JWST's PEARLS: Transients in the MACS J0416.1−2403 Field

With its unprecedented sensitivity and spatial resolution, the James Webb Space Telescope (JWST) has opened a new window for time-domain discoveries in the infrared. Here we report observations in the only field that has received four epochs (spanning 126 days) of JWST NIRCam observations in Cycle 1. This field is toward MACS J0416.1−2403, which is a rich galaxy cluster at redshift z = 0.4 and is one of the Hubble Frontier Fields. We have discovered 14 transients from these data. Twelve of these transients happened in three galaxies (with z = 0.94, 1.01, and 2.091) crossing a lensing caustic of the cluster, and these transients are highly magnified by gravitational lensing. These 12 transients are likely of a similar nature to those previously reported based on the Hubble Space Telescope (HST) data in this field, i.e., individual stars in the highly magnified arcs. However, these 12 could not have been found by HST because they were too red and too faint. The other two transients are associated with background galaxies (z = 2.205 and 0.7093) that are only moderately magnified, and they are likely supernovae. They indicate a demagnified supernova surface density, when monitored at a time cadence of a few months to a ∼3–4 μm survey limit of AB ∼28.5 mag, of ∼0.5 arcmin−2 integrated to z ≈ 2. This survey depth is beyond the capability of HST but can be easily reached by JWST.


INTRODUCTION
New capabilities in multi-messenger and time-domain astronomy will open outstanding vistas for discovery, as highlighted, for example, in the Decadal Survey on Astronomy and Astrophysics 2020 (Astro2020) 1 .A core challenge is in localizing sources on the sky and in redshift, with the pri-1 https://nap.nationalacademies.org/resource/26141/interactive/mary technique being searches for electromagnetic counterparts, which calls for observatories with the best flux sensitivity and angular resolution possible.
Until recently, one of the leading observatories for this purpose was the Hubble Space Telescope (HST), which had many successes.For example, it has found high-redshift supernovae, especially those of type Ia, which constrain cosmological models.In many cases, these observations were integrated with large, general-purpose extragalactic surveys (e.g., Riess et al. 2004;Amanullah et al. 2010;Suzuki et al. 2012;Riess et al. 2018).Observations of high-redshift clusters have been important for increasing yields (e.g., Dawson et al. 2009;Hayden et al. 2021), while observations of lowredshift clusters have led to the first discovery of a supernova that is gravitationally lensed into multiple images (Kelly et al. 2015(Kelly et al. , 2016)).The light curves of such supernovae, and in particular the time delay between images, provide a new route to measure the Hubble-Lemaître constant H 0 (Vega-Ferrero et al. 2018;Grillo et al. 2018Grillo et al. , 2020;;Kelly et al. 2023a,b).For another example, a novel type of transient phenomenacaustic-crossing transients-has been identified through HST observations (Kelly et al. 2018;Rodney et al. 2018;Chen et al. 2019;Kaurov et al. 2019).These are individual stars in highly magnified background galaxies lying very close to the critical curve of the lensing cluster, which are further magnified-temporarily-by intracluster stars that act as microlenses.These transients have provided a completely unexpected method to study individual stars at cosmological distances.
The advent of the James Webb Space Telescope (JWST) has brought dramatically better opportunities because of its more than an order of magnitude sensitivity increase relative to HST.The Prime Extragalactic Areas for Reionization and Lensing Science program (PEARLS; Windhorst et al. 2023), one of the programs under the JWST Interdisciplinary Scientists' Guaranteed Time Observations (GTO), has a major time-domain science component.One of its fields is MACS J0416.1−2403(hereafter M0416), which is a lensing cluster at z ∼ 0.4 and one of the Hubble Frontier Fields (HFF: Lotz et al. 2017).The redshift of M0416 as a whole is still uncertain at the level of ±0.003, mainly because this is a merging cluster whose sub-components might have large peculiar motions.Spectroscopic campaigns on this cluster are described by Balestra et al. (2016); Caminha et al. (2017); Vanzella et al. (2021); Bergamini et al. (2021).We adopt z = 0.397 as the fiducial redshift of this cluster.HST has previously revealed several caustic-crossing transients near two causticstraddling arcs in M0416.Rodney et al. (2018) discovered two fast transients in an arc identified at z = 1.0054 (Caminha et al. 2017;Rodney et al. 2018), which was nicknamed "Spock" by the authors.The transient sources themselves are consistent with being supergiant stars with temperatures between 3500 K and 18000 K residing in the strongly lensed galaxy that constitutes the Spock arc (Diego et al. 2023a).Chen et al. (2019) and Kaurov et al. (2019) found a transient of similar nature in another arc identified at z = 0.94 (Hoag et al. 2016;Caminha et al. 2017), which is named "Warhol."In addition, the ultra-deep, UV-to-visible HST program "Flashlights" detected two high-significance caustic transients in the Spock arc and four in the Warhol arc (Kelly et al. 2022).Highly lensed regions such as these are expected to produce caustic transients continually.
To take advantage of opportunities enabled by JWST, PEARLS incorporated three epochs of NIRCam observations of M0416.We expected these data to be particularly powerful for detecting red supergiant stars at z ≳ 1 because red supergiants are bright at λ ≳ 2 µm.The design was also motivated by the possibility of detecting individual Population III stars through caustic transits at z > 7 (Windhorst et al. 2018).Another JWST GTO program, the CAnadian NIRISS Unbiased Cluster Survey (CANUCS; Willott et al. 2022), also observed M0416 with NIRCam in a separate epoch.All these data have been taken, making M0416 the only field in JWST Cycle 1 that has four epochs of NIRCam observations.This makes M0416 the best region in the sky to date for studying infrared transients.
This paper reports a transient search using the unique 4epoch data.The search has gone beyond the aforementioned two arcs, as we also intend to assess the general infrared transient rate in less magnified regions at depths that have never been probed before.This paper is the first in a series on this subject and presents an overview of the transients found in this field.The paper is organized as follows.The NIRCam observations and data are described in Section 2. The transient search is detailed in Section 3. Section 4 discusses the transient, and Section 5 summarizes results.All magnitudes are in the AB system, and all coordinates are in the ICRS frame (equinox 2000).

