# Retrospective Search for Strongly Lensed Supernovae in the DESI Legacy
Imaging Surveys

William Sheu Department of Physics & Astronomy, University of California, Los
Angeles
430 Portola Plaza, Los Angeles, CA 90095, USA  Physics Division, Lawrence
Berkeley National Laboratory
1 Cyclotron Road, Berkeley, CA 94720, USA  Xiaosheng Huang Physics Division,
Lawrence Berkeley National Laboratory
1 Cyclotron Road, Berkeley, CA 94720, USA  Department of Physics & Astronomy,
University of San Francisco
2130 Fulton Street, San Francisco, CA 94117-1080, USA  Aleksandar Cikota
Gemini Observatory / NSF’s NOIRLab
Casilla 603, La Serena, Chile  European Southern Observatory
Alonso de Cordova 3107, Vitacura, Casilla 19001, Santiago de Chile, Chile  Nao
Suzuki Physics Division, Lawrence Berkeley National Laboratory
1 Cyclotron Road, Berkeley, CA 94720, USA  Kavli Institute for the Physics and
Mathematics of the Universe, University of Tokyo
Kashiwa 277-8583, Japan  David Schlegel Physics Division, Lawrence Berkeley
National Laboratory
1 Cyclotron Road, Berkeley, CA 94720, USA  Christopher Storfer Physics
Division, Lawrence Berkeley National Laboratory
1 Cyclotron Road, Berkeley, CA 94720, USA  Institute for Astronomy, University
of Hawaii
2680 Woodlawn Drive, Honolulu, HI 96822-1897, USA

###### Abstract

The introduction of deep wide-field surveys in recent years and the adoption
of machine learning techniques have led to the discoveries of
$\mathcal{O}(10^{4})$ strong gravitational lensing systems and candidates.
However, the discovery of multiply lensed transients remains a rarity. Lensed
transients and especially lensed supernovae are invaluable tools to cosmology
as they allow us to constrain cosmological parameters via lens modeling and
the measurements of their time delays. In this paper, we develop a pipeline to
perform a _targeted_ lensed transient search. We apply this pipeline to 5807
strong lenses and candidates, identified in the literature, in the DESI Legacy
Imaging Surveys (Dey et al., 2019) Data Release 9 (DR9) footprint. For each
system, we analyze every exposure in all observed bands (DECam _g_ , _r_ , and
_z_). Our pipeline finds, groups, and ranks detections that are in sufficient
proximity temporally and spatially. After the first round of inspection, for
promising candidate systems, we further examine the newly available DR10 data
(with additional _i_ and Y bands). Here we present our targeted lensed
supernova search pipeline and seven new lensed supernova candidates, including
a very likely lensed supernova — probably a Type Ia — in a system with an
Einstein radius of $\sim 1.5^{\prime\prime}$.

Strong Lensing — Lensed Supernovae — Lensed Transient Pipeline

††software: Astropy (Astropy Collaboration et al., 2013, 2018), Montage (Jacob
et al., 2010), SEP (Bertin & Arnouts, 1996; Barbary, 2018), SNCosmo (Barbary,
2014), NumPy (Harris et al., 2020), Matplotlib (Hunter, 2007)

##  1 Introduction

The flat $\Lambda$CDM cosmological model is highly successful in describing
our universe from the time of photon decoupling (at a redshift $z\approx$
1100) to the present time. According to this model, our universe has a flat
geometry and is expanding at an accelerating rate (Riess et al., 1998,
Perlmutter et al., 1999). The present day expansion rate of the universe is
known as the Hubble constant ($H_{0}$). The inferred value for $H_{0}$ from
the Planck CMB measurements is $67.4\pm 0.5$ km/s/Mpc (Planck Collaboration et
al., 2020). On the other hand, direct measurements of $H_{0}$ by using local
distance ladders is higher by $\gtrsim 4\sigma$ (e.g., Riess et al., 2021).
Thus if this inconsistency is not due to systematic effects (e.g., Freedman,
2021), then at a minimum, $\Lambda$CDM needs revision.

If a transient event were to occur in a strongly lensed background galaxy, it
can be potentially observed multiple times, in each of the lensed images. The
time delay $\Delta t$ between the different images consists of a geometric
component and a gravitational component (e.g., Narayan & Bartelmann, 1996).
Competitive $H_{0}$ constraint can be achieved if the time delays can be
measured precisely and the lensing potential can be modelled accurately,
providing an independent method of measuring the Hubble constant (e.g., Suyu
et al., 2020). If the observed transient is a lensed Type Ia supernova (L-SN
Ia), their standardizability can also significantly reduce the main systematic
effect for lensing-based $H_{0}$ measurements: the mass sheet degeneracy
(e.g., Birrer et al., 2022).

Currently, there have been seven confirmed lensed SNe: Quimby et al. (2014;
PS1-10afx), Kelly et al. (2015; “SN Refsdal”), Goobar et al. (2017; SN
2016geu), Rodney et al. (2021; “SN Requiem”), Kelly et al. (2022; AT 2022riv),
Goobar et al. (2022; “SN Zwicky”), and Chen et al. (2022; C22). Out of the
seven, four are lensed by a galaxy cluster (“SN Refsdal”, “SN Requiem”, AT
2022riv, C22). Compared with galaxy-scale lenses, cluster-scale strong lenses
typically have much longer time delays and are much harder to model well to
predict time delays accurately and precisely. Of the remaining three which
were lensed by single galaxies, two were found live (SN 2016geu, “SN Zwicky”).
Both happen to be Type Ia. However, both have short time delays of $\lesssim
0.5$ days, making them not useful for $H_{0}$ measurements (Dhawan et al.,
2019; Goobar et al., 2022; Pierel et al., 2022). In this paper, we develop a
targeted lensed transient pipeline. Applying our pipeline to the DESI Legacy
Imaging Surveys (Dey et al., 2019) in a retrospective search, we have
discovered seven new lensed supernovae candidates. Along with the discoveries
of many lensed quasars (which will be presented in a separate publication), we
are confident our pipeline is capable of finding live lensed transients for
present (e.g., Pan-STARRS; Chambers et al., 2016) and future surveys (e.g.,
LSST and the Roman Space Telescope; Ivezić et al., 2019 and Spergel et al.,
2015 respectively).

##  2 Observation

Figure 1: The Legacy Imaging Surveys DR9 footprint, color coded by the _z_
band observation depth. We perform a targeted search for lensed transients
within the DECaLS region (dec $<32^{\circ}$). Exposures from the MzLS and BASS
surveys (blue dashed outline) are excluded.

The DESI Legacy Imaging Surveys is composed of three surveys: the Dark Energy
Camera Legacy Survey (DECaLS), the Beijing Arizona Sky Survey (BASS), and the
Mayall _z_ -band Legacy Survey (MzLS). DECaLS is observed by the Dark Energy
Camera (DECam; Flaugher et al., 2015) on the 4-m Blanco telescope, which
covers $\sim 9000\text{ deg}^{2}$ of the sky in the range of
$-18^{\circ}\lesssim\delta\lesssim+32^{\circ}$. BASS/MzLS are observed in the
_g_ and _r_ bands by the 90Prime camera (Williams et al., 2004) on the Bok
2.3-m telescope and in the _z_ band by the Mosaic3 camera (Dey et al., 2016)
on the 4-m Mayall telescope. Together BASS/MzLS cover the same $\sim
5000\text{ deg}^{2}$ of the northern subregion of the Legacy Surveys. For this
search, we exclude BASS and MzLS data as the number of exposures from each of
the component surveys are fewer, with inferior seeing in $gr$ bands for
reliable detection of transients. Data Release 9 (DR9) contains additional
DECam data reprocessed from the Dark Energy Survey (DES; Dark Energy Survey
Collaboration et al., 2016) for $\delta\lesssim-18^{\circ}$. This provides an
additional $\sim 5000\text{ deg}^{2}$, resulting in a total footprint of $\sim
19,000\text{ deg}^{2}$. The DECam surveys will hereafter be referred to in its
entirety as DECaLS, within which we distinguish DES and non-DES regions. The
pipeline deployment will mostly focus on the exposures in DECaLS, in _g_ , _r_
, and _z_ filters, with a nominal DES exposure time of 90 seconds, and non-DES
exposure time ranging from 60 to 200 seconds. In addition, the Legacy Surveys
contain deep field DECam observations (from surveys such as COSMOS, XMM-LSS,
and SN-X3), with 800+ exposures for any given target in these fields. Our
pipeline has been applied to DECaLS and these deep observations.

As we take the approach of a targeted search, we compile a database of 5807
strong lenses and candidates found within DECaLS, with the majority from Huang
et al., 2020, Huang et al., 2021, and Storfer et al., 2022, and the rest from
Moustakas, 2012, Carrasco et al., 2017, Diehl et al., 2017, Jacobs et al.,
2017, Pourrahmani et al., 2018, Sonnenfeld & Leauthaud, 2018, Wong et al.,
2018, and Jacobs et al., 2019. Note that Storfer et al., 2022 only included
C-grade or above candidates. However on the project
website111https://sites.google.com/usfca.edu/neuralens, they also included
D-grade candidates. These receive numerical scores of 1 or 1.5222C. Storfer,
private communication.. Here we include those with the higher numerical score
of 1.5, which in this paper we will call D+.

##  3 Pipeline

The general framework of the pipeline consists of image reprojection and
reference image generation (§ 3.1), image subtraction (§ 3.2), and source
detection and grouping (§ 3.3) for each of 5807 lensing systems and
candidates.

###  3.1 Image Reprojection and Reference Image Generation

The pipeline first collects all relevant exposures from DR9 for all targets.
The images are then reprojected onto the same World Coordinate System (WCS)
orientation, with the system centered in each 801$\times$801 pixel
($216.27^{\prime\prime}\times 216.27^{\prime\prime}$) cutout. For each filter,
we use the median coadd as the reference image, in order to reduce the
influence of a potential transient (and other time-dependent systematics such
as cosmic rays). These steps are done using the Montage software package
(Jacob et al., 2010). For exposures of the same band within 1.5 days of each
other, we combine them as a mean coadd, as we do not expect significant change
in flux for an astrophysical transient in that short of a time frame, while
increasing detection efficiency.

###  3.2 Image Subtraction

To find transients, we perform image subtraction between each exposure and
reference image for the same filter. This pipeline uses two different image
subtraction algorithms: that of Bramich (2008; henceforth B08), and Saccadic
Fast Fourier Transform (SFFT; Hu et al., 2022).

