al. 2011). On the other hand,
ILRTs discovered to date have been strictly confined within the luminosity Gap
(–10 mag$<$MV$<$ –15 mag).

Figure 6: Colour curves for the ILRTs belonging to our sample, with the
addition of SN 2008S and AT 2017be. In the top two panels the optical colours
are shown. In the bottom panel, it is possible to appreciate the NIR colour
evolution.

##  4 Reddening Estimate

Estimating the reddening affecting ILRTs is a challenging task, and different
approaches can be found in the literature, depending on the available data. A
first method consists in using the empirical relation between the Na ID
Equivalent Width (EW) and the absorption along the line of sight (Turatto et
al., 2003; Poznanski et al., 2012), as was done by Cai et al. (2018). This
method has the advantage of not requiring any assumption on the intrinsic
properties of the target, but it needs high S/N spectroscopy in order to be
reliable. Furthermore, the EW of Na ID observed may saturate, preventing the
application of empirical relations (e.g. Stritzinger et al. 2020).
Furtheremore, the EW of the Na ID varies with time in ILRTs (e.g. Byrne et al.
2023, and further discussed in Paper II), increasing the uncertainty
associated with this method. A second method is based on the observation that
the spectral features of ILRTs resemble those of F-type stars (Humphreys et
al., 2011; Jencson et al., 2019). It is then assumed that all ILRTs reach a
temperature of $\sim$7500 K at maximum luminosity, and a reddening correction
is applied to the Spectral Energy Distribution (SED) at peak in order to
obtain a blackbody continuum corresponding to such temperature. Yet another
strategy is adopted for SN 2008S by Botticella et al. (2009), who estimate the
extinction affecting the target based on an IR echo model of the SED at early
stages.

In this work we adopt the same procedure carried out by Stritzinger et al.
(2020), who notes that the observed $V$–$r$ and $r$–$i$ colour curves of
several ILRTs have a similar shape. Assuming that ILRTs should display a
similar evolution of optical colours, a reddening estimate can be obtained by
attempting to match the colour evolution of the bluest objects. While this is
likely an approximation, it is not baseless. In fact, these transients present
a marked homogeneity in their optical spectra (which will be further discussed
in Paper II): since similar conditions in temperature and ionization state are
required to produce the same spectral features, we can expect the optical
colours of these transients to be at least compatible in their photospheric
phases. Following this reasoning, we consider the bluest object in our sample,
AT 2019udc, together with AT 2017be, which shows remarkably similar colours,
and we apply a reddening correction to all the other objects in our sample in
order to superimpose their $B-V$, $g-r$ and $r-i$ colour curves through a
least squares minimization procedure. Only the values measured within 100 days
after maximum are considered. The absorption values for each transient
inferred in this way are reported in the last column of Table 1. AT 2019abn is
by far the most reddened object in our sample, with an estimated internal
absorption of AV=2.34 $\pm$ 0.06 mag. AT 2019udc, by construction, is assumed
to be reddening-free, since it is among the bluest ILRT observed. In Figure 6
we report the colour evolution for our sample of ILRTs after applying the
reddening correction. The optical colours present an initial decrease (i.e.
the objects become bluer) during the rise to maximum. This is particularly
clear in AT 2019udc and AT 2019abn, thanks to their high cadence monitoring
pre-maximum. After peak luminosity, ILRTs become steadily more red in the
following months. This trend may invert as the flux becomes dominated by
emission lines rather than continuum emission, as seen for NGC 300 OT $r-i$
after 150 days post maximum. We note that we are using a conservative estimate
for the reddening affecting SN 2008S, for which we adopt just the Milky Way
absorption of AV=1.13 mag. This is a lower limit to the total reddening along
the line of sight: adopting a light echo model, Botticella et al. (2009) infer
an internal absorption of AV $\sim$ 1 mag. This leads to a peak temperature of
8400$\pm$120 K, closer to an A type star, rather than an F type star. In any
case, even with minimal absorption, SN 2008S is among the bluest ILRTs to
date: therefore if the colour evolution of ILRTs is indeed perfectly
homogeneous, our adopted absorption is likely a lower limit of the actual
value. On the other hand, it is reasonable to expect some scatter in the
temperature and consequently in the colours of ILRTs, granted that all of them
should fulfill the physical requirements for producing the spectrum of an F
type star (Humphreys et al., 2011). In this context, the absorption estimated
so far can be seen as a first order correction, crucial for heavily extincted
targets such as AT 2019abn.

Figure 7: From left to right SED evolution of NGC 300 OT, AT 2019abn and AT
2019ahd. In the upper panel, a single black body is sufficient to fit the
data, represented in blue. At later phases, shown in the lower panel, a second
black body is needed to reproduce the NIR flux excess. Epochs are reported
with respect to maximum light. Flux shifts have been applied for clarity.

For the sake of completeness we compare the reddening estimates just obtained
(which will be adopted for this work) with a straightforward application of
the linear relations between Na ID EW and E(B-V) presented by Turatto et al.
(2003). The detailed evolution of the Na ID EW for this sample of ILRTs will
be shown and discussed in Paper II: here we simply consider the first measured
value for each transient, specifically 0.7$\pm$0.1 Å for NGC 300 OT,
1.1$\pm$0.1 Å for AT 2019abn, 0.9$\pm$0.1 Å for AT 2019ahd and 5.4$\pm$0.2 Å
for AT 2019udc. The two different linear relations provided by Turatto et al.
(2003) allow to determine both a lower and upper estimates of E(B-V) for each
object. The resulting AV range obtained for NGC 300 OT spans between 0.3 and
0.9 mag, in good agreement with our previous estimation of 0.78 mag. In case
of the lowest reddening inferred, the peak luminosity of NGC 300 OT in $r$
band would be 0.4 mag fainter, leading to a peak absolute magnitude Mr= -12.4
mag. For AT 2019ahd we obtain 0.4 mag$<$AV$<$1.3 mag, with the lower limit
being compatible with our previous measurement of 0.37 mag. If we accepted the
larger estimate of AV$\sim$1.3 mag, the peak $r$ band absolute magnitude of AT
2019ahd would increase from -13.3 mag to -14.1 mag. For the other two ILRTs in
the samples the two methods for estimating AV yield more substantial
differences. According to the empirical relations obtained by Turatto et al.
(2003), the EW of the Na ID observed in the early phases of AT 2019abn would
imply an extinction of 0.5 mag$<$AV$<$1.6 mag, significantly lower than the
value 2.34 mag previously obtained. The peak absolute magnitude of AT 2019abn
would decrease from Mr= -15.1 mag to -14.4 mag, or even -13.5 mag in the case
of lowest extinction. On the contrary, AT 2019udc initially displays a
remarkably large Na ID EW of 5.4$\pm$0.2 Å (however, we note that the Na ID EW
rapidly declines to 1.3 Å in just two days, and even below 1 Å after that
phase): this would imply an extinction AV of at least 2.6 mag. The resulting
peak magnitude would be at least Mr= -16.5 mag, firmly within the luminosity
realm of full-fledged SNe. Such critical discrepancies in AV would also lead
remarkable variations in temperature, in particular a hotter AT 2019udc and a
much cooler AT 2019abn, especially around peak luminosity (compared to the
results discussed in the next section and displayed in Figure 8). This is an
unlikely circumstance, given the already mentioned spectral homogeneity of
ILRTs.

##  5 SED Evolution

In order to extract physical quantities of our targets, we perform blackbody
fits on the SED at different epochs. This analysis is carried out through
Monte Carlo simulations, using the python tool
curve_fit555https://docs.scipy.org/doc/scipy/reference/generated/
scipy.optimize.curve_fit.html to perform fits on 200 sets of fluxes randomly
generated with a Gaussian distribution centered at the measured flux value,
and $\sigma$ equal to the error associated to the measurement. Such procedure
was already adopted and described in Pastorello et al. (2021); Valerin et al.
(2022). The blackbody fit to the SED of the target yields the estimated
temperature, and by integrating over the wavelength we obtain the total flux
emitted. Adopting the distances discussed in Section 3 and assuming spherical
symmetry, we calculate the bolometric luminosity of the source. Finally, the
radius is estimated through the Stefan–Boltzmann law. This whole procedure is
repeated for each epoch with suitable photometric coverage, in order to study
the evolution of the inferred physical parameters with time. During the first
phase of evolution all the objects are well fitted by a single black body,
associated to the photosphere, throughout the optical and NIR domains. We
refer to this component as the ”hot” blackbody, in contrast with the ”cold”
blackbody which emerges at later stages. The phase in which only the hot
blackbody is visible has a variable duration: up to 180 days for AT 2019abn,
110 days for AT 2019ahd and only 80 days for NGC 300 OT (Figure 7). The SED of
AT 2019udc is well fit by a single black body at all epochs observed, but it
is possible that the cold black body emerged after the end of our follow-up
campaign.

The values of temperature, luminosity and radius obtained for this hot
blackbody are displayed in Figure 8. The temperature evolution of our sample
is especially homogeneous between 25 and 75 days after maximum, due to our
reddening estimate through colour curves superposition (Section 4). However we
still find interesting differences between the various targets in the
pre–maximum phases. AT 2019abn displays an almost constant temperature of
$\sim$4600 K for several days before slowly reaching the peak temperature of
$\sim$5900K in $\sim$20 days. AT 2019udc qualitatively follows the same
behaviour, but in a shorter timescale (less than 10 days) and reaching 7000 K
at peak. This initial increase in temperature could be explained with the
injection of additional energy provided by the interaction between ejecta and
CSM, as happens for interacting SNe (e.g. Dessart et al. 2016). AT 2019ahd, on
the other hand, starts from a temperature of $\sim$7500 K, before quickly
cooling to 6000 K at peak luminosity. From this point onward, AT 2019ahd
closely follows the behaviour of AT 2019abn. In this respect, the early
temperature evolution of AT 2019ahd is reminiscent of that of SN 2005cs
(displayed in Figure 8 for comparison) and LL SN IIP in general, where the
temperature quickly declines during the rapid expansion of the ejecta. NGC 300
OT shows a very simple, monotonic temperature evolution, but in this case we
miss the pre–maximum photometric coverage.

Figure 8: Temperature, luminosity and radius evolution of the hot black body
of the four ILRTs in our sample. The same values measured for SN 2005cs are
shown as a dotted line for comparison.  Figure 9: Temperature, luminosity and
radius evolution of the cold black body of the three ILRTs in our sample that
present a NIR excess in their SED. In the third panel, the dashed line
represents the position of material expanding with velocity of 550 km s-1.

In the middle panel of Figure 8 we present the bolometric luminosity obtained
for the ”hot” blackbody. The bolometric luminosity behaves in a similar way to
what is described in Sect 3.5, with AT 2019abn being the brightest ILRT,
showing a peak luminosity of 1.9$\pm$ 0.3 $\times$ 1041 erg s-1. As previously
pointed out, its decline rate is slower compared to other objects of the same
class, but it is not flat like the plateau of SNe IIP. AT 2019udc is
characterized by a marked peak (1.4$\pm$0.5 $\times$ 1041 erg s-1) followed by
a fast decline. AT 2019ahd and NGC 300 OT display more modest peak
luminosities, respectively of 4.4$\pm$1.1 and 2.7$\pm$1.0 $\times$ 1040 erg
s-1. As for the evolution of the radius of the emitting source, shown in the
bottom panel of Figure 8, it appears that all ILRTs in our sample follow a
similar behaviour. After maximum, the transients show a roughly constant
radius with time, although with different values. AT 2019abn again stands out
from the group, showing a blackbody radius that at first quickly increases
from 21$\pm$2 to 36$\pm$3 AU from discovery to peak luminosity, and then
remains at 30 to 40 AU in the following 125 days. These values are roughly two
to three times those obtained for the other three targets. AT 2019ahd shows
qualitatively the same behaviour, with a radius growing from 7$\pm$1 to
15$\pm$1 AU from discovery to peak magnitude, and a subsequent slow evolution
ranging from 14$\pm$1 to 18$\pm$1 AU within 110 days after maximum. AT 2019udc
on the other hand does not show an increase in the radius during the
pre–maximum phase, but rather a marginal decrease, from 23$\pm$3 to 19$\pm$2
AU. The following slow evolution of the blackbody radius between 16$\pm$2 and
21$\pm$2 AU over the course of 90 days is reminiscent of those of the other
two ILRTs already presented. Finally, for NGC 300 OT we do not have
pre–maximum data, but the evolution of the blackbody radius after the observed
maximum is again slow, spanning from 11$\pm$1 to 16$\pm$1 AU in 90 days. This
tendency of the hot blackbody radius to linger around a constant value is in
stark contrast with the monotonic increase in radius for SNe IIP and Low
Luminosity SNe IIP during the first 80 days, as shown by the radial evolution
of SN 2005cs.

Figure 10: Bolometric light curves of our sample of ILRTs, with the addition
of SN 2008S and AT 2017be. Coloured dotted lines show the 56Ni decline rates
for the upper limits estimated for each object in our sample.