OBSERVATIONS AND DATA
The four epochs of NIRCam observations all used the same eight bands, namely, F090W, F115W, F150W, and F200W in the "short wavelength" (SW) channel and F277W, F356W, F410M, and F444W in the "long wavelength" (LW) channel.The native NIRCam pixel scales are 0. ′′ 031 pix −1 in the SW channel and 0. ′′ 063 pix −1 in the LW channel.As the SW channel is made up of four detectors, the observations used the INTRAMODULEBOX dithers to cover the gaps.The PEARLS observations adopted the MEDIUM8 readout pattern with "up-the-ramp" fitting to determine the count rate, while those of CANUCS used a combination of the SHALLOW4 and DEEP8 patterns.The total exposure times, dates of observation, and 5 σ depths of these observations are summarized in Table 1.
NIRCam has two nearly identical modules ("A" and "B") that subtend two adjacent, square fields.As the spatial orientations of the JWST instruments vary in time on an annual basis, these two fields cannot both be on the same region in the sky within a year.For this reason, all four epochs of NIR-Cam observations were designed to center the B module on the cluster, leaving the A module mapping different regions in the flanking area.This transient study uses only the module B data because only these are spatially overlapped.The data were retrieved from the Mikulski Archive for Space Telescopes (MAST).Reduction started from the socalled Stage 1 "uncal" products, which are the single exposures from the standard JWST data reduction pipeline (Bushouse et al. 2023) after Level 1b processing.We further processed these products using the version 1.9.4 pipeline in the context of jwst 1063.pmap.A few changes and augmentations were made to the pipeline to improve the reduction quality; most importantly, these included enabling the use of an external reference catalog for image alignment and implementing a better background estimate for the final stacking.The astrometry of each single exposure was calibrated using the public HFF products 2 .These single im-2 https://archive.stsci.edu/prepds/frontier/macs0416.htmlages were projected onto the same grid and were stacked in each band and in each epoch.We produced two versions of stacks, one at the pixel scale of 0. ′′ 06 (hereafter the "60mas" version) and the other at the scale of 0. ′′ 03 (the "30mas" version), to best match the native pixel scales in the LW and the SW channels, respectively.The mosaics are in surface brightness units of MJy sr −1 .The AB magnitude zeropoints are 26.581 and 28.087 for the 60mas and the 30mas stacks, respectively.Figure 1 shows a composite color image using the data from all four epochs.For convenience, we refer to the three epochs from the PEARLS program as Ep1, Ep2, and Ep3, respectively, where "p" stands for "PEARLS."The epoch from the CANUCS program, which was between Ep2 and Ep3, is referred to as Ec ("c" for "CANUCS").