The B08 algorithm fits for a spatially varying kernel that attempts to
convolve the reference image to appear comparable to the image of each
exposure (“science” image). B08 uses delta functions as its basis functions,
and thus fits for every pixel in the kernel to minimize the $\chi^{2}$ of the
difference image between the science image and the convolved reference image.
Because it fits for every pixel in the kernel, it makes no assumption on the
functional form of the fitted kernel.

SFFT is a fully Fourier implementation of image subtraction. SFFT performs
Fourier transforms on both reference and science images, and fits for a
convolutional, also spatially varying kernel for the reference image (thus
similar to B08, but in the Fourier space).

We have experimented with other well-known image subtraction algorithms
(Alard, 2000, Zackay et al., 2016), but found that B08 and SFFT best suit this
pipeline’s application. Alard (2000, henceforth A00), implemented in the
HOTPANTS package (Becker, 2015), is widely used for large surveys and is very
similar to B08. The main difference is that A00 uses a set of Gaussian priors,
and thus assumes a functional form of the convolutional kernel. Rather than
fitting for each pixel of the kernel (as with B08), A00 only has to fit for
the Gaussian parameters, which leads to significant speed-up for large scale
surveys. But since we are conducting a targeted search, our pipeline can
afford to use the slower, more flexible B08 algorithm. Zackay et al., 2016
(also known as ZOGY) takes a different approach to the image subtraction
problem, by utilizing the concept of cross-filtering (i.e., two separate
convolutional kernels) for the difference image generation and solving for
both kernels in Fourier space. We opt to use the SFFT algorithm, as their
results indicate an improvement to addressing photometric mismatch within
image subtraction over ZOGY. Despite appearing as a publication only recently,
SFFT has been extensively applied to time-domain observations 333L. Wang,
private communication.. For almost all cases, we find that the SFFT algorithm
produces cleaner and more accurate image subtraction compared to B08. Thus,
though both algorithms are used for transient detection, we use the SFFT
difference images for all subsequent photometry and detection presentation in
this paper.

###  3.3 Source Detection and Grouping

After generating difference images with both image subtraction algorithms, we
use a Python implementation (SEP; Barbary, 2018) of the source extraction
algorithm from Bertin & Arnouts (1996) to detect any potential sources in all
difference images, with thresholds ranging from 1.0 to 2.5$\sigma$ in 0.25
increments as determined by SEP (with detections $>$ 2.5$\sigma$ treated as
the same detection level as 2.5$\sigma$). Henceforth, we denote a detection in
a single difference algorithm as a “sub-detection” (a given transient event in
a single exposure can generate two sub-detections, by being detected in
difference images produced by both the B08 and SFFT algorithms). All sub-
detections (from both subtraction algorithms, across all bands and across all
exposures) are then grouped together spatially and temporally. These groupings
contain all sub-detections that are within three pixels ($0.8^{\prime\prime}$)
of one another, and are within 50 days of other sub-detections in the group.
If a given group has less than three sub-detections, the pipeline disregards
them. If a group has three or more difference image sub-detections, it is
labelled as a possible transient detection. That is, an event must be observed
by DECaLS at least twice, in at least two separate exposures, to be labelled
as a possible transient detection444For example, at the threshold (inclusive),
a group with three sub-detections can correspond to two or three detections
(i.e., in two or three exposures). In the case of two detections, one of them
is detected by both subtraction algorithms. In the case of three detections,
each are detected by a single subtraction algorithm.. This is to reduce the
number of false detections (from noise, cosmic rays, CCD artifacts, etc.) and
inconclusive events, and improve the overall quality of detections that will
be visually examined. Had we conducted this search live, $\mathcal{O}(100)$ 2+
sub-detection groups would have been identified, most of which would warrant
follow-up observations.

The entire process typically takes about two hours to run per system, with
approximately one hour for data collection and reprojection and one hour for
image subtraction. To run this pipeline on 5807 systems (approximately 120,000
individual exposure cutouts), parallelization is necessary. The full
deployment is performed on the National Energy Research Scientific Computing
Center (NERSC) Cori supercomputer. Using 20 nodes, 32 CPUs per node, and 1
thread per CPU, this requires that each thread run 9 to 10 systems, taking a
total of 18 to 20 hours. SFFT is capable of being run on GPUs with significant
speed gain. We will take advantage of this capability in our pipeline in the
near future.

Twenty-five of the 5807 candidate systems lies within a deep field survey
footprint, and thus each has 800+ individual exposures. For these systems, the
amount of memory and time required makes naively running the pipeline
infeasible. Instead, we opt to split up the exposures from these systems into
smaller groups of temporally-similar exposures, and running the pipeline on
each possible pair of groups, for all permutations. The groups were created
such that every exposure appears in at least three groups, as to ensure that
the pipeline does not miss a possible lensed transient in any exposure. We do
not find any lensed transients within the 25 deep field systems.

###  3.4 Selection Criteria

Human inspection of the pipeline results is necessary to validate the pipeline
detections. For first round visual inspection, for each system, two initial
grades are assigned regarding its most convincing group of detections.
Firstly, we assign a location grade to assess how close the detection location
lies relative to any putative lensed features. We use this grade to filter out
transient candidates that are clearly not lensed. Secondly, a transient grade
is given by how likely the detection is a transient.

Most systems were not given any grades; i.e., there were no convincing
detections for these systems. As our pipeline’s focus is to detect transients
that are lensed, very obvious transients far from any lensing features are
given high transient grades, but low location grades. By using these metrics,
we identified the most promising lensed transient candidates.

We apply our pipeline to these select candidates a second time, with the
change of removing all exposures that contain the suspected transient
detection from the median coadd, in order to generate a reference free of
possible transient light. Preliminary Legacy Surveys Data Release 10 (DR10)
data are included in this second run. The new data also includes observations
from the DECam _i_ and Y bands. Using Point Spread Functions (PSFs) modelled
from isolated stars within the entire CCD exposure
brick555https://www.legacysurvey.org/dr10/description/, PSF photometry is then
applied to all SFFT difference images. For exposures that we are not able to
fit with a PSF at the detection location (i.e., non-detections that take place
well before or after the peak of the suspected transient event), aperture
photometry is applied to the location of the possible transient in order to
establish a baseline flux for light curve fitting. For promising candidates,
we apply our own final set of criteria to select the candidates with the
highest potential of being a L-SN:

  1. 1.

_Strong Lensing Plausibility_ \- Because the lens candidates included in the
search are from multiple publications and different search efforts, we
determine how likely a candidate is a strong lensing system. The criteria we
use are similar to those in Huang et al. (2021).

  2. 2.

_Asteroid Filtering_ \- If there are only a few detections minutes apart in a
given night, and no detections after that night, this is an indication that
transient is possibly an asteroid. To confirm this, we can approximate the
speed of the asteroid between detections (using PSF fitting to precisely
locate the punitive asteroid), and compare it to the speed of a typical main-
belt asteroid.

  3. 3.

_Location Consideration_ \- In combination with the location grade above, we
also take into consideration surrounding objects (in some cases, modeling
their light profiles) and assess the overall probability of the transient
candidate being lensed based on the detection location.

  4. 4.

_Light Curve Fit Quality_ \- To narrow the possible identities of the
detection, we fit a SALT3 (Kenworthy et al., 2021) SN Ia light curve model,
and 161 different core-collapse (CC) SN models to the observed photometry. As
the survey data is sparse and the search is retrospective, we use a
photometric redshift prior or a spectroscopic redshift in the fitting process.
A fit with low $\chi^{2}/$DOF is an indication of a possible identity. When a
light curve model fits the photometry well, we also assess whether the best-
fit light curve model parameters are reasonable (e.g., the SALT2 $x_{1}$
parameter is generally between $-3$ and $3$).

  5. 5.

_Amplification/Hubble Diagram Residual_ \- From the best-fit light curve
models, we can further deduce whether the transient is amplified, and if the
amplification is reasonable given the system configuration. For the case of a
SN Ia, we can find its Hubble residual and determine the amplification (if
any).

##  4 Expectations

To assess the feasibility of finding L-SNe Ia in the DESI Legacy Imaging
Surveys, we can simulate SNe Ia light curves at various redshifts and lensing
amplifications of a lensed SN, and calculate the amount of time a given
simulated SNe will be detectable in the DECam _g_ , _r_ , and _z_ bands. We
will be using the following values: 23.47, 23.43, and 21.63 for _g_ , _r_ ,
and _z_ bands respectively, based on the 5$\sigma$ PSF detection thresholds
from Dey et al. (2019), adjusted to the nominal time of 90 seconds per
exposure in DR9. We use SNCosmo (Barbary, 2014) to simulate SNe Ia light
curves, based on the SALT3 model (Guy et al., 2007; Kenworthy et al., 2021).
We assume $x_{1}=0$ and $c=0$ for the SALT3 parameters. Figure 2 illustrates
the length of time that a L-SN Ia is detectable in the DECam _g_ , _r_ , and
_z_ filters across a range of reasonable redshifts and amplifications. This
initial investigation indicated that L-SN Ia are discoverable in the Legacy
Surveys and motivated this search.

Figure 2: Number of days when a L-SN Ia is detectable as a function of
redshift and lensing amplification in DECam _g_ , _r_ , and _z_ bands. Every
pixel in each plot represents a simulated SALT3 light curve model, color-coded
by the number of days it exceeds the corresponding filter’s $5\sigma$ PSF
detection limit.

As a careful forecast of lensed SN rates is beyond the scope of this paper, we
use the formulation of Shu et al. (2018, 2021; henceforth S18) to provide a
first-order estimation. Following S18, we simulate the star formation rate for
a source galaxy at a given redshift in order to sample SN rates.

We can now estimate the number of lensed Type Ia and CC SNe we expect to find
in our retrospective search. We start by simulating the source redshift of a
given lensing system. As most of our lens candidates are from Huang et al.
(2020), Huang et al. (2021), and Storfer et al. (2022), we generalize the lens
galaxy spectroscopic or photometric redshifts from those candidates as the
lens galaxy redshift666https://sites.google.com/usfca.edu/neuralens
distribution in our simulations. We then multiply this with a truncated normal
distribution $\mathcal{N}(2,0.5)$, with a lower bound at 1, to represent the
source galaxy redshift distribution. Figure 3 shows the source galaxy redshift
distribution from which we sample for our simulations.

