# Two peculiar fast transients in a strongly lensed host galaxy

S. A. Rodney, I. Balestra, M. Bradac, G. Brammer, T. Broadhurst, G. B.

Caminha, G. Chirivì, J. M. Diego, A. V. Filippenko, R. J. Foley, et al.

► To cite this version:

S. A. Rodney, I. Balestra, M. Bradac, G. Brammer, T. Broadhurst, et al. Two peculiar fast transients in a strongly lensed host galaxy. Nature Astronomy, 2018, 2, pp.324-333. 10.1038/s41550-018-0405-4. insu-03711229

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https://insu.hal.science/insu-03711229v1

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# Two peculiar fast transients in a strongly lensed host galaxy

S. A. Rodney<fnref n="1" />*, I. Balestra², M. Bradac³, G. Brammer⁴, T. Broadhurst⁵,⁶, G. B. Caminha<fnref n="1" />,⁷,⁸, G. Chirivi⁹, J. M. Diego¹⁰, A. V. Filippenko¹¹,¹², R. J. Foley¹³, O. Graur¹⁴,¹⁵,¹⁶, C. Grillo¹⁷,¹⁸, S. Hemmati¹⁹, J. Hjorth¹⁸, A. Hoag¹⁰, M. Jauzac²⁰,²¹,²², S. W. Jha²³, R. Kawamata²⁴, P. L. Kelly¹¹,²⁵, C. McCully²⁶,²⁷, B. Mobasher²⁸, A. Molino²⁹,³⁰, M. Oguri³¹,³²,³³, J. Richard³⁴, A. G. Riess⁴,³⁵, P. Rosati⁷, K. B. Schmidt²⁷,³⁶, J. Selsing¹⁸, K. Sharon³⁷, L.-G. Strolger⁴, S. H. Suyu⁹,³⁸,³⁹, T. Treu⁴⁰, B. J. Weiner⁴¹, L. L. R. Williams²⁵ and A. Zitrin⁴²

A massive galaxy cluster can serve as a magnifying glass for distant stellar populations, as strong gravitational lensing magnifies background galaxies and exposes details that are otherwise undetectable. In time-domain astronomy, imaging programmes with a short cadence are able to detect rapidly evolving transients, previously unseen by surveys designed for slowly evolving supernovae. Here, we describe two unusual transient events discovered in a Hubble Space Telescope programme that combined these techniques with high-cadence imaging on a field with a strong-lensing galaxy cluster. These transients were faster and fainter than any supernovae, but substantially more luminous than a classical nova. We find that they can be explained as separate eruptions of a luminous blue variable star or a recurrent nova, or as an unrelated pair of stellar microlensing events. To distinguish between these hypotheses will require clarification of the cluster lens models, along with more high-cadence imaging of the field that could detect related transient episodes. This discovery suggests that the intersection of strong lensing with high-cadence transient surveys may be a fruitful path for future astrophysical transient studies.

The transients presented here are designated HFF14Spo-NW (northwest) and HFF14Spo-SE (southeast) and collectively nicknamed 'Spock'. As shown in Fig. 1, the HFF14Spo events appeared in Hubble Space Telescope (HST) imaging collected as part of the Hubble Frontier Fields (HFF) survey<fnref n="1" />, a multicycle programme for deep imaging of six massive galaxy clusters and associated 'blank sky' fields observed in parallel. One of these clusters was the Massive Cluster Survey (MACS) cluster MACS J0416.1-2403 (hereafter, MACS0416), and the two HFF14Spo

events appeared behind MACS0416 in separate images (labeled 11.1 and 11.2, as in Fig. 1) of the same strongly lensed galaxy at redshift $z=1.0054 \pm 0.0002$. HFF14Spo-SE appeared 223 days after HFF14Spo-NW. Both transients reached peak luminosities of ~$10^{41}$ ergs$^{-1}$ (absolute magnitude using the AB magnitude system $M_{AB} < -14$ mag) in 5 rest-frame days or fewer, and then faded below detectability in roughly the same timespan.

Although recent surveys are beginning to discover progressively more categories of rapidly changing optical transients²,³, most

<footnote n="1">¹Department of Physics and Astronomy, University of South Carolina, Columbia, SC, USA. ²University Observatory Munich, Munich, Germany.
³Department of Physics, University of California, Davis, CA, USA. ⁴Space Telescope Science Institute, Baltimore, MD, USA. ⁵Fisika Teorikoa, Zientzia eta Teknologia Fakultatea, Euskal Herriko Unibertsitatea UPV/EHU, Leioa, Spain. ⁶IKERBASQUE, Basque Foundation for Science, Alameda Urquijo, Bilbao, Spain. ⁷Dipartimento di Fisica e Scienze della Terra, Università degli Studi di Ferrara, Ferrara, Italy. ⁸Kapteyn Astronomical Institute, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands. ⁹Max-Planck-Institut für Astrophysik, Garching, Germany. ¹⁰IFCA, Instituto de Física de Cantabria (UC-CSIC), Santander, Spain. ¹¹Department of Astronomy, University of California, Berkeley, CA, USA. ¹²Miller Institute for Basic Research in Science, University of California, Berkeley, CA, USA. ¹³Department of Astronomy and Astrophysics, University of California, Santa Cruz, CA, USA. ¹⁴Center for Cosmology and Particle Physics, New York University, New York, NY, USA. ¹⁵Department of Astrophysics, American Museum of Natural History, New York, NY, USA. ¹⁶Harvard-Smithsonian Center for Astrophysics, Cambridge, MA, USA. ¹⁷Dipartimento di Fisica, Università degli Studi di Milano, Milan, Italy. ¹⁸Dark Cosmology Centre, Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark. ¹⁹Infrared Processing and Analysis Center, California Institute of Technology, Pasadena, CA, USA. ²⁰Centre for Extragalactic Astronomy, Department of Physics, Durham University, Durham, UK. ²¹Institute for Computational Cosmology, Durham University, Durham, UK. ²²Astrophysics and Cosmology Research Unit, School of Mathematical Sciences, University of KwaZulu-Natal, Durban, South Africa. ²³Department of Physics and Astronomy, Rutgers, The State University of New Jersey, Piscataway, NJ, USA. ²⁴Department of Astronomy, Graduate School of Science, The University of Tokyo, Tokyo, Japan. ²⁵School of Physics and Astronomy, University of Minnesota, Minneapolis, MN, USA. ²⁶Las Cumbres Observatory Global Telescope Network, Goleta, CA, USA. ²⁷Department of Physics, University of California, Santa Barbara, CA, USA. ²⁸Department of Physics and Astronomy, University of California, Riverside, CA, USA. ²⁹Universidade de São Paulo, Cidade Universitária, Instituto de Astronomia, Geofísica e Ciências Atmosféricas, São Paulo, Brazil. ³⁰Instituto de Astrofísica de Andalucía (CSIC), Granada, Spain. ³¹Research Center for the Early Universe, University of Tokyo, Tokyo, Japan. ³²Department of Physics, University of Tokyo, Tokyo, Japan. ³³Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU, WPI), University of Tokyo, Kashiwa, Japan. ³⁴Univ Lyon, Univ Lyon¹, Ens de Lyon, CNRS, Centre de Recherche Astrophysique de Lyon UMR5574, F-69230 Saint-Genis-Laval, France. ³⁵Department of Physics and Astronomy, The Johns Hopkins University, Baltimore, MD, USA. ³⁶Leibniz-Institut für Astrophysik Potsdam (AIP), Potsdam, Germany. ³⁷Department of Astronomy, University of Michigan, Ann Arbor, MI, USA. ³⁸Institute of Astronomy and Astrophysics, Academia Sinica, Taipei, Taiwan. ³⁹Physik-Department, Technische Universität München, Garching, Germany. ⁴⁰Department of Physics and Astronomy, University of California, Los Angeles, CA, USA. ⁴¹Department of Astronomy, University of Arizona, Tucson, AZ, USA. ⁴²Ben-Gurion University of the Negev, Beer-Sheva, Israel. *e-mail: srodney@sc.edu</footnote>
<figure><img src="image_2.png" /><figcaption>**Fig. 1** | Detection of HFF14Spo-NW and HFF14Spo-SE in HST imaging from the HFF. **a–c**, Panel **c** shows the full field of the MACS0416 cluster, in a combined image using optical and infrared bands from HST, with the orientation and angular size of the image in arcseconds indicated at the bottom. The two white boxes in **c** demarcate the regions where the HFF14Spo host-galaxy images appear, shown in **a** and **b**, with increased angular resolution as indicated by the scale bar in **b**. Panels **a** and **b** highlight the three images of the host galaxy, which are caused by the cluster gravitational lensing. Dashed ellipses in **b** mark host-galaxy images 11.1 and 11.2, while the dashed circle in **a** marks host image 11.3. **d–i**, Discovery of the two transient events in optical (**d–f**) and infrared (**g–i**) light. Panels **d,g** show the template images, **e,h** show the epoch when each transient appeared and **f,i** show the difference images. Arrows in **d–f** indicate the location of the HFF14Spo-NW transient, and arrows in **g–i** indicate the location of the HFF14Spo-SE transient. Images in **a–c** ESA/Hubble, NASA, HST Frontier Fields. Data for **d–i** from the Hubble Space Telescope data archive.</figcaption></figure>