TRANSIENT DISCOVERIES 3.1. Search method
The search for transients was done in the usual way by detecting positive peaks on difference images between epochs.Thanks to the excellent image alignment and stable image quality, we were able to form the difference images by direct subtraction, for which we used the 60mas images.Due to the intense human labor in the visual inspection step (see below), this work is limited to these pairs of difference images: Ep1 − Ep2 for the search of decaying sources in Ep1, Ep2 − Ep1 for new sources appearing in Ep2, and Ep3 − Ep1 for new sources appearing in Ep3.Ec was not used to initiate transient searches, as it was only 13.3 days after Ep2; however, it was used when studying the light curves of the identified transients.When building a difference image, its "root mean square" (RMS) map was also constructed by adding the RMS maps of the parent images in quadrature.As compared to the SW images, the LW images are less affected by defects and therefore their difference images are cosmetically cleaner.We used the F356W band as the basis of our search because its data are the deepest.
The initial transient search was to run SExtractor (Bertin & Arnouts 1996) on the 60mas F356W difference images.The RMS maps were used in the process to estimate the signal-tonoise ratios (S/N) of the peaks in the difference images.Only the peaks that have S/N ≥ 5 were further considered.This left thousands of peaks in each difference image, which were then visually inspected.Not surprisingly, the vast majority of these peaks are not transient objects but are residuals caused by imperfect subtraction of bright stars and galaxies for two reasons: (1) the values of the pixels occupied by bright objects fluctuate over different epochs because of Poisson noise, which often results in positive peaks accompanied by negative peaks in a difference image; (2) the position angle of the point spread function (PSF) is different in different epochs owing to the different field orientations.This leads to spurious sources around bright objects that appear in different positions in different epochs.
After the initial visual inspection, only a few tens of transient candidates survived.To ensure their reliability, we further required that the selected transients should be detected at S/N ≥ 5 in the difference image of at least one more band Color composite image of M0416 using the data from four epochs of NIRCam observations as described in the text.The color scheme is F090W+F115W+F150W as blue, F200+F277W as green, and F356W+F410M+F444W as red.The regions where the transients are found are also marked.
in addition to F356W.Applying this requirement gave a total of 14 robust transients.In most cases, these sources are embedded in a highly nonuniform background and/or are affected by contamination from nearby objects, and PSF fitting had to be used to obtain reliable photometry.For this purpose, the 30mas images are more appropriate.To be consistent, we used PSF fitting for all objects on the 30mas images, and the detailed process is explained in the Appendix.

Transients in the Warhol region
Figure 2 shows the positions of the seven transients discovered in this region.The first three letters in their IDs indicate the difference images on which they were first detected in our process; for example, "Dc2" stands for the difference image constructed by subtracting the Ep2 image from the Ec image, and so on.The letter "W" indicates that these are in the Warhol region.The photometric results are listed in Table 2. Figure 3 shows three of them (D21-W1, D21-W2 and D21-W3) that were seen in multiple epochs, while Fig- NOTE-The R.A. and Decl.coordinates are in decimal degrees for the J2000.0equinox.The magnitudes are based on the PSF-fitting results.
The upper limits are measured within 11×11 pixels (to match the size of the PSF-fitting area) centered at the source location on the RMS maps.The limits labeled with * are 5σ upper limits (appropriate for the measurements in the original image where the background is high and non-uniform), otherwise 2σ (more appropriate for the measurements in the difference images where the background is largely subtracted).The quoted magnification factors µ are the 68% confidence level intervals from Bergamini et al. (2023).
• D21-W1 This transient was visible in Ep1, reached its maximum brightness in Ep2, became fainter in Ec, and further declined in brightness in Ep3 but remained visible.It faded more rapidly in the red bands than in the blue ones.At its peak (m 277 = 27.10 mag), it was the brightest among all transients in this region.As it was visible in all epochs, its photometry was done in each epoch individually.
• D21-W2 This transient was invisible in Ep1, appeared in Ep2, and slowly varied in the following two epochs.Interestingly, its behaviors in the SW and the LW bands differed: while it decayed with time in the LW bands, it became much brighter in the SW bands in Ep3, especially in the two bluest bands.The photometry was done on the difference images between these epochs and Ep1 (i.e., the D21, Dc1 and D31 images), as this offers a more reliable determination of the background.
• D21-W3 This transient was only 0. ′′ 28 away from D21-W2 and was also invisible in Ep1.It appeared in Ep2 in F150W and redder bands.It was much weaker in Ec and barely (if at all) visible in Ep3.The photometry was done on the difference images between all other epochs and Ep1.The decline in brightness from Ep2 to Ec is very obvious in the blue bands.The F444W photometry weakly suggests that it might have slightly brightened from Ep2 to Ec, but this is inconclusive because of the large uncertainties.The extracted signals in Ep3 all have S/N < 2, which we consider as nondetections.
• Dc2-W4 This event appeared as a sudden brightening in Ec, particularly in the LW bands.As mentioned earlier, Ec was not used to initiate the transient search; this event was found on the difference images involving Ec when inspecting other transients in the Warhol region.While there seems to be a "source" in other epochs at this location, there is no detectable signal in the difference images between Ep1, Ep2, and Ep3.This means that the event happened only in Ec, and it left no trace in any other epochs, including Ep2, which was only 13.3 days prior.The photometry was done on the difference images between Ec and Ep1 (i.e., the Dc1 images).
• D31-W5 This transient was seen only in Ep3, as it was only visible in the difference images involving Ep3.It was very close to D21-W3 but was a different transient.It was invisible in the three bluest bands.The photometry was done on the difference images between Ep3 and Ep1 (the D31 images).
• D31-W6 and D31-W7 These two transients were also seen only in Ep3.Like D31-W5, the photometry was done on the difference images between Ep3 and Ep1 (the D31 images).