Figure 3: Distributions used to simulate necessary parameters for calculating
the expected results of our pipeline’s deployment. Top Left: star formation
rate versus redshift, with the polynomial fit (degree of 3) to the data (Bell
et al., 2007, Sobral et al., 2012, Smit et al., 2012). The uncertainty bounds
(shown in grey) is generated using the the covariance matrix of the resulting
fit. Top Right: the assumed source redshift distribution (see text). Bottom
Left: CC SNe rates verses redshift. The same polynomial fit and uncertainty
bounds are used to calculate these rates, according to equation 1 and 2.
Bottom Right: SNe Ia rates versus redshift. The same polynomial fit and
uncertainty bounds are used to calculate these rates, according to equations
2, 3, and 4.

Using SFR estimations of varying redshifts (from $z=0.2$ to $z=6.8$) from Bell
et al. (2007), Smit et al. (2012), and Sobral et al. (2012), we fit a
polynomial function (degree of three, using Numpy’s polyfit algorithm) to
$\log_{10}($SFR$)$, with the uncertainties given by the polynomial fit
covariance matrix. We sample SFRs at a given source redshift from this
polynomial model.

From S18, we can convert SFRs to CC SNe rates:

$R_{CC}=0.0068M^{-1}_{\odot}\frac{\text{SFR}}{1+z_{S}}[\text{yr}^{-1}]$ (1)

The CC SNe rates are the broken down into sub-rates for the different types,
based on the percentages in Table 4.

We can estimate the SFH from the functional form (Madau & Dickinson, 2014),
normalized by the recent SFR (S18):

$\text{SFR}(t(z))=\text{SFR}\times\left(\frac{1+z(t)}{1+z_{S}}\right)^{2.7}\left(\frac{1+\left(\frac{1+z_{S}}{2.9}\right)^{5.6}}{1+\left(\frac{1+z(t)}{2.9}\right)^{5.6}}\right)$
(2)

From S18, by assuming a delay time ($t_{D}$) distribution, $f_{D}$:

$f_{D}(t_{D})\propto t_{D}^{-1.07},$ (3)

we can estimate SN Ia rates:

$R_{Ia}=0.00084M^{-1}_{\odot}\frac{\int^{t(z_{S})}_{0.1}\text{SFR}(t(z_{S})-t_{D})f_{D}(t_{D})\,dt_{D}}{(1+z_{S})\int_{0.1}^{t(z=0)}f_{D}(t_{D})\,dt_{D}}[\text{yr}^{-1}],$
(4)

Each system is assumed to have two or four lensed images (with probabilities
of 0.7 and 0.3 respectively; Oguri & Marshall, 2010), and each image has a
magnification sampled from a lognormal distribution (mean = 1.5 and standard
deviation = 0.35), with an expected magnification of 4.765. As context, Shu et
al. (2021) used a constant magnification of 5 for their targeted rates
estimations, whereas Craig et al. (2021) performs a targeted estimate on a set
of 40 strong lenses (from Shu et al., 2017) with magnifications ranging [2,
105], with a median of 6.5. We sample time delays between each lensed image
from $\mathcal{N}(36,4)$ days (Craig et al., 2021).

We do not simulate the times of exposures, but rather use the true exposure
times of our 5807 targets, observed in the DECam _g_ , _r_ , and _z_ bands.
Conservatively, we assume 90 seconds for each exposure (since while
occasionally an exposure can be as low as 60 seconds, the vast majority of the
exposures are 90 seconds or longer).

Table 1: Supernova simulation percentages and brightness parameters

SNe Type | $\overline{M_{B}}$ | $\sigma$ |  % Rate of |  |
---|---|---|---|---|---
| SNCosmo Template | Template | CC Occurrence |  |
IIp | $-16.75\pm 0.37$ | 0.98 | 55.83 | nugent-sn2p | Gilliland et al. (1999)
Ic | $-17.66\pm 0.40$ | 1.18 | 17.00 | nugent-sn1bc | Levan et al. (2005)
IIb | $-16.99\pm 0.45$ | 0.92 | 12.43 | v19-2006t-corr | Vincenzi et al. (2019)
Ib | $-17.45\pm 0.33$ | 1.12 | 9.00 | nugent-sn1bc | Levan et al. (2005)
IIL | $-17.98\pm 0.34$ | 0.86 | 3.34 | nugent-sn2l | Gilliland et al. (1999)
IIn | $-18.53\pm 0.32$ | 1.36 | 2.40 | nugent-sn2n | Gilliland et al. (1999)
Ia | $-19.25\pm 0.20$ | 0.50 | - | salt3 | Kenworthy et al. (2021)

Note. — This table shows the supernova-related parameters used in the pipeline
simulated results. As with Craig et al. (2021), the rate for 87A-like SNe (1%)
is uniformly distributed across IIp, IIb, and IIL SNe. All $\overline{M_{B}}$
and $\sigma$ values are reported in Richardson et al. (2014). CC SNe
percentages are reported in Eldridge et al. (2013).

Assuming all 5807 systems in our catalog are real lensing systems, we simulate
the expected results for each system, using their time of exposures in the
DECam _g_ , _r_ , and _z_ bands for our search. We sample their source
redshifts, number of lensed images, lensing amplifications, lensing time
delays, and star formation rates. Using these sampled values, we calculate the
Ia and CC SN rates. Based on these rates, we simulate SNe across the duration
of the DR9 observation range (from the date of the first exposure $-$100 days
to the date of the last exposure +100 days; the time frame being significantly
larger than the typical width of Ia and CC light curve widths). In Table 4 are
the SNCosmo light curve models used during simulations, as well as the
absolute _B_ band magnitude distributions. For simulated SNe Ia, we sample the
following parameters as: $c\sim\mathcal{N}(0,0.1)$ and
$x_{1}\sim\mathcal{N}(0,1)$ (Guy et al., 2010; Scolnic et al., 2021). For CC
SNe, we subdivide and simulate them as Ib, Ic, IIn, IIp, IIb, or IIL, with
their $M_{B}$ sampled from Table 4. For all simulated SNe, we assume a small
amount of host galaxy dust ($E(B-V)\lesssim 0.02$). Finally, we check if a
lensed SN image for a given system in a given band is above the detection
limit.

The full simulation of our pipeline (on the 5807 target systems) was
parallelized and run 1000 times on NERSC to estimate the expected SNe rates.
The final results are shown in Figure 4 and Table 2. In order to reliably find
transients, we require a threshold of three sub-detections or more. As
mentioned earlier (§ 3.3), depending on the system, this means at least two or
three detections, corresponding to the highlighted rows in Table 2.

Table 2: Expected numbers of lensed SN detections

Number of detections | L-SNe Ia | L-CC SNe
---|---|---
1 or more | $16.49\pm 4.14$ | $22.74\pm 4.85$
2 or more | $\mathbf{6.58\pm 2.57}$ | $\mathbf{9.35\pm 3.08}$
3 or more | $\mathbf{2.90\pm 1.68}$ | $\mathbf{4.53\pm 2.12}$
4 or more | $1.31\pm 1.16$ | $2.43\pm 1.55$
5 or more | $0.63\pm 0.80$ | $1.42\pm 1.16$
6 or more | $0.30\pm 0.53$ | $0.82\pm 0.87$
7 or more | $0.14\pm 0.36$ | $0.48\pm 0.68$

Note. — This table shows the final results of the 1000 simulated for finding
lensed supernovae in the 5807 lenses and candidates. To compare this forecast
with our targeted search, we highlight the rows for two and three detections
or more (see text).

Figure 4: Results of the 1000 simulated runs for finding lensed SNe in the
5807 targeted systems. Left: A histogram illustrating the average number of
systems (out of 5807) with three or more detections verses redshift, as well
as the scaled sampled source redshift distribution outlined in green. The
redshift distribution of detectable systems clearly is lower than the
distribution we sample from, due to detection limits. The integrals of the
distributions are shown in Table 2. Center: A histogram illustrating the
number of systems with three or more detections verses magnification, as well
as the magnification distribution we sample from outlined in green. There is a
slight bias towards higher magnifications, as would be expected. Right: A bar
diagram illustrating the representation of each type of simulated SNe in the
systems with three or more detections.

##  5 Testing Detection and Photometry Pipelines on Known SNe Ia

To test the performance of our pipeline, we apply it to photometric data from
known SNe Ia discovered in DES (Smith et al., 2020; Abbott et al., 2021). From
the DES SNe Ia, we select well observed and modelled SNe that had at least two
DR10 exposures within $-$15 to +30 days of the time of peak brightness in _B_
band (or $t_{0}$). This results in a set of 32 SNe Ia. The SNe were previously
modelled using SALT2 (extended by Hounsell et al., 2018)
parameterization777https://github.com/sam-dixon/sncosmo_lc_fits, with a host
galaxy dust extinction model (Fitzpatrick, 1999). Modelled SALT2 parameters
include redshift $z$, $t_{0}$, the normalization factor $x_{0}$ (normalized so
that the peak _B_ band apparent magnitude is $10.5$ when $x_{0}=1$, per
SNCosmo), the “stretch” factor $x_{1}$, and the color parameter $c$. We plot
our photometry together with previously observed photometry and the SALT2
models. All coadded RGB images are made with the Legacy Surveys’ RGB image
generation
scheme888https://github.com/legacysurvey/imagine/blob/main/map/views.py. Below
we present the results for four SNe Ia systems at different redshifts
($z=[0.18,0.40,0.53,0.69]$). Results for the full 32 DES SNe Ia test systems
are shown in Appendix A. All light curves presented are in the observer frame.

Figure 5: Detection and photometry results of our pipeline, for a known SN Ia
at (RA, dec) = (7.6006, $-$42.2977), $z=0.1838$. Top Left: The mean coadded
RGB (generated from _g_ , _r_ , _i_ , and _z_ bands; see text) image,
generated using exposures that include the SN event. Top Middle: The mean
coadded RGB image, generated using exposures that exclude the supernova event.
The dotted red circle indicates the location of the SN Ia event. Top Right:
Photometry for the detected SN from the SFFT difference images (solid points),
plotted with DES photometry (fainter points) for this SN and the best-fit DES
light curve. We note the good agreement between our results and DES. Below the
dotted line: examples of single band images in chronological order, alongside
its corresponding SFFT difference image (bottom) and SN detection, labelled
with band, date of exposure, the phase, and the $\sigma$-level of detection.
Figure 6: Detection and photometry results of our pipeline, for a known SN Ia
at (RA, dec) = (41.0802, $-$0.4498), $z=0.397$. For the arrangement of panels,
see the caption of Figure 5. Figure 7: Detection and photometry results of our
pipeline, for a known SN Ia at (RA, dec) = (41.2919, $-$1.5649), $z=0.5308$.
For the arrangement of panels, see the caption of Figure 5. Figure 8:
Detection and photometry results of our pipeline, for a known SN Ia at (RA,
dec) = (53.3699, $-$28.4430), $z=0.6894$. For the arrangement of panels, see
the caption of Figure 5. Note that there is no detection for the last
exposure. We therefore performed aperture photometry at the detected location
of the transient.

