# A Spitzer Survey for Dust-Obscured Supernovae

Ori D. Fox1,2, Harish Khandrika1, David Rubin3, Chadwick Casper4,5, Gary Z.
Li4,6, Tamás Szalai7,8, Lee Armus9, Alexei V. Filippenko4,10, Michael F.
Skrutskie11, Lou Strolger1, Schuyler D. Van Dyk9
1Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD
21218, USA.
<EMAIL_ADDRESS>
3Department of Physics and Astronomy, University of Hawai‘i at Mānoa,
Honolulu, Hawai‘i 96822, USA.
4Department of Astronomy, University of California, Berkeley, CA 94720-3411,
USA.
5Glint Photonics, 1520 Gilbreth Rd., Burlingame, CA 94010, USA.
6The Aerospace Corporation, 2310 E. El Segundo Blvd., El Segundo, CA 90245,
USA.
7Department of Optics and Quantum Electronics, University of Szeged, H-6720
Szeged, Dóm tér 9, Hungary.
8Konkoly Observatory, Research Centre for Astronomy and Earth Sciences, H-1121
Budapest, Konkoly Thege Miklós út 15-17, Hungary.
9IPAC, Caltech, 1200 E. California Blvd., Pasadena, CA 91125, USA.
10Miller Institute for Basic Research in Science, University of California,
Berkeley, CA 94720, USA.
11Department of Astronomy, P.O. Box 3818, University of Virginia,
Charlottesville, VA 22903-0818, USA

###### Abstract

Supernova (SN) rates serve as an important probe of star-formation models and
initial mass functions. Near-infrared seeing-limited ground-based surveys
typically discover a factor of 3–10 fewer SNe than predicted from far-infrared
(FIR) luminosities owing to sensitivity limitations arising from both a
variable point-spread function (PSF) and high dust extinction in the nuclear
regions of star-forming galaxies. This inconsistency has potential
implications for our understanding of star-formation rates and massive-star
evolution, particularly at higher redshifts, where star-forming galaxies are
more common. To resolve this inconsistency, a successful SN survey in the
local universe must be conducted at longer wavelengths and with a space-based
telescope, which has a stable PSF to reduce the necessity for any subtraction
algorithms and thus residuals. Here we report on a two-year Spitzer/IRAC 3.6
$\mu$m survey for dust-extinguished SNe in the nuclear regions of forty
luminous infrared galaxies (LIRGs) within 200 Mpc. The asymmetric Spitzer PSF
results in worse than expected subtraction residuals when implementing
standard template subtraction. Forward-modeling techniques improve our
sensitivity by several $\sim 1.5$ magnitudes. We report the detection of 9
SNe, five of which were not discovered by optical surveys. After adjusting our
predicted rates to account for the sensitivity of our survey, we find that the
number of detections is consistent with the models. While this search is
nonetheless hampered by a difficult-to-model PSF and the relatively poor
resolution of Spitzer, it will benefit from future missions, such as Roman and
JWST, with higher resolution and more symmetric PSFs.

###### keywords:

supernovae: general — dust, extinction — infrared: stars

##  1 Introduction

The observed rate at which stars more massive than $\sim 8$ M⊙ explode as
core-collapse supernovae (CCSNe) can be used to determine chemical evolution
and feedback processes (Matteucci et al., 2006; Scannapieco & Bildsten, 2005),
progenitor-mass distributions (Smith et al., 2011), star-formation rates
(Iben, 1983; Mannucci et al., 2007), and dust yields (Maiolino et al., 2004a,
b; Rho et al., 2009). Given the intrinsic brightness of SNe, they serve as
useful probes of the above characteristics at higher redshifts where other
techniques are less feasible (e.g., Dahlén & Fransson, 1999; Dahlen et al.,
2004; Strolger et al., 2015).

SN rates are useful probes, however, only if we understand the models linking
the initial mass function (IMF), star-formation rates (SFRs), and SNe. For
example, Mattila & Meikle (2001) derive the expected CCSN rate (CCSNr) as a
function of a galaxy’s far-infrared (FIR) luminosity, $L_{\rm
FIR}=L_{{\rm(8-1000)}~{}\micron}$ (which is used as a proxy for star
formation):

${\rm CCSNr}=\frac{2.7\,L_{\rm FIR}}{10^{10}~{}{\rm L_{\odot}}}{\rm
SN}\,(100~{}{\rm yr})^{-1}.\\\ $ (1)

Figure 1: The effects of dust on the intensity and shape of a blackbody
spectrum. The SED here is that of a 5000 K blackbody assumed to represent the
photosphere of a SN IIP several months post-explosion. The 3.6 µm flux is
normalised to $M=-16$ mag Vega (see Fig. 2). Since more absorption occurs at
shorter wavelengths, the peak of the spectrum shifts beyond the NIR (i.e., 2.6
µm) as $A_{V}$ increases beyond 25 mag. Spitzer is more efficient than HST at
these higher extinction levels.

While Equation 1 is an empirical relationship, Mattila & Meikle (2001) derive
a similar relation (their Eq. 5) from first principles and show that Equation
1 both has a basis in and is consistent with the theoretical connection
between the FIR luminosity and SFR. Mattila et al. (2012) add that this
empirical relationship could have a significant uncertainty owing to a small
sample size. We further note that the theoretically derived relationship also
has significant uncertainty since it assumes a scaling factor between the
intrinsic FIR-specific luminosity and the SFR, with no correction for
extinction or other effects111This includes the an unknown efficiency in
reprocessing UV radiation from stars into dust emission in the far-IR, which
for starbursts with high optical depths is around $100\%$., of about
$\kappa_{\rm FIR}\approx 4\times 10^{-10}\,{\rm M}_{\odot}\,{\rm
yr}^{-1}\,{\rm L}_{\odot}^{-1}$. This is about twice as large as the value
determined for dusty galaxies by Madau & Dickinson (2014) and Kennicutt
(1998), at ages of above around 300 Myr.222Younger galaxies ($\lesssim 300$
Myr) have higher emission-to-star-formation ratios as short-lived massive
stars still dominate UV emission that is reprocessed and re-emitted in the IR.
The derivation also assumes the fraction of stars ultimately successful in
producing CCSNe is $k\approx 0.007~{}{\rm M}_{\odot}^{-1}$. This value is
$\sim 30$% larger than estimated for average galaxies by Strolger et al.
(2015), but also carries some assumptions on progenitor mass ranges an/d
average shape of the high-mass IMF. Considering the relationship between all
of these variables, the observed CCSNr therefore gives a useful constraint on
the model by providing some leverage on our theoretical understanding of $k$
and $\kappa_{\rm FIR}$.