So far we described the physical properties of the hot blackbody, which is
associated to the photosphere of the transient and is usually well visible for
$\sim$100-150 days after maximum. At later phases however, as the gas cools
down and expands, an excess in the NIR flux is detected (extending to the MIR,
when such measures are available). Such feature can be associated with the
formation of dust, which contributes to the SED with a second emission
component characterised by a low temperature compared to the hot continuum
observed in the first months of evolution (T $\lesssim$ 1500 K, Botticella et
al. 2009; Cai et al. 2018). In the bottom panels of Figure 7 are shown
blackbody fits performed to the SED of our targets at epochs when two
components coexist. At the latest phases, as the objects shift from the
photospheric to the nebular phase, the optical flux is entirely supported by
emission lines (H$\alpha$, H$\beta$, [CaII], Ca NIR triplet), and there is no
more evidence of a hot spectral continuum. At these epochs we still identify a
contribution from the ”cold” black body associated with dust emission. This
feature is especially clear in AT 2019abn and NGC 300 OT (at 761 days after
maximum, see Section 6.1) thanks to the MIR measurements. In Figure 9 we
present the physical parameters obtained for the “cold” blackbody component
associated with dust emission. In principle this cold blackbody could be the
result of a NIR light echo (e.g. Miller et al. 2010). However, the timing of
the appearance of this NIR excess (80 days for NGC 300 OT being the shortest)
would imply that the dust causing the light echo is located at least
$\sim$6900 AU away from the transient. Botticella et al. (2009) show that the
flash from SN 2008S is able to create a dust-free cavity of just $\sim$2000
AU: it appears unlikely that the energy radiated by our ILRTs can bring such a
distant body of dust close to its sublimation temperature ($\sim$1400 K for
silicates and $\sim$1800 K for graphite, e.g. Jiang et al. 2016). Therefore,
we favour the interpretation that this cold blackbody component is emitted by
newly condensed dust rather than by a light echo. AT 2019abn and AT 2019ahd
show very similar cold components, with temperatures cooling from $\sim$1600
to $\sim$1200 K over a timescale of hundreds of days. The luminosity of both
components evolve slowly, starting from $\sim$3 $\times$ 1039 erg s-1. The
radius of the emitting source is around 60 AU for AT 2019ahd and 75 AU for AT
2019abn. The most relevant difference between the two transients is that AT
2019ahd develops the ”cold” component sooner, at around 110 days. We stress
that the blackbody fits at these epochs are affected by large errors, due to
the uncertainty in disentangling the hot and cold components in the SED.

This is true also for NGC 300 OT, but in this case we have a higher cadence of
NIR observations (also accounting for previously published observations),
allowing us to better constrain the evolution of the cold component. A first,
fast decline in temperature is observed between 71 days and 130 days after
maximum, when the dust cools from 1550$\pm$170 K to 1150$\pm$90 K. The
subsequent temperature decline is slower, reaching 570$\pm$10 K at 761 days.
Such late estimate is possible thanks to publicly available WISE data. The
other two late measurements at 398 and 582 days were performed on MIR data
taken by Ohsawa et al. (2010). The luminosity of this ”cold” component fades
from 5.5$\pm$1.9 $\times$ 1039 erg s-1, just after its emergence, to
9.5$\pm$0.9 $\times$ 1038 erg s-1 at 761 days. The radius inferred for the
dust emission at first shrinks from $\sim$100 AU to $\sim$40 AU, but around
180 days the trend inverts and the radius grows to 235$\pm$20 AU at 761 days.
The initial shrinking of the emitting source can be qualitatively explained as
follows: we are observing dust formation far from the star, with dust
condensing at progressively smaller radii as the transient becomes dimmer and
the temperature decreases. Indeed, we know that the progenitor star was
enshrouded in dust (Thompson et al., 2009) before the transient event caused
its sublimation, and we may be witnessing the rebirth of this dusty cocoon. On
the other hand, the increase in radius of emitting dust observed after 200
days can be found also in SNe, where the dust expands together with the ejecta
(e.g. Wesson et al. 2015). As a simple comparison, in the bottom panel of
Figure 9 we mark with a dashed line the position of matter expanding with a
velocity of 550 km s-1, and we note that the three latest measures of radius
for NGC 300 OT are compatible with such trend. As will be shown in Paper II,
the velocity of 550 km s-1 is also well in line with the full width at half
maximum velocity estimated from the emission lines of NGC 300 OT,
corroborating the idea that the dust is moving jointly with the expanding gas
seen during the photospheric phase. As previous observations displayed, part
of the dusty cocoon surrounding ILRTs may survive the explosion, avoiding
sublimation thanks to a large distance from the star (Botticella et al., 2009;
Prieto et al., 2009). However, in the present work we lack the mid and far-
infrared coverage at early phases necessary to detect the emission from such
dust component.

In order to obtain the bolometric luminosity of ILRTs, we combine the
contribution of the “hot”, photospheric component, and the ”cold”, dusty
component. At late epochs, a blackbody continuum is no longer discernible in
the optical domain, with only emission lines dominating the spectra.
Therefore, to measure the bolometric luminosity in those cases we integrate
the fluxes in the optical domain using the trapezoidal rule. On the other
hand, at longer wavelengths it is still possible to perform a blackbody fit
and integrate the flux even beyond the observed spectral region. In fact,
while the optical domain only displays emission lines at late time, there
still is still evidence of thermal continuum in the NIR and MIR domain. The
bolometric luminosity obtained for our sample of ILRTs is reported in Figure
10. We analysed an unprecedented amount of NIR and MIR data for ILRTs, which
allow us to better infer the luminosity contribution at longer wavelengths,
crucial at late times. The dotted lines in Figure 10 show the expected
behaviour of a light curve powered exclusively by 56Co decay: it is evident
that AT 2019abn, AT 2019ahd and NGC 300 OT are characterised by a late time
decline shallower than what is expected if only 56Co decay is supporting their
late time luminosity. Of course a more shallow slope in the light curve does
not exclude the presence of 56Co, but rather it requires an additional
mechanism to explain the late time luminosity of ILRTs. In order to estimate
an upper limit to the 56Ni mass powering the late linear decline of ILRTs, we
employ the analytical formulation provided by Hamuy (2003) for the luminosity
of 56Ni and 56Co decay. By considering the first data points available during
each linear decline, we obtain upper limits to the 56Ni mass of 6.7x10-3 M⊙
for AT 2019abn, 2.0x10-3 M⊙ for AT 2019ahd and 1.2x10-3 M⊙ for NGC 300 OT. AT
2019udc is the only object that shows a linear decline compatible with the one
expected from 56Co decay, resulting in an estimate of 3.3$\pm$0.3 x10-3 M⊙ of
56Ni.

Model L [1038 erg s-1] T [K] R [AU] $\tau_{5}$ Md [10-4 M⊙] Graphite 0.1 $\mu
m$ 9.1 (1.4) 576 (5) 228 (18) 5.9 (0.7) 1.9 (0.5) Graphite 1.0 $\mu m$ 9.1
(1.4) 579 (5) 225 (18) 4.9 (0.6) 0.45 (0.11) Silicate 0.1 $\mu m$ 9.2 (1.4)
585 (6) 222 (17) 19.4 (2.4) 19 (5) Silicate 1.0 $\mu m$ 9.2 (1.4) 586 (6) 222
(18) 16.5 (2.0) 9.5 (2.4)

Table 2: Parameters obtained for the different SED fit models of NGC 300 OT at
761 d. Errors are reported in brackets.

Figure 11: Fits to the late time SED of NGC 300 OT. In the different panels
are reported the fits for the different dust compositions and grain sizes. The
best fit to the data is shown as a solid blue line, while the dashed lines
show the effect of changes in the optical depth while keeping temperature and
radius of the source fixed.

We can also provide values of the total energy radiated by our ILRTs during
the time they were monitored: NGC 300 OT emitted 2.5$\times$1047 erg over the
course of 760 days, with 1.5$\times$1047 erg released in the first 120 days
after maximum. Similarly, AT 2019ahd radiated 4.0$\times$1047 erg in 440 days,
2.3$\times$1047 erg in the first 100 days, while AT 2019udc emitted
4.0$\times$1047 erg in about 100 days. Finally, AT 2019abn radiated
1.7$\times$1048 erg in 480 days, the vast majority (1.6$\times$1048 erg)
emitted in the first 240 days. Aside from the total energy released by these
transients, the decline rate of their bolometric luminosity at late time
appears particularly interesting.

##  6 Late time mid-infrared monitoring of ILRTs

###  6.1 Dust evolution and composition

Figure 12: SED of AT 2019abn 1956 days after discovery. Circles represent flux
measurements obtained with JWST on 2024-05-31, while squares represent data
extrapolated from the measurements on 2023-06-08. Solid lines trace the best
fits for dust with different composition and grain size. The gray dashed line
displays a scaled emission spectrum of PAH+ with size 14 Å (Draine & Li,
2007).

Ohsawa et al. (2010) monitored the evolution of NGC 300 OT in the IR domain
(2-5 $\mu m$) at 398 and 582 days, finding that the hot dust component had
progressively cooled down to 810 K and ultimately to 680 K. The probed
wavelength range did not provide information on the cool, pre-existing dust
component, which by that time could only contribute $\sim$1% of the observed
flux. Ohsawa et al. (2010) also set lower limits for the optical depth of the
dust: $\tau_{\nu}>$ 12 at 398 days and $\tau_{\nu}>$ 6 at 582 days,
effectively stating that the dust remains optically thick even at very late
phases. In this condition, the lower limit to the mass of emitting dust was
estimated to be $\sim$10-5 M⊙.

Thanks to the WISE data collected on 2010-06-17 in the $W1$, $W2$, $W3$ and
$W4$ filters, we are able to expand the analysis on the late time evolution of
the dust in NGC 300 OT, 761 days after maximum. To correct these values for
absorption, we extend the reddening law to 22 $\mu m$ by employing the
tabulated values and prescriptions found in Rieke & Lebofsky (1985) and Draine
(1989). The late time K band coverage with SOFI obtained 853 days after
maximum allows us to linearly extrapolate the K-band flux at 761 days in order
to have a more detailed SED of the transient. We fit our flux measures through
the same procedure detailed in Section 5. Following in the footsteps of Ohsawa
et al. (2010), instead of a simple Planck function we use
$f(\nu)\propto(1-e^{-\tau_{\nu}})B_{v}(T_{d})$ as a fitting function, where
$\tau_{\nu}$ is the optical depth, $B_{\nu}$ is the Planck function and
$T_{d}$ is the dust temperature. The multiplicative factor in front of the
Planck function aims to account for the different opacity of dust at different
wavelengths. It is relevant to point out that this model is isothermal, while
a cloud of optically thick dust would present a temperature gradient, so this
is already an approximation.

To better differentiate the properties of the dust depending on the size of
the dust grains and their chemical composition, we perform the fits using four
different sets of opacity kν, tabulated by Fox et al. (2010). Two sets are
opacity values for graphite dust, with grain size of 0.1 and 1 $\mu m$
respectively, while the other two sets of opacity assume the same grain size,
but present a silicate composition. Since the values presented by Fox et al.
(2010) only cover up to 13 $\mu m$ while our data reach 22 $\mu m$ (thanks to
the W4 channel), we have to extrapolate the behaviour of kν in that region.
For the graphite dust we follow the prescription from Draine (2016), using a
$\lambda^{-2}$ scaling. The silicate opacity is instead characterised by an
additional bump in opacity around 19 $\mu m$: to reproduce it, we adopt the
opacity behaviour reported by Draine & Lee (1984). Beyond 9 $\mu m$, graphite
dust tends to have a lower opacity compared to graphite dust (see Figure 17 in
Appendix). Silicate dust stands out because of the ”bumps” in opacity in the
MIR domain, in contrasts with the smooth behaviour of the graphite opacity.

Model L [1038 erg s-1] T [K] R [AU] $\tau_{5}$ Md [10-4 M⊙] Graphite 0.1 $\mu
m$ 2.8 (0.1) 347 (9) 350 (15) 96 (33) 71 (24) Graphite 1.0 $\mu m$ 2.8 (0.1)
347 (10) 349 (17) 198 (87) 46 (20) Silicate 0.1 $\mu m$ 2.8 (0.1) 379 (15) 290
(18) 1.2 (0.6) 1.8 (0.8) Silicate 1.0 $\mu m$ 2.8 (0.1) 372 (10) 303 (13) 1.6
(0.9) 1.6 (0.9)

Table 3: Parameters obtained for the different SED fit models of AT 2019abn at
1956 days. Errors are reported in brackets. Figure 13: Left panel: images of
NGC 300 OT in the [4.5] $\mu m$ channel of Spitzer from the progenitor until
the disappearance of the transient. Right panel: updated version of the figure
shown in Adams et al. (2016), with their measurements in the [4.5] $\mu m$
channel shown with circles. Additional data points for NGC 300 OT and AT
2019abn are shown with stars (upper limits are represented as empty symbols).
We also show the JWST data point of AT 2019abn obtained by Rose et al. (2024).
The progenitor luminosity of each transient is shown as a horizontal dashed
line.