From these results, we found that our detection pipeline can detect known SN
events within the DR9/DR10 data, with a 100% detection rate for the 32 test
SNe Ia from DES. Furthermore, the new photometry points from our pipeline are
consistent with the DES photometry for these SNe Ia.

##  6 Results and Discussion

We have identified seven lensed SN candidates, one unlensed SN, and two
asteroids detections with our pipeline. This section will focus on one Grade A
and two Grade B lensed SN candidates, with the lower grade lensed SN
candidates and the unlensed SN in Appendix B, and the asteroid detections in
Appendix C. We would also note that all eight SN detections (summarized in
Table 6) would have warranted additional follow-up observations if found live.

=0.8cm

Table 3: Lensed and Unlensed Supernova Candidates

System Name |  Overall |  |  |  |  |  |  |  |  |  |  |  |
---|---|---|---|---|---|---|---|---|---|---|---|---|---
|  Total Number |  |  |  |  |  |  |  |  |  |  |  |
of Exposures |  |  |  |  |  |  |  |  |  |  |  |  |
|  Number of PSF |  |  |  |  |  |  |  |  |  |  |  |
Photometry Exposures |  |  |  |  |  |  |  |  |  |  |  |  |
(_g_ , _r_ , _i_ , _z_ , Y) |  |  |  |  |  |  |  |  |  |  |  |  |
|  Distance |  |  |  |  |  |  |  |  |  |  |  |
|  Postulation |  Shown |  Redshift |  |  |  |  |  |  |  |  |  |
used in |  |  |  |  |  |  |  |  |  |  |  |  |
|  Best-fit |  | LC Prior |  |  |  |  |  |  |  |  |  |
|  $\chi^{2}/$DOF |  Hubble |  |  |  |  |  |  |  |  |  |  |
|  Required | Residual |  |  |  |  |  |  |  |  |  |  |
|  Model |  |  |  |  |  |  |  |  |  |  |  |
Fitting |  |  |  |  |  |  |  |  |  |  |  |  |
|  Reason |  |  |  |  |  |  |  |  |  |  |  |
DESI-344.6252-48.8977 | A | (10, 8, 7, 7, 7) | (1, 2, 1, 0, 1) | A | uL-SN Ia | Y | 0.374 $\pm$ 0.053 | 0.299 $\pm$ 0.021 | 5.47 | 1.10 $\pm$ 0.24 | - | D | [1] [2]
|  |  |  |  | L-SN Ia | Y | 1.188 $\pm$ 0.255 | 0.833 $\pm$ 0.042 | 2.81 |  $-$2.29 $\pm$ 0.30 | $8.23^{+2.61}_{-1.98}$ | A |
|  |  |  |  | uL-CC SN |  | 0.374 $\pm$ 0.053 | 0.393 $\pm$ 0.026 | 4.93 | - | - | D | [1]
|  |  |  |  | L-CC SN | Y | 1.188 $\pm$ 0.255 | 0.731 $\pm$ 0.049 | 2.75 | - | $40.28^{+52.80}_{-22.89}$ | B |
DESI-058.6486-30.5959 | B | (10, 11, 9, 9, 6) | (2, 2, 0, 0, 0) | B | uL-SN Ia | Y | 0.1702 | 0.1702 | 1.73 | 0.66 $\pm$ 0.20 | - | B$-$ |
|  |  |  |  | L-SN Ia |  | 0.6735 | 0.6735 | 4.61 |  $-$3.00 $\pm$ 0.04 | $15.82^{+0.54}_{-0.52}$ | C | [1]
|  |  |  |  | uL-CC SN |  | 0.1702 | 0.1702 | 3.40 | - | - | C | [1]
|  |  |  |  | L-CC SN | Y | 0.6735 | 0.6735 | 2.43 | - | $27.91^{+82.66}_{-20.92}$ | B+ |
DESI-308.7726-48.2381 | B | (12, 12, 10, 15, 8) | (0, 1, 1, 1, 0) | A | uL-SN Ia |  | 0.473 $\pm$ 0.032 | 0.448 $\pm$ 0.034 | 4.59 |  $-$1.54 $\pm$ 0.61 | - | D | [1] [2]
|  |  |  |  | L-SN Ia | Y | - | 0.869 $\pm$ 0.021 | 2.05 |  $-$2.91 $\pm$ 0.32 | $14.62^{+5.02}_{-3.74}$ | B+ |
|  |  |  |  | uL-CC SN | Y | 0.473 $\pm$ 0.032 | 0.465 $\pm$ 0.026 | 4.88 | - | - | C | [1]
|  |  |  |  | L-CC SN | Y | - | 0.828 $\pm$ 0.057 | 2.98 | - | $15.61^{+45.94}_{-11.66}$ | B$-$ |
DESI-034.3625-35.3563 | C | (11, 11, 10, 8, 9) | (2, 2, 1, 0, 0) | A | uL-SN Ia | Y | 0.240 $\pm$ 0.008 | 0.238 $\pm$ 0.011 | 1.31 | 0.20 $\pm$ 0.25 | - | A |
|  |  |  |  | L-SN Ia |  | - | 0.294 $\pm$ 0.026 | 1.64 |  $-$0.09 $\pm$ 0.24 | $1.09^{+0.27}_{-0.22}$ | D | [3]
|  |  |  |  | uL-CC SN |  | 0.240 $\pm$ 0.008 | 0.242 $\pm$ 0.011 | 1.71 | - | - | B |
|  |  |  |  | L-CC SN | Y | - | 0.530 $\pm$ 0.218 | 1.97 | - | $35.16^{+50.83}_{-20.79}$ | C | [1]
DESI-035.1374+00.4676 | C | (21, 16, 7, 14, 9) | (1, 0, 1, 1, 0) | C | uL-SN Ia | Y | 0.269 $\pm$ 0.007 | 0.269 $\pm$ 0.008 | 1.20 | 0.27 $\pm$ 0.33 | - | A |
|  |  |  |  | L-SN Ia |  | 0.776 $\pm$ 0.118 | 0.727 $\pm$ 0.056 | 1.25 |  $-$1.90 $\pm$ 0.41 | $5.74^{+2.63}_{-1.81}$ | B |
|  |  |  |  | uL-CC SN |  | 0.269 $\pm$ 0.007 | 0.269 $\pm$ 0.005 | 1.84 | - | - | B |
|  |  |  |  | L-CC SN | Y | 0.776 $\pm$ 0.118 | 0.795 $\pm$ 0.050 | 0.44 | - | $18.97^{+55.29}_{-14.13}$ | A |
DESI-052.0083-37.2049 | C | (43, 11, 64, 9, 4) | (3, 2, 1, 2, 0) | A | uL-SN Ia | Y | 0.292 $\pm$ 0.029 | 0.333 $\pm$ 0.023 | 1.48 | 0.47 $\pm$ 0.16 | - | B |
|  |  |  |  | L-SN Ia |  | - | 0.357 $\pm$ 0.013 | 1.46 | 0.37 $\pm$ 0.10 | $0.71^{+0.07}_{-0.07}$ | D | [3]
|  |  |  |  | uL-CC SN |  | 0.292 $\pm$ 0.029 | 0.316 $\pm$ 0.018 | 2.07 | - | - | D | [1]
|  |  |  |  | L-CC SN | Y | - | 0.450 $\pm$ 0.018 | 1.54 | - | $12.60^{+18.20}_{-7.45}$ | B |
DESI-084.8493-59.3586 | D | (9, 10, 6, 9, 3) | (3, 3, 0, 2, 0) | D | uL-SN Ia | Y | 0.361 $\pm$ 0.015 | 0.365 $\pm$ 0.008 | 1.61 |  $-$0.15 $\pm$ 0.09 | - | B |
|  |  |  |  | L-SN Ia |  | 0.593 $\pm$ 0.146 | 0.391 $\pm$ 0.011 | 1.41 |  $-$0.20 $\pm$ 0.12 | $1.20^{+0.12}_{-0.11}$ | D | [3]
|  |  |  |  | uL-CC SN |  | 0.361 $\pm$ 0.015 | 0.406 $\pm$ 0.006 | 3.64 | - | - | D | [1]
|  |  |  |  | L-CC SN | Y | 0.593 $\pm$ 0.146 | 0.819 $\pm$ 0.064 | 2.02 | - | $86.05^{+153.15}_{-55.10}$ | C | [1]
DESI-015.8465-50.5450 | N/A | (9, 7, 4, 9, 5) | (1, 1, 0, 0, 0) | N/A | uL-SN Ia | Y | 0.301 $\pm$ 0.026 | 0.373 $\pm$ 0.131 | 0.58 |  $-$0.91 $\pm$ 1.52 | - | B |
|  |  |  |  | L-SN Ia |  | - | - | - | - | - | - |
|  |  |  |  | uL-CC SN | Y | 0.301 $\pm$ 0.026 | 0.289 $\pm$ 0.036 | 1.30 | - | - | B |
|  |  |  |  | L-CC SN |  | - | - | - | - | - | - |

Note. — Summary table for our eight lensed and unlensed supernova candidates.
Column 2: A wholistic grade on how likely a detection is a L-SN, based on the
criteria in § 3.4. Column 5: The distance grade, based on the location of the
transient (for first round visual inspection, § 3.4). Column 6: The four
postulations for each candidate, uL-SN Ia, L-SN Ia, uL-CC SN, L-CC SN. Column
7: Only light curve models for postulations marked with “Y” in this column are
shown (in § 6.1 and Appendix B, above and below the horizontal line,
respectively). Column 8: For redshift prior in the fitting process, we use
photometric redshifts from Zhou et al. (2020, shown with three decimal places
and uncertainties), or fix them to be the spectroscopic redshifts from Cikota
et al. (in prep, shown with four decimal places and no uncertainties). Columns
14 and 15: Each postulation is given a grade based on the light curve fitting
and/or the Hubble residuals, as well as reasons for a C or D grade. The
reasons correspond to the following: [1] poor fit in comparision to the other
postulations, [2] large Hubble residual in the case of uL-SN Ia, and [3] best-
fit $z_{SN}$ too close to the lens photo-$z$, and hence inconsistent with a
lensing postulation (Note that, to be complete, we nevertheless include the
best-fit $z_{SN}$ and magnification information).

