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# Shock cooling of a red-supergiant supernova at redshift 3 in lensed images

## Abstract

The core-collapse supernova of a massive star rapidly brightens when a shock, produced following the collapse of its core, reaches the stellar surface. As the shock-heated star subsequently expands and cools, its early-time light curve should have a simple dependence on the size of the progenitor1 and therefore final evolutionary state. Measurements of the radius of the progenitor from early light curves exist for only a small sample of nearby supernovae2,3,4,5,6,7,8,9,10,11,12,13,14, and almost all lack constraining ultraviolet observations within a day of explosion. The several-day time delays and magnifying ability of galaxy-scale gravitational lenses, however, should provide a powerful tool for measuring the early light curves of distant supernovae, and thereby studying massive stellar populations at high redshift. Here we analyse individual rest-frame exposures in the ultraviolet to the optical taken with the Hubble Space Telescope, which simultaneously capture, in three separate gravitationally lensed images, the early phases of a supernova at redshift z ≈ 3 beginning within 5.8 ± 3.1 hours of explosion. The supernova, seen at a lookback time of approximately 11.5 billion years, is strongly lensed by an early-type galaxy in the Abell 370 cluster. We constrain the pre-explosion radius to be $$53{3}_{-119}^{+154}$$ solar radii, consistent with a red supergiant. Highly confined and massive circumstellar material at the same radius can also reproduce the light curve, but because no similar low-redshift examples are known, this is unlikely.

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## Data availability

The HST data used for this study can be retrieved from the NASA Mikulski Archive for Space Telescopes (http://archive.stsci.edu). The supernova is found in the HST imaging of the Abell 370 field acquired from programme GO-11591 (PI J.-P. Kneib). The LBT spectroscopy data are available from the LBT archive (http://archive.lbto.org). The Keck MOSFIRE data can be retrieved from the Keck Observatory Archive (https://www2.keck.hawaii.edu/koa/public/koa.php). The HFF data and models can be downloaded from https://archive.stsci.edu/prepds/frontier/lensmodels/#modelsandinput. Additional data including the MMT spectroscopic data, the HST coaddition and image differencing data, the GALFIT scripts and resulting models, the HST photometry data of the SN host galaxy, the SN light curve fitting script and resulting MCMC data, and our best-fit GLAFIC lens model are available from https://doi.org/10.5281/zenodo.6725770.

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## Acknowledgements

This work was supported by the HST Cycle 27 Archival Research programme (grant AR-15791), as well as by GO-15936 and GO-16278. We utilize gravitational lensing models produced by the GLAFIC group. The lens modelling was partially funded by the HST Frontier Fields programme conducted by STScI. The lens models were obtained from the Mikulski Archive for Space Telescopes. Some of the observations reported here were obtained at the MMT Observatory, a joint facility of the Smithsonian Institution and the University of Arizona. The data presented here were obtained in part at the LBT Observatory. The LBT is an international collaboration among institutions in the USA, Italy and Germany. Some of the data presented herein were obtained at the W. M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California, and the National Aeronautics and Space Administration (NASA). The Observatory was made possible by the generous financial support of the W. M. Keck Foundation. We wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Maunakea has always had within the Indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain. P.L.K. is supported by US National Science Foundation (NSF) grant AST-1908823. J.M.D. acknowledges support from projects PGC2018-101814-B-100 and MDM-2017-0765. M.O. acknowledges support from World Premier International Research Center Initiative, MEXT, Japan, and JSPS KAKENHI grants JP20H00181, JP20H05856, JP22H01260 and JP18K03693. A.Z. acknowledges support by grant 2020750 from the USA–Israel Binational Science Foundation (BSF) and grant 2109066 from the US NSF, and by the Ministry of Science & Technology, Israel. A.V.F. is grateful for assistance from the Christopher R. Redlich Fund, the UC Berkeley Miller Institute for Basic Research in Science (where he was a Miller Senior Fellow), and many individual donors. We acknowledge the help of W. Zheng with the Keck MOSFIRE observations.

## Author information

Authors

### Contributions

W.C. analysed the HST, Keck, LBT and MMT data, wrote the manuscript and developed simulations. P.L.K. aided the interpretation of the events, planned the Keck, LBT and MMT observations, edited the manuscript and cross-checked the results. M.O. constructed the gravitational-lensing model for this work. T.J.B., J.M.D. and A.Z. helped with the HST proposal and reviewed the manuscript. P.L.K., N.E. and A.Z. acquired the Keck observation. P.L.K. and N.E. acquired the LBT observation. A.Z. constructed independent lens models for the cluster to verify the time-delay results. A.V.F. obtained the Keck time, helped acquire the Keck MOSFIRE observations, and edited the HST proposal and this manuscript. T.L.T. contributed to the manuscript and interpretation.

