SN REFSDAL: CLASSIFICATION AS A LUMINOUS AND BLUE SN 1987A-LIKE TYPE II SUPERNOVA

Refsdal (1964) first considered the possibility that a gravitational lens might create multiple images of a background supernova (SN) explosion. He showed that the time delays between the images of the SN should depend on the distribution of matter in the lens and, geometrically, on the cosmic expansion rate. In Kelly et al. (2015b), we reported the first example of a strongly lensed SN resolved into multiple images, which we found in near-infrared (NIR) Hubble Space Telescope (HST) WFC3 exposures of the MACS J1149+2223 cluster (Ebeling et al. 2001) taken as part of the Grism Lens-Amplified Survey from Space (GLASS; PI T. Treu; GO-13459; see Schmidt et al. 2014; Treu et al. 2015). The data revealed a total of four images of the SN in an Einstein cross surrounding an early-type galaxy in the cluster. Here we use photometry and spectroscopy from the first year after discovery to classify the SN and characterize its basic properties.

The explosion site of SN Refsdal is close to the tip of a spiral arm of a galaxy at redshift z = 1.49 (Smith et al. 2009), which is inclined at an angle i = 45 ± 10° (Yuan et al. 2011) and is multiply imaged (Zitrin & Broadhurst 2009) by the potential of the massive MACS J1149+2223 cluster ((1.4 ± 0.3) × 10¹⁵ M_⊙; Applegate et al. 2014; Kelly et al. 2014; von der Linden et al. 2014) at z = 0.54. The cluster lens forms three images of the SN host galaxy that include the explosion site of the SN.

Light that travels toward us on a direct route through the center of the cluster arrives last owing to the greater spatial curvature and gravitational time dilation near the center of the potential (see Treu & Ellis 2015 for a review). In Kelly et al. (2015b), we predicted that the 2014 appearances were only the next-to-last arrival and that the SN would reappear within several years closer to the center of the cluster. Modeling efforts (Diego et al. 2015; Oguri 2015; Sharon & Johnson 2015) sought to make more precise predictions by collecting improved data sets (Grillo et al. 2016; Jauzac et al. 2016; Kawamata et al. 2015; Treu et al. 2016). An imaging campaign with HST (PI P. Kelly; GO-14199) detected the predicted reappearance on December 11, 2015 (UT dates are used throughout this paper; Kelly et al. 2015a), and deep follow-up images will measure the relative time delay with 1%–2% precision.

Either a thermonuclear SN Ia or a core-collapse SN provided a reasonable match to the light curve and colors of SN Refsdal during the first month after discovery, which was made on 2014 November 11. After a 1 hr Keck-I MOSFIRE observation (PI C. Steidel) was not able to detect the SN, an HST Director's Discretionary (DD) time program was carried out from 2014 December 23 through 2015 January 5 (PI P. Kelly; GO-14041) to acquire WFC3 spectra. Instead of fading as would have been expected for a SN Ia, SN Refsdal continued a slow rise in brightness, which made ground-based NIR spectroscopy possible near the peak of the light curve. We obtained Very Large Telescope (VLT) X-shooter spectra through an ESO DD program (PI J. Hjorth; 295.D-5014) in 2015 May and June, approximately six months after discovery. Keck-II DEIMOS observations taken in 2015 December, March, and May yielded no detection of the SN at optical wavelengths.

Here we show that the spectra and light curve of SN Refsdal are consistent with those of SN 1987A-like SNe, whose prototype was the best-studied SN explosion in recent history. A companion paper (Rodney et al. 2016) presents measurements of the relative time delays and magnifications of the four images in the Einstein cross, and magnitudes measured using point-spread-function (PSF) fitting photometry. In Section 2, we describe the MOSFIRE, DEIMOS, HST grism, and X-shooter spectra that we have collected. The photometric classification of the light curve is discussed in Section 3. Section 4 presents an analysis of the SN spectra, and Section 5 contains measurements of the host-galaxy environment. We summarize the results in Section 6. The methods that we use to process and extract spectra of SN Refsdal, compute K-corrections of photometry of SN Refsdal, and a comparison with the spectra of superluminous SNe (SLSNe) are presented in the Appendix.