###  6.1 Grade A & B Lensed Supernova Candidates

The first seven systems (of eight) in Table 6 are identified by the pipeline
and determined by visual inspection to be lensed SN candidates. For the eighth
system, we believe that it is almost certainly not a strongly lensed system,
and have given it an overall grade of “N/A”. In this section, we will present
the best three lensed SN candidates, with the remaining four (and one unlensed
SN) candidates presented in Appendix B.

For each system, we attempt to narrow the identity of the transients by
fitting different light curve models to the photometry. We test for four
different postulations for each system: unlensed SN Ia (uL-SN Ia), lensed SN
Ia (L-SN Ia), unlensed CC SN (uL-CC SN), and unlensed CC SN (uL-CC SN). In
this paper, we present figures only for the most probable scenarios (systems
with “Y” in the “Shown” column 7 of Table 6).

We account for Milky Way extinction according to Schlafly & Finkbeiner (2011).
When fitting a SN Ia light curve model (for uL-SN Ia and L-SN Ia), we use the
SALT3 model (Kenworthy et al., 2021), and fit for the parameters: redshift
$z$, time of _B_ band peak $t_{0}$, the normalization factor $x_{0}$, the
“stretch” factor $x_{1}$, and the color parameter $c$. We do not fit for host-
galaxy dust, as the $c$ parameter would be largely degenerate with small
amounts of reddening. We use the following priors in the fitting process:
$c\sim\mathcal{N}(0,0.1)$ and $x_{1}\sim\mathcal{N}(0,1)$. We then use the
best-fit SALT parameters for “stretch” and color corrections, and find the
Hubble residual for the given model. This is plotted together with SNe Ia from
Suzuki et al. (2012). Though this data is modelled with SALT2, we expect
negligible differences in Hubble residuals of $7\pm 11$ mmag (Kenworthy et
al., 2021). To model CC SNe light curves, we fit for 161 separate CC SNe
templates (as provided by SNCosmo). All CC templates are parameterized by only
$t_{0}$, $z$, and amplitude (a scaling term with arbitrary units), allowing
for a small amount of host galaxy dust. In all the CC SN light curves shown in
this paper, the best-fit $E(B-V)$ values are very small ($\lesssim 0.01$), and
therefore we do not report the reddening parameters. Except for one system,
redshift priors used for both CC SNe and SNe Ia postulations (see column 8 of
Table 6) are photometric redshifts of objects identified by the forward
modeling source extraction algorithm, the Tractor (Lang et al., 2016). All
photometric redshifts in this paper are from Zhou et al. (2020). For
DESI-058.6486-30.5959, we fix the redshifts to be the spectroscopic redshifts
(Cikota et al. in prep).

In the figures below, if a lensed scenario is postulated, we estimate the
amplification, $\mu$. If a CC SN scenario is postulated, the expected peak _B_
band magnitude for a given SN type (“X”) is represented with
“$\emph{E}(\text{M}_{\text{B}}~{}|~{}\text{X})$,” where the values from Table
4 are used.

####  6.1.1 DESI-344.6252-48.8977

DESI-344.6252-48.8977 is a strong lensing candidate discovered in Storfer et
al. (2022) and assigned a C-grade. In our analysis, we find this relatively-
low grade was given because in the Legacy Surveys coadded image, the arc and
counterarc (objects 2 and 3 respectively, in Figure 9) appear to have somewhat
different colors due to the transient. However, with an improved analysis of
the color of the arc and counterarc by the criteria laid out in Huang et al.
(2021), taking into account of the presence of the transient and photo-$z$
(see below), we now regrade this system as an A-grade lensing candidate.

Figure 9: Coadded RGB images (using _g_ , _r_ , _i_ , and _z_ bands) of L-SN
Ia candidate DESI-344.6252-48.8977 with and without the transient detection
(red dotted circle) exposures. The arrows are color-coded as the following
postulated scenario: red for the lens galaxy, green for the lensed source
galaxy, and purple for a possible second lensed source or an interloper.
Photometric redshifts are displayed on the top right. Figure 10: Detection
exposures for the transient in DESI-344.6252-48.8977 in chronological order.
Top row: single pass images. Bottom row: corresponding differencing images
from SFFT, where the red circle indicates the location of the detected
transient.

The lensed arc in DESI-344.6252-48.8977 is located Southwest of the lens, with
its counterimage appearing Northeast of the lens. The color and photo-$z$’s of
the two lensed images agree with each other (within uncertainties), with both
photo-$z$’s being significantly higher than the lens photo-$z$. We note that
for object 3, as the majority of the exposures do not contain the transient,
its light is unlikely to significantly affect the photo-$z$ of object 3. As
the lens and source galaxies appear to be red elliptical galaxies, we consider
their photo-$z$’s to be reliable. The image-counterimage arrangement indicates
a strong lensing configuration. The detected transient lies directly on the
counterimage. As with all other light curves presented, the light curves below
are constrained by both detection and non-detection exposures.

##### Postulation 1: uL-SN Ia

Figure 11 shows the best-fit light curve model for the uL-SN Ia scenario. We
see that it is not a good fit ($\chi^{2}/\text{DOF}=5.47$), especially in the
_r_ band. Additionally, the resulting SALT3 model has a statistically
significant Hubble residual. Thus, we believe this detection is unlikely to be
an uL-SN Ia. Not shown is the uL-CC SN scenario, which also (as with the uL-SN
Ia scenario) has a large $\chi^{2}/\text{DOF}$ (see Table 6).

Figure 11: Best-fit SALT3 model for DESI-344.6252-48.8977 with a lens
photo-$z$ redshift prior of $0.374\pm 0.053$. For this and Figures 12 and 13,
solid photometry points correspond to the detection passes shown in Figure 10.

##### Postulation 2: L-SN Ia

Figure 12 shows the best-fit light curve model for the L-SN Ia scenario. Due
to the high redshift, SALT3 cannot model the _g_ band observation and it is
ignored in the fitting process. For the three redder bands, the best-fit SALT3
curve model agrees well with the photometric data. Based on the Hubble
residual, the implied amplification is $8.23^{+2.61}_{-1.98}$. This is
consistent with the expectation of a multiply imaged SN by a galaxy scale lens
(e.g., Shu et al., 2018). Finally, the best-fit SN redshift, $z_{SN}=8.333\pm
0.042$, is consistent with the photo-$z$ of the source galaxy. We note that
this redshift value is in line with our preliminary investigation of the
feasibility of our search (see Figure 2).

Figure 12: Best-fit SALT3 model for DESI-344.6252-48.8977 with a source
photo-$z$ redshift prior of $1.188\pm 0.255$.

##### Postulation 3: L-CC SN

Figure 13 shows the best-fit light curve model for the L-CC SN scenario. As
with the previous postulation, this model cannot fit the _g_ band datapoint
due to the high redshift, and thus is ignored in the fitting process. The
best-fit model (the “nugent-sn2l” SN IIL template) is in good agreement with
the photometric data from the redder bands. However, the implied magnification
is quite large. Despite this, we note that 1.) such a magnification is not
impossible (e.g., Quimby et al., 2014), and 2.) since CC SNe have a large
range of $M_{B}$, the uncertainties of the amplification is large. Therefore
the L-CC SN scenario is still plausible for this system.

Figure 13: Best-fit core collapse template model for DESI-344.6252-48.8977
with a lensed source photo-$z$ redshift prior $1.188\pm 0.255$.

##### Conclusion

Any unlensed SN postulation seems unlikely, due to the poor agreement between
the light curve model and the data. Additionally, for the uL-SN Ia scenario,
the Hubble residual would be too high. With all the evidence considered, this
is very likely a lensed SN. A L-SN CC is possible. But, we believe it is most
likely a L-SN Ia. This conclusion is based on the following:

  1. 1.

The red color and morphology seem to indicate that the putative lensed source
is an elliptical galaxy. The foreground galaxy is clearly an elliptical
galaxy. Thus, the photo-$z$’s for the punitive lens and source are both likely
reliable, with the later being significantly higher than the former. Based on
this, combined with the classic image-counterimage configuration, we regard
this system as a grade-A lens candidate.

  2. 2.

The putative SN is situated directly on the counterimage.

  3. 3.

Given the source galaxy is likely an elliptical galaxy, the SN is more likely
a Ia than CC.

  4. 4.

The SN Ia light curve model is a good fit to the photometry and the Hubble
residual is most consistent with it being lensed. For this scenario, the
amplification is also consistent with galaxy-scale strong lensing.

If it is indeed a lensed SN, this would be the first galaxy-scale strongly
lensed SN resolved by ground-based observations. Furthermore, either for the
case of L-CC SN or L-SN Ia, it is at a significantly higher redshift
($z_{SN}\gtrsim 0.8$) than the other two resolved galaxy-scale strongly lensed
SNe (Goobar et al., 2017, Goobar et al., 2022). Given the Einstein radius is
$\sim 1.5^{\prime\prime}$, the expected time delay would be on the order of
weeks. If caught live, it could have resulted in a $H_{0}$ measurement
competitive with those from lensed quasars (e.g., Wong et al., 2019).
Additionally, if it were a L-SN Ia, the systematic effect of the mass sheet
degeneracy could be significantly reduced due to the standardizability of its
brightness (e.g., Birrer et al., 2022). Therefore, if discovered live, this
system would make a strong case for high resolution imaging and spectroscopic
follow-up observations.999At the present, it is still possible to obtain the
source galaxy spectra to measure its star formation rate. This in turn would
more precisely quantify the SN Ia likelihood.

####  6.1.2 DESI-058.6486-30.5959

DESI-058.6486-30.5959 was discovered in Huang et al. (2021), as a grade-A
strong lensing candidate.

Figure 14: Coadded RGB images (using _g_ , _r_ , _i_ , and _z_ bands) of
DESI-058.6486-30.5959 with and without the transient detection (red dotted
circle) exposures. Labelled objects are color-coded as the following
postulated scenario: red as the lenses and green as the source galaxy.
Photometric (shown with uncertainties) and spectroscopic (shown without
uncertainties; Cikota et al. in prep) redshifts for the labelled objects are
displayed on the top right. Figure 15: Detection exposures for the transient
in DESI-058.6486-30.5959 in chronological order. See caption of Figure 10 for
the full description. Figure 16: Mean coadded images of DESI-058.6486-30.5959
across different observed bands. These deeper images (especially the _r_ and
_i_ bands) seem to support the possibility of a faint lensed image between the
detection (red dotted circle) and the arc.