The ability to detect all CCSNe in a survey limits the completeness of any
rate study. This is particularly true in galaxies with high SFRs, where gas
and dust obscure many CCSNe. In fact, optical-wavelength surveys in dusty,
star-forming (ultra)-luminous IR galaxies (LIRGs and ULIRGs) have routinely
established CCSNr values that are unexpectedly similar to those in more normal
galaxies (Richmond et al., 1998; Navasardyan et al., 2001). Strolger et al.
(2015) derive the CCSNr from the Hubble Space Telescope (HST) CANDELS and
CLASH programs, two extragalactic multicycle treasury programs using the WFC3
IR channel with sensitivities down to 25.5 magVega out to 1.6 µm. The
observations are notably different from the ultraviolet (UV)/optical SFR
(Madau & Dickinson, 2014), and even less so with the mid-IR (MIR) and FIR
predictions (Chary & Elbaz, 2001). Strolger et al. (2015) link the low CCSNr
(and the subsequent source of discrepancy between the UV/optical and IR-
derived SFRs) to dust obscuration, particularly in galaxies with high SFRs,
where gas and dust obscure most of the SNe, in agreement with Mattila et al.
(2012).

The highest SFRs in the local Universe are found in LIRGs and ULIRGs ($L_{\rm
FIR}>10^{11}$ L⊙ and $10^{12}$ L⊙, respectively; Sanders et al. 2003).
Although one must account for the contribution from hidden active galactic
nuclei (AGNs), star formation tends to contribute most of the IR luminosity
(Sanders & Mirabel, 1996; Genzel et al., 1998), and estimates of the relative
AGN power have been made using a variety of MIR tracers in hundreds of local
IR galaxies (e.g., Díaz-Santos et al., 2017). (U)LIRGs account for only a
small fraction of the local ($<100$ Mpc) galaxy population (Sanders et al.,
2003), so obscuration in these galaxies does not have a detrimental effect on
local CCSNr studies. At higher redshifts, however, obscured star formation in
(U)LIRGs dominates over star formation traced by UV and optical light (e.g.,
Floc’h et al., 2005; Magnelli et al., 2009, 2011; Strolger et al., 2015). To
accurately measure the CCSNr as a function of redshift, the local CCSNr in
starburst galaxies, such as (U)LIRGs, must be fully characterised.

Figure 2: Early-time MIR evolution of all historical SNe obtained from Spitzer archival data by Szalai et al. (2019). Filled and open symbols denote SNe where photometry was obtained with or without image subtraction, respectively. SN subtypes (e.g., Filippenko, 1997) are denoted in the legend, and “SN imp" refers to SN impostors. Table 1: Target Galaxies Name | RA (J2000) | Dec (J2000) | Distance | $L_{\rm FIR}$ | # of SNe | # of SNe | Detections
---|---|---|---|---|---|---|---
|  |  | (Mpc) | (log L⊙) |  | (Corrected) |
NGC 34 | 00:11:06.612 | -12:06:28.33 | 83.33 | 11.43 | 1.45 | 0.42 | 0
NGC 232 | 00:42:45.814 | -23:33:40.69 | 91.66 | 11.23 | 0.92 | 0.28 | 0
MCG+12-02-001 | 00:54:03.943 | +73:05:05.23 | 66.67 | 11.29 | 1.05 | 0.71 | 0
IC 1623 | 01:07:47.2 | -17:30:25 | 79.17 | 11.38 | 1.30 | 0.35 | 0
UGC 2369 | 02:54:00.9 | +14:58:31 | 129.17 | 11.44 | 1.49 | 0.09 | 0
IRAS 03359+1523 | 03:38:46.9 | +15:32:55 | 145.83 | 11.38 | 1.30 | 0.04 | 1
MCG-03-12-002 | 04:21:20.0 | -18:48:45 | 133.33 | 11.30 | 1.08 | 0.05 | 0
NGC 1572 | 04:22:42.814 | -40:36:03.50 | 83.33 | 11.16 | 0.78 | 0.34 | 0
NGC 1614 | 04:34:00.027 | -08:34:44.57 | 66.67 | 11.41 | 1.39 | 0.56 | 0
NGC 2623 | 08:38:24.093 | +25:45:16.70 | 75.00 | 11.47 | 1.59 | 0.82 | 0
UGC 4881 | 09:15:55.54 | +44:19:58.2 | 166.67 | 11.57 | 2.01 | 0.01 | 0
UGC 5101 | 09:35:51.694 | +61:21:10.52 | 162.50 | 11.90 | 4.29 | 0.02 | 0
MCG+08-18-012 | 09:36:30.7 | +48.28:10 | 108.33 | 11.19 | 0.84 | 0.14 | 0
IC 563/IC 564 | 09:46:20.361 | +03:02:43.86 | 83.33 | 11.10 | 0.68 | 0.29 | 1
NGC 3110 | 10:04:02.124 | -06:28:29.12 | 66.67 | 11.10 | 0.68 | 0.44 | 0
NGC 3256 | 10:27:51.60 | -43:54:18.0 | 37.50 | 11.44 | 1.49 | 1.25 | 1
IRAS 10565+2448 | 10:59:18.153 | +24:32:34.30 | 175.00 | 11.87 | 4.00 | 0.03 | 0
Arp 148 | 11:03:53.892 | +40:50:59.89 | 141.67 | 11.50 | 1.71 | 0.06 | 1
MCG+00-29-0023 | 11:21:12.261 | -02:59:03.00 | 100.00 | 11.36 | 1.24 | 0.26 | 0
IC 2810/UGC 6436 | 11:25:45.055 | +14:40:35.98 | 141.67 | 11.50 | 1.71 | 0.06 | 0
NGC 3690 | 11:28:33.13 | +58:33:58.0 | 45.83 | 11.72 | 2.83 | 0.24 | 0
ESO507-G070 | 13:02:52.354 | -23:55:17.65 | 87.50 | 11.31 | 1.10 | 0.39 | 0
UGC 8335 | 13:15:32.8 | +62:07:37 | 129.17 | 11.60 | 2.15 | 0.06 | 0
UGC 8387 | 13:20:35.380 | +34:08:21.84 | 95.83 | 11.52 | 1.79 | 0.23 | 0
NGC 5256 | 13:38:17.69 | +48:16:33.9 | 112.50 | 11.37 | 1.27 | 0.16 | 0
NGC 5257 | 13:39:52.273 | +00:50:22.48 | 91.67 | 11.37 | 1.27 | 0.40 | 1
Mk 273 | 13:44:42.070 | +55:53:13.17 | 158.33 | 12.10 | 6.80 | 0.08 | 0
NGC 5331 | 13:52:16.15 | +02:06:03.3 | 137.50 | 11.43 | 1.45 | 0.06 | 0
UGC 8782 | 13:52:17.7 | +31:26:44 | 187.50 | 12.27 | 10.06 | 0.00 | 0
Arp 302 | 14:57:00.4 | +24:36:44 | 141.67 | 11.59 | 2.10 | 0.05 | 0
Mk 848 | 15:18:06.123 | +42:44:44.59 | 166.67 | 11.72 | 2.83 | 0.03 | 0
Arp 220 | 15:34:57.272 | +23:30:10.48 | 75.00 | 12.12 | 7.12 | 3.52 | 0
NGC 6090 | 16:11:40.39 | +52:27:21.5 | 120.83 | 11.35 | 1.21 | 0.11 | 1
NGC 6240 | 16:52:58.97 | +02:24:01.7 | 100.00 | 11.85 | 3.82 | 0.65 | 2
IRAS 17208-0014 | 17:23:21.943 | -00:17:00.96 | 179.17 | 12.30 | 10.77 | 0.05 | 0
IC 4687/86 | 18:13:39.829 | -57:43:31.25 | 70.83 | 11.35 | 1.21 | 0.68 | 0
IRAS 18293-3413 | 18:32:40.2 | -34:11:26 | 75.00 | 11.63 | 2.30 | 0.97 | 1
NGC 6926 | 20:33:06.108 | -02:01:39.07 | 83.33 | 11.11 | 0.70 | 0.29 | 0
NGC 7130 | 21:48:19.490 | -34:57:04.73 | 66.67 | 11.21 | 0.88 | 0.48 | 0
IRAS 23128-5919 | 23:15:46.772 | -59:03:15.94 | 183.33 | 11.80 | 3.41 | 0.01 | 0
Figure 3: Comparison of sample data products, in this case for the first epoch
of NGC 6240, used in our transient search. (Top left:) Original, unsubtracted
MOPEX processed data. (Top right:) Standard alignment and subtraction of two
epochs. (Bottom left:) Forward modeling subtraction, where the circle
corresponds to our forward modeling radius. (Bottom right:) Subtraction of two
epochs that have been forward modeled, but in this case are spaced nearly one
year apart so that the telescope roll angle is similar. The colour scale and
stretch is constant for all subtracted images shown in this figure. The point
source is SN 2013dc. It is present in all the images, but is most clearly
detected in the bottom right. The central source is the galaxy nucleus. As
described in the text, there are a number of caveats for modeling the inner
core, including nonlinearity concerns. Correcting those issues is beyond the
scope of this paper, but we account for them in our statistics.