2.1. Keck-I MOSFIRE Spectra

On 2014 November 23, approximately two weeks after discovery, we obtained a 1 hr H-band integration with the Multi-Object Spectrometer for Infrared Exploration (MOSFIRE; McLean et al. 2010, 2012) mounted on the 10 m Keck-I telescope. As we show in Figure 1, a 07 wide slit was oriented at position angle (PA) 10968 to place the slit across both images S1 and S2. The resolving power of the setup was R = 3660 in the H band (1.48–1.81 μm), chosen to be able to have sensitivity to Hα emission at the redshift (1.49) of the face-on spiral galaxy. Table 1 provides an overview of the MOSFIRE observations.

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Table 1.  Details of Keck-I MOSFIRE Observations

Date	F160W AB	α(J2000)	δ(J2000)	Position	Para.	Airmass	Total	Slit	Seeing
(MJD)	(±0.1 mag)			Angle	Angle		Exp. (s)	Width
56984	∼25.45 (S1); ∼25.5 (S2)	11:49:35.574	+22:23:44.06	10968	82°	1.56	3578.8	07	07a

Notes. Magnitudes listed are total and do not account for slit losses, and are extrapolated from the first F160W observations by ∼6 days in the observed frame (∼2.5 days in the rest frame). Observations were acquired in a sequence of thirty 119.29 s exposures.

^aDetermined from the J-band image; the FWHM in the H band should be smaller.

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The data were obtained using mask nodding in thirty 119.29 s exposures, split evenly between integration at positions A and B separated by 12'' along the slit in an alternating sequence, for a total integration of 3578.8 s. The full width at half-maximum (FWHM) intensity of the J-band PSF was estimated to be 07 during the observations, and the H-band FWHM is expected to have smaller size. The data were reduced using the MOSFIRE Data Reduction Pipeline.²¹

We extract the spectra of images S1 and S2 using a 4 pixel (072) width aperture centered on the expected positions of the images of the SN. The locations of S1 and S2 show narrow nebular emission from the host galaxy.

2.2. Keck-II DEIMOS Data

2.3. HST G141 Grism Spectra

2.4. HST Light Curves

2.5. VLT X-shooter Spectra

Data were acquired with the X-shooter echelle spectrograph (Vernet et al. 2011) mounted on Unit Telescope 2 (UT2) of the VLT in three observation blocks (OBs) executed on 2015 May 16 (OB1), June 15 (OB2), and June 16 (OB3). X-shooter covers the entire spectral range 3100–25000 Å by directing incoming light simultaneously to three arms with complementary wavelength coverage. The observations of SN Refsdal were taken in nodding mode where positions A and B were separated by 7'' along the slit.

The fraction of light from a well-centered point source that enters a spectrograph slit depends on the slit width and the FWHM of the PSF. From an R-band acquisition image, we can directly estimate the PSF FWHM through X-shooter at the beginning of each OB. The European Southern Observatory (ESO) Ambient Conditions Database²² archives an estimate of the seeing at Cerro Paranal from the differential image motion monitor (DIMM). However, the DIMM seeing differs, in general, from the seeing achieved through X-shooter. The DIMM shows that conditions changed significantly during each of the three OBs.

In Table 2, we list estimates for the average seeing during each OB. We measure the seeing through X-shooter at the beginning of the OB from the FWHM of stars in the acquisition image. We then find the average FWHM recorded by the DIMM during the entire OB, and rescale this average value by the ratio between the DIMM FWHM at the start of the OB and the FWHM measured from the X-shooter acquisition image. The DIMM PSF measured a degradation from a FWHM of ∼08 to ∼16 and then settling at ∼14 over the course of the OB1 observations. During the OB2 observation, the seeing gradually improved from ∼075 to ∼065. During the OB3 observation, the seeing evolved from ∼07 to ∼09 to ∼08.

An overview of the observations is given in Table 3, and we show the slit positions in Figure 1. Observations of SN Refsdal were acquired at a high airmass almost orthogonal to the parallactic angle, so we need to consider carefully the effects of atmospheric dispersion (Filippenko 1982). The telescope tracks the target in images taken at 4700 Å, and a tip-tilt mirror corrects for the atmospheric refraction between 4700 Å and the middle of the atmospheric dispersion range for the NIR arm at 13100 Å. Since the atmospheric dispersion in the NIR is comparatively small, X-shooter does not have an atmospheric dispersion corrector (ADC) to correct the NIR arm. The relative shift between 13100 Å and Hα (∼16330 Å) is expected to be only ∼01. The relative atmospheric dispersion across the visible (VIS) arm is greater, and the ADC is not operational. We expect a ∼05 shift at [O ii] (∼9274 Å) relative to 4700 Å, the tracking wavelength where the target is centered on the slit. The slit width in the VIS spectroscopic arm is 09 for OB1 and 12 for OB2 and OB3. We test that the emission-line ratios in the NIR arm are not significantly affected by comparing spectra from OB1 and OB2 to OB3, for which the PA was closer to the parallactic angle.