Transients in the Spock region
Figure 5 shows the positions of the four transients in this region.Due to the high brightness of this arc, these transients can only be revealed in the difference images, and none of them is clearly seen in the original images.Their IDs follow the convention of §3.2.1 with "S" to indicate that these transients are in the Spock region.Figures 6 to 9 show the details of these transients.Their photometry (except for D23-S3, see below) is presented in Table 3.
• D21-S1 This transient is best detected in the difference images between Ep2 and Ep1 (the D21 images) but is seen only in the LW bands.It became significantly weaker in the difference images between Ec and Ep1 (the Dc1 images) and almost completely disappeared from between Ep3 and Ep1 (the D31 images).All this indicates that it reached the maximum in Ep2 and then faded.Assuming that it was invisible in Ep1, we obtained its magnitudes in Ep2 and Ec by photometry on the difference images between Ep2 and Ep1 (D21) and those between Ec and Ep1 (Dc1).
• D21-S2 This transient was detected in the difference images involving Ep2 but not otherwise.Therefore, it is rea-  sonable to assume that this event was caught in Ep2 only.
The photometry was done on the difference images between Ep2 and Ep3 (i.e., the D23 images) because this combination offers a cleaner background than others (e.g., the D21 images).
• D23-S3 This transient was best detected in the difference images between Ep2 and Ep3 (D23).It appears in the D23 images in F150W through F410M, is barely visible in F444W, and is invisible in F115W and F090W.This transient presents a complicated case that is difficult to understand.First of all, it seems to be an elongated system in the D23 F356W image.In the D23 F200W and F150W images, which have better resolution, this elongated structure is resolved into two components.However, it does not maintain such a two-component structure (or the elongated morphology) consistently in all bands: one of the components (the southern one) is missing from the D23 F277W and F410M images.Second, in the difference images between Ep2 and Ep1 (D21), only the southern component appears, and it appears only in F200W and F150W.Taking the above at the face value, one would infer the following picture: (1) D21-S3 was made of two components; (2) the northern one maintained its brightness from Ep1 to Ep2 and then decayed (not visible in the D21 images but showing up in the D23 images); (3) the southern component brightened in Ep2 but only in F150W and F200W (in the D21 images visible only in F150W and F200W) and then decayed; (4) however, this southern component maintained its brightness from Ep1 through Ep3 in F277W, F356W, and F410M.The last point is inconsistent with the observation that the southern component seems to be present in the D23 F356W image.It is possible to attribute this inconsistency to the weakness of the signals.We attempted PSF fitting on the two components  in the D23 images, but the fitting failed in all bands.We have to give up photometry on this transient.
• D31-S4 This transient was only detected in the difference images involving Ep3, implying that it appeared in Ep3.It is only 0. ′′ 39 away from D21-S1, which already decayed and was invisible in Ep3.The photometry was done on the difference images between Ep3 and Ep1 (D31).
Detecting four transients in this arc in the four epochs is consistent with expectations for this particular arc.Diego et al. (2023a) found that microlensing should produce between one and five transients per pointing in the Spock arc when reaching ∼29 mag.