The IR, which can be up to 10 times less affected by extinction than visible
light, offers an optimised window for SN searches in these starburst galaxies.
Already, a number of near-IR (NIR) searches have been performed with mixed
success. Early NIR ground-based surveys were hampered by poor resolution and
limited telescope time (van Buren & Greenhouse, 1994; Grossan et al., 1999;
Maiolino et al., 2002; Mannucci et al., 2003; Mattila et al., 2004, 2005a,
2005b; Miluzio et al., 2013). These studies resulted in an inferred CCSNr that
was still a factor of 3–10 lower than expected from the SFR (Mannucci et al.,
2003). Furthermore, no SNe were detected within the galaxy nuclei. Ground-
based high-resolution adaptive optics (AO) NIR searches have had some
additional success in their discovery of several CCSNe within $<300$ pc from
the LIRG nuclei (e.g. Mattila et al., 2007; Kankare et al., 2008, 2012; Kool
et al., 2018; Kankare et al., 2021; Pérez-Torres et al., 2021). Kool et al.
(2018) note their high-spatial-resolution search uncovered a larger
concentration of nuclear SNe in (U)LIRGs than previous low-resolution
searches, while Kankare et al. (2021) showed that a sample of 29 CCSNe at
$<$2.5 kpc from (U)LIRG nuclei showed a correlation between the startburst age
and SN subtype. In general, these gorund-based surveys either did not find
their rates consistent with the predictions or had limited statistics. The
overall conclusion was that a majority of SNe likely occur within the nuclei,
but the extinction is so high ($A_{V}>25$ mag) and the nuclei are so bright
that longer-wavelength observations are necessary. Even several space-based
surveys (e.g., Bregman et al., 2000), including a HST/NICMOS (Cresci et al.,
2007), turned up no confirmed detections, concluding that the ULIRG dust-
extinction values are too high ($A_{V}>25$ mag). Results from the SPitzer
InfraRed Intensive Transients Survey (SPIRITS; Kasliwal et al. 2017) between
2014 and 2018 find the fraction of CCSNe in nearby galaxies missed by optical
surveys could be as high as 38.5% (Jencson et al., 2019). High-resolution
ground-based radio surveys, by contrast, have successfully discovered nuclear
SNe with rates consistent with the galaxy IR luminosities, but not all SNe are
sufficiently bright at radio wavelengths to conduct a complete survey (Pérez-
Torres et al., 2021).

Until the James Webb Space Telescope (JWST) is launched, the Spitzer Space
Telescope (Spitzer) Infrared Array Camera (IRAC; Fazio et al. 2004) offered
the best combination of long-wavelength sensitivity, stable point-spread
function (PSF), moderate resolution, and sensitivity to SN radiation. Here we
describe a post-cryogenic Warm-Spitzer/IRAC survey conducted in the years
2012–2014 for dust-extinguished SNe in, but not limited to, the nuclear
regions of nearby star-forming (U)LIRGs (PID 90031; PI: O. Fox). (A similar,
but more limited survey was conducted during the cryogenic Spitzer mission by
Lawrence & Gautier 2004, PID 108; however, the data analysis and results were
never published.) The MIR is optimised for dust-extinction levels $A_{V}>25$
mag. The improved sensitivity offers an improved estimate of the number of SNe
missed by visible (and NIR) surveys and tighter constraints on our
understanding of star-formation models out to high redshifts. The direct
product of this study is the connection between FIR luminosity and massive-
star formation. Such results naturally connect to the high-redshift universe,
where a fundamental observable is the FIR galactic flux. Given a future which
includes the LSST, EUCLID, the Nancy Grace Roman Space Telescope (NGRST), and
JWST, local measurements characterising the properties of galaxies selected
from FIR samples have large-scale implications.

Our observations are presented in Section 2. Section 3 describes the data
reduction, data processing, and analysis techniques. Our results are discussed
in Section 4, and Section 5 summarises our conclusions.