In Figure 11 are reported the results of the SED fitting procedure for the
different dust compositions and grain sizes considered. The parameters
obtained are reported in Table 2. The parameters of the best fitting black
body are similar regardless of dust particles size. There is, instead, a small
variation on whether we adopt graphite dust or silicate dust. The dust
temperature obtained for graphite is slightly lower than the temperature
obtained for silicate dust, with a radius that is consequently larger. All
things considered, the differences between the black body parameters of
silicate dust and graphite dust are negligible: the real difference lies in
the optical depth inferred. We consider the optical depth at 5 $\mu m$
($\tau_{5}$), to perform a comparison between the different models. As shown
by the dotted lines in Figure 11, at low optical depth ($\tau_{5}<$1), the
models deviate significantly from the Planck function: silicate dust shows a
double peaked emission, while the emission of graphite dust with grains of 1.0
$\mu m$ is characterised by a ”shoulder” at around 3.2 $\mu m$. Graphite dust
with grains of 0.1 $\mu m$ do not show such clear features, but the SED model
is systematically too narrow to properly fit the observed data in the
optically thin case. Indeed, all the best fit yield optically thick dust at
all wavelengths considered. However, in the case of silicate dust the best fit
is obtained with an optical depth of $\tau_{5}$=19.4 for 0.1 $\mu m$ grains
and $\tau_{5}$=16.5 for 1.0 $\mu m$ grains, basically returning to a Planck
function. On the other hand, the optical depth inferred for graphite dust are
$\tau_{5}$=5.9 for 0.1 $\mu m$ grains and $\tau_{5}$=4.9 for 1.0 $\mu m$
grains: optically thick, but still distinguishable from a pure Planck
function. We notice that none of the models can accurately fit the point at 22
$\mu m$: we speculate that this infrared excess is produced by the cold dust
component that further cooled down since its detection by Prieto et al.
(2009). Finally, through our measures of the optical depth, it is possible to
obtain an estimate of the dust mass using the equation (as done by
Hosseinzadeh et al. 2022):

$\hskip 71.13188ptM_{dust}=\frac{4\pi R_{dust}^{2}\tau_{\nu}}{3k_{\nu}}.$ (1)

Here we are assuming a constant density profile in the dust cloud, which is of
course an additional approximation. Depending on the composition and grain
size considered, the inferred dust mass spans from 4.5$\times$10-5 M⊙ up to
1.9$\times$10-3 M⊙ (see Table 2). It is interesting to note that such values,
obtained at $\sim$800 days after explosion, are perfectly in line with the
amount of dust found in the ejecta of core-collapse SNe
666https://nebulousresearch.org/dustmasses/ (e.g. Fabbri et al. 2011; Bevan et
al. 2020). We remark that this fitting procedure was performed on the dust
which was identified by Prieto et al. (2009) 93 days after discovery at a
temperature of 1510 K (and named ”warm” dust), and whose cooling is tracked in
the upper panel of Figure 9. The initial temperature of this dust component is
close to the dust sublimation temperature: this behaviour is compatible with
newly formed dust which condensed few months after the peak luminosity of NGC
300 OT, and by the time of our fit has cooled down to $\sim$580 K. Similarly,
also the third blackbody component with a temperature of 485 K detected by
Prieto et al. (2009) at 93 days (identified as circumstellar dust that
survived the explosion) must have cooled down, and the peak of its emission
has shifted outside the monitored domain. As mentioned above, this component
may be the origin of the exceeding flux observed at 22 $\mu m$.

We replicate this SED analysis on AT 2019abn, thanks to publicly available
images of M51 taken by the JWST on 2022-12-13 (proposal 1240, PI M.E.
Ressler), 2023-06-08, 2023-06-14 (proposal 1783 PI A. Adamo) and 2024-05-31
(3435 PI K.M. Sandstrom). The object is still visible even five years after
its peak luminosity: we report the magnitudes obtained with PSF fitting
through ecsnoopy in Table 21. The wavelength coverage of the first three
epochs is too scarce to provide a well sampled SED, therefore we focus on the
measurements obtained on 2024-05-31, 1956 days after discovery. To fill the
gap between the F430M and F1000W filters, we infer the behaviour of the F560W
and F770W filters observed the previous year (2023-06-08). To do so, we assume
a constant colour evolution using the filters F444W (observed on 2023-06-08)
and F430M (observed on 2024-05-31) as anchors. The flux in these overlapping
filters decreases by a factor of 1.5 between the two epochs, and we assume the
same holds true for the F560W and F770W filters. Since cooling objects tend to
become redder, this is likely an underestimation of the fluxes in F560W and
F770W on 2024-05-31, yet this simple approximation allows us to constrain a
crucial spectral region. The resulting SED is displayed in Figure 12. Firstly,
we point out that the Pa$\alpha$ line is located within the F182M filter, and
this could account for the relative brightness of the transient in this band,
which is therefore excluded from the following discussion.

In Figure 12 we show as solid lines the various fits to the observed SED of AT
2019abn with dust models characterised by different chemical composition and
grain size. Parameters of each fit are shown in Table 3. The luminosity of the
transient is consistently found to be (2.8$\pm$0.1$)\times$1038 erg s-1 (in
Figure 17 this result is added to the bolometric light curve of AT 2019abn,
updating Figure 10). There is instead a discrepancy in the resulting
temperature and radius depending on the dust composition: in the case of
graphite, the best fits yield a temperature of $\sim$350 K and a radius of
$\sim$350 AU, while for the silicate dust the temperature found is $\sim$375
K, with a blackbody radius of $\sim$300 AU. Grain size only plays a marginal
role in shaping these results. Graphite dust models yield high optical depth
($\tau_{5}$$>>$1), leading to infer lower limits to the dust masses in the
order of several 10-3 M⊙. On the other hand, the best fitting silicate dust
models are closer to the optically thin regime ($\tau_{5}$$\sim$1), with
inferred dust masses of the order of $\sim$2$\times$10-4 M⊙. These results,
however, need to be interpreted with caution, since even the best fits
struggle to accurately reproduce the observed data. Particularly puzzling is
the flux “depression” in the F1000W band compared to the flux values found in
the F770W and F1130W bands. A possible explanation for this departure from a
simple blackbody emission may be the presence of polycyclic aromatic
hydrocarbon (PAH). In fact, PAH are characterised by emission features around
7 $\mu m$ and 11 $\mu m$. In Figure 12 we display a scaled emission spectrum
of ionized PAH with size of 14 Å (Draine & Li, 2007) to show the match between
the PAH emission features and the peculiarities of the observed SED. The
presence of PAH is also corroborated by MIR spectroscopy of AT 2019abn
obtained on 2022 Rose et al. (2024). Accurate PAH modelling is beyond the
scope of this study and is deferred to later works. Beyond these
considerations on the shape of the SED, JWST observations provide valuable
information on the MIR luminosity evolution of AT 2019abn five year after its
discovery, as discussed in the following section.

###  6.2 Photometric decline below progenitor luminosity

Adams et al. (2016), monitored the two ILRTs NGC 300 OT and SN 2008S with the
Spitzer telescope for several years, until they both faded below the
luminosity of their respective progenitor. We update this follow-up campaign
by analysing the Spitzer images collected between 2015-10-20 and 2019-11-24
with the Spitzer [4.5] $\mu m$ channel. A visual inspection of the images
shows that NGC 300 OT has faded below the detection threshold (Figure 13, left
panel). We measure the flux on all public Spitzer [4.5] $\mu m$ images through
PSF fitting employing ecsnoopy. Our results are in good agreement with the
values measured with aperture photometry by Adams et al. (2016), with the
exception of the very last detection, on 2015-02-09: we find a value of
600$\pm$300 L⊙ against the 140$\pm$110 L⊙ obtained with aperture photometry
(the difference can be appreciated on the right panel of Figure 13). The
complex background surrounding the target, as seen in the left panel of Figure
13, contributes to the uncertainty of this measure. All the images collected
from that moment only provide upper limits to the luminosity of NGC 300 OT: in
particular, in the right panel of Figure 13 we show the 1$\sigma$ limits
obtained from PSF fitting. We therefore confirm that since 2015 NGC 300 OT has
faded below the detection threshold, well below the progenitor luminosity.

We are also able to include AT 2019abn among the ILRTs with MIR coverage
spanning several years. The light curve up to $\sim 500$ days is provided by
the Spitzer and WISE monitoring already shown in Figure 1, while the last two
epochs are provided by the late JWST observations obtained 1598 and 1956 days
after discovery and presented in the previous section. Despite the slight
mismatch in the covered wavelength, the JWST filters F444W and F430M are
sufficiently close to the [4.5] $\mu m$ and W2 filters to provide a coherent
light curve, which is shown with red stars symbols in Figure 13. The behaviour
of AT 2019abn is similar to that of SN 2008S, where the initial decline rate
significantly slows down after $\sim 200$ days. It is interesting to consider
the evolution of the transient compared to its progenitor luminosity in the
[4.5] $\mu m$ channel provided by Jencson et al. 2019, which is marked in
Figure 13 as a red horizontal dashed line. It is possible to notice that on
2023-06-08 AT 2019abn has already faded below its progenitor luminosity, with
the latest measure obtained on 2024-05-31 being over two times dimmer than the
luminosity of the star before the event. All three ILRTs that were monitored
for multiple years in the MIR domain eventually became dimmer than their
progenitor star, and so far none of them has shown sign of stopping their
steady luminosity decline: this fact supports the interpretation that ILRTs
are terminal events.

Figure 14: The solid black line represents the ILRTs template light curve,
while the gray shaded area shows the 1 $\sigma$ deviation from the mean. The
coloured dashed lines display the interpolation performed on each object. In
the bottom panels the ILRTs are separated between slow and fast declining
objects.

##  7 Template Light curve

In order to better characterize this class of objects, we produce an $r$ band
template light curve for ILRTs. We are motivated also by the potential
usefulness of such templates in our future attempts to classify new transients
discovered by the Vera Rubin Observatory (formerly Large Synoptic Survey
Telescope, Ivezić et al. 2019) and released by dedicated science brokers such
as Lasair (Smith et al., 2019) and Alerce (Förster et al., 2021). With the
foreseen amount of data, it will be impossible to study in detail every single
target, and template light curves for different classes of transient could
prove to be useful tools for filtering the data stream, in addition to the
classification algorithms and tools that are currently being developed (e.g.
Fraga et al. 2024; de Soto et al. 2024). Apart from NGC 300 OT, AT 2019abn, AT
2019ahd and AT 2019udc, which were presented above, we broaden our sample
including SN 2002bu (Smith et al., 2011), SN 2008S (Botticella et al., 2009),
AT 2017be (Cai et al., 2018), SNHunt120 (Stritzinger et al., 2020), AT 2010dn,
AT 2013jc, AT 2013la, AT 2013lb, AT 2018aes (Cai et al., 2021) and AT 2022fnm
(Moran et al. 2024, submitted). We chose to focus on the $r$-band, since it is
typically well-sampled and allows for a reliable comparison between objects.
The peak absolute magnitude of different ILRTs can span at least three
magnitudes (from -12 mag to -15 mag, see Figure 5): however, here we are
interested in recovering just the expected light curve shape of ILRTs. For
this reason we normalised the peak magnitude of all objects considered to the
same arbitrary value. Both the light curve shape and the absolute magnitude at
peak can then be used as filters to identify future ILRTs candidates.

As a first step to produce a light curve template we make use of Gaussian
Processes to interpolate the light curves of each object (see e.g. Inserra et
al. 2018 for a more detailed description of the procedure). In particular, we
employ the Matern 3/2 kernel found in the python package george (Ambikasaran
et al., 2015), and as for the mean function we adopt equation 1 given by Bazin
et al. (2011). It is worth noticing that we performed the interpolation
procedure in the ”luminosity - time” space. Given the different sampling of
each event, this first step is performed to ensure that each objects holds the
same weight in the construction of the template, regardless of how many data
points were collected at a given phase. After interpolating the light curve of
each object, we recover the mean value and the standard deviation of the ILRTs
luminosity within temporal bins of 3 days, which we empirically choose as a
good compromise that yields a rather smooth template which still has a
reasonable time resolution. The resulting ”mean light curve” of an ILRT is
shown as a black solid line in the upper panel of Figure 14, with the grey
shaded area representing the 1 $\sigma$ deviation from the mean.

Due to the low number of available ILRTs, the rising part of the template
becomes reliable only at about -10 days with respect to maximum luminosity:
before that phase the template is dominated by the widely different behaviours
of AT 2019abn and AT 2018aes. The overall template light curve rises of about
0.5 mag from -10 days to 0 days, and fades by 1 mag from maximum to 50 days.
As time progresses, the 1 $\sigma$ region gets wider, with objects evolving at
different rates. Objects fading below the detection threshold can result in a
jagged profile of the template, as happens at about 100 days due to the
disappearing of AT 2018aes and AT 2022fnm. There is a variety of properties in
the light curves of the considered ILRTs, but we can roughly divide them in
two subclasses, based on their behaviour in the 50 days after maximum. The
first group of objects present slowly declining, convex light curves, which on
average only fade by 0.8 mag from day 0 to day 50. The second group of objects
display fast declining, concave light curves, which on average fade by more
than 1.3 mag in the same time span (see Figure 14, lower panels). While this
distinction is clear in some cases (AT 2019abn and AT 2019ahd are slow
decliners, while AT 2019udc and AT 2022fnm are fast decliners), there are some
objects with intermediate properties, such as AT 2013la, whose light curve
quickly fades in the first two months, only to flatten after 75 d, ultimately
becoming even brighter than AT 2019abn after 130 d. Another outlier is AT
2018aes, which is characterised by the shallowest rise to maximum light,
followed by a rather ”standard” slow decline for 40 days before abruptly
fading by 3.2 mag in 60 days. The dichotomy between slow and fast declining
ILRTs is reminiscent of the division between SNe IIP and IIL (e.g. Anderson et
al. 2014), with the progenitors of the slow declining ILRTs retaining larger
hydrogen envelopes compared to the progenitors of fast declining ILRTs. Of
course, a larger sample of ILRTs is needed to verify if this analogy holds
true or if it is a mere coincidence.

Figure 15: Bolometric light curves of our sample of ILRTs (represented with
black circles) with a toy model reproducing their shape. The errors on the
data points, dominated by the uncertainty on distance and reddening
estimations, are reported as a gray shaded area. The toy models attempting to
reproduce the behaviour of each transient is shown as a solid light blue line.
The energy sources powering the different phases of the light curves are shown
as dashed lines.

##  8 A toy model for ILRTs light curves

Transient 56Ni Mbulk Vbulk Ebulk Rbulk Menv Venv Eenv Renv tCSM [M⊙] [M⊙] [km
s-1] [erg] [cm] [M⊙] [km s-1] [erg] [cm] [days] AT 2019abn 6.7x10-3 7.0 2000
6.5x1049 2x1013 1 5500 2.7x1048 1x1014 12 AT 2019ahd 1.8x10-3 3.5 4500
4.1x1049 5x1012 0.5 5000 7.0x1046 1x1014 3 NGC 300 OT 1.2x10-3 4.2 3500
3.9x1049 4.5x1012 - - - - 3 AT 2019udc 3.5x10-3 0.9 12000 3.7x1049 1.0x1013 -
- - - 2

Table 4: Parameters used in the models displayed in Figure 15.