programmes remain largely insensitive to transients with luminosities and timescales similar to the HFF14Spo events⁴. Such ‘peculiar’ transients may be generated by the tumultuous atmospheres of massive stars or the interactions of close stellar binaries. These systems are valuable for understanding extreme outcomes of stellar evolution and the physical processes that lead to stellar explosions. Future wide-field observatories such as the Large Synoptic Survey Telescope⁵ are expected to reveal many new examples of such astrophysical transients. The HST is not an efficient wide-field survey telescope, but in the HFF programme, the combination of gravitational lensing magnification and a rapid observation cadence made it possible to catch intrinsically faint and rapidly evolving transient sources. In this way, the HFF survey has provided a glimpse of the potential discovery space available to high-cadence imaging surveys in the future.

## Results

To evaluate the impact of gravitational lensing from the MACS0416 cluster on observable properties of the two HFF14Spo events, we use seven independently constructed cluster mass models. These models indicate that the gravitational time delay between the locations of HFF14Spo-NW and HFF14Spo-SE is <60 days (Table 1 and Supplementary Fig. 1). As shown in Fig. 2, the observed span of 223 days separating the two events is inconsistent with the model-predicted time delays if one assumes that HFF14Spo-SE is a gravitationally delayed image of HFF14Spo-NW. However, if these were independent events, then a time delay of the order of tens of days between images 11.1 and 11.2 could have resulted in time-delayed events that were missed by the HST imaging of this field.

The models also predict absolute magnification values between $\mu \approx 10$ and $\mu \approx 200$ for both events. This wide range is caused primarily by the close proximity of the lensing critical curve (the region on the image plane of theoretically infinite magnification) for sources at $z=1$. The lensing configuration consistently adopted for this cluster assumes that the arc comprises two mirror images of the host galaxy (labelled 11.1 and 11.2 in Fig. 1)⁶⁻¹⁴. This implies that a single critical curve passes roughly midway between the

<table><caption>**Table 1** | Lens model predictions for time delays and magnifications at the locations of the HFF14Spo transients</caption><thead><tr><th>Model</th><th>|μ<sub>NW</sub>|</th><th>|μ<sub>SE</sub>|</th><th>|μ<sub>11.3</sub>|</th><th>Δt<sub>NW/SE</sub><br>(days)</th><th>Δt<sub>NW/11.3</sub><br>(yr)</th></tr></thead><tbody><tr><td>CATS</td><td>196<sup>+140</sup><sub>-53</sub></td><td>46<sup>+2</sup><sub>-1</sub></td><td>3.3<sup>+0.0</sup><sub>-0.0</sub></td><td>-1.7<sup>+2.0</sup><sub>-1.9</sub></td><td>-3.7<sup>+0.1</sup><sub>-0.2</sub></td></tr><tr><td>GLAFIC</td><td>29<sup>+43</sup><sub>-10</sub></td><td>84<sup>+103</sup><sub>-38</sub></td><td>3.0<sup>+0.2</sup><sub>-0.2</sub></td><td>4.1<sup>+5.5</sup><sub>-3.4</sub></td><td>-5.0<sup>+0.5</sup><sub>-0.6</sub></td></tr><tr><td>GLEE</td><td>182<sup>+203</sup><sub>-83</sub></td><td>67<sup>+31</sup><sub>-16</sub></td><td>2.9<sup>+0.1</sup><sub>-0.1</sub></td><td>36<sup>+6</sup><sub>-7</sub></td><td>-6.1<sup>+0.3</sup><sub>-0.2</sub></td></tr><tr><td>GRALE</td><td>13<sup>+11</sup><sub>-6</sub></td><td>12<sup>+9</sup><sub>-5</sub></td><td>3.1<sup>+2.2</sup><sub>-0.9</sub></td><td>-10<sup>+1</sup><sub>-7</sub></td><td>-2.5<sup>+1.0</sup><sub>-3.1</sub></td></tr><tr><td>SWUnited</td><td>38 ± 8</td><td>13 ± 1</td><td>2.9 ± 0.1</td><td>NA</td><td>NA</td></tr><tr><td>WSLAP+</td><td>35 ± 20</td><td>30 ± 20</td><td>NA</td><td>-48 ± 10</td><td>0.8</td></tr><tr><td>ZLTM</td><td>103<sup>+48</sup><sub>-40</sub></td><td>32<sup>+8</sup><sub>-10</sub></td><td>3.5 ± 0.3</td><td>43<sup>+12</sup><sub>-10</sub></td><td>-3.7 ± 0.3</td></tr></tbody></table>

Each lens model is identified by the name of the modelling team or tool. From left to right, columns 2, 3 and 4 give predicted magnification factors for the NW position, SE position, and host image 11.3, respectively. Columns 5 and 6 give predicted time delays for appearance at the SE location (host image 11.1, column 5) and at the third image of the host galaxy (image 11.3, column 6) relative to an appearance in the NW host image, 11.2. Positive (negative) values indicate that the NW image is the leading (trailing) image of the pair. The observed time lag between the NW and SE events was $\Delta t_{NW/SE} = 234 \pm 6$ days. NA: no data available.

two HFF14Spo locations. The location of the critical curve varies substantially among the models (Fig. 3) and is sensitive to many parameters that are poorly constrained. We find that it is possible to make reasonable adjustments to the lens model parameters so that the critical curve does not bisect the HFF14Spo host arc, but instead intersects both of the HFF14Spo locations (see Supplementary Information). Such lensing configurations can qualitatively reproduce the observed morphology of the HFF14Spo host galaxy, but they are disfavoured by a purely quantitative assessment of the positional strong-lensing constraints.

