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# A gravitationally lensed supernova with an observable two-decade time delay

## Abstract

When the light from a distant object passes very near to a foreground galaxy or cluster, gravitational lensing can cause it to appear as multiple images on the sky1. If the source is variable, it can be used to constrain the cosmic expansion rate2 and dark energy models3. Achieving these cosmological goals requires many lensed transients with precise time-delay measurements4. Lensed supernovae are attractive for this purpose because they have relatively simple photometric behaviour, with well-understood light curve shapes and colours—in contrast to the stochastic variation of quasars. Here we report the discovery of a multiply imaged supernova, AT 2016jka (‘SN Requiem’). It appeared in an evolved galaxy at redshift 1.95, gravitationally lensed by a foreground galaxy cluster5. It is probably a type Ia supernova—the explosion of a low-mass stellar remnant, whose light curve can be used to measure cosmic distances. In archival Hubble Space Telescope imaging, three lensed images of the supernova are detected with relative time delays of <200 d. We predict that a fourth image will appear close to the cluster core in the year 2037 ± 2. Observation of the fourth image could provide a time-delay precision of ~7 d, <1% of the extraordinary 20 yr baseline. The supernova classification and the predicted reappearance time could be improved with further lens modelling and a comprehensive analysis of systematic uncertainties.

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## Data availability

All HST images used in this work are available from the Mikulski Archive for Space Telescopes (mast.stsci.edu). HST data from 2016 when the transient was active are from the programme HST-GO-14496 (archive.stsci.edu/proposal_search.php?id=14496&mission=hst). Data collected in 2019 are from the REQUIEM programme, HST-GO-15663 (archive.stsci.edu/proposal_search.php?id=15663&mission=hst). All VLT/MUSE spectroscopic data used in this work are available from the ESO Archive Science Portal (archive.eso.org/dataset/ADP.2019-10-07T18:14:24.762, archive.eso.org/dataset/ADP.2019-10-07T18:14:24.751 and archive.eso.org/dataset/ADP.2019-10-07T18:14:24.776). All derived data supporting the findings of this study (photometry, lens model inputs and so on) are available within this Letter and Supplementary Information. Source data are provided with this paper.

## Code availability

All software tools used in the analysis are publicly available, as indicated in the text. The software used for figure creation, including input data files, can be downloaded from github.com/gbrammer/mrg0138_supernova.

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## Acknowledgements

We thank P. Kelly and L. Moustakas for helpful commentary on earlier drafts of this work. Data are based on observations made with the NASA/ESA HST, obtained from the data archive at the Space Telescope Science Institute, and on observations collected at the European Organisation for Astronomical Research in the Southern Hemisphere under ESO programme 0103.A-0777(A). Support for this work was provided by NASA through grant numbers HST-GO-14622 (K.E.W.), HST-AR-15050 (J.D.R.P.), HST-GO-15663 (M.A.) and HST-GO-16264 (S.A.R.) from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc. under NASA contract NAS 5-26555. The Cosmic Dawn Center of Excellence is funded by the Danish National Research Foundation under grant no. 140. Support was provided by NASA Headquarters under the NASA Future Investigators in Earth and Space Science and Technology (FINESST) awards 80NSSC19K1414 (M.A.) and 80NSSC19K1418 (J.D.R.P.). K.E.W. acknowledges funding from the Alfred P. Sloan Foundation.

## Author information

Authors

### Contributions

Conceptualization, S.A.R., G.B.B. and S.T.; methodology, S.A.R., J.D.R.P., J.R. and K.F.O.; investigation, G.B.B., J.R., S.T., M.A. and K.E.W.; writing—original draft, G.B.B. and S.T.; writing—review and editing, S.A.R., G.B.B., J.D.R.P., J.R., S.T., K.F.O., M.A. and K.E.W.; visualization, S.A.R., G.B.B., J.D.R.P., J.R. and K.F.O.; supervision, S.A.R., G.B.B., S.T. and K.E.W.; funding acquisition, M.A., K.E.W., J.D.R.P. and S.A.R.

### Corresponding authors

Correspondence to Steven A. Rodney or Gabriel B. Brammer.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature Astronomy thanks Ariel Goobar, Anupreeta More and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Extended data

### Extended Data Fig. 1 Elements of the MRG0138 cluster lens model.

The model comprises 37 potentials in total: the BCG (red), 32 cluster members (yellow), three perturbers (cyan), and the main cluster potential (pink). Labeled × symbols indicate the positions of the SN, host, and one additional multiply imaged galaxy with a secure redshift used as model constraints (Supplemental Table 3). The filters used to generate the color image are as in Fig. 1, and tick marks are separated by 10 arcsec.