In this section we present a simple model in the attempt to reproduce the
shape of the bolometric light curves of ILRTs in the context of a weak SN
explosion. The end goal is to obtain a rough estimate of parameters such as
the amount of mass ejected and its velocity. The basic concepts are taken from
Chatzopoulos et al. (2012), which in turn expand the approach introduced by
Arnett (1980, 1982). First of all, 56Ni radioactive decay is expected to be a
relevant power source for SNe, and its luminosity over time is given by the
equation:

$\hskip
42.67912ptL_{Ni}(t)=\frac{2M_{Ni}}{t_{d}}e^{-[\frac{t^{2}}{t^{2}_{d}}+\frac{2R_{0}t}{vt^{2}_{d}}]}[(\epsilon_{NI}-\epsilon_{Co})\times\\\
\hskip
42.67912pt\times\int^{t}_{0}[\frac{R_{0}}{vt_{d}}+\frac{t^{\prime}}{t_{d}}]e^{[\frac{t^{\prime
2}}{t^{2}_{d}}+\frac{2R_{0}t^{\prime}}{vt^{2}_{d}}]}e^{-t^{\prime}/t_{Ni}}dt^{\prime}+\\\
+\epsilon_{Co}\int^{t}_{0}[\frac{R_{0}}{vt_{d}}+\frac{t^{\prime}}{t_{d}}]e^{[\frac{t^{\prime
2}}{t^{2}_{d}}+\frac{2R_{0}t^{\prime}}{vt^{2}_{d}}]}e^{-t^{\prime}/t_{Co}}dt^{\prime}](1-e^{-At^{-2}}),$
(2)

where MNi is the mass of synthesised 56Ni, tNi and tCo are the half lives of
56Ni and 56Co, while $\epsilon_{Ni}$ and $\epsilon_{Co}$ are the energy
generation rates of 56Ni and 56Co released during the radioactive decay. $A$
is a constant that accounts for the opacity of the ejecta to $\gamma$-rays,
with large values of $A$ corresponding to complete trapping. The constant
values are the same reported in Chatzopoulos et al. (2012). This equation
takes into account the diffusion time through an homologously expanding gas of
mass $M$, initial radius $R_{0}$ and characteristic expansion velocity $v$. As
discussed in Paper II, the velocity inferred from the width of the emission
lines of our sample of ILRTs can reach only up to $\sim$103 km s-1. However,
the observed emission lines of ILRTs originate in a dense CSM which is
obscuring the underlying material: as happens for SNe IIn, fast ejecta may be
hiding below this layer of dense gas. Theoretical expectations for ECSNe
suggest that their ejecta should be less energetic than a standard SN ($v$
$\lesssim$ 104 km s-1). The characteristic timescale $t_{d}$ of the light
curve can be written as a combination of the diffusion timescale $t_{0}$ and
the hydrodynamical timescale $t_{h}$:

$\hskip 42.67912ptt_{d}=\sqrt{t_{0}t_{h}}\hskip
28.45274ptt_{0}=\frac{kM}{\beta cR_{0}}\hskip
28.45274ptt_{h}=\frac{R_{0}}{v},$ (3)

where $\beta$ is a constant linked to the density profile of the mass, and $k$
is the opacity of the ejecta, for which we adopt a value of 0.33 cm2 g-1.
As an additional source of luminosity, we consider the radiation emitted by
the expanding and cooling gas, which was heated by the blast wave that
followed the explosion. This term was already introduced by Arnett (1980) to
reproduce the slowly declining light curves of SNe IIP. Using the formalism of
Chatzopoulos et al. (2012), such luminosity term is written as:

$\hskip
71.13188ptL_{blast}(t)=\frac{E_{th}}{t_{0}}e^{-[\frac{t^{2}}{t^{2}_{d}}+\frac{2R_{0}t}{vt^{2}_{d}}]},$
(4)

where Eth is the internal energy which was deposited in the ejecta during the
explosion. To better reproduce the observed shape of the light curve, we
consider two blast terms: one associated with the envelope, less massive and
more extended, characterized by a short diffusion time, and another associated
with the bulk of the ejecta, more massive and dense, with a much longer
diffusion timescale. Dividing the ejecta in two regions is not a novelty: such
approach has been successfully used, for example, by Nagy & Vinkó (2016). The
total time dependent luminosity is therefore the sum of these three
contributions:

$\hskip 56.9055ptL_{tot}=L_{Ni}+L_{bulk}+L_{envelope}.$ (5)

The final piece of the model is the thick CSM surrounding the transient, which
is a key feature observed in ILRTs spectra. This element does not provide
additional energy, but it simply reprocesses the total luminosity emitted by
the ejecta and 56Ni, delaying its appearance. To reproduce this effect, we use
the fixed photosphere approximation presented by Chatzopoulos et al. (2012):

$\hskip
28.45274ptL_{final}(t)=\frac{1}{t_{CSM}}e^{-\frac{t}{t_{CSM}}}\int^{t}_{0}e^{\frac{t^{\prime}}{t_{0}}}L_{tot}(t^{\prime})dt^{\prime},$
(6)

where $t_{CSM}$ is the diffusion time through the thick CSM shell surrounding
the transient. Its effect is crucial in the first phases, during which the
blast terms Lbulk and Lenvelope start abruptly from the maximum luminosity,
without a rising phase. A CSM shell with a diffusion time of few days allow
the model to reproduce the rise observed in ILRTs. In Figure 15 are shown the
models and the bolometric light curves they are trying to emulate. The
contribution of each component is shown with different colours: the parameters
relative to each of them are reported in Table 4. One weakness of the approach
outlined above is the large number of free parameters, as well as the
degeneracy between some of them: similar solutions can be obtained while
inputting different parameters. Instead of blindly applying a fitting
procedure, we tried to input reasonable parameters in the context of SNe,
gradually modifying them to improve the agreement with the data. An additional
fragility of this approach is the assumption of spherical symmetry, which may
be a crude approximation in the case of these transients (e.g. Soker & Kashi
2012).

AT 2019abn is definitely the most successful example within our sample. The
emission from a rather massive envelope, combined with a CSM diffusion time of
10 days, seems to properly reproduce the rise and the maximum phases. The
subsequent slow decline can be explained by slow ejecta which trap the photons
for almost 200 days. The 56Ni contribution is not significant until the late
phases, and it is definitely too faint to explain the evolution after 200
days: as mentioned in the previous section, an additional source of energy is
likely needed to explain the late time luminosity of ILRTs.
The parameters used to model AT 2019ahd do not differ significantly from the
ones used for AT 2019abn: they are mainly scaled down in mass and internal
energy of the ejecta. The blast term associated with the envelope is not as
crucial, but the overall evolution appears to be reproduced sufficiently well,
excluding of course the late shallow decline. Since we miss the first
evolutionary phases of NGC 300 OT, we only use a single blast (associated to
the bulk of the ejecta) term plus 56Ni decay to reproduce the data: the blast
term associated with the envelope is relevant during the early phases, so it
is difficult to constrain in this case. Apart from this, the parameters used
for NGC 300 OT are very similar to the ones used for AT 2019ahd.

The same conclusions cannot be reached for AT 2019udc, which is definitely an
outlier in this sample. First of all, the fast decline hints at the presence
of a single blast term. Most strikingly, the evolution of AT 2019udc is much
faster compared to the other transients considered so far. For this reason the
diffusion time within the ejecta must be remarkably lower: this leads to a low
ejected mass and a high scale velocity, several times larger compared to the
other ILRTs mentioned so far. Finally, it is worth noticing that in the case
of AT 2019udc, 56Ni decay is a key element to reproduce the observed late time
data points. All the masses mentioned so far are just relative to the ejected
material: a compact remnant is expected to be left behind, in the scenario in
which ILRTs arise from a core collapse event. Since the mass of the remnant
can be estimated to be 1.3–2.0 M⊙ (Pumo et al., 2017), the inferred mass of
our sample of ILRTs right before the explosion adds up to 5.3–6.0 M⊙ for AT
2019ahd, 5.5–6.2 M⊙ for NGC 300 OT and 9.3–10 M⊙ for AT 2019abn. Such values
are compatible with the expectations for SAGB stars and consequently ECSN
events, especially accounting for the fact that some mass was likely lost
during the evolution of the star, therefore leading to a slightly higher ZAMS.
AT 2019udc, with its estimated progenitor mass of just 2.2–2.9 M⊙ at the time
of explosion, sets itself apart from the rest of the sample, although its
origin could be tentatively explained as an ECSN arising from a SAGB star that
underwent extreme mass loss. We remark that the toy model presented in this
section is a simplified approach to the light curve modelling of ILRTs: more
detailed models envisioning hydrodynamical modelling should be used to
retrieve more robust estimates of the explosion parameters of these objects.
Accounting for the possible luminosity contribution from ejecta-CSM
interaction will also be an important step forward: while ILRTs never display
spectral signatures typically associated with shocks, there may be hidden CSM
interaction powering their light curve (Paper II). The puzzling results
obtained for AT 2019udc may be significantly revised by using a more refined
approach.

##  9 Summary and Conclusions

In this work we present data sets for NGC 300 OT, AT 2019abn, AT 2019ahd and
AT 2019udc. AT 2019abn and AT 2019udc stand out for their bright peak
magnitude (Mr=–15 mag and –14.5 mag respectively). On the other hand, NGC 300
OT and AT 2019ahd are characterised by a more modest peak magnitude (Mr= –12.7
mag and –13.2 mag). We detect a NIR excess in the SED of three of our ILRTs,
tentatively associated with dust formation, in three out of four targets. The
only exception is AT 2019udc, characterised by the fastest evolution timescale
among the ILRTs observed. At late phases, the contributions in the NIR and MIR
domains to the bolometric light curve cause a decline shallower than the
luminosity decline supported by the 56Ni decay, hinting at the presence of an
additional powering mechanism.

The late time monitoring of NGC 300 OT with WISE allows us to build the SED of
the transient 761 days after maximum. From its study, we infer a dust mass of
the order of $\times$10-5-$\times$10-3 M⊙, depending on the composition and
size of the grains adopted. Furthermore, the evolution of NGC 300 OT has been
monitored with Spitzer for several years, showing a steady dimming of the flux
at the transient position over 4 years. This strengthens the argument
suggested by Adams et al. (2016) that NGC 300 OT was a terminal event. Thanks
to JWST observations we were able to show that also AT 2019abn faded below its
progenitor luminosity in the MIR domain. Its SED appears to depart from a
simple blackbody, possibly due to the presence of PAH emission features.
Finally, a simple model is presented in the context of a SN explosion, with
the goal to estimate the parameters characterising the transients. For AT
2019abn, 2019ahd and NGC 300 OT, the low masses ejected (between 4 and 8 M⊙)
and low velocity of the material (up to 4500 km s-1) are compatible with a
weak explosion from a low mass star. AT 2019udc is an outlier in this sense,
since its very fast decline rate leads to inferring high velocity (12000 km
s-1) and remarkably low ejected mass (0.9 M⊙). Overall, due to their low
energy and their apparent terminal nature, ILRTs remain solid candidates for
being ECSNe.

## Acknowledgements

We thank the staff of the various observatories where data were obtained for
their assistance. 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. Observations from the Nordic Optical Telescope were obtained through
the NUTS2 collaboration which are supported in part by the Instrument Centre
for Danish Astrophysics (IDA). The data presented here were obtained in part
with ALFOSC, which is provided by the Instituto de Astrofisica de Andalucia
(IAA). This work makes use of data from the Las Cumbres Observatory network.
The LCO team is supported by NSF grants AST–1911225 and AST–1911151, and NASA
SWIFT grant 80NSSC19K1639. Data were also obtained at the Liverpool Telescope,
which is operated on the island of La Palma by Liverpool John Moores
University in the Spanish Observatorio del Roque de los Muchachos with
financial support from the UK Science and Technology Facilities Council. Part
of the observations were collected at Copernico and Schmidt telescopes
(Asiago, Italy) of the INAF – Osservatorio Astronomico di Padova. Based on
observations made with the Gran Telescopio Canarias (GTC), installed in the
Spanish Observatorio del Roque de los Muchachos of the Instituto de
Astrofísica de Canarias, in the island of La Palma This work has made use of
data from the Asteroid Terrestrial-impact Last Alert System (ATLAS) project.
Time domain research by the University of Arizona team and D.J.S. is supported
by NSF grants AST-1821987, 1813466, 1908972, & 2108032, and by the Heising-
Simons Foundation under grant #20201864. G.V., N.E.R. and I.S. acknowledge
financial support from PRIN-INAF 2022 “Shedding light on the nature of gap
transients: from the observations to the models”. N.E.R. also acknowledge
support from the Spanish MICINN grant PID2019-108709GB-I00 and FEDER funds,
and from the program Unidad de Excelencia Maria de Maeztu CEX2020-001058-M.
A.R. acknowledges financial support from the GRAWITA Large Program Grant (PI
P. D’Avanzo) and the PRIN-INAF 2022 ”Shedding light on the nature of gap
transients: from the observations to the models. Y.-Z. Cai is supported by the
National Natural Science Foundation of China (NSFC, Grant No. 12303054), the
Yunnan Fundamental Research Projects (Grant No. 202401AU070063) and the
International Centre of Supernovae, Yunnan Key Laboratory (No.
202302AN360001). T.E.M.B. acknowledges financial support from the Spanish
Ministerio de Ciencia e Innovacion (MCIN), the Agencia Estatal de
Investigacion (AEI) 10.13039/501100011033, and the European Union Next
Generation EU/PRTR funds under the 2021 Juan de la Cierva program
FJC2021-047124-I and the PID2020-115253GA-I00 HOSTFLOWS project, from Centro
Superior de Investigaciones Cientificas (CSIC) under the PIE project
20215AT016, and the program Unidad de Excelencia Maria de Maeztu
CEX2020-001058-M. MF is supported by a Royal Society - Science Foundation
Ireland University Research Fellowship. The Aarhus supernova group is funded
by the Independent Research Fund Denmark (IRFD, grant numbers 8021-00170B,
10.46540/2032-00022B). L.G. acknowledges financial support from the Spanish
Ministerio de Ciencia e Innovación (MCIN), the Agencia Estatal de
Investigación (AEI) 10.13039/501100011033, and the European Social Fund (ESF).
This work was funded by ANID, Millennium Science Initiative, ICN12_009 M.N. is
supported by the European Research Council (ERC) under the European Union’s
Horizon 2020 research and innovation programme (grant agreement No. 948381).
Part of the funding for GROND (both hardware as well as personnel) was
generously granted from the Leibniz-Prize to Prof. G. Hasinger (DFG grant HA
1850/28-1). H.K. was funded by the Academy of Finland projects 324504 and
328898. R.K. acknowledges support from the Research Council of Finland
(340613).