**Ruling out common astrophysical transients.** Several categories of astrophysical transients can be rejected solely on the basis of characteristics of the HFF14Spo-NW and HFF14Spo-SE light curves, shown in Fig. 4. Neither of the HFF14Spo events is periodic as expected for stellar pulsations such as Cepheids, RR Lyrae
<figure><img src="image_3.png" /></figure>

**Fig. 2** | Predictions for the reappearance episodes of HFF14Spo-NW and HFF14Spo-SE caused by gravitational lensing time delays. Time delays are listed in Table 1. **a**, Photometry collected at the NW position (host-galaxy image 11.2) where the first event (HFF14Spo-NW) appeared in January 2014. Optical measurements from the ACS are in blue and green, and infrared observations from the WFC3-IR are in red and orange, with error bars indicating $1\sigma$ measurement uncertainties. The colour key indicates the HST bandpasses used. **b**, Photometry from the SE position (image 11.1) with the same colour coding and uncertainties as **a**. The horizontal grey dashed line in **a**, **b** marks zero flux. Each blue bar in **b** shows one lens model prediction for the dates when that same physical event (HFF14Spo-NW) would have also appeared in the SE location (galaxy image 11.1), as a result of a gravitational lensing time delay. On the right-hand side of **b** is the measured appearance of the second event (HFF14Spo-SE). The red bars in **a** show model predictions for when the NW host image 11.2 would have exhibited the gravitationally delayed image of the HFF14Spo-SE event. The width of each bar encompasses the 68% confidence region for a single model, and darker regions indicate an overlap from multiple models.

or Mira variables. Stellar flares can produce rapid optical transient phenomena, but the total energy released by even the most extreme stellar flare¹⁵ falls far short of the observed energy release from the HFF14Spo transients. We can also rule out active galactic nuclei, which are disfavoured by the quiescence of the HFF14Spo sources between the two observed episodes and the absence of any of the broad emission lines that are often observed in active galactic nuclei. Additionally, no X-ray-emitting point source was detected in seven epochs from 2009 to 2014, including Chandra X-ray space telescope imaging that was coeval with the peak of infrared emission from HFF14Spo-SE.

Many types of stellar explosions can generate isolated transient events, and a useful starting point for classification of such objects is to examine their position in the phase space of peak luminosity ($\nu L_{\nu, pk}$) versus decline time¹⁶. Figure 5 shows our two-dimensional constraints on $\nu L_{\nu, pk}$ and the decline timescale $t_2$ (the time over which the transient declines by 2 mag) for the HFF14Spo events, accounting for the range of lensing magnifications ($10 < \mu < 200$) derived from the cluster lens models. The HFF14Spo-NW and HFF14Spo-SE events are largely consistent with each other, and if both events are representative of a single system (or a homogeneous class) then the most likely peak luminosity and decline time (the region with the most overlap) would be $\nu L_{\nu, pk} \approx 10^{41} \text{ erg s}^{-1}$ and $t_2 \approx 1 \text{ day}$, respectively.

The relatively low peak luminosities and the very rapid rise and fall of both HFF14Spo light curves are incompatible with all categories of stellar explosions for which a sufficient sample of observed events exists. This includes the common type Ia supernovae (SNe) and core-collapse SNe, as well as the less well-understood classes of superluminous SNe¹⁷, type Iax SNe¹⁸, fast optical transients³, calcium-rich SNe¹⁹ and luminous red novae¹⁶.

The SN-like transients that come closest to matching the observed light curves of the two HFF14Spo events are the ‘kilonova’ class and the ‘Ia’ class. Kilonovae are a category of optical/near-infrared (NIR) transients generated by the merger of a neutron star binary²⁰⁻²². The Ia class is produced by helium shell explosions that are expected to arise from AM Canum Venaticorum binary star systems undergoing helium mass transfer onto a white dwarf primary star²³. The HFF14Spo light curves exhibited a slower rise time than a kilonova event²⁴⁻²⁶, and a faster decline time than is anticipated for a Ia event²⁷.

Another problem for all of these catastrophic stellar explosion models is that they cannot explain the appearance of repeated transient events. The kilonova progenitor systems are completely disrupted at explosion, as is the case for all normal SN explosions. For Ia events, even if an AM Canum Venaticorum system could produce repeated helium shell flashes of similar luminosity, the period of recurrence would be ~10⁵ yr, making these effectively non-recurrent sources. Models invoking a stellar merger or the collision of a planet with its parent star have a similar difficulty. In these cases, the star may survive the encounter, but the rarity of these collision events makes it highly unlikely that two such transients will be detected from the same galaxy in a single year.

Dynamically induced stellar collisions or close interactions in a dense stellar cluster²⁸ could in principle produce a series of optical transients. Similarly, the collision of a jovian planet with a main-sequence star²⁹,³⁰ or a terrestrial planet with a white dwarf star³¹ could generate an optical transient with a peak luminosity comparable to that observed for the HFF14Spo events, although it is unclear whether the ultraviolet (UV)/optical emission could match the observed HFF14Spo light curves. These scenarios warrant further scrutiny, so that predictions of the light-curve shape
<figure><img src="image_4.png" /><figcaption>**Fig. 3** | Locations of the lensing critical curves relative to the positions of the two HFF14Spo sources. **a**, HFF composite NIR image of the full MACS0416 field. The magnification map for a source at $z=1$ is overlaid with orange and black contours<sup>14</sup>. **b**, Closer view of the HFF14Spo host galaxy (the region indicated by the white box in **a**). **c**, A trace of the lensing critical curve from the GRALE model. **d-i**, Magnification maps for the six other primary models, all for a source at the HFF14Spo redshift. The magnification maps are plotted with log scaling such that white is $\mu=1$ and black is $\mu=10^3$. **j-m**, The same magnification maps, extracted from the lens model variations (described in Methods). In **b-m**, a magenta + marks the position of HFF14Spo-SE, and a magenta x marks the position of HFF14Spo-NW.</figcaption></figure>

and anticipated rates can be more rigorously compared with the HFF14Spo observations.