Table 2.  Seeing During X-shooter Observation Blocks

OB	Acquisition Image	Estimated Average
	(FWHM)
1	069	100
2	062	07
3	054	09

Note. To estimate the seeing at the beginning of each OB, two bright stars in the acquisition image are fit with a two-dimensional Gaussian. For all observations a significant worsening of the seeing occurred during the observations. To estimate the average seeing during each OB, we scale the average DIMM seeing by the difference between the measured FWHM in the acquisition images and the DIMM FWHM recorded at the beginning of the OB.

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Table 3.  Details of VLT X-shooter Observations

OB	Date	$F160W$ AB	α(J2000)	δ(J2000)	Position	Para.	Airmass	Total	NIR Slit
	(MJD)	(±0.1 mag)			Angle	Angle		Exp. (s)	Width
1	57158	24.75 (S1); 24.47 (S2)	11:49:35.520	+22:23:44.44	1082	175°	1.47	4800	06
2	57188	24.75 (S1); 24.60 (S2)	11:49:35.511	+22:23:44.65	1082	165°	1.51	4800	09
3	57189	24.60 (S2); 24.60 (S3)	11:49:35.406	+22:23:44.40	516	162°	1.53	4800	09

Note. Magnitudes listed are total and do not account for slit losses. Observations were acquired in a sequence of four 1200 s exposures.

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Table 4.  Predicted Magnifications

Model	μS1	${\mu }_{{\rm{S}}2}$	μS3
Kelly et al. (2015b)	∼10	∼10	∼10
Oguri (2015)	15.30	17.66	18.29
Sharon & Johnson (2015)	${18.5}_{-4.5}^{+6.4}$	${14.4}_{-5.5}^{+7.5}$	${20.5}_{-3.9}^{+19.1}$
Grillo et al. (2016) (G12F)	${16.0}_{-5.7}^{+1.4}$	${14.3}_{-6.4}^{+4.5}$	${15.2}_{-4.9}^{+4.0}$
Jauzac et al. (2016)	22.4 ± 2.0	18.9 ± 2.3	19.7 ± 1.7
Kawamata et al. (2015)	${15.4}_{-1.6}^{+1.6}$	${17.7}_{-2.0}^{+2.0}$	${18.4}_{-2.0}^{+2.0}$

Note. Magnifications of images S1–S3 (for which we have spectra) predicted by models of the combined gravitational potential of the early-type galaxy and the MACS1149 galaxy cluster lenses.

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During the first three months of observations after discovery on 2014 November 11, SN Refsdal continued to rise in brightness well beyond the time where any normal SN Ia, Ib, or Ic would have reached its peak luminosity (Kelly et al. 2015b). Continued monitoring showed that the light curve rose for ∼150 days, and the SN became similarly incompatible with most normal SN II light curves, which brighten to a "luminosity plateau" over only several days to weeks in the rest frame (Barbon et al. 1979; Doggett & Branch 1985). In Figure 2, we plot a comparison between the full SN light curves for S1–S4 against the light curves of a typical SN Ia (SN 1994D), SN Ib/c (SN 1994I), SN IIP (SN 1999em), and SN IIn (SN 1998S).

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To identify potential matches to the light curve of SN Refsdal, we have performed an extensive search of published SN photometry. While SLSNe have a very small volumetric rate (Quimby et al. 2013), they can exhibit light curves whose peaks are broad (e.g., SN 2008es; SN 2013hx; Miller et al. 2009; Inserra et al. 2016). However, as we show in the Appendix, the equivalent width of Hα emission from SLSNe is substantially too small to match that of SN Refsdal. Furthermore, for the expected magnification listed in Table 4 (μ ≈ 15), SN Refsdal would have an absolute V-band magnitude of −16.9 ± 0.1, while SLSNe have absolute magnitudes of ≲−21. A high extinction (A_V ≳ 3.5 mag) would allow a sufficient luminosity, but the corresponding reddening would require the SN to be significantly more blue than known SLSNe. Even without lensing magnification, SN Refsdal would have an absolute V-band magnitude of only −19.8 ± 0.1.