## References

  * Adams et al. (2016) Adams, S. M., Kochanek, C. S., Prieto, J. L., et al. 2016, Monthly Notices of the Royal Astronomical Society, 460, 1645
  * Ambikasaran et al. (2015) Ambikasaran, S., Foreman-Mackey, D., Greengard, L., Hogg, D. W., & O’Neil, M. 2015, IEEE Transactions on Pattern Analysis and Machine Intelligence, 38, 252
  * Anderson et al. (2014) Anderson, J. P., González-Gaitán, S., Hamuy, M., et al. 2014, ApJ, 786, 67
  * Arnett (1980) Arnett, W. D. 1980, APJ, 237, 541
  * Arnett (1982) Arnett, W. D. 1982, APJ, 253, 785
  * Bazin et al. (2011) Bazin, G., Ruhlmann-Kleider, V., Palanque-Delabrouille, N., et al. 2011, A&A, 534, A43
  * Berger et al. (2009) Berger, E., Soderberg, A. M., Chevalier, R. A., et al. 2009, The Astrophysical Journal, 699, 1850
  * Bevan et al. (2020) Bevan, A. M., Krafton, K., Wesson, R., et al. 2020, ApJ, 894, 111
  * Bond et al. (2009) Bond, H. E., Bedin, L. R., Bonanos, A. Z., et al. 2009, The Astrophysical Journal, 695, L154
  * Botticella et al. (2009) Botticella, M. T., Pastorello, A., Smartt, S. J., et al. 2009, MNRAS, 398, 1041
  * Byrne et al. (2023) Byrne, R. A., Fraser, M., Cai, Y. Z., Reguitti, A., & Valerin, G. 2023, MNRAS, 524, 2978
  * Cai et al. (2021) Cai, Y. Z., Pastorello, A., Fraser, M., et al. 2021, A&A, 654, A157
  * Cai et al. (2018) Cai, Y. Z., Pastorello, A., Fraser, M., et al. 2018, MNRAS, 480, 3424
  * Cappellaro (2014) Cappellaro, E. 2014, http://sngroup.oapd.inaf.it/snoopy.html
  * Cardelli et al. (1989) Cardelli, J. A., Clayton, G. C., & Mathis, J. S. 1989, ApJ, 345, 245
  * Chambers et al. (2016) Chambers, K. C., Magnier, E. A., Metcalfe, N., et al. 2016, arXiv e-prints, arXiv:1612.05560
  * Chatzopoulos et al. (2012) Chatzopoulos, E., Wheeler, J. C., & Vinko, J. 2012, APJ, 746, 121
  * de Soto et al. (2024) de Soto, K. M., Villar, A., Berger, E., et al. 2024, arXiv e-prints, arXiv:2403.07975
  * de Vaucouleurs et al. (1991) de Vaucouleurs, G., de Vaucouleurs, A., Corwin, Herold G., J., et al. 1991, Third Reference Catalogue of Bright Galaxies
  * Dessart et al. (2016) Dessart, L., Hillier, D. J., Audit, E., Livne, E., & Waldman, R. 2016, MNRAS, 458, 2094
  * Doherty et al. (2015) Doherty, C. L., Gil-Pons, P., Siess, L., Lattanzio, J. C., & Lau, H. H. B. 2015, MNRAS, 446, 2599
  * Draine (1989) Draine, B. T. 1989, in Infrared Spectroscopy in Astronomy, ed. E. Böhm-Vitense, 93
  * Draine (2016) Draine, B. T. 2016, APJ, 831, 109
  * Draine & Lee (1984) Draine, B. T. & Lee, H. M. 1984, ApJ, 285, 89
  * Draine & Li (2007) Draine, B. T. & Li, A. 2007, ApJ, 657, 810
  * Fabbri et al. (2011) Fabbri, J., Otsuka, M., Barlow, M. J., et al. 2011, MNRAS, 418, 1285
  * Fixsen et al. (1996) Fixsen, D. J., Cheng, E. S., Gales, J. M., et al. 1996, ApJ, 473, 576
  * Förster et al. (2021) Förster, F., Cabrera-Vives, G., Castillo-Navarrete, E., et al. 2021, AJ, 161, 242
  * Fox et al. (2010) Fox, O. D., Chevalier, R. A., Dwek, E., et al. 2010, APJ, 725, 1768
  * Fraga et al. (2024) Fraga, B. M. O., Bom, C. R., Santos, A., et al. 2024, arXiv e-prints, arXiv:2404.08798
  * Gardner et al. (2006) Gardner, J. P., Mather, J. C., Clampin, M., et al. 2006, Space Sci. Rev., 123, 485
  * Gogarten et al. (2010) Gogarten, S. M., Dalcanton, J. J., Williams, B. F., et al. 2010, ApJ, 712, 858
  * Graham et al. (2019) Graham, M. J., Kulkarni, S. R., Bellm, E. C., et al. 2019, Publications of the Astronomical Society of the Pacific, 131, 078001
  * Greiner et al. (2008) Greiner, J., Bornemann, W., Clemens, C., et al. 2008, PASP, 120, 405
  * Hamuy (2003) Hamuy, M. 2003, ApJ, 582, 905
  * Hiramatsu et al. (2021) Hiramatsu, D., Howell, D. A., Van Dyk, S. D., et al. 2021, Nature Astronomy, 5, 903
  * Holmbo et al. (2019) Holmbo, S., Stritzinger, M., Nowack, G., et al. 2019, The Astronomer’s Telegram, 12661, 1
  * Hosseinzadeh et al. (2022) Hosseinzadeh, G., Sand, D. J., Jencson, J. E., et al. 2022, arXiv e-prints, arXiv:2210.06499
  * Howell (2019) Howell, D. 2019, in American Astronomical Society Meeting Abstracts, Vol. 233, American Astronomical Society Meeting Abstracts #233, 258.16
  * Humphreys et al. (2011) Humphreys, R. M., Bond, H. E., Bedin, L. R., et al. 2011, The Astrophysical Journal, 743, 118
  * Inserra et al. (2018) Inserra, C., Prajs, S., Gutierrez, C. P., et al. 2018, ApJ, 854, 175
  * Ivezić et al. (2019) Ivezić, Ž., Kahn, S. M., Tyson, J. A., et al. 2019, ApJ, 873, 111
  * Janka et al. (2008) Janka, H. T., Müller, B., Kitaura, F. S., & Buras, R. 2008, A&A, 485, 199
  * Jencson et al. (2019) Jencson, J. E., Adams, S. M., Bond, H. E., et al. 2019, ApJ, 880, L20
  * Jha (2019) Jha, S. 2019, Transient Name Server Classification Report, 2019-1237, 1
  * Jiang et al. (2016) Jiang, N., Dou, L., Wang, T., et al. 2016, ApJ, 828, L14
  * Jones et al. (2013) Jones, S., Hirschi, R., Nomoto, K., et al. 2013, ApJ, 772, 150
  * Karachentsev et al. (1985) Karachentsev, I., Lebedev, V., & Shcherbanovski, A. 1985, Bulletin d’Information du Centre de Donnees Stellaires, 29, 87
  * Karambelkar et al. (2023) Karambelkar, V. R., Kasliwal, M. M., Blagorodnova, N., et al. 2023, ApJ, 948, 137
  * Kozyreva et al. (2021) Kozyreva, A., Baklanov, P., Jones, S., Stockinger, G., & Janka, H.-T. 2021, MNRAS, 503, 797
  * Lacy et al. (2005) Lacy, M., Wilson, G., Masci, F., et al. 2005, ApJS, 161, 41
  * Landolt (1992) Landolt, A. U. 1992, AJ, 104, 340
  * Limongi et al. (2024) Limongi, M., Roberti, L., Chieffi, A., & Nomoto, K. 2024, ApJS, 270, 29
  * McQuinn et al. (2016) McQuinn, K. B. W., Skillman, E. D., Dolphin, A. E., Berg, D., & Kennicutt, R. 2016, ApJ, 826, 21
  * McQuinn et al. (2017) McQuinn, K. B. W., Skillman, E. D., Dolphin, A. E., Berg, D., & Kennicutt, R. 2017, AJ, 154, 51
  * Miller et al. (2010) Miller, A. A., Smith, N., Li, W., et al. 2010, AJ, 139, 2218
  * Miyaji et al. (1980) Miyaji, S., Nomoto, K., Yokoi, K., & Sugimoto, D. 1980, PASJ, 32, 303
  * Monard (2008) Monard, L. A. G. 2008, International Astronomical Union Circular, 8946, 1
  * Moriya et al. (2014) Moriya, T. J., Tominaga, N., Langer, N., et al. 2014, A&A, 569, A57
  * Nagy & Vinkó (2016) Nagy, A. P. & Vinkó, J. 2016, AAP, 589, A53
  * Nasonova et al. (2011) Nasonova, O. G., de Freitas Pacheco, J. A., & Karachentsev, I. D. 2011, A&A, 532, A104
  * Nomoto (1984) Nomoto, K. 1984, ApJ, 277, 791
  * Nugent et al. (2011) Nugent, P. E., Sullivan, M., Cenko, S. B., et al. 2011, Nature, 480, 344
  * Ohsawa et al. (2010) Ohsawa, R., Sakon, I., Onaka, T., et al. 2010, ApJ, 718, 1456
  * Pastorello et al. (2019a) Pastorello, A., Chen, T. W., Cai, Y. Z., et al. 2019a, A&A, 625, L8
  * Pastorello & Fraser (2019) Pastorello, A. & Fraser, M. 2019, Nature Astronomy, 3, 676
  * Pastorello et al. (2021) Pastorello, A., Fraser, M., Valerin, G., et al. 2021, A&A, 646, A119
  * Pastorello et al. (2019b) Pastorello, A., Mason, E., Taubenberger, S., et al. 2019b, A&A, 630, A75
  * Pastorello et al. (2009) Pastorello, A., Valenti, S., Zampieri, L., et al. 2009, MNRAS, 394, 2266
  * Poelarends et al. (2008) Poelarends, A. J. T., Herwig, F., Langer, N., & Heger, A. 2008, ApJ, 675, 614
  * Poznanski et al. (2012) Poznanski, D., Prochaska, J. X., & Bloom, J. S. 2012, MNRAS, 426, 1465
  * Prieto et al. (2009) Prieto, J. L., Sellgren, K., Thompson, T. A., & Kochanek, C. S. 2009, The Astrophysical Journal, 705, 1425
  * Pumo et al. (2009) Pumo, M. L., Turatto, M., Botticella, M. T., et al. 2009, ApJ, 705, L138
  * Pumo et al. (2017) Pumo, M. L., Zampieri, L., Spiro, S., et al. 2017, MNRAS, 464, 3013
  * Reguitti et al. (2021) Reguitti, A., Pumo, M. L., Mazzali, P. A., et al. 2021, MNRAS, 501, 1059
  * Rieke & Lebofsky (1985) Rieke, G. H. & Lebofsky, M. J. 1985, ApJ, 288, 618
  * Roming et al. (2005) Roming, P. W. A., Kennedy, T. E., Mason, K. O., et al. 2005, Space Sci. Rev., 120, 95
  * Rose et al. (2024) Rose, S., Lau, R. M., Jencson, J. E., et al. 2024, arXiv [arXiv:2407.20430]
  * Schlafly & Finkbeiner (2011) Schlafly & Finkbeiner, D. P. 2011, The Astrophysical Journal, 737, 103
  * Siebert et al. (2019) Siebert, M. R., Dimitriadis, G., Kilpatrick, C. D., et al. 2019, Transient Name Server Classification Report, 2019-2287, 1
  * Skrutskie et al. (2006) Skrutskie, M. F., Cutri, R. M., Stiening, R., et al. 2006, AJ, 131, 1163
  * Smartt et al. (2015) Smartt, S. J., Valenti, S., Fraser, M., et al. 2015, A&A, 579, A40
  * Smith et al. (2020) Smith, K. W., Smartt, S. J., Young, D. R., et al. 2020, PASP, 132, 085002
  * Smith et al. (2019) Smith, K. W., Williams, R. D., Young, D. R., et al. 2019, Research Notes of the American Astronomical Society, 3, 26
  * Smith (2013) Smith, N. 2013, MNRAS, 434, 102
  * Smith et al. (2011) Smith, N., Li, W., Silverman, J. M., Ganeshalingam, M., & Filippenko, A. V. 2011, MNRAS, 415, 773
  * Soker & Kashi (2012) Soker, N. & Kashi, A. 2012, ApJ, 746, 100
  * Spergel et al. (2007) Spergel, D. N., Bean, R., Doré, O., et al. 2007, ApJS, 170, 377
  * Spiro et al. (2014) Spiro, S., Pastorello, A., Pumo, M. L., et al. 2014, MNRAS, 439, 2873
  * Steele et al. (2004) Steele, I. A., Smith, R. J., Rees, P. C., et al. 2004, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 5489, Ground-based Telescopes, ed. J. Oschmann, Jacobus M., 679–692
  * Stritzinger et al. (2020) Stritzinger, M. D., Taddia, F., Fraser, M., et al. 2020, A&A, 639, A103
  * Tartaglia et al. (2018) Tartaglia, L., Sand, D. J., Valenti, S., et al. 2018, ApJ, 853, 62
  * Thompson et al. (2009) Thompson, T. A., Prieto, J. L., Stanek, K. Z., et al. 2009, ApJ, 705, 1364
  * Tody (1986) Tody, D. 1986, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 627, Instrumentation in astronomy VI, ed. D. L. Crawford, 733
  * Tonry et al. (2019) Tonry, J., Denneau, L., Heinze, A., et al. 2019, Transient Name Server Discovery Report, 2019-161, 1
  * Tonry et al. (2018) Tonry, J. L., Denneau, L., Heinze, A. N., et al. 2018, PASP, 130, 064505
  * Tully & Fisher (1988) Tully, R. B. & Fisher, J. R. 1988, Catalog of Nearby Galaxies
  * Tully et al. (2009) Tully, R. B., Rizzi, L., Shaya, E. J., et al. 2009, AJ, 138, 323
  * Tully et al. (1992) Tully, R. B., Shaya, E. J., & Pierce, M. J. 1992, ApJS, 80, 479
  * Turatto et al. (2003) Turatto, M., Benetti, S., & Cappellaro, E. 2003, in From Twilight to Highlight: The Physics of Supernovae, ed. W. Hillebrandt & B. Leibundgut, 200
  * Tylenda et al. (2011) Tylenda, R., Hajduk, M., Kamiński, T., et al. 2011, A&A, 528, A114
  * Valerin et al. (2022) Valerin, G., Pumo, M. L., Pastorello, A., et al. 2022, MNRAS, 513, 4983
  * Wanajo et al. (2009) Wanajo, S., Nomoto, K., Janka, H. T., Kitaura, F. S., & Müller, B. 2009, ApJ, 695, 208
  * Wesson et al. (2015) Wesson, R., Barlow, M. J., Matsuura, M., & Ercolano, B. 2015, MNRAS, 446, 2089
  * Williams et al. (2015) Williams, S. C., Darnley, M. J., Bode, M. F., & Steele, I. A. 2015, ApJ, 805, L18
  * Williams et al. (2020) Williams, S. C., Jones, D., Pessev, P., et al. 2020, A&A, 637, A20
  * Woosley et al. (2002) Woosley, S. E., Heger, A., & Weaver, T. A. 2002, Reviews of Modern Physics, 74, 1015
  * Wright et al. (2010) Wright, E. L., Eisenhardt, P. R. M., Mainzer, A. K., et al. 2010, AJ, 140, 1868
  * York et al. (2000) York, D. G., Adelman, J., Anderson, John E., J., et al. 2000, AJ, 120, 1579