Although the two events were most probably not temporally coincident, all of our lens models indicate that it is entirely

plausible for the two HFF14Spo events to be spatially coincident: a single location at the source plane can be mapped to both HFF14Spo locations to within the positional accuracy of the model reconstructions (~0.6" in the lens plane). This is supported by

<figure><img src="image_5.png" /><figcaption>**Fig. 4** | Light curves for the two transient events. **a**, The HFF14Spo-NW light curve. The colour key indicates the HST bandpasses used. **b**, The HFF14Spo-SE light curve. AB-based apparent magnitudes are plotted against rest-frame time at $z=1.0054$, relative to the time of the peak observed flux for each event. The corresponding MJD in the observer frame is marked on the top axis for each panel. Optical observations using the HST ACS-WFC detector are shown as circles, while infrared measurements from the WFC3-IR detector are shown as squares. Error bars give $1\sigma$ uncertainties and downward arrows indicate $3\sigma$ upper limits for epochs in which the HFF14Spo transients were not detected.</figcaption></figure>
<figure><img src="image_6.png" /></figure>

**Fig. 5** | Peak luminosity versus decline time for HFF14Spo and assorted categories of explosive transients. **a, b,** The observed constraints of the HFF14Spo events plotted as overlapping coloured bands along the left-hand side. HFF14Spo-NW is shown as cyan and blue bands, corresponding to independent constraints drawn from the F435W and F814W light curves, respectively. For HFF14Spo-SE, the scarlet and maroon bands display constraints from the F125W and F160W light curves, respectively. The width and height of these bands incorporate the uncertainty due to magnification (we adopt $7 < \mu_{NW} < 485$ and $7 < \mu_{SE} < 185$; see Table 1) and the time of peak. In **a,** ellipses and rectangles mark the luminosity and decline-time regions occupied by various explosive transient classes. Closed shapes show the empirical bounds for transients with a substantial sample of known events. Regions surrounded by dashed lines mark theoretical expectations for rare transients that lack a sufficient sample size: the .Ia class of white dwarf helium shell detonations and the kilonova class from neutron star mergers. Grey bands in **a,b** represent the MMRD relation for classical novae. Panel **b** zooms in on the lower-left quadrant of **a** and changes to a linear scale for the time axis. Circles mark the observed peak luminosities and decline times for classical novae, while black + symbols mark RNe in our own Galaxy. The large cross labelled at the bottom shows the rapid-recurrence nova M31N 2008-12a. Each orange diamond marks a separate short transient event from the two rapid LBV outburst systems, SN 2009ip (ref. ³⁵) and NGC 3432-LBV1 (also known as SN 2000ch)³⁶. These LBV events are plotted with left-pointing arrows because they provide only upper limits on the decline time owing to limited photometric sampling.

the fact that the host-galaxy colours and spectral indices at each HFF14Spo location are indistinguishable within the uncertainties (see Supplementary Figs. 5 and 6 and Supplementary Tables 3 and 4). Thus, to accommodate all of the observations of the HFF14Spo events with a single astrophysical source, we turn to two categories of stellar explosion that are sporadically recurrent: luminous blue variables (LBVs) and recurrent novae (RNe).

**LBV star.** The transient sources categorized as LBVs are the result of eruptions or explosive episodes from massive stars (>10 solar masses ($M_\odot$)). The class is exemplified by P Cygni, $\eta$ Carinae ($\eta$ Car) and S Doradus$^{32,33}$. Although most giant LBV eruptions have been observed to last much longer than the HFF14Spo events$^{32}$, some LBVs have exhibited repeated rapid outbursts that are broadly consistent with the very fast HFF14Spo light curves (see Supplementary Fig. 7). Because of this common stochastic variability, the LBV hypothesis does not have any trouble accounting for the HFF14Spo events as two separate outburst episodes of the same star.

Two well-studied LBVs that provide a plausible match to the observed HFF14Spo events are SN 2009ip (refs ³⁴,³⁵) and NGC 3432-LBV1 (ref. ³⁶). Both exhibited multiple brief transient episodes over a span of months to years. Unfortunately, for these outbursts, we have only upper limits on the decline timescale owing to the relatively sparse photometric sampling (see Supplementary Fig. 7). Recent studies have shown that SN 2009ip-like LBV transients have remarkably similar light curves, leading up to a final terminal SN explosion$^{37,38}$. Figure 5b shows that both HFF14Spo events are consistent with the observed luminosities and decline times of these fast and bright LBV outbursts—although the HFF14Spo events would be among the most rapid and most luminous LBV eruptions ever seen.

In addition to those relatively short and very bright giant eruptions, most LBVs also commonly exhibit a slower underlying variability. P Cygni and $\eta$ Car, for example, slowly rose and fell in brightness by ~1–2 mag over a timespan of several years before and after their historic giant eruptions. Such variation has not been

detected at the HFF14Spo locations. Nevertheless, given the broad range of light-curve behaviours seen in LBV events, we cannot reject this class as a possible explanation for the HFF14Spo system.

The total radiated energy of the HFF14Spo events is $10^{44}$ erg $< E_{\text{rad}} < 10^{47}$ erg (see Methods), which falls well within the range of plausible values for a major LBV outburst. From this measurement, we can derive constraints on the luminosity of the progenitor star, by assuming that the energy released is generated slowly in the stellar interior and is in some way 'bottled up' by the stellar envelope, before being released in a rapid mass ejection (see Methods). With this approach, we derive a quiescent luminosity of $L_{\text{qui}} \approx 10^{39.5}$ erg s⁻¹ (absolute magnitude in the V band $M_V \approx -10$ mag). This value is fully consistent with the expected range for LBV progenitor stars (for example, $\eta$ Car has $M_V \approx -12$ mag, and the faintest known LBV progenitors such as SN 2010dn have $M_V \approx -6$ mag).

**Recurrent nova.** Novae occur in binary systems in which a white dwarf star accretes matter from a less massive companion, leading to a burst of nuclear fusion in the accreted surface layer that causes the white dwarf to brighten by several orders of magnitude, but does not completely disrupt the star. The mass transfer from the companion to the white dwarf may restart after the explosion, so the cycle may begin again and repeat after a period of months or years. When this recurrence cycle is directly observed, the object is classified as a recurrent nova (RN).

The light curves of many RN systems in the Milky Way are similar in shape to the HFF14Spo episodes, exhibiting a sharp rise (<10 days in the rest frame) and a similarly rapid decline (see Supplementary Fig. 8). This is reflected in Fig. 5, where novae are represented by a grey band that traces the empirical constraints on the maximum magnitude versus rate of decline (MMRD) relation for classical novae$^{39,40}$.

The RN model can provide a natural explanation for having two separate explosions that are coincident in space but not in time. However, the recurrence timescale for HFF14Spo in the rest
frame is 120±30 days, which would be a singularly rapid recurrence period for an RN system. The RNe in our own Galaxy have recurrence timescales of 10–98 yr (ref. ⁴¹). The fastest measured recurrence timescale belongs to M31N 2008-12a, which has exhibited a new outburst every year from 2008 to 2016¹⁴,⁴³ Although this M31 record holder demonstrates that very rapid recurrence is possible, classifying HFF14Spo as an RN would still require a very extreme mass-transfer rate to accommodate the <1 yr recurrence.

Another major concern with the RN hypothesis is that the two HFF14Spo events are substantially more luminous than all known novae—perhaps by as much as two orders of magnitude. This is exacerbated by the observational and theoretical evidence indicating that rapid-recurrence novae have less energetic eruptions³⁴ (see Supplementary Fig. 9). Although the RN model is not strictly ruled out, we can deduce that, if the HFF14Spo transients are caused by a single RN system, then that progenitor system would be among the most extreme white dwarf binary systems yet known.