### Corresponding author

Correspondence to Wenlei Chen.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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## Extended data figures and tables

### Extended Data Fig. 1 Photometry of the multiply imaged SN: image differencing and the blackbody fitting.

We used GALFIT51 to fit bright sources in the lensing system and subtracted the best-fit model from the field prior to measuring the flux. ac, The template image (a), the best-fit GALFIT model (b), and the residual through the HST ACS-WFC F814W filter (c). d, The WFC3-IR F160W difference image by subtracting the template from the event image directly. e, The difference image using our GALFIT-based method, where we subtracted the PSF-convolved best-fit GALFIT source models from the images, and then calculated the difference from GALFIT residuals between the coadded images and the event images. We can see that this method can reduce the significant residual from the mismatched PSFs around bright sources as shown in d. fh, Distributions of effective temperature and luminosity from the MCMC samples from fitting the blackbody emission into the photometry of each SN image.

### Extended Data Fig. 2 Photometry and photometric redshift of the SN host galaxy.

ac, Broadband spectral energy distributions and best-fitting BPZ17 templates for G1, G2 and G3. The coloured circles designate the observed AB magnitudes with ±1σ uncertainties measured from ACS-WFC (green) and WFC3-IR (red) images, and arrows correspond to 95% upper limits. Dark-blue curves plot the best-fit spectral templates. Grey rectangles mark the magnitudes calculated from the best-fitting BPZ templates (with approximate uncertainties) for those filters95. df, Broadband spectral energy distributions and best-fitting EAZY17 templates for G1, G2 and G3. The data points are the observed flux with ±1σ uncertainties. Blue curves show the best-fit spectral template. The three panels on the right display the posterior probability distribution of the photometric redshift. g,h, Photometric redshift probability distributions for G1 (green dashed line), G2 (blue dashed line), G3 (red dashed line), and the joint analysis (solid line) derived from BPZ and EAZY fitting. i, The distribution of CCSN host-galaxy stellar mass (M) and star-formation rate (SFR)55, where the red star marks M and SFR of the host galaxy of the SN reported in this work.

### Extended Data Fig. 3 Modelling the strongly lensed images.

a, Best-fit multiple-image geometry from the published Keeton V4 (left), GLAFIC V4 (middle) and Sharon V4 (right) models, by minimizing the r.m.s. angular separation of the predicted images from the real images in the image plane, for z = 3. b, Best-fit r.m.s. angular separation of the predicted images as a function of z from the published Keeton V4, GLAFIC V4 and Sharon V4 models. c, Best-fit multiple-image geometry from our revised GLAFIC model. d, Distribution of μS1, μS2 and μS3 from the MCMC samples given by our revised GLAFIC model, where μ1, μ2 and μ3 are predicted magnifications of images S1, S2 and S3, respectively. Cyan, yellow and magenta markers show the distribution projected on the μS1μS3, μS1μS2 and μS2μS3 planes, where red-dashed lines are the best-fit lines from linear regressions on the projected distribution. e, Correlations between Δt13 and Δt23 from the MCMC samples, where Δt13 and Δt23 are the time delay of S1 and S2 relative to S3, respectively.

### Extended Data Fig. 4 Distribution of parameters from fitting the RSG model to the observations.

Here R is the extended envelope radius, M is the envelope mass, v is the shock velocity, t0 is the initial time, and Δt13 and μS1 are, respectively, the time delay and magnification of the S1 image. We set t = 0 at the observation time of the S3 image in the ACS-WFC F814W band. The time delay of each image is defined as the difference of its light-travel time from that of S3. The result is for RV = 3.1.

### Extended Data Fig. 5 Distribution of parameters from fitting the CSM-homologous model to the observations.

The result is for a prior on the CSM mass of M < 1M. The parameters are the same as in Extended Data Fig. 5. Data of the MCMC samples for all models with all our choices of RV and priors are available from an online repository75.