A transient in yet another arc
There is one transient identified on an arc at z = 2.091 (Bergamini et al. 2021) where no previous transient has been reported.Dubbed "Mothra," this transient is discussed in detail by Diego et al. (2023b).Figure 10 shows the details of this transient.The knot in which it is located is the faintest among five knots on the arc, but the knot was visible in all four epochs.This transient is best explained by the intrinsic variability of a red supergiant star (in a binary system with a blue supergiant) that is being magnified by a dark milli-lens (Diego et al. 2023b).
The transient behavior is best seen in the difference images between Ep3 and Ep1 (D31) and as well as in those between Ec and Ep1 (Dc1), where it shows up as a strong, red source with decreasing amplitude towards the blue end.It is even  NOTE-As for Table 2 but for the transient in the "Mothra" arc region.The lensing magnification factor µ is from Bergamini et al. (2023).
visible in the difference images between Ec and Ep2 (Dc2; 13.3 days apart), albeit being much weaker.It is almost invisible in the difference images between Ep3 and Ec (D3c; 29.4 days apart).In other words, this knot was slowly increasing in brightness and reached maximum at around Ec (96.7 days between Ep1 and Ec), and it stayed more or less at its maximum through Ep3 (29.4 days between Ec and Ep3).
Because this transient was caused by the variability of a source that was visible in all epochs, ideally its photometry should be done on the images taken in each epoch.As it is almost blended with a brighter knot 0. ′′ 12 to the southeast, one should do PSF fitting on both simultaneously.However, we were only able to obtain reasonable PSF fitting results in Ep1.(The Appendix gives details.)The procedure failed in other epochs, mostly because the light of brightened transient blended with the nearby knot more severely.Therefore, we performed PSF fitting on the difference images between Ep1 and other epochs (Figure 10) and then added the excess fluxes extracted in this way to the Ep1 SED to obtain the SEDs in other epochs.The results are presented in Table 4 and are also shown in the bottom row of Figure 10.

Two likely supernovae
There were two transients associated with galaxies that are only moderately magnified.Both transients were detected in multiple epochs, and neither was seen in the HFF data.Based on their light curves, we believe that they are SNe.Their physical interpretations will be detailed in a forthcoming paper (Wang et al., in prep.).Their photometry is presented in Table 5.
• SN01 We initially reported this event (Yan et al. 2023) based on the data from Ep1 and Ep2. Figure 11 shows the color images of the transient and its vicinity in the four epochs.The transient appeared as a blue source in Ep1 and then became very red in the subsequent epochs.The difference images show that its F200W and redder light reached  maximum in Ep2.The source is very close to an irregular galaxy, which presumably is the host.The CANUCS NIRISS slitless spectroscopy shows that this galaxy is at z = 2.205 (C.Willot, private communication).Because the transient was visible in all epochs, its photometry should be done on the images in individual epochs.To minimize the impact of the contamination from the host galaxy, the photometry was done by PSF fitting.The results are shown in Figure 11.
• SN02 This transient was found within a spiral galaxy identified at z = 0.7093 (redshift based on Caminha et al. 2017).The transient was invisible in Ep1 and appeared in Ep2.From the difference images, this transient was bright-est in most bands in Ep2 and then slightly decayed in Ec and Ep3.The photometry in Ep2, Ec, and Ep3 was done on the difference images between Ep2 and Ep1 (D21), Ec and Ep1 (Dc1), and Ep3 and Ep1 (D31).In these difference images, the transient's neighbourhood is affected by the strong residuals from imperfect subtraction of the hostgalaxy bulge.PSF-fitting photometry reduced but did not eliminate the contamination.