DESI-058.6486-30.5959 is a galaxy-group lensing system, with a prominent red
arc Southeast of the lens. Including additional observations from DR10, there
appears to be a faint, highly magnified blue arc Northwest of the lens as
well, somewhat further from the estimated center of mass for the foreground
galaxy group than the red arc. For this system, we have obtained VLT MUSE
spectroscopy with preliminary redshifts (Cikota et al. in prep) for objects 1,
2, 3, and 4 in Figure 14. The clearly detected transient lies $\sim
3^{\prime\prime}$ from the tip of the red arc (object 4, spectroscopically
confirmed to be in the background) in the deep _i_ band image (Figure 16,
lower left panel). The deep _z_ band image (Figure 16, lower right panel)
seems to show that the arc curves towards the direction of the transient.
There also seems to be a very faint galaxy (object 6) between the red arc and
the transient location. The source extraction code for the Legacy Surveys, the
Tractor, also identifies this object. It has similar photo-$z$ (Zhou et al.,
2020) as the aforementioned blue arc (object 3, also spectroscopically
confirmed to be in the background), and therefore could possibly be its
counter-image.

##### Postulation 1: uL-SN Ia

Figure 17 shows the best-fit light curve model for the uL-SN Ia scenario. We
see that the second _r_ band photometry point is not well accounted for in
this SALT3 model, but not at an unreasonable level. Additionally, the Hubble
residual indicates that this scenario is unusually faint.

Figure 17: Best-fit SALT3 model for DESI-058.6486-30.5959 with a lens
photo-$z$ redshift of $0.1702$. For this and Figure 18, solid photometry
points correspond to the detection passes shown in Figure 15.

##### Postulation 2: L-CC SN

Figure 18 shows the best-fit light curve model (with the best-fitting
parameters of the best-fitting CC SN templates) for the L-CC SN scenario. The
best CC SN template to the data is the “nugent-sn2n” SN IIn model. This model
seems to provide the best overall fit. The implied amplification would be
$27.91^{+82.66}_{-20.92}$. Depending on the location of the SN relative to the
lensing critical curve, a large amplification for a group-scale lens is not
impossible (e.g., SN Refsdal; Kelly et al., 2016 and Rodney et al., 2016). We
also note the large uncertainty, as typical for CC SNe.

Figure 18: Best-fit core collapse template model for DESI-058.6486-30.5959
with a source photo-$z$ redshift of $0.6735$.

##### Conclusion

The rise time for the transient in DESI-058.6486-30.5959 is consistent with it
being a SN. If so, there are three possibilities for the host galaxy – objects
2, 4, or 6. Object 2 is clearly an elliptical galaxy. Thus, if it hosts a SN,
it is more likely a Ia than CC. Figure 17 shows that the SALT3 fit for a SN Ia
at its spectroscopic redshift cannot account well for the _r_ band photometry
near maximum light. Furthermore, the Hubble residual of 0.66 mag, is unusually
large at $>3\sigma$. Object 4 appears to be at the greatest angular separation
from the transient. However, given the high degree of distortion due to
lensing, without lens modeling, it is difficult to meaningfully assess how far
away the SN is from object 4 — e.g., in terms of half-light radius or
directional light radius (Sako et al., 2018) if the delensed source is highly
elliptical. Object 6 has the least angular separation from the transient. By
color, location, and photo-$z$, it appears to be the possible counterarc of
the large arc (spectroscopically confirmed) to the Northwest of the lens. The
L-CC SN postulation is also consistent with object 6 appearing to be a blue,
and therefore likely star-forming, galaxy. Given the sparsity of the
photometric data, it is difficult to be certain. All factor considered, we
assigned a grade of B to this transient as a lensed SN (more likely a CC than
Ia). Additional spectroscopic observation of object 6 can test whether it is a
lensed counterimage. We also note that if this transient was detected live,
real time photometric and spectroscopic follow-up observation could be
triggered to determine the nature of this transient.

####  6.1.3 DESI-308.7726-48.2381

DESI-308.7726-48.2381 was discovered in Storfer et al. (2022), and is given a
D+ grade strong lensing candidate (see § 2). If it turns out to be a lensing
system, the location of the detection would lie directly on the arc (Figure
19).

Figure 19: Coadded RGB images (using _g_ , _r_ , _i_ , and _z_ bands) of
DESI-308.7726-48.2381 with and without the transient detection (red dotted
circle) exposures. Labelled objects are color-coded as the following
postulated scenario: red as the lens galaxy and green as the source galaxy.
Photometric redshifts are displayed on the top right. Figure 20: Detection
exposures for the transient in DESI-308.7726-48.2381 in chronological order.
See caption of Figure 10 for the full description.

For DESI-308.7726-48.2381, there is a possible arc stretching from object 3 to
4 (in Figure 19), with object 2 as a counterimage; all three objects are
identified by the Tractor. The transient candidate is only detected twice: in
the _r_ -band, and four days later in the _z_ -band. This system serves as an
example of how our pipeline is able to detect transients with only two
detections, as the event was captured in at least three sub-detections (see §
3.3). These detections are visually comparable to the difference and detection
images of known high-redshift SNe Ia in the § 5 (e.g., Figures 7 and 8). While
there are only two detections, we are reasonably confident that this is an
astrophysical transient, as forced photometry in other bands at the detection
location supports this postulation (Figures 21 to 23).

##### Postulation 1: L-SN Ia

Figure 21 shows the best-fit light curve model for the L-SN Ia scenario with
no prior on the redshift (given how broad the photometric redshifts of the
punitive lensed images are). The SALT3 parameters are all reasonable with a
best-fit redshift of 0.869. The resulting SALT3 model seems to fit the
photometric data reasonably well, with an amplification of
$14.62^{+5.02}_{-3.74}$.

Figure 21: Best-fit SALT3 model for DESI-308.7726-48.2381 with no redshift
prior. For this and Figures 22 and 23, solid photometry points correspond to
the detection passes shown in Figure 20, hollow points correspond to other
exposures with PSF photometry, and crosses correspond to measurements using
aperture photometry (§ 3.4).

##### Postulation 2: uL-CC SN

Figure 22 shows the best-fit light curve model for the uL-CC SN scenario,
which appears to be far worse compared with Postulation 1. To reiterate, this
is the best-fitting CC SN template model of 161 templates supplied by SNcosmo.

Not shown is the uL-SN Ia fit, which results in a model too bright for what is
expected of a SN Ia (see Table 6).

Figure 22: Best-fit core collapse template model for DESI-308.7726-48.2381
with a lens photo-$z$ redshift prior of $0.473\pm 0.032$.

##### Postulation 3: L-CC SN

Figure 23 shows the best-fit light curve model for the L-CC SN scenario. The
best-fit redshift is at 0.828, and the required amplification is 15.61, albeit
with a large uncertainty, as is typical for CC SNe. The data appear to rise
more rapidly than the model, but this scenario may still be possible.

Figure 23: Best-fit core collapse template model for DESI-308.7726-48.2381
with no redshift prior.

##### Conclusion

The transient found in DESI-308.7726-48.2381 is likely a lensed SN (more
likely a Ia than CC). As with the previous two candidates, to be more
confident of the lensing nature of this system, higher resolution and/or
spectroscopic observations are needed.

##  7 Conclusion

We have developed a pipeline for a _targeted_ search for lensed transients.
For 5807 strong lensing systems and candidates observed by the DESI Legacy
Imaging Surveys, this pipeline first generates a median coadd for each
observed band as a reference image. It then employs two image subtraction
algorithms to identify transient detections that are in close proximity both
spatially and temporally. By applying this pipeline to the DESI Legacy Imaging
Surveys DR9/10, we have found seven lensed SN candidates, one unlensed SN, and
two asteroids. We have also confirmed the variability of a large number of
lensed quasars, which we will present in a subsequent paper (Sheu et al. in
prep). Of the seven lensed SN candidates, the one in DESI-344.6252-48.8977 is
very likely a galaxy-scale strongly lensed SN, probably a Type Ia. Follow-up
high resolution imaging and spectroscopy, as well as lens modeling, can help
reach a more definitive conclusion on whether some of these transient
candidates are lensed.

Of our grade A and B candidates, the transients in DESI-344.6252-48.8977 and
DESI-308.7726-48.2381 are likely L-SNe Ia, whereas the transient in
DESI-058.6486-30.5959 is likely a L-CC SN. Preliminary results indicate that
half of the 5807 systems, for which we have conducted the search, are actually
strong lenses (Tabares-Tarquinio et al. in prep). Since the uncertainties of
our forecast results in Table 2 are Poisson in nature, we adjust the number of
L-SNe Ia and L-CC SNe with two or more detections to be $3.29\pm 1.82$ and
$4.68\pm 2.18$, respectively, and the corresponding numbers for three or more
detections to be $1.45\pm 1.19$ and $2.27\pm 1.50$. The results from our grade
A and B candidates are broadly consistent with these forecasts.

We believe that these results demonstrate the very promising viability of our
pipeline and its applicability to future surveys such as the Vera C. Rubin
Observatory Legacy Survey of Space and Time (LSST) and the Nancy Grace Roman
Space Telescope (RST) to find live lensed SNe and other types of transients,
as well as lensed quasars. Assuming the trend of three high grade lensed SN
candidates for every $5807/2\approx 3000$ systems found in our search, we can
estimate the lower-bound for the number of lensed SN candidates in these
upcoming surveys: 17 for RST ($\sim 17,000$ strong lensed systems; Weiner et
al., 2020) and $\mathcal{O}(10^{2})$ for LSST ($\sim 10^{5}$ strong lensed
systems; e.g., Collett, 2015). These bounds do not account for the obvious
improvements to seeing and cadence these surveys have over the DESI Legacy
Imaging Surveys. Lensed transient searches in these future surveys will likely
realize the potential to dramatically improve lens modeling and possibly
resolve the $H_{0}$ tension.