The slow rise in brightness of SN Refsdal to a broad peak is consistent with the light curve of SN 1987A, a peculiar SN II in the Large Magellanic Cloud (LMC) that is the nearest and brightest SN observed in the last four centuries (Arnett et al. 1989, and references therein). After excluding SLSNe on the basis of their Hα emission, luminosity, and color, only SN 1987A-like SNe as well as a single example of a SN IIn (SN 2005cp) provide approximate matches to the light curve of SN Refsdal.

SN 1987A brightened steadily in the rest-frame optical after initial emission from the shock breakout subsided to reach peak luminosity ∼84 days after first light; see Figure 3 of Filippenko (1997) for a comparison with the light curve of a typical SN IIP. The progenitor of SN 1987A was identified as a blue supergiant (Sk −69°202; Gilmozzi et al. 1987; Sonneborn et al. 1987) in the LMC (d ≈ 50 kpc), and more recent SNe with similar light-curve shapes and spectra are understood to be the result of the explosions of these compact massive stars. Well-studied examples of nearby SN 1987A-like events include SN 1998A (Pastorello et al. 2005), SN 2000cb and SN 2005ci (Kleiser et al. 2011), SN 2006V and SN 2006au (Taddia et al. 2012), and SN 2009E (Pastorello et al. 2012). These show a wide range of light-curve shapes and colors, explosion energies, and expansion velocities (e.g., Pastorello et al. 2012; Taddia et al. 2012).

In a search of SNe IIn with published photometry, we found a single example, SN SN 2005cp (Kiewe et al. 2012), that shows a light curve similar to that of SN 1987A. SNe IIn are characterized by relatively narrow H emission lines originating in the interaction between the expanding ejecta and pre-existing circumstellar material (CSM; e.g., Filippenko 1997). The interaction produces narrow Balmer emission and can power a strong underlying continuum.

In Figure 3, we compare the F160W (rest-frame ∼R-band) light curves of the four SN Refsdal images with the R-band light curves of SN 1987A-like SNe (PTF 12gcx, SN 2006V, NOOS-005, SN 1987A) and the Type IIn SN 2005cp. The broad-peaked shapes of the light curves of PTF 12gcx and NOOS-005 provide the best matches to that of SN Refsdal. The PTF 12gcx light curve from Taddia et al. (2016) has dense sampling for 50 days after discovery followed by a 42 day gap in coverage which likely spans the date of maximum brightness. However, the substantial flattening of the light curve before the gap in coverage (see Figure 4 of Taddia et al. 2016) strongly indicates that it has a broad, flat peak similar to that of SN Refsdal.

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NOOS-005 was one of the events considered likely to be a SN 1987A-like SN by Pastorello et al. (2012), although its light curve was measured only in the I band and no spectra were taken. Its I-band absolute magnitude (M_I = −17.51 mag) would make it one of the most luminous of SN 1987A-like SNe. For the purpose of computing time delays among the images of SN Refsdal forming the Einstein cross, Rodney et al. (2016) used the light curves of several SN 1987A-like SNe as templates for fitting the multiple light curves of SN Refsdal.

In Figure 4, we show that SN Refsdal has a $F125W-F160W$ ($\sim V-R$ in the rest frame of the SN) color comparable to those of nearby SN 1987A-like SNe. At an early phase, SN Refsdal has a $F105W-F125W$ ($\sim B-V$) color comparable to those of SN 2006V and SN 2006au, the bluest SN 1987A-like SN, but near maximum brightness the color of SN Refsdal is blue in comparison to even SN 2006V and SN 2006au. At almost all epochs and in both colors, SN 2005cp is bluer than SN Refsdal. Here we have applied K-corrections to the extinction-corrected colors of the comparison sample (see Table 6). We apply no correction for possible dust extinction to the colors of SN Refsdal, since the low signal-to-noise ratio (S/N) or low resolution of the spectra do not allow any constraint on absorption by, for example, Na I D or diffuse interstellar bands.