##  2 Observations

The original proposal called for a Warm-Spitzer/IRAC survey of 40 galaxies to
maximise the number of expected SNe and generate a statistically significant
sample to minimise the statistical effects of undetected SNe. We selected the
nearest 40 (U)LIRGs ($L_{\rm FIR}>10^{10}$ L⊙) from Sanders et al. (2003),
which ultimately extended our sample out to 200 Mpc. Table 1 summarises the
targets and also lists the number of SNe predicted by Equation 1 over the two-
year survey window. For each galaxy, eight epochs of observations were
obtained, spaced approximately 1–6 months apart depending on the visibility
window.

To minimise observing time, all observations were obtained in only a single
filter with IRAC Channel 1 (3.6 µm). The spectral energy distribution (SED)
for a 5000 K blackbody peaks at $>2.0$ µm for $A_{V}>25$ mag (Fig. 1).
Increasing the extinction pushes the peak of the SED to longer wavelengths,
but also lowers the overall flux substantially enough that it becomes
inefficient to observe these targets at larger distances. Channel 1 (3.6 µm)
is also slightly more sensitive than Channel 2 (4.5 µm). These are the only
two channels available during the Warm-Spitzer mission and, at the time of the
survey, Spitzer/IRAC was the only MIR observing capabilities accessible from
space.

Figure 4: A residual map of UGC 8782 illustrating complications and
limitations of our algorithm to detect interconnected groups of pixels within
a given epoch with fluxes $\gtrsim 3\sigma$ of their average value. The
original image has the forward model subtracted, resulting in the ringed
structure corresponding to the model itself. The color scale units are
$\sigma$, defined by the statistics of each individual pixel across all eight
epochs. The poorly subtracted nuclear region in this example is typical of
many of the targets in our sample for a variety of issues beyond forward
modeling that we describe and account for in the text.

To calculate our integration times, we consider the distribution of CCSN
magnitudes. MIR light curves of CCSNe are sparse, but Szalai et al. (2019)
present comprehensive plots of all existing Spitzer observations. Figures 6
and 7 from Szalai et al. (2019) show that CCSNe plateau in the MIR for $\sim
300$ days post-explosion, and often even longer. Figure 2 plots the photometry
as a function of distance, separated by explosion type and age. A majority of
CCSNe fall within a range of $-16<M_{3.6\,\mu m}<-18$ over the first few
months. Most of these SNe are at distances $<60$ Mpc, since the proposed
Spitzer observations generally targeted nearby, bright SNe.

Figure 5: Sensitivity of our search algorithm derived from the artificial
source tests for each galaxy as a function of the galaxy distance. Each galaxy
in our sample has four data points, corresponding to recovery rates for
artificial sources placed at various radii from the nucleus as defined by the
legend. The detection limit, or cutoff magnitude, is defined as the magnitude
at which we can achieve a 50% recovery rate for all of our sources. The solid
line corresponds to the more realistic empirical cutoff magnitude derived
qualitatively from Figure 10, as we discuss in the text. Figure 6 plots the
consolidated results for all galaxies shown in this plot.

Given that the typical time between consecutive observations is anywhere in
the range 1–6 months, we assumed a magnitude of $M_{3.6\,\mu m}\approx-17$
when designing our observations. In general, photon-counting statistics from
the underlying galaxy dominate the uncertainty, and we therefore require
longer integration times. We also account for possible extinction ranging up
to $A_{V}=35$ mag. Figure 1 shows the effects of extinction by plotting the
SED for a 5000 K blackbody for various values of $A_{V}$. At 3.6 µm, the
effects of extinction are minimal, decreasing the brightness only $\sim 2$ mag
for $A_{V}=45$ mag. Despite this planning, however, subtraction effects
ultimately dominated our error budget, which we discuss in more detail below.

##  3 Reduction Techniques

###  3.1 Forward Modeling and Subtraction

Despite the absence of atmospheric effects when working with images taken by
space telescopes, there are three features of the Spitzer data that combine to
make precise galaxy subtraction difficult. (1) The PSF is undersampled (only
$\sim 1$ pixel per full width at half-maximum intensity). (2) The PSF is
highly azimuthally asymmetric. (3) The data are taken over a range of
spacecraft roll angles, with no two epochs matching exactly. To enable precise
galaxy subtraction, we turn to forward modeling.

Forward modeling infers an analytic galaxy model on the sky by tracing the
light (“forward”) through convolution with the PSF and pixel, and then
sampling by the detector (e.g., Holtzman et al., 2008; Suzuki et al., 2012;
Hayden et al., 2021; Rubin et al., 2021). Each of the epochs is fit
simultaneously with a model of the galaxy background plus SN. This model is
inferred using a set of dithers and/or rotations, bypassing the traditional
step of resampling the images for pixel-by-pixel subtraction, which would
introduce artifacts. In testing, we found that the given model of the Point
Response
Function333https://irsa.ipac.caltech.edu/data/SPITZER/docs/irac/calibrationfiles/psfprf/
(PRF, the covolution of the PSF and the pixel response) was not accurate
enough for our purposes, so we derived our own PRF from high signal-to-noise-
ratio observations of field stars.

For each of the eight epochs in which a search is performed, the forward model
is derived from reference observations of the galaxy obtained before the SN
appears or after the SN fades. In other words, we exclude observations
obtained $<20$ days prior or $>330$ days to account for the possibility that a
rising/falling SN component may contribute to the model. In addition to the
galaxy model, we also fit small tweaks to the astrometry and differences in
the sky level. Once a model is generated, it is subtracted from each corrected
Basic Calibrated Data (cBCD) file, which are then stacked with the MOsaicker
and Point source EXtractor
(MOPEX)444https://irsa.ipac.caltech.edu/data/SPITZER/docs/dataanalysistools/tools/mopex/
(Fig. 3).

Figure 6: Overall detection rate as a function of radius from the galactic
nucleus for forward model subtracted images based on artificial star tests

.

###  3.2 Detecting Transient Sources

To quantify the success of the forward-modeling algorithm, we use grids of
artificial star tests. Owing to the IRAC mosaic’s large pixel scale ($\sim
0.6$″), however, the flux density within any single pixel tends to vary from
epoch to epoch, particularly in rapidly changing (i.e., nuclear) environments.
This could lead to false positives. We therefore developed an approach that
considers the variance in each pixel over all eight epochs and then searches
for a cluster of interconnected pixels within a given epoch that are all
$>3\sigma$ from their average value (e.g., Fig. 4). For each galaxy, we
calculate the percent of SNe recovered using this method as a function of
magnitude and distance from the centre of the galaxy. The detection limit, or
cutoff magnitude, is defined as the magnitude at which we can achieve a 50%
recovery rate and varies significantly depending on the individual features of
the host galaxy (Fig. 5).