## AFFILIATIONS

1INAF – Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5,
I-35122 Padova, Italy
2INAF – Osservatorio Astronomico di Brera, Via E. Bianchi 46, 23807, Merate
(LC), Italy
3Yunnan Observatories, Chinese Academy of Sciences, Kunming 650216, P.R. China
4Key Laboratory for the Structure and Evolution of Celestial Objects, Chinese
Academy of Sciences, Kunming 650216, P.R. China
5International Centre of Supernovae, Yunnan Key Laboratory, Kunming 650216,
P.R. China
6 Graduate Institute of Astronomy, National Central University, 300 Jhongda
Road, 32001 Jhongli, Taiwan
7SRON, Netherlands Institute for Space Research, Niels Bohrweg 4, 2333 CA,
Leiden, The Netherlands
8Department of Astrophysics/IMAPP, Radboud University Nĳmegen, P.O. Box 9010,
6500 GL, Nĳmegen, The Netherlands
9Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans
s/n, E-08193 Barcelona, Spain
10School of Physics, O’Brien Centre for Science North, University College
Dublin, Belfield, Dublin 4, Ireland
11The Oskar Klein Centre, Department of Astronomy, Stockholm University,
AlbaNova, 10691 Stockholm, Sweden
12Hiroshima Astrophysical Science Center, Hiroshima University, Higashi-
Hiroshima, Japan
13Department of Physics, Florida State University, 77 Chieftan Way,
Tallahassee, FL 32306, USA
14Las Cumbres Observatory, 6740 Cortona Dr. Suite 102, Goleta, CA, 93117, USA
15Department of Physics, University of California, Santa Barbara, CA, 93106,
USA
16School of Physics & Astronomy, Cardiff University, Queens Buildings, The
Parade, Cardiff, CF24 3AA, UK
17INAF, Osservatorio Astronomico di Capodimonte, Salita Moiariello 16, I-80131
Napoli, Italy
18DARK, Niels Bohr Institute, University of Copenhagen, Jagtvej 128, 2200
Copenhagen, Denmark
19Caltech, Mail Code 220-6, Pasadena, CA 91125
20Tuorla Observatory, Department of Physics and Astronomy, University of
Turku, 20014, Turku, Finland
21Astrophysics Research Institute, Liverpool John Moores University, IC2,
Liverpool Science Park, 146 Brownlow Hill, Liverpool L3 5RF, UK
22Max-Planck-Institut für Astrophysik, Karl-Schwarzschild Str. 1, D-85748
Garching, Germany
23Aryabhatta Research Institute of observational sciences, Manora Peak,
Nainital, 263001, India
24Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7D, Arica,
Chile
25School of Physics, Trinity College Dublin, College Green, Dublin 2, Ireland
26Steward Observatory, University of Arizona, 933 North Cherry Avenue, Tucson,
AZ 85721-0065, USA
27Department of Physics, University of Oxford, Keble Road, Oxford, OX1 3RH
28Astrophysics Research Centre, School of Mathematics and Physics, Queens
University Belfast, Belfast BT7 1NN, UK
29Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120,
DK-8000 Aarhus C, Denmark
30INAF – Osservatorio Astronomico d’Abruzzo, via M. Maggini snc, Teramo,
I-64100, Italy
31Department of Physics, University of California, Davis, CA 95616, USA
32 European Southern Observatory, Alonso de Córdova 3107, Casilla 19,
Santiago, Chile
33Millennium Institute of Astrophysics, Nuncio Monsenor Sótero Sanz 100,
Providencia, 8320000 Santiago, Chile
34INAF-Osservatorio Astrofisico di Catania, Via Santa Sofia 78, I-95123
Catania, Italy
35Instituto de Astrofísica, Universidad Andres Bello, Fernandez Concha 700,
Las Condes, Santiago RM, Chile
36 ICRANet, Piazza della Repubblica 10, I-65122 Pescara, Italy
37Institut für Theoretische Physik, Goethe Universität, Max-von-Laue-Str. 1,
60438 Frankfurt am Main, Germany
38INFN-TIFPA, Trento Institute for Fundamental Physics and Applications, Via
Sommarive 14, I-38123 Trento, Italy
39Institut d’Estudis Espacials de Catalunya (IEEC), E-08034 Barcelona, Spain.
40Center for Astrophysics, Harvard & Smithsonian, Cambridge, Massachusetts, MA
02138, US
41The NSF AI Institute for Artificial Intelligence and Fundamental
Interactions, USA
42Finnish Centre for Astronomy with ESO (FINCA), University of Turku,
Väisäläntie 20, 21500 Piikkiö, Finland
43DTU Space, National Space Institute, Technical University of Denmark,
Elektrovej 327, 2800Kgs. Lyngby, Denmark
44Dipartimento di Fisica e Astronomia “G. Galilei”, Università degli studi di
Padova Vicolo dell’Osservatorio 3, I-35122 Padova, Italy
45IAASARS, National Observatory of Athens, Metaxa & Vas. Pavlou St., 15236,
Penteli, Athens, Greece
46Department of Astronomy, University of Virginia, Charlottesville, VA 22904,
USA
47Department of Physics and Astronomy, University of North Carolina at Chapel
Hill, Chapel Hill, NC 27599, USA
48Cosmic Dawn Center (DAWN), Denmark
49Niels Bohr Institute, University of Copenhagen, Jagtvej 128, 2200 København
N, Denmark
50Manipal Centre for Natural Sciences, Manipal Academy of Higher Education,
Manipal - 576104, Karnataka, India
51Indian Institute Of Astrophysics, 100 Feet Rd, Santhosapuram, 2nd Block,
Koramangala, Bengaluru, Karnataka 560034, India

##  Appendix A Additional tables and figures

Figure 16: Opacity of dust with different composition (graphite and silicates)
and grain size (0.1 and 1 $\mu m$). Reported values were tabulated by Fox et
al. (2010) and extended to $22$ $\mu m$ as detailed in Section 6.1.

Figure 17: Updated version of Figure 10 including the late time luminosity of
AT 2019abn measured on JWST data collected on 2024-05-31. Table 5: Instruments
and facilities used in our follow-up campaigns.

Code Diameter [m] Telescope Instrument Site PROMPT 0.41 PROMPT Telescope
Apogee Alta Cerro Tololo Inter-American Observatory, Cerro Tololo, Chile REM
0.6 REM ROSS ESO La Silla Observatory, La Silla, Chile Swope 1.0 Swope
Telescope SITe # 3 Las Campanas Observatory, Atacama Region, Chile fl03-fl15
1.0 LCO (LSC site) Sinistro LCO node at Cerro Tololo Inter-American
Observatory, Cerro Tololo, Chile fl05-fl07 1.0 LCO (ELP site) Sinistro LCO
node at McDonald Observatory, Texas, USA fl06-fl14 1.0 LCO (CPT site) Sinistro
LCO node at South African Astronomical Observatory, Cape Town, South Africa
fl12 1.0 LCO (COJ site) Sinistro LCO node at Siding Spring Observatory, New
South Wales, Australia ZTF 1.22 Oschin Telescope ZTF Palomar Observatory,
United States DFOT 1.3 Devasthal Fast Optical Telescope DZ436 Devasthal,
Nainital, India AFOSC 1.82 Copernico Telescope AFOSC Osservatorio Astronomico
di Asiago, Asiago, Italy HCT 2.0 Hymalayan Chandra Telescope A7iii Indian
Astronomical Observatory, Hanle, India IO:O 2.0 Liverpool Telescope IO:O
Observatorio Roque de Los Muchachos, La Palma, Spain IO:I 2.0 Liverpool
Telescope IO:I Observatorio Roque de Los Muchachos, La Palma, Spain GROND 2.2
MPG Telescope GROND ESO La Silla Observatory, La Silla, Chile GRONDIR 2.2 MPG
Telescope GRONDIR ESO La Silla Observatory, La Silla, Chile ALFOSC 2.56 Nordic
Optical Telescope ALFOSC Observatorio Roque de Los Muchachos, La Palma, Spain
NOTCam 2.56 Nordic Optical Telescope NOTCam Observatorio Roque de Los
Muchachos, La Palma, Spain SOFI 3.58 New Technology Telescope SOFI ESO La
Silla Observatory, La Silla, Chile ACAM 4.20 William Hershel Telescope ACAM
Observatorio Roque de Los Muchachos, La Palma, Spain LIRIS 4.20 William
Hershel Telescope LIRIS Observatorio Roque de Los Muchachos, La Palma, Spain

AT 2019abn $\gamma_{1}$ [-25 to -11] $\gamma_{2}$ [0 to 110] $\gamma_{3}$ [110
to 185] $\gamma_{4}$ [¿185] $B$ -21.8 $\pm$ 1.0 2.72 $\pm$ 0.05 – – $V$ -20.5
$\pm$ 0.9 1.70 $\pm$ 0.02 2.85 $\pm$ 0.10 – $g$ -19.7 $\pm$ 1.3 2.27 $\pm$
0.03 – – $r$ -21.0 $\pm$ 1.0 1.37 $\pm$ 0.01 2.49 $\pm$ 0.04 0.80 $\pm$ 0.06
$i$ -20.2 $\pm$ 1.2 1.04 $\pm$ 0.01 2.14 $\pm$ 0.07 1.45 $\pm$ 0.05 $z$ -16.0
$\pm$ 2.3 0.82 $\pm$ 0.01 1.67 $\pm$ 0.03 1.32 $\pm$ 0.09 $J$ – 0.84 $\pm$
0.08 – 1.56 $\pm$ 0.12 $H$ – 0.65 $\pm$ 0.02 – 1.07 $\pm$ 0.07 $K$ – 0.67
$\pm$ 0.07 – 0.72 $\pm$ 0.04

Table 6: Rise and decline rates for the various bands of AT 2019abn. All
quantities are reported in [mag/100 days]. For more detailed discussion of
these values, see Sect 3.1.

|  | AT 2019ahd |
---|---|---|---
|  $\gamma_{1}$ [0 to 45] |  $\gamma_{2}$ [45 to 105] |  $\gamma_{3}$ [¿ 105]
$g$ | 1.29 $\pm$ 0.11 | 2.51 $\pm$ 0.12 | –
$r$ | 1.12 $\pm$ 0.09 | 2.31 $\pm$ 0.10 | 1.05 $\pm$ 0.03
$i$ | 0.61 $\pm$ 0.06 | 2.18 $\pm$ 0.15 | 1.21 $\pm$ 0.04
$z$ | 0.51 $\pm$ 0.06 | 1.70 $\pm$ 0.09 | 1.16 $\pm$ 0.04
$J$ | 0.71 $\pm$ 0.06 | – | 0.97 $\pm$ 0.03
$H$ | 0.58 $\pm$ 0.03 | – | 0.57 $\pm$ 0.04
$K$ | 0.64 $\pm$ 0.10 | – | 0.37 $\pm$ 0.03

|  | AT 2019udc |
---|---|---|---
|  $\gamma_{1}$ [-10 to -8] |  $\gamma_{2}$ [0 to 35] |  $\gamma_{3}$ [¿ 35]
$U$ | -79.3 $\pm$ 8.7 | 8.19 $\pm$ 0.46 | –
$B$ | -62.1 $\pm$ 5.9 | 6.46 $\pm$ 0.27 | 2.69 $\pm$ 0.24
$V$ | -30.2 $\pm$ 6.2 | 4.37 $\pm$ 0.15 | 3.19 $\pm$ 0.09
$g$ | -57.4 $\pm$ 5.4 | 5.60 $\pm$ 0.12 | 2.88 $\pm$ 0.16
$r$ | -47.5 $\pm$ 4.8 | 3.93 $\pm$ 0.09 | 2.22 $\pm$ 0.12
$i$ | -17.8 $\pm$ 4.3 | 3.41 $\pm$ 0.17 | 2.12 $\pm$ 0.14
$z$ | – | 3.0 $\pm$ 0.2 | 1.71 $\pm$ 0.22
$H$ | – | – | 0.91 $\pm$ 0.15