### Extended Data Fig. 6 Reconstructed light curves from the best-fit model parameters from all the light curve models for RV = 3.1.

af, Data shown are from the RSG model (a), the BSG model (b), the CSM-homologous model for a prior on the CSM mass of M < 0.1M (c), the CSM-homologous model for a prior on the CSM mass of M < 1M (d), the CSM-planar model for a prior on the CSM mass of M < 0.1M (e), and the CSM-planar model for a prior on the CSM mass of M < 1M (f). Data points and error bars correspond to the measured values and ±1σ uncertainties of the flux densities, respectively. Reconstructed light curves with all our choices of RV are available from an online repository75.

### Extended Data Fig. 7 Comparisons of the reconstructed SN light curve with early UV light curves from other SNe.

a, The early-time evolution of the effective blackbody temperature of the SN reported here (green data points, where error bars are 68% confidence intervals), where the effective temperatures of the SN images are obtained by independently fitting the blackbody emission into the photometry of each SN image. The green solid line is from the best-fit RSG model. Red and blue dashed lines are two examples from the RSG model with progenitor radius of 200R and 1,000R, respectively, for the same envelope mass and shock velocity from our best-fit RSG model for the SN reported here. Red, yellow, blue and cyan data points show the early-time evolution of SN 2018fif14 (type IIP), SN 2013ej6 (type IIP/L), SN 2017eaw11,12 (type IIP), SN 1987A80 and SN 2016gkg7,8,9,10 (type IIb). bf, Stars and solid curves show the absolute magnitude of the SN reported here and reconstructed light curves from the best-fit RSG model, respectively, with arbitrary magnitude offsets for better visualization. For this SN, orange, teal and purple points and lines are for ACS-WFC F814W, WFC3-IR F110W and WFC3-IR F160W, respectively. In the rest frame of the SN, central wavelengths of these three filters fall into the B, UVW1, and UVW2 bands of Swift-UVOT. In b, we compare the SN’s early light curve to the Swift-UVOT observations of SN 2018fif14 and SN 2021yja81—two type-II SNe whose early light curves indicate only small amounts of CSM around their progenitors14,81. c,d, Comparison to the two type-II SNe, SN 2013fs82 and ASASSN-14gm83, which are believed to have dense CSM shells around their progenitors. In c,d, we plot the light curve from our best-fit CSM-homologous model for the SN of this work (dash-dotted lines) and light curves from the CSM-homologous model for the CSM radius and mass given by the analyses of CSM-rich CCSNe28,29 (dotted lines) for the two type-II SNe. e,f, Comparisons to the early UV light curves of SN 2016gkg8 (type IIb), SN 2020bvc84 (type Ib/c), SN 2018gv85 (type Ia), and ZTF18abvkwla86 (fast blue optical transient). ZTF-g band light curve is shown for ZTF18abvkwla at z = 0.27, corresponding to the rest-frame wavelength of 3,820 Å. All magnitudes are AB magnitudes. BB, blackbody.

### Extended Data Fig. 8 Estimating the CCSN rate based on observations of the multiply imaged SNe.

a, Cumulative distribution of CCSN host galaxies as a function of the host-galaxy extinction AV43. The black solid line shows the cumulative distribution function of the exponential distribution P(AV) = λVexp(−λVAV) with best-fit λV = 0.98. Black, red and blue dashed lines show the cumulative distribution function of the exponential distribution with λV = 1, λV = 0.187 and λV = 2, respectively. b, Differential comoving volume (dV/dz) for the strongly lensed sources as a function of redshift z. Blue curve shows the lensed volume for all the sources in the six Hubble Frontier Fields within a 0.03° × 0.03° search window for each cluster field. Orange curve shows the effective lensing volume for sources that can be significantly (>5σ) detected by HST in the last decade. c, Differential number of detectable multiply imaged core-collapse supernovae (dN/dz) above the 5σ signal-to-noise-ratio level by HST in the last decade as a function of z. d, Volumetric CCSN rate (RCC) as a function of redshift. Contents are the same as in Fig. 4, but for λV = 0.187. e. Volumetric CCSN rate (RCC) as a function of redshift for different choices of λV and RV. Red, green and blue shaded regions are for λV = 0.187, λV = 1 and λV = 2, respectively, for RV = 4.05. Red, green and blue lines are from the MLE kCC for the three λV options. The green dotted line is the same as the green solid line, but for RV = 3.1.

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Chen, W., Kelly, P.L., Oguri, M. et al. Shock cooling of a red-supergiant supernova at redshift 3 in lensed images. Nature 611, 256–259 (2022). https://doi.org/10.1038/s41586-022-05252-5

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• DOI: https://doi.org/10.1038/s41586-022-05252-5