Figures 6 and 7 consolidate the results from Figure 5 and show the evolution
of the detection rate as a function of magnitude for the different radii bins.
Generally, the detection limit improves at larger radii owing to less
complicated subtraction residuals. For comparison, results for the traditional
(i.e., non-forward modeling) subtraction images are also plotted in Figure 7.
Note how the forward modeling improves our relative fraction of faint SNe
($>14$ mag) recovered.

Using this $3\sigma$ interconnected pixel detection algorithm, however, is
limited given only eight epochs of data per pixel and the fact that SNe can
span multiple epochs, thereby influencing the statistics of the pixels that we
are trying to isolate. Any single threshold does not equally apply to all
pixels because the asymmetric PSF impacts the noise in the model subtractions
of some pixels in a non-Gaussian way. We also notice a subtle nonlinearity in
the pixel response that evolves over the two-year lifetime of the survey
(i.e., later epochs have lower fluxes). Pixels may therefore exhibit $3\sigma$
deviations that are not due to Poisson statistics alone (Fig. 4). Furthermore,
we have prior knowledge of the artificial source locations, so recovering the
sources is not hampered with false positives or nearby noise effects.

Figure 7: Overall detection rate for 0–5″ comparing the standard and forward
model subtraction techniques based on artificial star tests

.

Figure 8: Histograms of flux-density variance per pixel in the inner $<$3″ of each galaxy using the two different reduction techniques: standard template subtraction and forward modeling. The histogram for the forward modeling is much narrower, suggesting less variance per pixel and overall increased sensitivity to detecting fainter sources. Table 2: Supernova Detections in this Survey Host | Source RA/Dec | Nuclear Offset | Date | $F_{\nu,[3.6\,\mu m]}$ | $m/M$ | Notes
---|---|---|---|---|---|---
Galaxy | (J2000) | (″N/E) | (MJD) | ($\mu$Jy) | ($3.6\,\mu m$) |
NGC 5257 | 13:39:52.2148, +0:50:25.328 | -11.8/0.3 | 56780 | 12(5) | 18.3/$-$16.5 (0.5) | –
IRAS 18293-3413 | 18:32:41.0980, $-$34:11:27.230 | -1.0/0.2 | 56455 | 55(5) | 16.8/$-$17.6 (0.1) | SN 2013if
56483 | 26(5) | 17.6/$-$16.8 (0.3)
56613 | 87(5) | 16.3/$-$18.1 (0.1)
56646 | 45(5) | 17.0/$-$17.4 (0.2)
Arp 148 | 11:03:53.1180, +40:51:09.385 | -8.8/9.5 | 56510 | 1(0) | 21.2/$-$14.6 (0.1) | –
NGC 6090 | 16:11:40.3172, +52:27:23.609 | -3.7/-3.3 | 56890 | 44(5) | 17.0/$-$18.4 (0.2) | –
NGC 3256 | 10:27:50.7987, $-$43:54:02.554 | -5.2/11.0 | 56875 | 610(10) | 14.1/$-$18.7 (0.1) | PSN J10275082-4354034
56925 | 142(20) | 15.7/$-$17.1 (0.2)
IRAS 03359 | 03:38:47.3486, +15:32:56.462 | 3.0/2.7 | 56964 | 24(2) | 17.7/$-$18.1 (0.1) | –
IC 563 | 09:46:20.7408, +3:02:38.346 | 5.7/-5.5 | 56687 | 31(3) | 17.4/$-$17.2 (0.3) | –
NGC 6240 | 16:52:57.6161, +02:23:36.731 | -18.7/-26.8 | 56795 | 46(4) | 17.0/$-$18.0 (0.3) | PS1-14xw
56833 | 20(5) | 17.8/$-$17.2 (0.4)
56953 | 5(2) | 19.4/$-$15.6 (0.8)
NGC 6240 | 16:52:58.9791, +02:24:25.587 | 1.8/22.0 | 56421 | 56(5) | 16.8/$-$18.2 (0.1) | SN 2013dc
56454 | 55(5) | 16.8/$-$18.2 (0.1)
56580 | 8(2) | 18.9/$-$16.1 (0.2)
56617 | 7(2) | 19.0/$-$16.0 (0.2)

All of this is to say that false positives could impact our interpretation of
Figures 6 and 7. To alleviate any of these concerns, Figure 8 plots the
distribution of variance in each pixel for the two different subtraction
techniques. The forward-modeling approach has a much narrower distribution,
which is consistent with an improved subtraction approach. We conclude that
the artificial star tests are most useful for guiding the relative success of
our forward modeling and subtraction algorithms, but the limitations of the
simulations are significant enough that we cannot use them as an absolute
quantification of the sensitivity of our search. Ultimately, we choose to
manually search for transient sources in the resulting images with limited
guidance from our algorithm.

Figure 9: Imaging of each SN detected in this survey, labeled by galaxy and
epoch. For each detection, two images are displayed. On the left is the
subtraction of the template derived using forward modeling. On the right is
the subtraction of two different epochs that have been forward modeled. Epochs
separated by $\sim 1$ yr have similar orientations and the relative
subtractions remove additional residuals that were still visible after forward
modeling, as well as the more diffuse, outer galaxy that was not forward
modeled. In general, this relative subtraction of epochs separated by about a
year provided optimal results.

##  4 Results

###  4.1 Detections

Table 2 lists, and Figures 9 and 10 show, all 9 detections from our sample. We
also indicate any corresponding ground-based discoveries, which help us
constrain the explosion dates. SN 2013if was discovered by the Supernova
UNmasked By Infra-Red Detection (SUNBIRD) project and had an associated near-
IR light curve (Kool et al., 2018). The best-fit light-curve template shows SN
2013if to be an SN IIP with almost no extinction, which is surprising given
its proximity to the nucleus. Kankare et al. (2021) reported the discovery of
PSN J10275082-4354034 near the nucleus of NGC 3256. The SN was also detected
in serendipitous Hubble Space Telescope high-resolution imaging. The
subsequent light curve was determined to be most consistent with an SN IIn,
although an SN IIP could not be ruled out. Again, only a small amount of
extinction ($A_{V}\lesssim 0.3$ mag) is present. PS1-14xw was first reported
by Benitez et al. (2014) and classified as an SN Ia, while SN 2013dc was first
reported by Block et al. (2013). We find no published analysis of either
PS1-14xw or SN 2013dc.