DISCUSSION
The NIRCam data used here were produced by only half of the NIRCam field of view (module B).Because of the differ- ent field orientations at different times, the area overlapped in all four epochs amounts to only 3.98 arcmin 2 .Those data resulted in 14 robust transients, the largest number of transients ever found within such a small area.There are two reasons for this high transient production rate.First, the high sensitivity of NIRCam allows searching for transients to an unprecedented depth.The vast majority of our transients were fainter than 27.0 mag even at their peaks and were fainter than 28.0 mag most of the time in most bands.The PEARLS observations had exposure times of ∼0.8-1 hours per band per epoch, and the data reach 5σ limits of ∼28.5-30.0mag (within a 0. ′′ 2-radius aperture).This is deep enough to validate the transients in multiple bands.Second, M0416 includes two regions extremely magnified by the cluster, the Warhol and the Spock arcs, which are known to have produced a number of caustic transients in the previous studies with HST.Both arcs are at relatively low redshifts (z ≈ 1), which facilitates the detection of luminous stars in them.In our data spanning 126 days, these two regions contributed seven and four transients, respectively, making them the most productive transient "factories" known.In addition, our search found a transient in another arc (the "Mothra" arc) where no transient had been seen previously.As mentioned above (and to be discussed in detail in forthcoming papers), these transients are most likely stars in the lensed arcs that were temporarily magnified by an extra factor by micro-lensing.Studying such transients remains the only direct way to study individual stars at cosmological distances and therefore should be pursued by JWST in the coming years.These transients might occur very frequently.For example, Dc2-W4 in the Warhol region appeared in Ec but was not seen in either Ep2 (13.6 days earlier) or Ep3 (29.4 days later).A monitoring cadence of ∼10 days (∼5 days in the rest frame) would potentially reveal more fast transients like Dc2-W4.This possibility is worth exploring with JWST in the near future.
In addition to the 12 transients in the highly magnified arcs, we also discovered two transients in regions that are only moderately magnified (µ ∼ 2-3).They are most likely SNe, and with intrinsic, post-peak brightnesses of ∼28.5 mag, they  were bright enough to have been discovered even without the lensing magnification.Taken at face value, discovering two SNe in 3.98 arcmin 2 implies a SN surface density of ∼0.5 arcmin −2 integrated to z ≈ 2.2 when monitored over ∼126 days.This frequency is broadly consistent with expectations (Wang et al. 2017;Regős & Vinkó 2019).Both SNe were caught near their maxima (in the rest-frame visible range) by the Ep2 observations, which were taken 83.4 days after Ep1.Owing to time dilation, neither transient changed significantly in brightness from Ep2 to Ec, which was 96.7 days after Ep1.This suggests that a time cadence of ∼90 days should be effective in discovering SN-like transients (integrated over all redshifts) and is likely to catch events near their peaks.
Finally, there could be a color bias in the transients reported here.The vast majority of them are very red with the only exception being SN01 in Ep1.Even that source transformed to a red object in Ep2.This may, at least in part, result from the initial selection being based on the F356W difference images.An initial selection based an SW band (e.g., F150W) is possible, although it would be more complex to validate because of the more numerous defects in the SW data.
5. SUMMARY M0416 has been observed by NIRCam for four epochs, making it the field most intensely monitored by JWST in its Cycle 1.The eight-band data also provide the best near-IR SED sampling to date.This work has identified 14 transients in these four epochs, which spanned 126 days.Twelve transients occurred in three regions highly lensed by the cluster (seven, four, and one in the Warhol, Spock, and Mothra regions, respectively), while the other two happened in two background galaxies that are only moderately magnified (by ∼2-3×).The eight-band photometry enables the construction of the transients' SEDs from 0.9 to 4.4 µm.This is the first time that time-domain studies have such detailed information for interpretation.Further analysis of SEDs and light curves will be presented in forthcoming papers.
This work demonstrates the power of JWST in the study of the transient IR sky.It is now expected that JWST will be able to function for about twenty years, enabling long-term monitoring programs addressing new science never before possible.A new era of IR time-domain science has begun.
The NIRCam data presented in this paper can be accessed via 10.17909/wmmd-ev74 after the respective proprietary periods.
This work is dedicated to the memory of our dear colleague Mario Nonino, a kind and gentle person and an example for many.We thank the CANUCS team for generously providing early access to their proprietary data of MACS0416.This project is based on observations made with the NASA/ESA/CSA James Webb Space Telescope and obtained from the Mikulski Archive for Space Telescopes, which is a collaboration between the Space Telescope Science Institute (STScI/NASA), the Space Telescope European Coordinating Facility (ST-ECF/ESA), and the Canadian Astronomy Data Centre (CADC/NRC/CSA).We thank our Program Coordinator, Tony Roman, for his expert help scheduling this complex program.This research made use of Photutils, an Astropy package for detection and photometry of astronomical sources.images between adjacent bands (the bluer image was always PSF-matched to the redder image when constructing the difference) to judge whether the extracted flux in each band was reasonable under each step of background estimate.For example, if the F150W − F115W difference image showed a distinct source at the transient location, it meant that the extracted flux in F150W must be higher than that in F115W.This added constraint, while tedious, allowed us to tweak the background values to obtain the most reasonable flux measurements.
In all cases, our PSF-fitting results have been properly normalized by aperture correction.As mentioned above, we used five stars to construct the EPSFs; these five stars were our basis for the aperture correction.We ran PSF fitting on these five stars to obtain their fitted fluxes and also derived their aperture fluxes within the same 11×11 pixel areas.The averaged ratio between the two in each band was the multiplicative aperture correction factor, which we applied to the outputs from BasicPSFPhotometry.
In the end, there are only marginal differences between the results based on the WPSFs and those based on the EPSFs.As the EPSFs were derived using only a small number of stars (total of five), we regard them as being less secure.Therefore, we adopted the WSPF results for our final photometry reported in the tables.