**Microlensing.** In the presence of strong gravitational lensing, it is possible to generate a transient event from lensing effects alone. In this case, the background source has a steady luminosity, but the relative motion of the source, lens and observer causes the magnification of that source (and therefore the apparent brightness) to change rapidly with time. An isolated strong-lensing event with a rapid timescale can be generated when a background star crosses over a lensing caustic (the mapping of the critical curve back on to the source plane). In the case of a star crossing the caustic of a smooth lensing potential, the amplification of the source flux would increase (decrease) with time *t*, following a characteristic $t^{-1/2}$ profile as it moves toward (away from) the caustic. This slowly evolving light curve then transitions to a very sharp decline (rise) when the star has moved to the other side of the caustic⁴⁵,⁴⁶. With a more complex lens comprising many compact objects, the light curve would exhibit a superposition of many such sharp peaks⁴⁷,⁴⁸.

The peculiar transient MACS J1149 LS1, observed behind the HFF cluster MACS J1149.6+2223, has been proposed as the first observed example of such a stellar caustic-crossing event⁴⁹. Such events may be expected to appear more frequently in strongly lensed galaxies that have small angular separation from the centre of a massive cluster. In such a situation, our line of sight to the lensed background galaxy passes through a dense web of overlapping microlenses caused by the intracluster stars distributed around the centre of the cluster. This has the effect of 'blurring' the magnification profile across the cluster's critical curve, making it more probable that a single (and rare) massive star in the background galaxy gets magnified by the required factor of ~10⁵ to become visible as a transient caustic-crossing event. On this basis, the HFF14Spo host-galaxy images are suitably positioned for caustic-crossing transients, as they are seen through a relatively high density of intracluster stars (see Methods)—comparable to that observed for the MACS J1149 LS1 transient.

The characteristic timescale of a canonical caustic-crossing event would be of the order of hours or days (see Supplementary Information), which is comparable to the timescales observed for the HFF14Spo events. Gravitational lensing is achromatic as long as the size of the source is consistent across the spectral energy distribution (SED). This means that the colour of a caustic-crossing transient will be roughly constant. Using simplistic linear interpolations of the observed light curves (see Methods), we find that the inferred colour curves for both HFF14Spo events are marginally consistent with this expectation of an unchanging colour (Supplementary Fig. 4).

In the baseline lensing configuration adopted above—where a single critical curve subtends the HFF14Spo host-galaxy arc—these events cannot plausibly be explained as stellar caustic crossings, because neither transient is close enough to the single critical curve

to reach the required magnifications of $\mu \approx 10^6$. Some of our lens models can, however, be modified so that instead of just two host images, the lensed galaxy arc is made up of many more images of the host, with multiple critical curves subtending the arc where the HFF14Spo events appeared (Fig. 3). If this alternative lensing situation is correct, then similar microlensing transients would be expected to appear at different locations along the host-galaxy arc, instigated by new caustic-crossing episodes from different stars in the host galaxy.

**The rate of similar transients.** Although we lack a definitive classification for these events, we can derive a simplistic estimate of the rate of HFF14Spo-like transients by counting the number of strongly lensed galaxies in the HFF clusters that have sufficiently high magnification that a source with $M_v = -14$ mag would be detected in HST imaging. Only six galaxies satisfy that criterion, all with $0.5 < z < 1.5$ (Methods). Each galaxy was observed by the high-cadence HFF programme for an average of 80 days. Treating HFF14Spo-NW and HFF14Spo-SE as separate events leads to a rough rate estimate of 1.5 HFF14Spo-like events per galaxy per year.

Derivation of a volumetric rate for such events would require a detailed analysis of the lensed volume as a function of redshift, and is beyond the scope of this work. Nevertheless, a comparison with rates of similar transients in the local Universe (within approximately 150 Mpc) can inform our assessment of the likelihood that the HFF14Spo events are unrelated. A study of very fast optical transients with the Pan-STARRS1 (Panoramic Survey Telescope and Rapid Response System 1) survey derived a rate limit of approximately $<0.05$ Mpc$^{-3}$yr$^{-1}$ for transients reaching $M \approx -14$ AB mag on a timescale of ~1 day (ref. ⁴). This limit, although several orders of magnitude higher than the constraints on novae or SNe, is sufficient to make it exceedingly unlikely that two unrelated fast optical transients would appear in the same galaxy in a single year. Furthermore, we have observed no other transient events with similar luminosities and light-curve shapes in high-cadence surveys of five other Frontier Fields clusters. Indeed, all other transients detected in the primary HFF survey have been fully consistent with normal SNe. Thus, we have no evidence to suggest that transients of this kind are common enough to be observed twice in a single galaxy in a single year.

## Discussion

We have examined three plausible explanations for the HFF14Spo events, but we cannot make a definitive choice between them because of the scarcity of observational data and the uncertainty in the location of the lensing critical curves. If there is just a single critical curve passing between the two HFF14Spo locations, then our preferred explanation for the HFF14Spo events is that we have observed two distinct eruptive episodes from a massive LBV star. These would be extreme LBV outbursts in several dimensions, and should add a useful benchmark for the theoretical challenge of developing a comprehensive physical model that accommodates both the η-Car-like great eruptions and the S-Doradus-type variation of LBVs.

If, instead, the MACS0416 lens has multiple critical curves that intersect both HFF14Spo locations, then our third proposal of a microlensing-generated transient would be preferred. Stellar caustic crossings have not been observed before, but the analysis of a probable candidate behind the MACS J1149 cluster⁴⁹ indicates that massive cluster lenses may generate such events more frequently than previously expected⁴⁸,⁴⁹. Resolving the uncertainty of the HFF14Spo classification will require refinement of the lens models to more fully address systematic biases and more tightly constrain the path of the critical curve. High-cadence monitoring of the MACS0416 field would also be valuable, as it could catch future LBV eruptions or microlensing transients at or near these locations.
## Methods

**Discovery.** The HFF14Spo transients were discovered in HST imaging collected as part of the HFF survey (HST General Observer (GO) programme 13496, principal investigator (PI) Lotz), a multicycle programme observing six massive galaxy clusters and associated 'blank sky' parallel fields¹. Several HST observing programmes have provided additional observations supplementing the core HFF programme. One of these is the FrontierSN programme (HST GO programme 13386, PI Rodney), which aims to identify and study explosive transients found in the HFF and related programmes⁵⁰. The FrontierSN team discovered HFF14Spo in two separate HFF observing campaigns for the galaxy cluster MACS0416. The first was an imaging campaign in January 2014 during which the MACS0416 cluster field was observed in the F435W, F606W and F814W optical bands using the Advanced Camera for Surveys Wide Field Camera (ACS-WFC). The second concluded in August 2014 and imaged the cluster with the infrared detector of HST's Wide Field Camera 3 (WFC3-IR) using the F105W, F125W, F140W and F160W bands.

To discover transient sources, the FrontierSN team processes each new epoch of HST data through a difference-imaging pipeline (https://github.com/srodney/ndrizpipe), using archival HST images to provide reference images (templates), which are subtracted from the astrometrically registered HFF images. For MACS0416, the templates comprise images collected as part of the Cluster Lensing And Supernova survey with Hubble (CLASH, HST GO programme 12459, PI Postman)⁵¹. The resulting difference images are visually inspected, and any new transients of interest (primarily SNe) are monitored with additional HST imaging or ground-based spectroscopic observations as needed.