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Table 6.  Nearby Supernovae with SN 1987A-like Light Curves

SN	Host	Milky Way	D	R- or r-band	Spectroscopy	Photometry
	$E(B-V)$ (mag)	$E(B-V)$ (mag)	(Mpc)	Max. (MJD)	Data Set	Data Set
SN 1987A	0.13 (1)	0.06 (2)	0.50 ± 0.005	46933.10 ± 1.0	3	4
SN 1998A	∼0 (5)	0.12	33 ± 10	50885.10 ± 3.9	5	6
SN 2005cp	0.02 (6)	0.03	120 ± 9.9	53581	7, 8	7
SN 2006V	∼0 (7)	0.029	72.7 ± 5	53824.23	9	9
SN 2006au	0.141 (8)	0.172	46.2 ± 3.2	53866.25	10	10
SN 2009E	0.02 (8)	0.02	29.97 ± 2.10 (8)	54927.8 ± 2.8	10	10
PTF 12gcx	∼0 (11)	0.045	198.3 ± 3.7	56133.2	11	11

Note. Publications containing data used for comparison. Many of the spectra were retrieved from WISEREP (http://wiserep.weizmann.ac.il/) (Yaron & Gal-Yam 2012). Welty et al. (2012) (1); Staveley-Smith et al. (2003) (2); Hamuy & Suntzeff (1990) (3); Phillips et al. (1988) (http://www.physics.unlv.edu/~jeffery/astro/sne/spectra/d1980/sn1987a/) (4); Phillips et al. (1990) (ftp://ftp.noao.edu/sn1987a) (5); Pastorello et al. (2005) (6); Kiewe et al. (2012) (7); Silverman et al. (2012) (8); Taddia et al. (2012) (9); Pastorello et al. (2012) (10); Taddia et al. (2016) (11). Distances taken from NASA/IPAC Extragalactic Database (https://ned.ipac.caltech.edu/) except if another citation is provided. Milky Way extinction from Schlafly & Finkbeiner (2011), except for the case of SN 1987A in the LMC.

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For the sample of SN 1987A-like SNe included in Pastorello et al. (2012), the SNe show a range of absolute magnitudes (in the V, R, and I bands) in an approximate range −15 to −17.5 mag. In Figure 5, we show that SN Refsdal may have bluer B − V and V − R colors near maximum light than the comparison sample of SN 1987A-like SNe. The magnifications predicted for sources S1, S2, and S3 are listed in Table 4. From its M_B and M_V absolute magnitudes, SN Refsdal would be one of the most luminous of the low-redshift SN 1987A-like SNe. For a peak magnitude of $F160W\approx 24.2$ mag AB (see Rodney et al. 2016), SN Refsdal would have had M_R = −16.9 mag for an assumed magnification of μ = 15.

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Taddia et al. (2016) found that PTF 12gcx reached an r-band peak on approximately 2012 August 14. The only photometric constraint on its color is from imaging taken more than three weeks after peak. To estimate the B − V and V − R colors of PTF 12gcx near peak, we instead average synthetic magnitudes measured from a Palomar 5 m spectrum taken on 2012 July 26 (B − V = 1.13 mag; $V-R=0.63$ mag) and a low-S/N Lick 3 m spectrum taken on 2012 August 23 ($B-V=0.77$ mag; $V-R=0.52$ mag). The gri photometry acquired on 2012 September 7 and 8 favor a redder g − r color ($g-r=1.4\pm 0.3$) than the synthetic magnitudes ($g-r=0.8$–1.1), but the r − i colors are in approximate agreement ($r-i\approx 0.3$–0.5). SN 2006V and SN 2006au were observed in the r band and not in the R band, so we used available spectra as close as possible to maximum light to compute the expected color conversion and find $(V-R)-(V-r)\approx 0.16$ mag for both SNe.

The light curve and colors of SN Refsdal can be matched approximately by those of SN 1987A-like SNe II or, alternatively, SN 2005cp. We next use the WFC3 grism and the VLT X-shooter spectra to confirm the Type II classification spectroscopically by identifying strong Hα emission. We find compelling evidence for broad and deep absorption by Hα and Na I D, and these features identify SN Refsdal as a SN 1987A-like SN without strong circumstellar interaction.

Figure 6 plots the binned WFC3 grism spectra of SN Refsdal taken in both the 111° and 119° telescope orientations at an average phase of −47 ± 8 days relative to maximum light. We plot the weighted average of the raw flux measurements (each 20 Å) within each 100 Å wavelength bin, and show an uncertainty computed using bootstrapping with replacement. We show, for comparison, a spectrum of SN 1987A obtained at −41 days, of SN 1998A at −40 days (Pastorello et al. 2005), of SN 2006V at −25 days, and of SN 2006au at −19 days (Taddia et al. 2012). These spectra are scaled so that F160W = 25.1 mag AB, the average flux of SN Refsdal during the grism observations.