Figure 10: Absolute magnitudes of the nine SNe discovered in our sample (green
symbols). The photometry corresponds to zero host galaxy extinction for all
the events and therefore their absolute magnitudes should be considered as
lower limits. Also plotted are early (i.e.,$<3$ month) photometry from Szalai
et al. (2019) of nearby ($<50$ Mpc) SNe IIP and some SNe Ia within 30 days of
explosion (black and red symbols, respectively). Dashed, dotted, and dotted-
dashed lines represent apparent brightness levels of 17, 18, and 19 mag,
respectively.

Figure 11 plots the MIR light curves along with previously published light
curves from Szalai et al. (2019). The MIR evolution of SNe Ia and SNe IIP
overlap substantially, especially at early times, but they do tend to diverge
a bit more at later times. Of the light curves that extend out to later
epochs, the evolution is most consistent with SNe IIP. Of course, PS1-14xw was
originally classified as an SN Ia. For the SNe for which we only have a single
epoch, the brightness is consistent with both SNe Ia and SNe IIP around peak
with very little to no extinction. The detection in Arp148 stands out for
being relatively faint, which could indicate significant extinction or perhaps
a poor constraint on the explosion time. It is difficult to draw any
conclusions on the extinction from just a single filter.

Even with the forward modeling, all of our SN detections are outside ($>3$″)
of the galactic nucleus. (SN 2013if is a nuclear event included in our tally
for rates purposes, but we do not have a convincing detection in Figure 9.)
The survey has limited follow-up observations to confirm the nature and
classification of each transient source, but the observed magnitudes are
consistent with those of other SNe (Fig. 10), bright enough to rule out most
other types of transients (see Fig. 4 of Kasliwal et al. 2017). For the
purposes of this analysis, we assume that each detection (except PS1-14xw) is
a CCSN.

###  4.2 Survey Sensitivity

Before we can interpret the statistics of our detections, it is important to
have an understanding of our survey’s sensitivity. We first consider our
search sensitivity from an empirical perspective. Figure 10 plots the
photometry of SNe detected in our survey (green points), as well as the
relatively early ($<3$ month) magnitudes of the nearby ($<50$ Mpc) CCSNe from
Figure 2 (black points) and some young SNe Ia from Szalai et al. (2019) (red
points). Overplotted are lines of constant apparent magnitude. The early-time
magnitude distribution of nearby CCSNe is $-16\lesssim M_{3.6\,\mu
m}\lesssim-18$, while known SNe Ia are a couple of magnitudes brighter. We
assume that the nearby distribution of magnitudes is relatively complete. If
our survey were also to be considered complete and the magnitude distribution
doesn’t change as a function of redshift, then to first order we should detect
a similar spread in our SN magnitude distribution out to 200 Mpc.

The actual distribution of our SN photometry in Figure 10, however, does not
reflect the more nearby distribution. Most of the SNe we detect are relatively
bright. In fact, as noted in Figure 11, an absolute magnitude $M_{\rm
3.6\,\micron}\approx-18$ may be interpreted as more consistent with the peak
magnitudes of SNe Ia rather than those of SNe IIP. Although our sample is
limited in size, we conclude that we are Malmquist biased and generally do not
detect SNe dimmer than $17.5\pm 0.5$ mag. This empirical limit is compared to
the results of our artificial-star tests in Figure 5. While in most cases the
empirical threshold is brighter than the artificial-star tests achieved, there
are a number of cases where the artificial-star tests are brighter than the
empirical limit, particularly in the innermost regions of the galaxies. As
noted in Section 3.2, there are a number of caveats in the sensitivity of the
artificial-star tests to the fainter stars. In general, we therefore define
our sensitivity limit for a given radial bin to be the brighter of these two
limits.

Figure 11: The 3.6 $\mu$m light curves of the four detected known transients
in our Survey (with black symbols), together with previously published light-
curves (grey symbols and shaded colored regions, adopted from Szalai et al.,
2019). Dark-grey transparent rectangles mark the single epoch of photometry
for the other five detected sources within the possible periods (taking into
account the dates of last non-detections). Widths and heights of the
rectangles denote the uncertainties of epochs and absolute magnitudes of the
five previously unknown transients, respectively.

###  4.3 Possible Causes for Decreased Sensitivity

This survey is not particularly sensitive to SNe in either the nuclear regions
of galaxies or galaxies at $>150$ Mpc. Cresci et al. (2007) offer some
explanations for their HST/NICMOS survey that could apply to our survey. For
example, the FIR flux used to calculate the expected CCSNr is dominated by
obscured AGNs and not by star formation. Estimates of the relative AGN power,
however, have been made using a variety of MIR tracers in hundreds of local IR
galaxies and, in most cases, do not suggest significant AGN contributions
(e.g., Díaz-Santos et al., 2017).

Another possibility is that the SNe may be more obscured by dust than
originally expected, or underluminous SNe (e.g., Pastorello et al., 2004) form
a significant fraction of all CCSNe. In the latter case, the SNe would stay
above our detection limit for a shorter time. In either case, the Gaussian
distribution of magnitudes would have a tail skewed toward dimmer objects and
our overall sensitivity would decrease, resulting in a decrease in our
expected CCSNr.

Figure 12: Relationship between predicted CCSN rate, actual CCSN rate, and
distance. (Top:) The number of actual detections compared to the predicted
number of CCSNe, where the colour bar corresponds to the distance (Mpc), for
both the uncorrected and corrected rates. (Bottom:) The predicted number of
SNe as a function of distance, where the colour bar corresponds to the number
of actual detections. Both plots show values for both the uncorrected and
corrected rates (as described in the text).

The most likely explanation, however, is a combination of worse than expected
subtraction residuals combined with relatively poor resolution, despite the
decreased extinction afforded by observations at 3.6 µm. Note that the mosaic
images have a pixel scale of $\sim 0.6^{\prime\prime}$ that corresponds to a
projected distance of $\sim 290$ pc at 100 Mpc (and the real resolution is a
factor of 2–3 worse). Our poor residual at $<3$″ corresponds to $\sim$1.5 kpc
at these distances. If most starburst activity is concentrated within the
galaxy nucleus, then our survey not being sensitive to a majority of these
events. We correct for the limitations in our survey sensitivity below.