Table 7: Rise and decline rates for various bands of AT 2019ahd and AT 2019udc. All quantities are reported in [mag/100 days]. For more detailed discussion of these values, see Sect 3.2 and 3.3. |  |  | NGC 300 OT |  |
---|---|---|---|---|---
|  $\gamma_{1}$ [0 to 35] |  $\gamma_{2}$ [35 to 75] |  $\gamma_{3}$ [75 to 120] |  $\gamma_{4}$ [120 to 255] |  $\gamma_{5}$ [¿255]
$U$ | 2.57 $\pm$ 0.16 | 4.20 $\pm$ 0.12 | – | – | –
$B$ | 2.16 $\pm$ 0.08 | 4.06 $\pm$ 0.08 | 6.30 $\pm$ 0.10 | 1.50 $\pm$ 0.08 | –
$V$ | 1.38 $\pm$ 0.06 | 3.77 $\pm$ 0.07 | 7.06 $\pm$ 0.20 | 1.49 $\pm$ 0.07 | –
$R$ | 0.81 $\pm$ 0.06 | 3.21 $\pm$ 0.05 | 5.24 $\pm$ 0.06 | 0.95 $\pm$ 0.05 | –
$I$ | 0.49 $\pm$ 0.06 | 2.66 $\pm$ 0.06 | 5.21 $\pm$ 0.10 | 1.35 $\pm$ 0.05 | –
$u$ | 3.38 $\pm$ 0.23 | – | – | – | –
$g$ | 1.73 $\pm$ 0.11 | 4.14 $\pm$ 0.34 | – | – | –
$r$ | 1.11 $\pm$ 0.05 | 3.32 $\pm$ 0.08 | – | 0.69 $\pm$ 0.07 | 1.56 $\pm$ 0.05
$i$ | 0.64 $\pm$ 0.07 | 3.09 $\pm$ 0.09 | – | 1.54 $\pm$ 0.09 | 1.38 $\pm$ 0.10
$z$ | 0.33 $\pm$ 0.07 | 2.24 $\pm$ 0.07 | – | 1.29 $\pm$ 0.09 | 1.71 $\pm$ 0.10
$J$ | 0.03 $\pm$ 0.10 | 1.90 $\pm$ 0.09 | 2.75 $\pm$ 0.09 | 1.94 $\pm$ 0.12 | 1.01 $\pm$ 0.23
$H$ | -0.28 $\pm$ 0.09 | 1.46 $\pm$ 0.14 | 2.00 $\pm$ 0.13 | 1.40 $\pm$ 0.08 | 1.21 $\pm$ 0.09
$K$ | -0.33 $\pm$ 0.30 | 0.98 $\pm$ 0.27 | 1.50 $\pm$ 0.20 | 0.64 $\pm$ 0.10 | 0.81 $\pm$ 0.06
Table 8: Decline rates for various bands of NGC 300 OT. All quantities are
reported in [mag/100 days]. For more detailed discussion of these values, see
Sect 3.4.

Table 9: Template light curves for ILRTs as described in Section 7.

Phase | Total | Slow declining | Fast declining
---|---|---|---
$[days]$ | $[mag]$ | $[mag]$ | $[mag]$
-15 | -14.21 ${}^{-0.48}_{+0.89}$ | -13.33 ${}^{-0.19}_{+0.23}$ | –
-12 | -14.31 ${}^{-0.39}_{+0.62}$ | -13.96 ${}^{-0.31}_{+0.43}$ | –
-9 | -14.60 ${}^{-0.17}_{+0.20}$ | -14.57 ${}^{-0.10}_{+0.11}$ | -14.52 ${}^{-0.19}_{+0.23}$
-6 | -14.81 ${}^{-0.08}_{+0.08}$ | -14.82 ${}^{-0.05}_{+0.05}$ | -14.80 ${}^{-0.09}_{+0.10}$
-3 | -14.94 ${}^{-0.05}_{+0.05}$ | -14.94 ${}^{-0.04}_{+0.05}$ | -14.93 ${}^{-0.06}_{+0.06}$
0 | -14.99 ${}^{-0.01}_{+0.01}$ | -14.99 ${}^{-0.01}_{+0.01}$ | -14.99 ${}^{-0.02}_{+0.02}$
3 | -14.94 ${}^{-0.07}_{+0.07}$ | -14.97 ${}^{-0.03}_{+0.04}$ | -14.89 ${}^{-0.08}_{+0.08}$
6 | -14.85 ${}^{-0.12}_{+0.13}$ | -14.90 ${}^{-0.08}_{+0.08}$ | -14.76 ${}^{-0.11}_{+0.13}$
9 | -14.77 ${}^{-0.15}_{+0.17}$ | -14.85 ${}^{-0.10}_{+0.11}$ | -14.65 ${}^{-0.13}_{+0.15}$
12 | -14.72 ${}^{-0.17}_{+0.21}$ | -14.82 ${}^{-0.11}_{+0.12}$ | -14.56 ${}^{-0.14}_{+0.15}$
15 | -14.66 ${}^{-0.19}_{+0.24}$ | -14.77 ${}^{-0.12}_{+0.14}$ | -14.46 ${}^{-0.13}_{+0.15}$
18 | -14.60 ${}^{-0.22}_{+0.27}$ | -14.74 ${}^{-0.13}_{+0.14}$ | -14.37 ${}^{-0.14}_{+0.16}$
21 | -14.55 ${}^{-0.22}_{+0.28}$ | -14.70 ${}^{-0.12}_{+0.14}$ | -14.28 ${}^{-0.13}_{+0.15}$
24 | -14.51 ${}^{-0.22}_{+0.27}$ | -14.65 ${}^{-0.10}_{+0.11}$ | -14.22 ${}^{-0.14}_{+0.16}$
27 | -14.47 ${}^{-0.22}_{+0.28}$ | -14.62 ${}^{-0.10}_{+0.11}$ | -14.16 ${}^{-0.16}_{+0.19}$
30 | -14.42 ${}^{-0.23}_{+0.29}$ | -14.58 ${}^{-0.10}_{+0.12}$ | -14.11 ${}^{-0.16}_{+0.19}$
33 | -14.36 ${}^{-0.24}_{+0.30}$ | -14.54 ${}^{-0.11}_{+0.12}$ | -14.03 ${}^{-0.16}_{+0.19}$
36 | -14.32 ${}^{-0.25}_{+0.33}$ | -14.50 ${}^{-0.11}_{+0.12}$ | -13.91 ${}^{-0.17}_{+0.20}$
39 | -14.27 ${}^{-0.25}_{+0.33}$ | -14.45 ${}^{-0.11}_{+0.13}$ | -13.86 ${}^{-0.17}_{+0.20}$
42 | -14.21 ${}^{-0.24}_{+0.31}$ | -14.38 ${}^{-0.11}_{+0.12}$ | -13.84 ${}^{-0.19}_{+0.22}$
45 | -14.15 ${}^{-0.24}_{+0.31}$ | -14.32 ${}^{-0.11}_{+0.12}$ | -13.79 ${}^{-0.21}_{+0.26}$
48 | -14.07 ${}^{-0.25}_{+0.32}$ | -14.25 ${}^{-0.11}_{+0.13}$ | -13.72 ${}^{-0.23}_{+0.30}$
51 | -13.99 ${}^{-0.26}_{+0.34}$ | -14.18 ${}^{-0.12}_{+0.14}$ | -13.63 ${}^{-0.25}_{+0.33}$
54 | -13.93 ${}^{-0.28}_{+0.38}$ | -14.13 ${}^{-0.14}_{+0.15}$ | -13.54 ${}^{-0.27}_{+0.36}$
57 | -13.87 ${}^{-0.30}_{+0.42}$ | -14.08 ${}^{-0.15}_{+0.18}$ | -13.46 ${}^{-0.28}_{+0.39}$
60 | -13.79 ${}^{-0.31}_{+0.43}$ | -14.02 ${}^{-0.16}_{+0.19}$ | -13.40 ${}^{-0.28}_{+0.38}$
63 | -13.72 ${}^{-0.32}_{+0.45}$ | -13.95 ${}^{-0.18}_{+0.22}$ | -13.33 ${}^{-0.29}_{+0.39}$
66 | -13.63 ${}^{-0.34}_{+0.49}$ | -13.86 ${}^{-0.20}_{+0.25}$ | -13.24 ${}^{-0.30}_{+0.43}$
69 | -13.53 ${}^{-0.36}_{+0.54}$ | -13.78 ${}^{-0.22}_{+0.28}$ | -13.12 ${}^{-0.32}_{+0.45}$
72 | -13.43 ${}^{-0.39}_{+0.62}$ | -13.71 ${}^{-0.26}_{+0.35}$ | -13.00 ${}^{-0.33}_{+0.47}$
75 | -13.35 ${}^{-0.43}_{+0.71}$ | -13.62 ${}^{-0.31}_{+0.43}$ | -12.90 ${}^{-0.36}_{+0.55}$
78 | -13.26 ${}^{-0.46}_{+0.80}$ | -13.52 ${}^{-0.34}_{+0.49}$ | -12.84 ${}^{-0.42}_{+0.70}$
81 | -13.17 ${}^{-0.48}_{+0.88}$ | -13.43 ${}^{-0.36}_{+0.54}$ | -12.78 ${}^{-0.45}_{+0.80}$
84 | -13.10 ${}^{-0.50}_{+0.97}$ | -13.37 ${}^{-0.38}_{+0.58}$ | -12.73 ${}^{-0.49}_{+0.92}$
87 | -13.06 ${}^{-0.53}_{+1.08}$ | -13.37 ${}^{-0.39}_{+0.61}$ | -12.68 ${}^{-0.53}_{+1.08}$
90 | -13.00 ${}^{-0.55}_{+1.17}$ | -13.31 ${}^{-0.41}_{+0.67}$ | -12.61 ${}^{-0.57}_{+1.28}$
93 | -12.92 ${}^{-0.57}_{+1.25}$ | -13.23 ${}^{-0.43}_{+0.71}$ | -12.55 ${}^{-0.61}_{+1.52}$

Phase | Total | Slow declining | Fast declining
---|---|---|---
$[days]$ | $[mag]$ | $[mag]$ | $[mag]$
96 | -12.83 ${}^{-0.59}_{+1.36}$ | -13.13 ${}^{-0.45}_{+0.78}$ | -12.49 ${}^{-0.64}_{+1.75}$
99 | -12.80 ${}^{-0.59}_{+1.39}$ | -13.06 ${}^{-0.47}_{+0.85}$ | -12.45 ${}^{-0.66}_{+1.92}$
102 | -12.83 ${}^{-0.57}_{+1.26}$ | -13.01 ${}^{-0.49}_{+0.91}$ | -12.41 ${}^{-0.67}_{+2.06}$
105 | -12.78 ${}^{-0.57}_{+1.29}$ | -12.96 ${}^{-0.49}_{+0.93}$ | -12.38 ${}^{-0.68}_{+2.25}$
108 | -12.84 ${}^{-0.49}_{+0.92}$ | -12.88 ${}^{-0.49}_{+0.92}$ | –
111 | -12.78 ${}^{-0.49}_{+0.90}$ | -12.81 ${}^{-0.49}_{+0.92}$ | –
114 | -12.74 ${}^{-0.48}_{+0.90}$ | -12.75 ${}^{-0.49}_{+0.93}$ | –
117 | -12.73 ${}^{-0.48}_{+0.87}$ | -12.70 ${}^{-0.50}_{+0.95}$ | –
120 | -12.75 ${}^{-0.46}_{+0.82}$ | -12.65 ${}^{-0.50}_{+0.97}$ | –
123 | -12.70 ${}^{-0.46}_{+0.82}$ | -12.58 ${}^{-0.50}_{+0.95}$ | –
126 | -12.63 ${}^{-0.46}_{+0.82}$ | -12.50 ${}^{-0.49}_{+0.92}$ | –
129 | -12.58 ${}^{-0.47}_{+0.84}$ | -12.43 ${}^{-0.49}_{+0.91}$ | –
132 | -12.52 ${}^{-0.48}_{+0.87}$ | -12.35 ${}^{-0.49}_{+0.93}$ | –
135 | -12.46 ${}^{-0.49}_{+0.92}$ | -12.27 ${}^{-0.50}_{+0.95}$ | –
138 | -12.40 ${}^{-0.50}_{+0.96}$ | -12.19 ${}^{-0.50}_{+0.96}$ | –
141 | -12.34 ${}^{-0.51}_{+1.00}$ | -12.12 ${}^{-0.50}_{+0.96}$ | –
144 | -12.30 ${}^{-0.52}_{+1.04}$ | -12.06 ${}^{-0.51}_{+0.99}$ | –
147 | -12.25 ${}^{-0.53}_{+1.06}$ | -12.01 ${}^{-0.51}_{+0.97}$ | –
150 | -12.21 ${}^{-0.53}_{+1.09}$ | -11.96 ${}^{-0.51}_{+0.97}$ | –
153 | -12.15 ${}^{-0.54}_{+1.12}$ | -11.89 ${}^{-0.50}_{+0.96}$ | –
156 | -12.09 ${}^{-0.55}_{+1.18}$ | -11.80 ${}^{-0.50}_{+0.95}$ | –
159 | -12.03 ${}^{-0.57}_{+1.27}$ | -11.72 ${}^{-0.50}_{+0.97}$ | –
162 | -12.06 ${}^{-0.56}_{+1.23}$ | -11.72 ${}^{-0.49}_{+0.93}$ | –
165 | -12.06 ${}^{-0.56}_{+1.20}$ | -11.70 ${}^{-0.48}_{+0.89}$ | –
168 | -12.01 ${}^{-0.57}_{+1.25}$ | -11.63 ${}^{-0.48}_{+0.87}$ | –
171 | -11.97 ${}^{-0.58}_{+1.32}$ | -11.57 ${}^{-0.47}_{+0.84}$ | –
174 | -11.93 ${}^{-0.58}_{+1.36}$ | -11.51 ${}^{-0.46}_{+0.81}$ | –
177 | -11.91 ${}^{-0.59}_{+1.37}$ | -11.49 ${}^{-0.46}_{+0.80}$ | –
180 | -11.88 ${}^{-0.59}_{+1.39}$ | -11.45 ${}^{-0.45}_{+0.79}$ | –
183 | -11.83 ${}^{-0.60}_{+1.49}$ | -11.37 ${}^{-0.43}_{+0.73}$ | –
186 | -11.80 ${}^{-0.61}_{+1.51}$ | -11.34 ${}^{-0.43}_{+0.72}$ | –
189 | -11.78 ${}^{-0.61}_{+1.56}$ | -11.30 ${}^{-0.43}_{+0.71}$ | –
192 | -11.73 ${}^{-0.63}_{+1.69}$ | -11.23 ${}^{-0.42}_{+0.69}$ | –
195 | -11.68 ${}^{-0.66}_{+1.95}$ | -11.13 ${}^{-0.41}_{+0.68}$ | –
198 | -11.63 ${}^{-0.69}_{+2.38}$ | -11.03 ${}^{-0.43}_{+0.73}$ | –
201 | -11.58 ${}^{-0.72}_{+3.04}$ | -10.93 ${}^{-0.47}_{+0.83}$ | –