## Acknowledgments

This work was supported in part by the Director, Office of Science, Office of
High Energy Physics of the US Department of Energy under contract No. DE-
AC025CH11231. This research used resources of the National Energy Research
Scientific Computing Center (NERSC), a U.S. Department of Energy Office of
Science User Facility operated under the same contract as above and the
Computational HEP program in The Department of Energy’s Science Office of High
Energy Physics provided resources through the “Cosmology Data Repository”
project (Grant #KA2401022). X. Huang acknowledges the University of San
Francisco Faculty Development Fund.

This paper is based on observations at Cerro Tololo Inter-American
Observatory, National Optical Astronomy Observatory (NOAO Prop. ID:
2014B-0404; co-PIs: D. J. Schlegel and A. Dey), which is operated by the
Association of Universities for Research in Astronomy (AURA) under a
cooperative agreement with the National Science Foundation.

This project used data obtained with the Dark Energy Camera, which was
constructed by the Dark Energy Survey collaboration. Funding for the DES
Projects has been provided by the U.S. Department of Energy, the U.S. National
Science Foundation, the Ministry of Science and Education of Spain, the
Science and Technology Facilities Council of the United Kingdom, the Higher
Education Funding Council for England, the National Center for Supercomputing
Applications at the University of Illinois at Urbana-Champaign, the Kavli
Institute of Cosmological Physics at the University of Chicago, the Center for
Cosmology and Astro-Particle Physics at the Ohio State University, the
Mitchell Institute for Fundamental Physics and Astronomy at Texas A&M
University, Financiadora de Estudos e Projetos, Fundação Carlos Chagas Filho
de Amparo à Pesquisa do Estado do Rio de Janeiro, Conselho Nacional de
Desenvolvimento Científico e Tecnológico and the Ministério da Ciência,
Tecnologia e Inovacão, the Deutsche Forschungsgemeinschaft, and the
Collaborating Institutions in the Dark Energy Survey. The Collaborating
Institutions are Argonne National Laboratory, the University of California at
Santa Cruz, the University of Cambridge, Centro de Investigaciones
Enérgeticas, Medioambientales y Tecnológicas-Madrid, the University of
Chicago, University College London, the DES-Brazil Consortium, the University
of Edinburgh, the Eidgenössische Technische Hochschule (ETH) Zürich, Fermi
National Accelerator Laboratory, the University of Illinois at Urbana-
Champaign, the Institut de Ciències de l’Espai (IEEC/CSIC), the Institut de
Física d’Altes Energies, Lawrence Berkeley National Laboratory, the Ludwig-
Maximilians Universität München and the associated Excellence Cluster
Universe, the University of Michigan, the National Optical Astronomy
Observatory, the University of Nottingham, the Ohio State University, the
OzDES Membership Consortium the University of Pennsylvania, the University of
Portsmouth, SLAC National Accelerator Laboratory, Stanford University, the
University of Sussex, and Texas A&M University.

The work of Aleksandar Cikota is supported by NOIRLab, which is managed by the
Association of Universities for Research in Astronomy (AURA) under a
cooperative agreement with the National Science Foundation.

We thank Alex Kim at the Lawrence Berkeley National Laboratory for insightful
discussions on difference image photometry, as well as Saul Perlmutter and
Greg Aldering for general commentary on our paper results.

##  Appendix A Photometry on Previously Discovered SNe Ia

Figure 24: Our photometry (solid data-points) for new detections of 9 (of 32;
for the rest see Figures 25 and 26) known SNe Ia from DES, shown along with
DES photometry (faint points) and their best-fit SALT2 light
curve111111https://github.com/legacysurvey/imagine/blob/main/map/views.py. For
all panels, we follow the color scheme of blue=_g_ band, green=_r_ band,
yellow=_i_ band, and red=_z_ band. The redshift and the (RA, dec) is given on
the top right of every plot. Note that our measurements match well with DES
photometry, and provide additional photometry points for these SNe Ia. Figure
25: Our photometry (solid data-points) for new detections of 12 (of 32) known
SNe Ia from DES. For additional details, see the caption of Figure 24. Figure
26: Our photometry (solid data-points) for new detections of 11 (of 32) known
SNe Ia from DES. For additional details, see the caption of Figure 24.

##  Appendix B Grade C & D Lensed Supernova and Unlensed Supernova Candidates

###  B.1 DESI-034.3625-35.3563

DESI-034.3625-35.3563 is a C-grade strong lensing candidate, discovered in
Storfer et al. (2022).

Figure 27: Coadded RGB images (using _g_ , _r_ , _i_ , and _z_ bands) of
DESI-034.3625-35.3563 with and without the transient detection (red dotted
circle) exposures. Labelled objects are color-coded as the following
postulated scenario: red as the lens galaxy, green as the source galaxy, and
cyan as an interloper or a second source. Photometric redshifts are displayed
on the top right. Figure 28: Detection exposures for the transient in
DESI-034.3625-35.3563 in chronological order. See caption of Figure 10 for the
full description. Figure 29: Residual image after lens light subtraction for
DESI-034.3625-35.3563, with the Sérsic light parameters (half-light radius,
axis ratio, semi-major axis orientation from the y axis) in the top left
(modelled in DECam _g_ filter), with the core of the lens galaxy masked out.

DESI-034.3625-35.3563 is a strong lensing candidate system with a single
massive galaxy as the main lens. There appear to be two faint arcs, located
North (identified by Tractor as objects 4 and 5 in Figure 27) and South
(objects 2 and 3) of the foreground galaxy, at approximately four arcseconds
away. Given the morphology and similarity in color, they quite possibly
correspond to the same background source. The transient lies directly at the
east end of the first arc (object 5). This transient is also only about 2.5
effective radii (Figure 29) away from the lens, and so it is possible that the
foreground galaxy is the host.

##### Postulation 1: uL-SN Ia

Figure 30 shows the best-fit SALT3 light curve model for the uL-SN Ia
scenario. This model agrees well with the data, with reasonable light curve
parameters. The inferred absolute magnitude is consistent with the expectation
for a SN Ia at the redshift of the foreground galaxy. Therefore, this seems to
be a likely identity the transient.

Figure 30: Best-fit SALT3 model for DESI-034.3625-35.3563 with a lens
photo-$z$ redshift prior of $0.240\pm 0.008$. For this and Figure 31, solid
photometry points correspond to the detection passes shown in Figure 28.

##### Postulation 2: L-CC SN

Figure 31 shows the best-fit light curve model for the L-CC SN scenario. This
SN IIP template fit has a slightly worse $\chi^{2}/$DOF compared to
Postulation 1 (see Table 6), but this scenario is nevertheless possible. The
model does require a fairly high amplification of $35.16^{+50.83}_{-20.79}$,
albeit with large uncertainties.

Figure 31: Best-fit core collapse template model for DESI-034.3625-35.3563
with no redshift prior.

##### Conclusion

The photometry seems to suggest that this detection is an uL-SN Ia. However,
if additional high resolution and/or spectroscopic observation can confirm the
faint lensed arc North of the lens, the data would strongly support the
postulation of a L-CC SN. This points to the importance of timely follow-up if
this were a live detection, as both the lensed and unlensed scenarios are
possible, given the location.

###  B.2 DESI-035.1374+00.4676

DESI-035.1374+00.4676 was discovered in Storfer et al. (2022), as a C-grade
strong lensing candidate. However, after viewing the Hyper Suprime-Cam (HSC;
Aihara et al. 2019) image (see Figure 32), we feel confident in moving this
into the A-grade lens candidate category.

Figure 32: Coadded RGB images (using _g_ , _r_ , _i_ , and _z_ bands) of
DESI-035.1374+00.4676 with and without the transient detection (red dotted
circle) exposures, as well as the HSC DR2 image. Labelled objects are color-
coded as the following postulated scenario: red as the lens galaxy, green as
the source galaxy, and cyan as an interloper or a member galaxy of the
foreground group. Photometric redshifts are displayed on the top right of the
second image. Figure 33: Detection exposures for the transient in
DESI-035.1374+00.4676 in chronological order. See caption of Figure 10 for the
full description. Figure 34: Residual image after lens light subtraction for
DESI-035.1374+00.4676, with the Sérsic light parameters (half-light radius,
axis ratio, semi-major axis orientation from the y axis) in the top left
(modelled in DECam _g_ filter), with the core of the lens galaxy masked out.

DESI-035.1374+00.4676 appears to be a galaxy group-scale strongly lensing
system, with the arc lying Northeast of the main lensing galaxy. The
transient’s location is somewhat far from both the lens and lensed image. From
the best-fit foreground galaxy light parameters shown in Figure 34, the
detection is approximately 4 half-light radii away from the lensing galaxy,
which does not exclude it from being the host galaxy of the transient. On the
other hand, if it is hosted by the lensed source galaxy, the distance between
the transient and its center would be stretched along the tangential
direction. Without lens modeling, which would provide the delensed source, it
is difficult to estimate how far the transient is from the source galaxy
center in meaningful terms (e.g., half-light radius or directional light
radius). Therefore neither is an impossible scenario based on the location.
The possibility of a faint galaxy hosting the transient seems remote, as such
a galaxy does not appear even in the HSC image with superior seeing
($0.58^{\prime\prime}$ in the _i_ band) and greater depth ($26.2$ _i_ band
limiting magnitude; see Figure 32).

##### Postulation 1: uL-SN Ia

Figure 35 shows the best-fit light curve model for the uL-SN Ia scenario. The
SALT3 model fits the four photometric data points well, and its Hubble
residual is consistent with the Union 2.1 best-fit cosmology. We consider this
to be a possible identity of this transient.

Figure 35: Best-fit SALT3 model for DESI-035.1374+00.4676 with a lens
photo-$z$ redshift prior of $0.269\pm 0.007$. For this and Figure 36, solid
photometry points correspond to the detection passes shown in Figure 33.

##### Postulation 2: L-CC SN

Figure 36 shows the best-fit light curve model for the L-CC SN scenario. This
model also fits the available data well for a Type IIn SN template (“nugent-
sn2n”), with an estimated amplification of $18.97^{+55.29}_{-14.13}$. As this
model is consistent with the data, we believe L-CC SN to be a possible
identity of the transient.

Figure 36: Best-fit core collapse template model for DESI-035.1374+00.4676
with a source photo-$z$ redshift prior of $0.776\pm 0.118$.

##### Conclusion

This transient in DESI-035.1374+00.4676 appears to be consistent with an uL-SN
Ia or a L-CC SN. With the data, it is difficult to discern which scenario is
more likely. In the case of a uL-SN Ia, the supernova would have occurred at
approximately four effective radii away from the lensing galaxy. On the other
hand, while the detection is far from the center of the lensed galaxy, this
separation may not rule out the background as the host due to the tangential
“stretching” from strong lensing. Lens modeling (using HSC DR2 data or follow-
up higher resolution observations) may shed more light on this possibility. If
detected live, this detection would warrant follow-up observations.