**Photometry.** The follow-up observations of HFF14Spo included HST imaging observations in infrared and optical bands using the WFC3-IR and ACS-WFC detectors, respectively. Supplementary Tables 1 and 2 present photometry of the HFF14Spo events from all available HST observations. The flux was measured in difference images, first using aperture photometry with a 0.3" radius, and by fitting with an empirical point spread function (PSF). The PSF model was defined using HST observations of the G2V standard star P330E, observed in a special calibration programme. A separate PSF model was defined for each filter, but owing to the long-term stability of the HST PSF, we used the same model in all epochs. All of the aperture and PSF-fitting photometry was carried out using the PythonPhot software package (https://github.com/djones1040/PythonPhot)⁵².

**Host-galaxy spectroscopy.** Spectroscopy of the HFF14Spo host galaxy was collected using three instruments on the Very Large Telescope (VLT). Observations with the VLT's X-shooter cross-dispersed echelle spectrograph⁵³ were taken on October 19, 21 and 23, 2014 (programme 093.A-0667(A), PI J. Hjorth) with the slit centred on the position of HFF14Spo-SE. The total integration time was 4.0h for the NIR arm of X-shooter, 3.6h for the VIS (visual wavelength) arm and 3.9h for the UVB arm. The spectrum did not provide any detection of the transient source itself, because it had faded below detectability. However, the spectrum did provide a redshift for the host galaxy of z = 1.0054 ± 0.0002 from Hα and the [O II] doublet in data from the NIR and VIS arms, respectively. This is consistent with the photometric redshift of the host: z = 1.00 ± 0.02 from the BPZ (Bayesian Photometric Redshift) algorithm⁵⁴, and z = 0.92 ± 0.05 from the EAZY (Easy and Accurate zphot from Yale) program⁵⁵. Both were derived from HST photometry of the host images 11.1 and 11.2, spanning 4,350–16,000 Å.

Additional VLT observations were collected using the Visible Multi-Object Spectrograph⁵⁶, as part of the CLASH-VLT large programme (186.A-0.798, PI P. Rosati)⁵⁷, which collected ~4,000 reliable redshifts over 600 arcmin² in the MACS0416 field¹¹,¹⁸. For the MACS0416 field, the CLASH-VLT programme collected 1h of useful exposure time in good seeing conditions with the Low Resolution Blue grism. Unfortunately, the wavelength range of this grism (3,600–6,700 Å) does not include any strong emission lines for a source at z = 1.0054, and the signal-to-noise ratio was not sufficient to provide any clear line identifications for the three images of the HFF14Spo host galaxy.

The VLT Multi-Unit Spectroscopic Explorer⁵⁹,⁶⁰ observed the northeast portion of the MACS0416 field—where the HFF14Spo host images are located— in December 2014 for 2h of integration time (European Southern Observatory programme 094.A-0115, PI J. Richard). These observations confirmed the redshift of the host galaxy with a clear detection of the [O II] doublet. Because the Multi-Unit Spectroscopic Explorer is an integral field spectrograph, these observations also provided a confirmation of the redshift of the third image of the host galaxy, 11.3, with a matching [O II] line at the same wavelength¹⁴.

A final source of spectroscopic information relevant to HFF14Spo is the Grism Lens-Amplified Survey from Space (GLASS, HST GO programme 13459, PI T. Treu)⁶¹,⁶². The GLASS programme collected slitless spectroscopy on the MACS0416 field using the WFC3-IR G102 and G141 grisms on HST, deriving redshifts for galaxies down to an H-band magnitude limit H < 23 mag on the AB photometric system. As with the VLT Visible Multi-Object Spectrograph data, the three sources identified as images of the HFF14Spo host galaxy are too faint in the GLASS data to provide any useful line identifications. There are also no other sources in the GLASS redshift catalogue (http://glass.astro.ucla.edu/) that have a spectroscopic redshift consistent with z = 1.0054.

**Gravitational lens models.** The seven lens models used to provide estimates of the plausible range of magnifications and time delays are as follows.

* CATS (Clusters As TelescopeS): the model of ref. ⁷, version 4.1, generated with the LENSTOOL software (https://projects.lam.fr/projects/lenstool/wiki)⁶³ using strong-lensing constraints. This model parameterizes cluster and galaxy components using pseudo-isothermal elliptical mass distribution density profiles⁶⁴,⁶⁵.

* GLAFIC: the model of ref. ⁶⁶, built using the GLAFIC software (http://www.slac.stanford.edu/~oguri/glafic)⁶⁷ with strong-lensing constraints. This model assumes simply parameterized mass distributions, and model parameters are constrained using the positions of more than 100 multiple images.

* GLEE: a new model built using the GLEE software⁶⁸,⁶⁹ with the same strong-lensing constraints used in ref. ¹⁴, representing mass distributions with simply parameterized mass profiles.

* GRALE: a free-form, adaptive grid model developed using the GRALE software tool¹³,⁷⁰⁻⁷², which implements a genetic algorithm to reconstruct the cluster mass distribution with hundreds to thousands of projected Plummer²³ density profiles.

* SWUnited: the model of ref. ¹², built using the SWUnited (Strong- and Weak-lensing United) modelling method⁷⁴,⁷⁵, in which an adaptive pixelated grid iteratively adapts the mass distribution to match both strong- and weak-lensing constraints. Time-delay predictions are not available for this model.

* WSLAP+: created with the WSLAP+ software (Weak- and Strong-Lensing Analysis Package plus member galaxies; http://www.ifca.unican.es/users/jdiego/LensExplorer)⁷⁶. (Note that no weak-lensing constraints were used for this MACS0416 model.)

* ZLTM: a model with strong- and weak-lensing constraints, built using the 'light-traces-mass' (LTM) methodology²⁷,²⁸, first presented for MACS0416 in ref. ⁶.

Early versions of the SWUnited, CATS, ZLTM and GRALE models were originally distributed as part of the HFF lens modelling project (https://archive.stsci.edu/prepds/frontier/lensmodels/), in which models were generated on the basis of data available before the start of the HFF observations, to enable rapid early investigations of lensed sources. The versions of these models applied here are updated to incorporate additional lensing constraints. In all cases, the lens modellers made use of strong-lensing constraints (multiply imaged systems and arcs) derived from HST imaging collected as part of the CLASH programme⁵¹). These models also made use of spectroscopic redshifts in the cluster field¹¹,¹⁴,⁷⁹,⁸⁰. Input weak-lensing constraints were derived from data collected at the Subaru Telescope⁸¹,⁸² and archival imaging.

Variations of these lens models, developed specifically for analysis of the HFF14Spo transients, are described in the Supplementary Information, and Supplementary Fig. 1 illustrates the multi-plane lensing constraints of the GLEE model.

**X-ray non-detections.** The MACS0416 field was observed by the X-ray and UV/ optical telescopes on the Neil Gehrels Swift Observatory in April 2013. No source was detected near the locations of the HFF14Spo events (N. Gehrels, personal communication). The field was also observed by Chandra with the Advanced CCD Imaging Spectrometer instrument for three separate programmes. On June 7, 2009, it was observed for GO programme 10800770 (PI H. Ebeling). It was revisited for Guaranteed Time Observer programme 15800052 (PI S. Murray) on November 20, 2013, and for GO programme 15800858 (PI C. Jones) on June 9, August 31, November 26 and December 17, 2014. These Chandra images show no evidence for an X-ray emitting point source near the HFF14Spo locations on those dates (S. Murray, personal communication).