Table 3: IR Integrated Luminosities (5–24 µm) Galaxy | 1″ | 3″ | 5″ | 10″
---|---|---|---|---
Name | L⊙ (Fraction of Total Luminosity)
NGC034 | 9.7 (0.1) | 10.4 (0.47) | 10.5 (0.62) | 10.7 (1.0)
NGC232 | 9.3 (0.05) | 9.9 (0.22) | 10.2 (0.44) | 10.6 (1.0)
MCG+12-02 | 9.2 (0.04) | 10.0 (0.24) | 10.3 (0.47) | 10.7 (1.0)
IC1623 | 8.9 (0.02) | 9.8 (0.15) | 10.1 (0.32) | 10.6 (1.0)
UGC2369 | 9.0 (0.02) | 9.6 (0.11) | 10.0 (0.25) | 10.6 (1.0)
IRAS03359 | 9.7 (0.07) | 10.3 (0.32) | 10.5 (0.46) | 10.8 (1.0)
MCG-03-12 | 9.4 (0.05) | 10.0 (0.27) | 10.3 (0.45) | 10.6 (1.0)
NGC1572 | 9.4 (0.09) | 10.1 (0.4) | 10.2 (0.52) | 10.5 (1.0)
NGC1614 | 9.5 (0.05) | 10.4 (0.38) | 10.6 (0.59) | 10.8 (1.0)
NGC2623 | 9.6 (0.09) | 10.2 (0.34) | 10.3 (0.5) | 10.6 (1.0)
UGC4881 | 9.7 (0.06) | 10.3 (0.26) | 10.5 (0.42) | 10.9 (1.0)
UGC5101 | 10.2 (0.11) | 10.8 (0.44) | 10.9 (0.56) | 11.1 (1.0)
MCG+08-18 | 8.2 (0.02) | 9.1 (0.16) | 9.3 (0.31) | 9.8 (1.0)
IC563 | 8.8 (0.03) | 9.6 (0.2) | 9.8 (0.36) | 10.3 (1.0)
NGC3110 | 9.1 (0.05) | 9.9 (0.3) | 10.1 (0.46) | 10.4 (1.0)
NGC3256 | 9.3 (0.04) | 10.1 (0.23) | 10.4 (0.43) | 10.7 (1.0)
IRAS10565 | 10.2 (0.1) | 10.8 (0.43) | 11.0 (0.54) | 11.2 (1.0)
Arp148 | 9.7 (0.08) | 10.3 (0.34) | 10.5 (0.49) | 10.8 (1.0)
MCG+00-29 | 9.6 (0.09) | 10.3 (0.42) | 10.4 (0.55) | 10.6 (1.0)
IC2810 | 9.6 (0.07) | 10.2 (0.3) | 10.4 (0.45) | 10.8 (1.0)
NGC3690 | 9.3 (0.04) | 10.1 (0.26) | 10.4 (0.45) | 10.7 (1.0)
ESO507-G070 | 9.4 (0.07) | 10.1 (0.32) | 10.3 (0.47) | 10.6 (1.0)
UGC8335 | 8.9 (0.12) | 9.6 (0.54) | 9.7 (0.78) | 9.8 (1.0)
UGC8387 | 9.7 (0.07) | 10.4 (0.35) | 10.6 (0.52) | 10.8 (1.0)
NGC5256 | 9.0 (0.02) | 9.8 (0.13) | 10.2 (0.35) | 10.7 (1.0)
NGC5257 | 9.0 (0.04) | 9.6 (0.17) | 9.9 (0.32) | 10.4 (1.0)
Mk273 | 10.4 (0.09) | 11.0 (0.35) | 11.1 (0.5) | 11.4 (1.0)
NGC5331 | 9.6 (0.06) | 10.3 (0.32) | 10.5 (0.47) | 10.8 (1.0)
UGC8782 | 9.3 (0.08) | 9.9 (0.35) | 10.1 (0.48) | 10.4 (1.0)
Arp302 | 9.7 (0.06) | 10.4 (0.3) | 10.6 (0.48) | 10.9 (1.0)
Mk848 | 10.0 (0.1) | 10.7 (0.41) | 10.8 (0.54) | 11.1 (1.0)
Arp220 | 9.8 (0.15) | 10.4 (0.69) | 10.5 (0.83) | 10.6 (1.0)
NGC6090 | 9.1 (0.02) | 9.9 (0.14) | 10.2 (0.3) | 10.7 (1.0)
NGC6240 | 10.0 (0.11) | 10.7 (0.47) | 10.8 (0.6) | 11.0 (1.0)
IRAS17208 | 10.4 (0.08) | 11.0 (0.35) | 11.2 (0.49) | 11.5 (1.0)
IC4687 | 9.3 (0.05) | 10.1 (0.34) | 10.4 (0.55) | 10.6 (1.0)
IRAS18293 | 9.7 (0.06) | 10.5 (0.32) | 10.7 (0.5) | 11.0 (1.0)
NGC6926 | 8.8 (0.04) | 9.5 (0.18) | 9.7 (0.32) | 10.2 (1.0)
NGC7130 | 9.4 (0.08) | 10.1 (0.34) | 10.2 (0.49) | 10.5 (1.0)
IRAS23128 | 10.1 (0.09) | 10.8 (0.38) | 10.9 (0.54) | 11.2 (1.0)

###  4.4 Observed vs. Expected

To properly compare the observed number of SNe detected to the predicted
value, we first have to correct for the number of expected SNe to account for
our decreased sensitivity. To properly correct, we must calculate both the
fraction of SNe we are sensitive to at any given location in a galaxy, $f_{\rm
SNe}$, and the fraction of light within that radius, $f_{\rm light}$.

We first define our detection threshold in Section 4.2. We then assume the
distribution of SN magnitudes to be consistent with observations in Figure 2,
which we take to be a Gaussian centred function at $M_{\rm 3.6\,\mu m}=-17$
mag and a standard deviation of $\sigma_{\rm SN~{}IIP}=0.7$. No extinction is
applied. This distribution should be considered an upper limit as the actual
function may have a lower-luminosity tail or be shifted to a somewhat less-
luminous centre in the case of high extinction. For each galaxy, we calculate
the respective apparent magnitude distribution for the given distance and the
corresponding fraction of SNe, $f_{\rm SNe}$, in the magnitude distribution
that is bright enough to be detected based on the detection threshold. This
fraction is calculated separately for each radial bin.

We next derive the fraction of light within each radial bin, $f_{\rm light}$,
from the integrated MIR lumninosity, which we measure using aperture
photometry performed on archival IRAC and MIPS data (when available). Although
the SFR and the CCSNr are tied to the FIR luminosity, we assume the MIR to be
a useful and convenient proxy, at least to first order. While most (U)LIRG
flux comes out at longer wavelengths (i.e., $\sim 70$ µm), the shape of a
(U)LIRG SED is roughly constant (Wright et al., 2014). Table 3 lists our
derived MIR luminosities and fractional luminosity for each aperture.