### Extended Data Fig. 2 The position of AT 2016jka in color-magnitude space.

Colored points show simulated photometry for normal SNe of Type Ia (red), Type Ib/Ic (gold), and Type II (green), with 10,000 simulated SNe in each subclass (not all apparent on this plot). Histograms above and below show the marginalized distributions that have been rescaled to represent posterior probability density functions. They are normalized to integrate to unity, then multiplied by the SN subclass priors based on the host galaxy stellar population (row b in Supplementary Table 2). Open markers show the observed photometry of the SN. Dotted vertical lines mark the magnification correction based on the preferred LENSTOOL model (model E, described in Methods: Lens Modeling). Closed markers show the resulting magnification-corrected photometry, with asymmetric error bars reflecting the systematic uncertainty derived from the five lens model variants. Horizontal error bars in the upper panel indicate the observed uncertainty in the SN color (not affected by lensing). The relevant SN photometry markers are repeated in the histogram side-panels with arbitrary vertical positions. All three SN images are located in regions of color-magnitude space that are expected to be dominated by Type Ia SNe.

### Extended Data Fig. 3 A representative set of light curve and color curve models from the STARDUST2 classification algorithm.

Panels a-f show F105W and F160W, as indicated, plotting the model light curves in black and photometry as red markers. Panels g-i show the F105W-F160W color curves and color data. All data points as shown have been corrected for magnification and shifted in time using the preferred LENSTOOL model (model E, described in Methods: Lens Modeling). Plotted error bars include the measurement uncertainty and the lens modeling magnification uncertainty. Data points in the right column also include this magnification uncertainty, even though cluster-scale lensing is achromatic, because the STARDUST2 analysis was done on the light curve data, not the color data directly. In all panels the first data point is SN image 2, followed by image 1 and image 3. In each panel the black curves show 200 SN light curve models drawn at random from the nested sampling sequence of the STARDUST2 (sncosmo) classification.

### Extended Data Fig. 4 Color-based age constraints for AT 2016jka.

Constraints are shown separately for Image SN1 (panels a and b), image 2 (c and d), and image 3 (e and f), using the methodology described in Methods: Color Curve Age Constraints. Large lower panels (b, d and f) show the observations and model fits. Each magenta shaded region shows the 1σ range of the measured F105W-F160W color, which corresponds to a U-V color in the rest-frame. The model fits are shown as grey shaded regions, indicating the 68% confidence interval of the best-fit SALT2 color curve, with the median model shown as a solid line. The small upper panels (a, c and e) show the posterior for the age of each image from SNTD, using a prior on the SALT2 color parameter (c) based on known population characteristics of SNIa. The effect of adding this prior is slight, with no significant deviation from the best-fit value of $$c = 0.02_{-0.05}^{+0.04}$$.

### Extended Data Fig. 5 Marginalized and joint posterior distributions for the color curve age constraints measured in this analysis.

Two-dimensional plots show MCMC sampling points as discrete dots, with contours for the high density regions, drawn at 0.5, 1, 1.5 and 2σ levels. Marginalized (1D) distributions are shown at the top of each column, with dashed vertical lines at the mean and ± 1σ (marking 16%, 50% and 84% levels). We use a weak prior on the SALT2 color parameter (c), and set the SALT2 stretch parameter (x1) to 0. This method is fully independent of lens modeling. The table in the upper right lists all priors, observations, and lens model information used for SN age estimates in this work. Only the highlighted components were used for the constraints shown here.

### Extended Data Fig. 6 Light-curve-based age constraints for AT 2016jka.

Constraints are shown separately for Image SN1 (panels a and b), image 2 (c and d), and image 3 (e and f), using the methodology described in Methods: Light Curve Age Constraints. Large lower panels (b, d and f) show the observations and model fits. Each orange shaded region shows the 1σ range of the measured F160W magnitude after lens model correction (see Table 1), which corresponds to roughly V band in the rest-frame. The model fits are shown as grey shaded regions, indicating the 68% confidence interval of the best-fit SALT2 light curve, with the median model shown as a solid line. Small upper panels (a, c and e) show the posterior distributions from SNTD for the age of each image that is independent of the lens model (magenta, same as Extended Data Figure 7), using the preferred lens model E (light blue), and the combination of both methods (orange).

### Extended Data Fig. 7 Marginalized and joint posterior distributions for the final age constraints measured in this analysis.

Two-dimensional plots show MCMC sampling points as discrete dots, with contours for the high density regions, drawn at 0.5, 1, 1.5 and 2σ levels. Marginalized (1D) distributions are shown at the top of each column, with dashed vertical lines at the mean and ± 1σ (marking 16%, 50% and 84% levels). We use the color curve posterior as the prior for light curve fitting with lens model E, and include weak priors on the absolute magnitude of a SNIa (MB) and the SALT2 color parameter (c), and set the SALT2 stretch parameter (x1) to 0.

## Supplementary information

### Supplementary Information

Supplementary Tables 1–6, Figs. 1 and 2 and Notes.

## Source data

### Source Data for Fig. 2

Measured photometry of the transient AT 2016jka, and predicted magnifications and time delays for the AT 2016jka images, from all lens model variants.

### Source Data for Extended Data Fig. 1

Locations for components of the LENSTOOL mass model of MACS J0138.

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Rodney, S.A., Brammer, G.B., Pierel, J.D.R. et al. A gravitationally lensed supernova with an observable two-decade time delay. Nat Astron (2021). https://doi.org/10.1038/s41550-021-01450-9

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• ### Back to the future with a supernova

• Anupreeta More

Nature Astronomy (2021)