The Chandra observations that were closest in time to the observed HFF14Spo events were those taken in August and November 2014. The August 31 observations were coincident with the observed peak of rest-frame optical emission for the HFF14Spo-SE event (on modified Julian date (MJD) 56900). The November 26 observations correspond to 44 rest-frame days after the peak of the HFF14Spo-SE event. If the HFF14Spo events are UV/optical nova eruptions, then these observations most probably did not coincide with the nova system's supersoft X-ray phase. For an RN system, the X-ray phase typically initiates after a short delay and persists for a span of only a few weeks. For example, the most rapid RN known, M31N 2008-12a, has exhibited a supersoft X-ray phase 6–18 days after the peak of the optical emission⁸³.

**Light-curve fitting.** Owing to the rapid decline timescale, no observations were collected for either event that unambiguously show the declining portion of the light curve. Therefore, we must make some assumptions for the shape of the light curve, to quantify the peak luminosity and the corresponding timescales for the rise and the decline. We first approach this with a simplistic model that is piecewise linear in magnitude versus time. Supplementary Fig. 3 illustrates examples of the resulting fits for the two events. For each fit, we use only the data collected within 3 days of the brightest observed magnitude, which allow us to fit a linear rise separately for the F606W and F814W light curves of HFF14Spo-NW and
the F125W and F160W light curves of HFF14Spo-SE. To quantify the covariance between the true peak brightness, the rise time and the decline timescale, we use the following procedure.

(1) Make an assumption for the date of peak, $t_{pk}$.

(2) Measure the peak magnitude at $t_{pk}$ from the linear fit to the rising light-curve data.

(3) Assume that the source reaches a minimum brightness (maximum magnitude) of 30 mag (AB) at the epoch of first observation after the peak.

(4) Draw a line for the declining light curve between the assumed peak and the assumed minimum brightness.

(5) Use that declining light-curve line to measure the timescale for the event to drop by 2 mag, $t_2$.

(6) Make a new assumption for $t_{pk}$, and repeat steps 2–6.

For further details, see the discussion of Supplementary Fig. 3 in the Supplementary Information.

At any assumed value for the time of peak brightness, this linear interpolation gives an estimate of the peak magnitude. We then convert that to a luminosity ($\nu L_\odot$ in ergs$^{-1}$) at frequency $\nu$ by first correcting for the luminosity distance assuming a standard $\Lambda$ cold dark matter cosmology, where $\Lambda$ is the cosmological constant, and then accounting for an assumed lensing magnification, $\mu$. The range of plausible lensing magnifications ($10 < \mu < 100$) is derived from the union of our seven independent lens models. This results in a grid of possible peak luminosities for each event as a function of magnification and time of peak. As we are using linear light-curve fits, the assumed time of peak is equivalent to an assumption for the decline time, which we quantify as $t_2$, the time over which the transient declines by 2 mag.

**LBV build-up timescale and quiescent luminosity.** To explore some of the physical implications of an LBV classification for the two HFF14Spo events, we first make a rough estimate of the total radiated energy, which can be computed using the decline timescale and the peak luminosity:

$$E_{rad} = \zeta t_2 2L_{pk} \quad (1)$$

where $\zeta$ is a dimensionless factor of order unity that depends on the precise shape of the light curve$^{15}$. Note that earlier work$^{12}$ has used $t_{1.5}$ instead of $t_2$, which amounts to a different light-curve-shape term, $\zeta$. Adopting $L_{pk} \approx 10^{41}$ ergs$^{-1}$ and $t_2 \approx 1$ day (as shown in Fig. 5), we find that the total radiated energy is $E_{rad} \approx 10^{46}$ erg. A realistic range for this estimate would span $10^{44} < E_{rad} < 10^{47}$ erg owing to uncertainties in the magnification, bolometric luminosity correction, decline time and light-curve shape. These uncertainties notwithstanding, our estimate falls well within the range of plausible values for the total radiated energy of a major LBV outburst.

The 'build-up' timescale$^{15}$, $t_{rad}$, matches the radiative energy released in an LBV eruption event with the radiative energy produced during the intervening quiescent phase:

$$t_{rad} = \frac{E_{rad}}{L_{\text{qui}}} = t_2 \frac{\zeta L_{\text{pk}}}{L_{\text{qui}}} \quad (2)$$

where $L_{\text{qui}}$ is the luminosity of the LBV progenitor star during quiescence.

The HFF14Spo events are not resolved as individual stars in their quiescent phase, so we have no useful constraint on the quiescent luminosity. Thus, instead of using a measured quiescent luminosity to estimate the build-up timescale, we assume that $t_{rad}$ for HFF14Spo corresponds to the observed rest-frame lag between the two events, roughly 120 days (this accounts for both cosmic time dilation and a gravitational lensing time delay of ~40 days). Adopting $L_{pk} = 10^{41}$ ergs$^{-1}$ and $t_2 = 2$ days (see Fig. 5), we infer that the quiescent luminosity of the HFF14Spo progenitor would be $L_{\text{qui}} \approx 10^{39.5}$ ergs$^{-1}$ ($M_V \approx -10$ mag).

**RN light-curve comparison.** There are ten known RNe in the Milky Way Galaxy, and seven of these exhibit outbursts that decline rapidly, fading by 2 mag in < 10 days (ref. $^{41}$). We compared the declining phase of these nova outbursts against the HFF14Spo transients by normalizing the nova light curves to the observed peak flux of the HFF14Spo light curves. As shown in Supplementary Fig. 8, this comparison demonstrates that the rapid decline of both of the HFF14Spo transient events is fully consistent with the eruptions of known RNe in the local Universe.

**RN luminosity and recurrence period.** To examine the recurrence period and peak brightness of the HFF14Spo events relative to RNe, we rely on a pair of papers that evaluated an extensive grid of nova models through multiple cycles of outburst and quiescence$^{44,84}$. We assume that the HFF14Spo events represent two outbursts of the same RN source, correct for the gravitational lensing time delay predicted by our lensing models, and derive the recurrence period from the observed separation in time between HFF14Spo-NW and HFF14Spo-SE. The nova recurrence models indicate that a recurrence period as fast as 1 yr is expected only for an RN system in which the primary white dwarf is very close to the Chandrasekhar mass limit ($1.4 M_\odot$) and has an extraordinarily rapid mass-transfer rate ($\sim 10^{-6} M_\odot$ yr$^{-1}$). The models of ref. $^{44}$ suggest that such systems should have a very low peak amplitude

(barely consistent with the lower limit for HFF14Spo) and a low peak luminosity ($\sim 100$ times less luminous than the HFF14Spo events). This comparison is presented in Supplementary Fig. 9, and the physical implications are discussed in the Supplementary Information.

**Intracluster light.** To estimate the mass of intracluster stars along the line of sight to the HFF14Spo events, we follow the procedure of refs $^{49,85}$. This entails fitting and removing the surface brightness of individual galaxies in the field, and next fitting a smooth profile to the residual surface brightness of intracluster light. The surface brightness is then converted to a projected stellar mass surface density by assuming a Chabrier$^{86}$ initial mass function and an exponentially declining star-formation history. This procedure leads to an estimate for the surface mass density of intracluster stars, $\Sigma_\odot$, of $\log(\Sigma_\odot/(M_\odot \text{kpc}^{-2})) = 6.9 \pm 0.4$, very similar to the value of $6.8^{+0.4}_{-0.3}$ inferred for the probable caustic-crossing star MACS J1149 LS1 (ref. $^{49}$).