Figure 1 .
Figure1.Color composite image of M0416 using the data from four epochs of NIRCam observations as described in the text.The color scheme is F090W+F115W+F150W as blue, F200+F277W as green, and F356W+F410M+F444W as red.The regions where the transients are found are also marked.
Our sample includes seven transients in the Warhol region, four in the Spock region, one in yet another arc, and two in other regions.Their locations are indicated in Figure 1.These objects and their photometry are described below.Their magnification factors based on the lens model of Bergamini et al. (2023, adopting their 68% confidence level intervals) are also quoted along with the photometry.

Figure 2 .
Figure2.Locations of the transients found in the Warhol region.The upper panel shows the color images of this region in the four epochs, while the lower panels show the inverted F356W difference images of the same region between relevant epochs that led to the discovery of these transients as labeled.All these images are 2. ′′ 4 on a side and are oriented north-up and east-left.

Figure 3 .
Figure 3. (top two rows) Transients D21-W1, D21-W2, and D21-W3 in the D21 (first row) and the D2c (second row) difference images in the eight NIRCam bands as labeled.The images are 2. ′′ 4 on a side and oriented north-up, east-left.The red arrows mark the locations of transients D21-W1, D21-W2, and D21-W3 from left to right in each image.D21-W1 (visible in all epochs) is fainter in D2c (13.3 days apart) than in D21 (83.4 days apart), suggesting that it faded rapidly after reaching its maximum in Ep2.D21-W2 (not visible in Ep1) is almost invisible in Dc2, suggesting that it decayed more slowly.D21-W3 (not visible in Ep1) was similar to D21-W2 (and is only 0. ′′ 28 away) but fainter.(bottom three rows, left to right) SEDs in each observable epoch, light curves in the SW bands, and light curves in the LW bands.D21-W1 was visible in all epochs, and the photometry was done on the original images.The other two transients were not seen in Ep1, and their photometry was done on the difference images with respect to Ep1, i.e., the D21, Dc1 and D31 images.

Figure 4 .
Figure 4. (top two rows) Transients Dc2-W4 in the Dc2 difference images (first row) and D31-W5, D31-W6, and D31-W7 in the D31 difference images (second row) in eight NIRCam bands.The images are 2. ′′ 4 on a side and oriented north-up, east-left.Dc2-W4 (position marked by the yellow arrow in each image) only appeared in Ec and was not visible in any other epoch, including Ep2 only 13.3 days prior.D31-W5, D31-W6, and D31-W7 (positions marked by the green arrows from left to right in each image) were visible only in Ep3, and their detections were significant only in the LW bands.(bottom two rows) SEDs of transients Dc2-W4 and D31-W5, D31-W6, and D31-W7.

Figure 5 .
Figure 5. Locations of the transients found in the Spock region.The upper panel shows the color images of this region in the four epochs, while the lower panels show the inverted F356W difference images of the same region.All images are 5 ′′ on a side and are oriented north-up and east-left.

Figure 6 .
Figure 6.(top two rows) Transient D21-S1 in the D21 (first row) and Dc1 (second row) difference images.The size of the images is labeled.The transient location is marked by the red arrow in each image.It is most prominent in the D21 images and becomes weaker in Dc1 images (but still visible), indicating that it reached maximum in Ep2 and then rapidly declined (disappearing from Ep3 entirely).It is almost invisible in the difference images in the SW bands.(bottom row) Photometric information of this transient, similar to those presented in Figure 3 but without the light curves in SW as it was not seen in these blue bands.The photometry in Ep2 and Ec is based on the D21 and Dc1 difference images, i.e., it assumes the object was invisible in Ep1.