###  B.3 DESI-052.0083-37.2049

DESI-052.0083-37.2049 was discovered in Storfer et al. (2022) as a C-grade
strong lensing candidate.

Figure 37: Coadded RGB images (using _g_ , _r_ , _i_ , and _z_ bands) of
DESI-052.0083-37.2049 with and without the transient detection (red dotted
circle) exposures. Labelled objects are color-coded as the following
postulated scenario: red as the lens galaxy and green as the source galaxy.
Photometric redshifts are displayed on the top right. Figure 38: Detection
exposures for the transient in DESI-052.0083-37.2049 in chronological order.
See caption of Figure 10 for the full description.

DESI-052.0083-37.2049 is a possible strong lensing candidate, although a ring
galaxy or a face-on spiral scenario is not ruled out. The transient, however,
is unmistakably present, with multiple detections lying directly on the arc-
like structure.

##### Postulation 1: uL-SN Ia

Figure 39 shows the best-fit light curve model for the uL-SN Ia scenario. Note
that the first _r_ band point is near the peak, almost coincidental with a _g_
band point. The SALT3 light curve model agrees reasonably well with the data.
The Hubble residual is somewhat large, but does not rule out this scenario. Of
note is that the first _z_ band point appears to be too bright for this model.

Figure 39: Best-fit SALT3 model for DESI-052.0083-37.2049 with a lens
photo-$z$ redshift prior of $0.292\pm 0.029$. For this and Figure 40, solid
photometry points correspond to the detection passes shown in Figure 38,
hollow points correspond to other exposures with PSF photometry, and crosses
correspond to measurements using aperture photometry.

##### Postulation 2: L-CC SN

Figure 40 shows the best-fit light curve model for the L-CC SN scenario. The
SN IIP template provides a reasonable fit for the photometry, with an
amplification of $12.60^{+18.20}_{-7.45}$. Similarly to Postulation 1, the
first _z_ band point is not well fit by this model; nor is the second point of
the _r_ band.

Figure 40: Best-fit core collapse template model for DESI-052.0083-37.2049
with no redshift prior.

##### Conclusion

The transient in DESI-052.0083-37.2049 appears to be either an uL-SN Ia or a
L-CC SN. If high resolution and/or spectroscopic observations reveal that the
arc-like structure is part of a spiral or ring galaxy, that would obviously
rule out the L-CC SN scenario. Conversely, if it is strongly lensed
arc/Einstein ring formation, then the L-CC SN possibility becomes quite
possible, considering the location of the detection. If found live, this
detection would warrant follow-up observations.

###  B.4 DESI-084.8493-59.3586

DESI-084.8493-59.3586 was discovered in Storfer et al. (2022), labelled as a
C-grade strong lensing candidate.

Figure 41: Coadded RGB images (using _g_ , _r_ , _i_ , and _z_ bands) of
DESI-084.8493-59.3586 with and without the transient detection (red dotted
circle) exposures. Labelled objects are color-coded as the following
postulated scenario: red as the lens galaxy, green as a source galaxy, and
purple as a second source. Photometric redshifts are displayed on the top
right. Figure 42: Detection exposures for the transient in
DESI-084.8493-59.3586 in chronological order. See caption of Figure 10 for the
full description.

DESI-084.8493-59.3586 is a single galaxy strongly lensed system. There is a
red lensed arc to the East of the lens, and the transient detection lies South
of the lens. Additionally, it is possible that objects 3 and 4 (Figure 41)
correspond to the same source galaxy, due to similarities in color and
photo-$z$, with the possibility that object 3 is the host.

##### Postulation 1: uL-SN Ia

Figure 43 shows the best-fit light curve model for the uL-SN Ia scenario, with
the foreground galaxy photo-$z$ used as the redshift prior. The SALT3 model
agrees well with the data, with reasonable light curve parameters and small
Hubble residual.

Figure 43: Best-fit SALT3 model for DESI-084.8493-59.3586 with a lens
photo-$z$ redshift prior of $0.361\pm 0.015$. For this and Figure 44, solid
photometry points correspond to the detection passes shown in Figure 42.

##### Postulation 2: L-CC SN

Figure 44 shows the best-fit light curve model for the L-CC SN scenario. The
fit is significantly inferior to the previous postulation in the _z_ band,
requiring a high magnification of $86.05^{+153.15}_{-55.10}$, albeit with
large uncertainties.

Figure 44: Best-fit core collapse template model for DESI-084.8493-59.3586
with a source photo-$z$ redshift prior of $0.593\pm 0.146$.

##### Conclusion

This transient in DESI-084.8493-59.3586 is likely an unlensed SN Ia, though
there is a small possibility of it being a lensed CC SN. Thus, we give this
system an appropriately low lensed SN grade of D. If found live, follow-up
spectroscopic observations at the transient location could easily distinguish
these two scenarios.

###  B.5 DESI-015.8465-50.5450

DESI-015.8465-50.5450 is a grade D$+$ strong lens candidate, discovered in
Storfer et al. (2022).

Figure 45: Coadded RGB images (using _g_ , _r_ , _i_ , and _z_ bands) of
DESI-015.8465-50.5450 with and without the transient detection (red dotted
circle) exposures. Labelled objects are color-coded as the following
postulated scenario: red as the main galaxy and cyan as surrounding galaxies.
Photometric redshifts are displayed on the top right. Figure 46: Detection
exposures for the transient in DESI-015.8465-50.5450 in chronological order.
See caption of Figure 10 for the full description.

Upon closer inspection of DESI-015.8465-50.5450, we believe it is more likely
a face-on spiral galaxy. In the detection coadd image in Figure 45, the
evidence for the spiral pattern (rather than lensed arcs) is especially strong
in the _g_ band. There are only two detections of this transient, observed two
minutes apart. However, we do not observe a shift in detection location above
the level of noise, and so we do not consider asteroid as a likely scenario.

##### Postulation 1: uL-SN Ia

Figure 47 shows the best-fit light curve model for the uL-SN Ia scenario. Due
to the sparsity of the photometric data, the uncertainties of the SALT3 model
parameters and Hubble residuals are large. While there are only two detection
exposures, the pipeline identified this transient with four sub-detections. As
with all other light curves presented, the light curves below are constrained
by both detection and non-detection exposures.

Figure 47: Best-fit SALT3 model for DESI-015.8465-50.5450 with a lens
photo-$z$ redshift prior of $0.301\pm 0.026$. For this and Figure 48,
photometry points correlate to the detections shown in Figure 46.

##### Postulation 2: uL-CC SN

Figure 48 shows the best-fit light curve model for the uL-CC SN scenario. This
SN Ic-LB template (“v19-2002ap-coor”) is one of many templates that are
consistent with the data.

Figure 48: Best-fit core collapse template model for DESI-015.8465-50.5450
with a lens photo-$z$ redshift prior of $0.301\pm 0.026$.

##### Conclusion

The most likely scenario for the transient in DESI-015.8465-50.5450 is an
unlensed supernova, as the system is probably a spiral galaxy and not a strong
lensing system. With the sparsity of photometric data, it is not possible to
determine the type. It could also be the case that the host galaxy is object 4
(which could be lensed, possibly with object 3 as its counterimage), as
opposed to object 1 (see Figure 45), but it is infeasible to determine with
current data.

##  Appendix C Asteroids

We have found two asteroid candidates. The detections are observed on the same
night (for each respective system), separated by approximately one to two
minutes. The locations of the two detections in each case are spatially close
enough for the pipeline to identify them as candidates (as a group of three to
four sub-detections). PSF fitting for the transient detections shows that the
movements between detections for both systems are significant. The approximate
speeds of transients are consistent with that of a main-belt asteroid (roughly
$0.5^{\prime\prime}$ per minute near opposition; Cicco, 2006).

###  C.1 DESI-008.6173+02.4228

Figure 49: Above the dotted line are coadded images of DESI-008.6173+02.4228
with and without the transient detection (red dotted circle) exposures. From
left to right, the images show 1.) The coadded image generated from mean
coadding from only the exposures with the transient detection, within each
band. 2.) The coadded image, generated from mean coadding all exposures
excluding the detection exposures within each band. 3.) The HST image of the
system (HST Proposal ID: 12884; H. Ebeling). The RGB image incorporates _g_ ,
_r_ , _i_ , and _z_ bands. Below the dotted line are detection exposures for
the transient. Each column is a single detection at the labelled date and
band. The top row is the single exposure image, whereas the bottom is the SFFT
difference image. The detection location is marked with a red dotted circle.
The first and second columns show _r_ and _g_ band detections on 01/18/2016
minutes apart, whereas the third column shows a set on nondetections six days
afterwards. Note the slight but significant shift in the transient location
between the two detections.

For DESI-008.6173+02.4228, we find that the transient has moved
$0.475^{\prime\prime}\pm 0.101$ between the _r_ and _g_ band detections; a
movement of $>4\sigma$ significance. As the exposures were taken $1.98$
minutes apart, the estimated speed of this asteroid is
$0.240^{\prime\prime}\pm 0.055$ per minute. This is slower than the typical
main-belt asteroid (near opposition) speed of $0.5^{\prime\prime}$ per minute,
but not unreasonably so. The coordinates and time observed does not correlate
with any known asteroid in the IAU’s Minor Planet Center database.

###  C.2 DESI-150.4863+15.4209

Figure 50: Above the dotted line are coadded images of DESI-150.4863+15.4209
with and without the transient detection (red dotted circle) exposures (see
Figure 49 caption). Below the dotted line are detection exposures for the
transient. The second and third columns show detections on 01/17/2016, while
the first column shows a nondetection on 01/12/2016 (5 days prior to
detection). The detection location is marked with a red dotted circle. As with
the previous system, there is a significant shift in detection location
between the exposures.

In DESI-150.4863+15.4209, we find that the transient has moved
$2.155^{\prime\prime}\pm 0.372$ between the _r_ and _g_ band detections, with
a significance of $>5\sigma$. The exposures were taken $1.23$ minutes apart.
Thus, the estimated speed of this asteroid is $0.475^{\prime\prime}\pm 0.082$
per minute, which is consistent with a main-belt asteroid near opposition. The
coordinates and time observed does not correlate with any known asteroid in
the IAU’s Minor Planet Center database.

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