**Colour curves.** At $z=1$, the observed optical and infrared bands translate to rest-frame UV and optical wavelengths, respectively. To derive rest-frame UV and optical colours from the observed photometry, we start with the measured magnitude in a relatively blue band (F435W and F606W for HFF14Spo-NW, and F105W, F125W and F140W for HFF14Spo-SE). We then subtract the coeval magnitude for a matched red band (F814W for HFF14Spo-NW, and F125W or F160W for HFF14Spo-SE), derived from the linear fits to those bands. To adjust these to rest-frame filters, we apply 'K corrections' $^{87}$, which we compute by defining a crude SED via linear interpolation between the observed broad bands for each transient event at every epoch. For consistency with past published results, we include in each K correction a transformation from AB- to Vega-based magnitudes. The resulting UV and optical colours are plotted in Supplementary Fig. 4. Both HFF14Spo-NW and HFF14Spo-SE show little or no colour variation over the period where colour information is available. This lack of colour evolution is compatible with all three of the primary hypotheses advanced, as it is possible to have no discernible colour evolution from either an LBV or an RN over this short timespan, and microlensing events inherently exhibit an unchanging colour.

If these two events are from a single source, then one could construct a composite SED from rest-frame UV to optical wavelengths by combining the NW and SE flux measurements, but only after correcting for the relative magnification. Figure 4 shows that the observed peak brightnesses for the two events agree to within ~30%. This implies that for any composite SED, the rest-frame UV/optical flux ratio is approximately equal to the NW/SE magnification ratio, and any extreme asymmetry in the magnification would indicate a very steep slope in the SED.

**Rates.** To derive a rough estimate of the rate of HFF14Spo-like transients, we first define the set of strongly lensed galaxies in which a similarly faint and fast transient could have been detected in the HFF imaging. The single-epoch detection limit of the HFF transient search was $m_{lim} = 26.7$ AB mag, consistent with the SN searches carried out in the CLASH and Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS) programmes$^{88,89}$. For a transient with peak brightness $M_V > -14$ mag to be detected, the host galaxy must be amplified by strong lensing with a magnification $\mu > 20$ at $z \approx 1$, growing to $\mu > 100$ at $z \approx 2$. Using photometric redshifts and magnifications derived from the GLAFIC lens models of the six HFF clusters, we find $N_{gal} = 6$ galaxies that satisfy this criterion, with $0.5 < z < 1.5$ (Supplementary Fig. 10).

We then define the control time, $t_c$, for the HFF survey, which gives the span of time over which each cluster was observed with a cadence sufficient for detection of such rapid transients. We define this as any period in which at least two HST observations were collected within every 10 day span. This effectively includes the entirety of the primary HFF campaigns on each cluster, but excludes all of the ancillary data-collection periods from supplemental HST imaging programmes. The average control time for a HFF cluster is $t_c = 0.22$ yr (80 days). Treating each HFF14Spo event as a separate detection, we can derive a rate estimate, $R$, using $R = 2/(N_{gal} t_c)$. This yields $R = 1.5$ events per galaxy per yr.

**Data availability.** The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request. All HST data utilized for this work are available through the Mikulski Archive for Space Telescopes (MAST).

Received: 7 October 2016; Accepted: 30 January 2018; Published online: 2 April 2018

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## Acknowledgements

The authors thank M. Livio and L. Chomiuk for discussion of this paper, as well as S. Murray and the late N. Gehrels for assistance with the Chandra and Swift data, respectively. Some of the data in this paper were obtained from the Mikulski Archive

for Space Telescopes (MAST). Support for MAST for non-HST data is provided by the NASA (National Aeronautics and Space Administration) Office of Space Science via grant NNX09AF08G, and by other grants and contracts. This research has made use of the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with NASA. Financial support for this work was provided to S.A.R., O.G. and L.-G.S. by NASA through grant HST-GO-13386 from the Space Telescope Science Institute (STScI), which is operated by Associated Universities for Research in Astronomy, Inc. (AURA), under NASA contract NAS 5-26555. G.B.C. and P.R. acknowledge financial support from PRIN-INAFT 2014 1.05.01.94.02. J.M.D. acknowledges support of projects AYA2015-64508-P (MINECO/ FEDER, UE) and AYA2012-39475-C02-01 and the consolider project CSD2010- 00064 funded by the Ministerio de Economía y Competitividad. A.V.F. and P.L.K. are grateful for financial assistance from the Christopher R. Redlich Fund, the TABASGO Foundation and NASA/STScI grants GO-14208, GO-14528, GO-14872 and GO-14922; A.V.F. is also grateful to the Miller Institute for Basic Research in Science (U.C. Berkeley). The work of A.V.F. was conducted in part at the Aspen Center for Physics, which is supported by NSF grant PHY-1607611. R.J.F. and the UCSC group are supported in part by NSF grant AST-1518052 and from fellowships to R.J.F. from the Alfred P. Sloan Foundation and the David and Lucile Packard Foundation. C.G. acknowledges support by the VILLUM FONDEN Young Investigator Programme through grant 10123. J.H. was supported by a VILLUM FONDEN Investigator grant (project number 16599). M.J. was supported by the Science and Technology Facilities Council (grant ST/L00075X/1) and used the DiRAC Data Centric system at Durham University, operated by the Institute for Computational Cosmology on behalf of the STFC DiRAC HPC Facility (www.dirac.ac.uk). M.J. was funded by BIS National E-infrastructure capital grant ST/K00042X/1, STFC capital grant ST/H008519/1, STFC DiRAC Operations grant ST/K003267/1 and Durham University. DiRAC is part of the National E-Infrastructure. R.K. was supported by Grant-in-Aid for JSPS Research Fellow (16J01302). A.M. acknowledges the financial support of the Brazilian funding agency FAPESP (Postdoc fellowship, process 2014/11806-9). M.O. acknowledges support in part by World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan, and JSPS KAKENHI grants 26800093 and 15H05892. J.R. acknowledges support from the ERC starting grant 336736-CALENDLS. G.C. and S.H.S. thank the Max Planck Society for support through the Max Planck Research Group of S.H.S. The GLASS team and T.T. were funded by NASA through NASA/STScI grant GO-13459. L.L.R.W. thanks the Minnesota Supercomputing Institute at the University of Minnesota for providing resources and support.

## Author contributions

S.A.R. designed the observations, processed the HST data, organized the analysis and wrote the manuscript. M.B., T.B., G.B.C., G.C., J.M.D., A.H., M.J., R.K., M.O., J.R., K.S., S.H.S., L.L.R.W. and A.Z. contributed to the lensing analysis with construction and/ or interpretation of a cluster lens model. I.B., G.B., G.B.C., C.G., S.H., B.M., A.M., P.R., K.B.S., J.S. and B.J.W. collected, processed and/or analysed data on the host galaxy and other galaxies in the cluster field. R.J.F., S.W.J., P.L.K., C.M., O.G., J.H., A.G.R. and L.-G.S. contributed to the evaluation of models of astrophysical transients. A.V.F and T.T. assisted with the observational programme design and editing of the manuscript.

## Competing interests

The authors declare no competing interests.

## Additional information

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