Figure 7 .
Figure 7. (top three rows) Transient D21-S2 in the D23 (first row), D2c (second row), and D31 (third row) difference images (negative).The size of the images is labeled.The location of the transient is marked by the red arrow in each image.It is visible in the difference images involving Ep2 but not otherwise, indicating that the event was caught only in Ep2.(bottom row) SED of the transient in Ep2 as measured from the D23 images.

Figure 8 .
Figure 8. Transient D23-S3 in the D23 (first row) and D21 difference images.The images have the same size as labeled.The transient location is marked by the red arrow in each image.This transient, however, is the most complicated of all, and the difference images of different epoch pairs reveal some inconsistencies.See text for details.

Figure 9 .
Figure 9. (top) Transient D31-S4 in the D31 (negative) difference images.The size of the images is labeled.The transient location is marked by the green arrow in each image.It was only seen in the difference images involving Ep3, indicating that it appeared only in that epoch.(bottom) SED of this transient in Ep3 as measured on the D31 difference images.

Figure 10 .
Figure 10."Mothra" transient identified in an unnamed arc.The top row shows the color images (4.′′ 8 on a side) of this region in four epochs.The red arrow in each image points to the knot that gave rise to the event.The second row zooms in to the arc and shows the Ep1 images (1.′′ 2 on a side) in the eight bands.The next three rows show the difference images between other epochs and Ep1, all displayed in negative.The last row shows the photometric information.See §3.2.3 and the Appendix for details of the photometry.
HY and BS acknowledge the partial support from the University of Missouri Research Council Grant URC-23-029.JMD acknowledges the support of project PGC2018-101814-B-100 (MCIU/AEI/MINECO/FEDER, UE) Ministerio de Ciencia, Investigación y Universidades.LW acknowledges support from NSF through grant #1813825.SHC, RAW, and RAJ acknowledge support from NASA JWST Interdisciplinary Scientist grants NAG5-12460, NNX14AN10G, and 80NSSC18K0200 from GSFC.ZM is supported in part by National Science Foundation grant #1636621.JFB was supported by NSF Grant No. PHY-2012955.CNAW acknowledges funding from the JWST/NIRCam contract NASS-0215 to the University of Arizona.CC is supported by the National Natural Science Foundation of China, No. 11803044, 12173045.AZ acknowledges support by Grant No. 2020750 from the United States-Israel Binational Science Foundation (BSF), Grant No. 2109066 from the United States National Science Foundation (NSF), and by the Ministry of Science & Technology, Israel.

Figure 11 .
Figure 11.(top row) Color images of SN01 in four epochs.Scale and orientation are labeled.The position of the SN is indicated by the red arrow in each image.The nearby irregular galaxy, which is at z = 2.205, is presumably the host.(middle two rows) D21 and D23 (negative) difference images.The location of the source is indicated by the red circle (0. ′′ 5 radius) in each image.The change of color from blue to green/yellow is obvious in the D21 images, where its location shows negative signals in the three bluest bands and positive signals in the rest.It largely maintained the same color from Ep2 through Ep3 (although becoming dimmer) as seen in the D23 images.(bottom row) SED evolution over four epochs (left panel) and the light curves in the SW bands (middle) and the LW bands (right).In Ep1, this transient was invisible in the three reddest bands, and the downward arrows in its Ep1 SED indicate the 5σ upper limits (calculated on the RMS maps within a 0. ′′ 165-radius circular aperture to best match the size within which the PSF fitting was done; see the Appendix).In F200W and the redder bands, the transient reached the maximum in Ep2 and then gradually faded.

Figure 12 .
Figure 12. (top row) Color images of SN02 in four epochs.Scale and orientation are labeled.The two red bars in each of the color images indicate SN02's location.It was not visible in Ep1.The host redshift is z = 0.7093.(middle two rows) D21 and D23 (negative) difference images.The location of the source is indicated by the red circle (0. ′′ 5 radius) in each image.From the difference images involving Ep2, it seems that this transient reached the maximum in Ep2 and then faded.(bottom row) SED evolution over four epochs (left panel) and the light curves in the SW bands (middle) and the LW bands (right).

Table 3 .
Catalog of transients in the Spock arc region Bergamini et al. (2023)or the transients in the Spock arc region.The lensing magnification factors µ are fromBergamini et al. (2023).

Table 4 .
Photometry for the transient "Mothra" in an arc at z = 2.091.

Table 5 .
Bergamini et al. (2023)SNe As for Table2but for the two SNe in less magnified regions.The lensing magnification factors µ are fromBergamini et al. (2023).