##  Appendix B Measured data

Table 10: Photometric data collected in Johnson bands for NGC 300 OT (Vega
mag).

Date | MJD | U (err) | B (err) | V (err) | R (err) | I (err) | Instrument
---|---|---|---|---|---|---|---
20080516 | 54602.89 | – (–) | 15.61 (0.05) | 14.69 (0.02) | 14.28 (0.02) | 13.83 (0.03) | PROMPT3+5
20080520 | 54606.88 | 15.92 (0.36) | 15.65 (0.02) | 14.70 (0.02) | 14.24 (0.01) | 13.85 (0.03) | PROMPT2+5
20080521 | 54607.84 | – (–) | – (–) | – (–) | 14.29 (60.00) | 13.83 (0.04) | REM
20080522 | 54608.83 | – (–) | – (–) | 14.82 (0.07) | 14.34 (84.00) | – (–) | REM
20080523 | 54609.55 | – (–) | – (–) | 14.82 (0.02) | 14.32 (0.01) | 13.84 (0.02) | PROMPT5
20080524 | 54610.87 | 16.09 (0.12) | 15.72 (0.02) | – (–) | – (–) | – (–) | PROMPT3
20080524 | 54610.87 | 16.07 (0.19) | 15.61 (0.02) | 14.89 (0.02) | 14.36 (0.01) | 13.85 (0.02) | PROMPT2+5
20080525 | 54611.87 | – (–) | 15.80 (0.04) | 14.87 (0.03) | – (–) | – (–) | PROMPT2
20080525 | 54611.87 | 16.09 (0.38) | 15.79 (0.08) | 14.87 (0.03) | 14.34 (0.03) | 13.83 (0.03) | PROMPT3+5
20080529 | 54615.82 | – (–) | – (–) | – (–) | – (–) | 13.85 (0.03) | REM
20080529 | 54615.66 | – (–) | – (–) | 14.90 (0.20) | 14.30 (0.20) | 13.80 (0.20) | Monard AAVSO
20080530 | 54616.85 | 16.13 (0.36) | 15.74 (0.02) | 14.89 (0.01) | 14.41 (0.01) | 13.90 (0.02) | PROMPT2+5
20080531 | 54617.85 | 16.15 (0.29) | 15.87 (0.02) | 14.90 (0.01) | 14.44 (0.01) | 13.90 (0.02) | PROMPT2+5
20080602 | 54619.67 | – (–) | – (–) | – (–) | 14.40 (0.20) | – (–) | Monard AAVSO
20080603 | 54620.63 | – (–) | – (–) | – (–) | 14.40 (0.20) | – (–) | Monard AAVSO
20080606 | 54623.80 | – (–) | – (–) | – (–) | – (–) | 13.91 (0.08) | REM
20080606 | 54623.90 | 16.40 (0.02) | 15.97 (0.01) | 14.98 (0.01) | 14.43 (0.01) | – (–) | EFOSC
20080607 | 54624.84 | – (–) | 16.06 (0.02) | 15.01 (0.02) | 14.47 (0.01) | 13.91 (0.01) | PROMPT2+5
20080608 | 54625.82 | – (–) | 16.02 (0.04) | 14.98 (0.05) | 14.45 (0.04) | 13.88 (0.03) | PROMPT3+5
20080609 | 54626.81 | – (–) | 16.00 (0.03) | 14.96 (0.02) | 14.40 (0.01) | 13.88 (0.01) | PROMPT4
20080609 | 54626.82 | – (–) | 16.02 (0.02) | 14.99 (0.02) | 14.51 (0.01) | 13.90 (0.03) | PROMPT2+5
20080610 | 54627.82 | – (–) | 16.03 (0.03) | 15.03 (0.02) | 14.42 (0.01) | 13.94 (0.01) | PROMPT3+5
20080611 | 54628.81 | – (–) | 16.11 (0.05) | 15.04 (0.02) | 14.41 (0.02) | 13.97 (0.02) | PROMPT4
20080611 | 54628.81 | – (–) | 16.01 (0.03) | 15.05 (0.02) | 14.45 (0.01) | 13.91 (0.01) | PROMPT3+5
20080612 | 54629.80 | – (–) | 16.13 (0.12) | 15.01 (0.02) | 14.43 (0.01) | 13.97 (0.01) | PROMPT4
20080612 | 54629.81 | – (–) | 16.18 (0.02) | 15.00 (0.01) | 14.48 (0.01) | 13.94 (0.01) | PROMPT2+5
20080613 | 54630.80 | – (–) | 16.22 (0.05) | 15.09 (0.02) | 14.49 (0.01) | 13.93 (0.02) | PROMPT4+5
20080613 | 54630.93 | 16.59 (0.01) | – (–) | – (–) | – (–) | – (–) | EFOSC
20080614 | 54631.81 | – (–) | – (–) | 15.12 (0.02) | 14.52 (0.01) | 13.92 (0.02) | PROMPT4
20080614 | 54631.81 | – (–) | – (–) | 15.10 (0.02) | 14.47 (0.01) | 13.97 (0.02) | PROMPT5
20080615 | 54632.80 | – (–) | 16.23 (0.03) | 15.16 (0.03) | 14.50 (0.01) | 13.95 (0.01) | PROMPT4
20080615 | 54632.80 | – (–) | 16.18 (0.02) | 15.08 (0.02) | 14.52 (0.01) | 13.94 (0.01) | PROMPT2+5

Table 11: Photometric data collected in Johnson bands for NGC 300 OT (Vega
mag).

Date | MJD | U (err) | B (err) | V (err) | R (err) | I (err) | Instrument
---|---|---|---|---|---|---|---
20080615 | 54632.92 | 16.60 (0.01) | – (–) | – (–) | – (–) | – (–) | EFOSC
20080616 | 54633.80 | – (–) | 16.20 (0.02) | – (–) | 14.52 (0.02) | 13.95 (0.01) | PROMPT2+5
20080617 | 54634.80 | – (–) | 16.14 (0.03) | 15.22 (0.02) | 14.59 (0.02) | 13.98 (0.01) | PROMPT2+5
20080620 | 54637.79 | – (–) | 16.26 (0.06) | 15.27 (0.03) | 14.53 (0.01) | 13.97 (0.02) | PROMPT4
20080622 | 54639.79 | – (–) | 16.27 (0.05) | 15.29 (0.04) | 14.61 (0.02) | 14.02 (0.04) | PROMPT4
20080622 | 54639.85 | – (–) | 16.31 (0.04) | 15.25 (0.03) | 14.60 (0.02) | 13.99 (0.02) | PROMPT2+5
20080623 | 54640.78 | – (–) | 16.35 (0.06) | 15.25 (0.02) | 14.56 (0.01) | 13.99 (0.02) | PROMPT4
20080623 | 54640.86 | – (–) | 16.43 (0.03) | 15.26 (0.02) | 14.60 (0.01) | 14.00 (0.01) | PROMPT2+5
20080624 | 54641.78 | – (–) | 16.46 (0.06) | 15.38 (0.03) | 14.64 (0.01) | 14.08 (0.01) | PROMPT4
20080624 | 54641.78 | – (–) | 16.48 (0.06) | 15.33 (0.02) | 14.57 (0.01) | 14.06 (0.01) | PROMPT2+5
20080625 | 54642.78 | – (–) | 16.42 (0.04) | 15.33 (0.02) | 14.63 (0.02) | 14.10 (0.02) | PROMPT4
20080625 | 54642.78 | – (–) | 16.43 (0.02) | 15.30 (0.02) | 14.60 (0.03) | 14.07 (0.01) | PROMPT2+5
20080626 | 54643.78 | – (–) | – (–) | 15.35 (0.05) | 14.65 (0.02) | 14.10 (0.03) | PROMPT4
20080626 | 54643.78 | – (–) | – (–) | 15.35 (0.05) | 14.68 (0.02) | 14.13 (0.02) | PROMPT5
20080627 | 54644.78 | – (–) | 16.59 (0.02) | 15.31 (0.02) | 14.70 (0.02) | 14.15 (0.02) | PROMPT2+5
20080628 | 54645.81 | – (–) | 16.57 (0.07) | 15.32 (0.03) | 14.72 (0.02) | 14.13 (0.01) | PROMPT4
20080628 | 54645.77 | – (–) | – (–) | 15.42 (0.02) | 14.69 (0.01) | 14.11 (0.01) | PROMPT5
20080629 | 54646.79 | – (–) | 16.58 (0.16) | 15.37 (0.03) | 14.78 (0.01) | 14.10 (0.02) | PROMPT4
20080629 | 54646.76 | – (–) | – (–) | 15.42 (0.04) | 14.74 (0.02) | – (–) | PROMPT5
20080630 | 54647.76 | – (–) | – (–) | 15.41 (0.02) | 14.82 (0.02) | – (–) | PROMPT5
20080701 | 54648.97 | 17.04 (0.29) | 16.63 (0.03) | 15.51 (0.02) | 14.85 (0.02) | 14.19 (0.01) | PROMPT5
20080703 | 54650.77 | – (–) | 16.65 (0.04) | 15.55 (0.02) | 14.92 (0.01) | 14.25 (0.01) | PROMPT3+5
20080704 | 54651.83 | – (–) | – (–) | 15.66 (0.04) | 14.91 (0.01) | 14.26 (0.01) | PROMPT3+5
20080705 | 54652.94 | 17.17 (0.01) | 16.75 (0.01) | 15.62 (0.01) | 14.95 (0.01) | – (–) | EFOSC
20080707 | 54654.75 | – (–) | – (–) | 15.65 (0.25) | 15.02 (0.17) | 14.33 (0.10) | REM
20080708 | 54655.75 | – (–) | 16.95 (0.11) | 15.75 (0.04) | 15.04 (0.01) | 14.34 (0.01) | PROMPT4
20080708 | 54655.75 | – (–) | 16.85 (0.05) | 15.79 (0.03) | 15.04 (0.02) | 14.35 (0.01) | PROMPT3+5
20080709 | 54656.81 | – (–) | 16.82 (0.10) | 15.83 (0.05) | 15.11 (0.03) | 14.36 (0.02) | PROMPT4
20080709 | 54656.74 | – (–) | 17.00 (0.08) | 15.81 (0.03) | 15.07 (0.02) | 14.33 (0.02) | PROMPT3+5
20080710 | 54657.74 | – (–) | 16.97 (0.14) | 15.83 (0.05) | 15.15 (0.03) | 14.41 (0.02) | PROMPT4
20080710 | 54657.73 | – (–) | 17.00 (0.12) | – (–) | 15.16 (0.02) | 14.38 (0.02) | PROMPT3+5
20080710 | 54657.70 | – (–) | – (–) | 15.84 (0.18) | – (–) | – (–) | REM
20080711 | 54658.82 | – (–) | 17.02 (0.06) | 15.86 (0.02) | 15.22 (0.02) | 14.42 (0.02) | PROMPT3+5
20080713 | 54660.86 | – (–) | 17.06 (0.06) | 15.95 (0.02) | 15.22 (0.02) | 14.52 (0.01) | PROMPT3+5
20080714 | 54661.73 | – (–) | 17.14 (0.11) | 16.01 (0.03) | 15.32 (0.02) | 14.49 (0.01) | PROMPT3+5
20080715 | 54662.93 | 17.60 (0.02) | 17.19 (0.02) | 16.03 (0.02) | 15.32 (0.01) | – (–) | EFOSC
20080715 | 54662.72 | – (–) | 17.17 (0.05) | 16.06 (0.03) | 15.33 (0.02) | 14.60 (0.01) | PROMPT3+5