The predicted CCSNr is finally corrected by multiplying by both the fraction
of SNe we are sensitive to, $f_{\rm SNe}$, and the fraction of light within
that radial bin, $f_{\rm light}$. Table 1 lists the corrected CCSNr
predictions, and Figure 12 compares the predicted and observed number of SNe
detected for each galaxy. Figure 12(a) compares the number of observed CCSNe
to the number of predicted CCSNe. Overplotted is a line corresponding to a 1:1
ratio, which is what we would expect in an ideal scenario. The two plots
correspond to the uncorrected and corrected number of predicted events,
respectively. Figure 12(b) plots the predicted number of CCSNe as a function
of distance. Again, the upper and lower panels correspond to the uncorrected
and corrected number of predicted events, respectively.

There are several qualitative takeaways. First, all of our detections occur at
$<150$ Mpc. Although our calculations suggest that we should be sensitive to
SNe out to 200 Mpc, other challenges arise at these distances. For example,
galaxies become less resolved and more compact, so the subtraction residuals
have a larger impact. These residuals correspond to larger projected distances
in, and therefore fraction of, the host galaxy. While there is no sharp
cutoff, the more distant galaxies in our sample are more luminous, but also
more compact and dustier.

Second, in almost every case the adjusted expected CCSNr ends up falling to
$<1$, which makes a comparison to the expected trend (black line) in Figure
12(a) difficult. Despite small-number statistics, we still see a slight
correlation between observed SNe versus predicted SNe that, although weak,
does provide a useful self-consistency check. The one exception is Arp 220,
which stands out from the other galaxies at $\sim 75$ Mpc for its large number
of predicted SNe. Despite this expectation, we don’t detect any SNe, possibly
due to the fact that most of the light is concentrated in the inner $<3$″.
Furthermore, like other IR-bright galaxies, Arp 220 may suffer from relatively
high local extinction.

Taken all together, these adjustments limit a significant fraction of the
phase space in which we can search for and detect an SN. The large number of
galaxies observed, however, compensates for these inefficiencies and provides
adequate statistics. In total, we expect 96 and 14$\pm$6 SNe before and after
corrections are made (respectively), where the error bars are dominated by
uncertainty assigned above to our detection threshold (i.e., $m_{\rm 3.6\,\mu
m}=17.5\pm 0.5$ mag). We discover 9 SNe (Table 2).

###  4.5 Statistical Implications

After all corrections are taken into account, our observations yield a
statistically significant sample that will enable us to differentiate between
(1) undetected SNe and (2) counting statistics. Assuming the counting
statistics are determined by the SN sample (i.e., $\sigma=\sqrt{N}$), then the
minimum number of SNe we must expect to detect is roughly sixteen. Any fewer
expected SNe would be statistically insufficient. For example, to identify a
$3\sigma$ deficit in the CCSNr when only 9 SNe are expected, one would need to
observe $<0$ SNe.

As noted above, we detect 9 SNe, whereas theory predicted 14$\pm$6 SNe. We
conclude that our observations are generally consistent with the predictions,
especially when considering the counting statistics, which for 14 SNe yield
$\sigma_{\rm counting}=\sqrt{14}=3.7$. Of course, the number of predicted SNe
is given after significant corrections in our sensitivity have been applied.

##  5 Conclusion

We have presented a Spitzer/IRAC MIR survey for dust-extinguished SNe to
resolve the discrepancy between theoretically predicted and optical/NIR
observed core-collapse SN rates. We searched 40 nearby ($<200$ Mpc) star-
forming galaxies using Spitzer/IRAC. The survey includes eight epochs of
observations obtained in the years 2012–2014.

Our ability to detect new SNe was dominated by subtraction residuals near the
nuclear regions ($<$3 ″) of each galaxy caused by an asymmetric PRF that
rotated throughout the year as the telescope circled the Sun. To optimise our
subtraction algorithm, we implemented a forward modeling technique that will
be employed on the NGRST; (Rubin et al., 2021).

While forward modeling improves our overall sensitivity, the number of
discovered SNe is still substantially lower than the expected intrinsic number
during the survey period. We compensate for the number of predicted SNe by
quantifying the inefficiencies, mostly arising from remaining residuals in the
inner $<3$″, where a majority of star formation occurs. The predicted rates
are particularly impacted by the fact that most of the galaxies with the
highest SN rates (2–11 SNe per year) are located at distances larger than 150
Mpc, where essentially zero SNe can be expected to be discovered owing to the
sensitivity limits of the search (Table 1). After all corrections are applied,
we expect to discover 14$\pm$6 SNe and actually find 9 SNe, which suggests
that our observations are consistent with the theoretical expectations.

While still hampered by high extinction, if most starburst activity is
concentrated within the inner nucleus of the galaxy (for this experiment
$<$1.5 kpc at 100 Mpc), a survey with both higher resolution and longer-
wavelength observations is necessary. A stable, space-based PSF is needed,
too. Figure 1 shows that the optimal wavelength is actually closer to 2.7 µm.
With the upcoming launch of JWST, with a PSF of $\sim 0.091$″ in its F277W
filter, such a survey to probe the nuclear regions of star-forming galaxies
for transients will finally be possible.

## Acknowledgements

The authors acknowledge an anonymous referee for helpful comments that led to
improvements in this paper. We also give tremendous thanks to the IRAC
instrument support team at the Spitzer Science Center (SSC) for their
continued assistance over the years. They are also grateful to Rick Arendt for
his helpful comments. O.D.F. additionally thanks Peter Capak, Sean Carey, and
Patrick Lowrance for useful technical discussions. This work is based on
observations made with the Spitzer Space Telescope (PID 90031), which is
operated by the Jet Propulsion Laboratory, California Institute of Technology,
under a contract with NASA. Support for this work was provided by NASA through
an award issued by JPL/Caltech, primarily supporting students C.C., G.L., and
H.K. Additional support was provided to D.R. and H.K. by STScI’s DDRF Grant
D0001.82477 and the TSRC program. T.S. is supported by the János Bolyai
Research Scholarship of the Hungarian Academy of Sciences, by the New National
Excellence Program (UNKP-20-5) of the Ministry of Technology and Innovation of
Hungary, by the GINOP-2-3-2-15-2016-00033 project of the National Research,
Development, and Innovation Office of Hungary (NKFIH) funded by the European
Union, and by NKFIH/OTKA FK-134432 grant. A.V.F. acknowledges support from the
TABASGO Foundation, the Christopher R. Redlich Fund, and the U.C. Berkeley
Miller Institute for Basic Research in Science (in which he is a Senior Miller
Fellow).

Data availability

The data underlying this article will be shared on reasonable request to the
corresponding author.

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