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In Figure 7, we plot the wavelength region 8195–10280 Å (5500–6900 Å in the rest frame) of the WFC3 G141 grism (−47 ± 8 days) and the VLT X-shooter (+16 ± 8 days) spectra. This spectral range shows strong, broad Hα absorption which is present in SN 1987A-like SNe and absent from SNe IIn, including SN 2005cp. Similarly, both the grism and X-shooter spectra show strong, broad Na I D absorption features. The spectrum of SN 2005cp (−14 days) plotted for comparison with the grism data contains no similar substantial feature near Na I D. While the post-maximum spectrum of SN 2005cp (+18 days) plotted for comparison with the VLT spectrum may contain a feature near Na I D, its minimum is not as deep as that present in the spectrum of SN 2006V and its shape does not appear to provide a good match to the VLT data.

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Figure 8 shows fits of the comparison SN spectra to the WFC3 grism spectrum restricted to respective wavelength regions bracketing Na I D and Hα. We vary the normalization of each comparison spectrum to find the best χ² agreement. The Akaike information criterion (AIC; Akaike 1974) yields very strong positive evidence that the SN 1987A-like SNe, which contain prominent Na I D and Hα absorption features, provide a better model than a spectrum of SN 2005cp. A change of 2 in the AIC gives evidence against the model having a greater AIC value, while a difference of 6 constitutes strong evidence (e.g., Kass & Raftery 1995; Mukherjee et al. 1998).

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Despite careful reduction and analysis of the X-shooter spectra, its background contains features we are not able to model. Therefore, we restrict statistical analysis of the X-shooter data to the spectral region containing Hα, which is expected to show stronger absorption than Na I D. In Figure 9, we compare the X-shooter data with spectra of SN 1987A-like SNe as well as SN 2005cp at a similar phase and calculate the χ² agreement within the wavelength range 15000–17000 Å surrounding Hα. We use the spectrum of an Sc galaxy redshifted to z = 1.49 (spiral host galaxy) as a model for the galaxy light, and vary its normalization to find the best match to the data. Using the spectrum of an S0 galaxy at z = 0.54 (early-type galaxy lens) yields almost identical results. All of the low-redshift comparison spectra are corrected for the Milky Way and host-galaxy extinction values listed in Table 6.

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4.1. Hα P-Cygni Absorption

A strong and wide Hα P-Cygni absorption feature is present in the spectra SN 1987A-like SNe II but absent from the spectra of SNe IIn. In SN 1987A-like SNe, the characteristic broad and deep P-Cygni absorption develops as the photosphere recedes into the ejecta. By constrast, the ejecta of SNe IIn collide with CSM and the photosphere generally forms in proximity to the heated, shocked material.

First, we smooth the SN spectrum using a σ = 2000 km s⁻¹ Gaussian kernel and variance weighting. After removing >5σ outliers from the data, we resmooth the spectrum with outliers removed using the same kernel. We search the smoothed spectrum across the wavelength range 15300–16100 Å to find the absorption minimum.

To determine the uncertainty of the wavelength of the absorption minimum, we use boostrap resampling. For the grism and X-shooter spectra, we assemble the set of all flux measurements at each wavelength taken in both orientations or in all combinations of OBs and SN images, respectively. We resample these sets of measurements with replacement to create the full set of bootstrapped spectra.

The distribution of absorption minima we measure from the bootstrapped WFC3 grism spectra is approximately Gaussian. After rejecting a small population of >5σ outliers, we find an absorption minimum of −8356 ± 1105 km s⁻¹ (15880 ± 60 Å). In contrast, the distribution of absorption minima we measure from the bootstrapped X-shooter spectra has a bimodal shape and is substantially broad, stretching over ∼15650–16050 Å. After removing a small number of outlying measurements close to 15300 Å, we constrain the absorption minimum to be −6465 ± 2918 km s⁻¹ (15983 ± 159 Å).

We next perform a data-driven simulation of the WFC3 grism spectrum to determine the statistical significance of finding the absorption feature we identify. As a first step, we smooth the grism spectrum using a σ = 2000 km s⁻¹ Gaussian kernel, and calculate the residuals of the data from the smoothed spectrum in the wavelength range 14000–16100 Å. Each simulated spectrum is created by replacing the flux at each wavelength in the grism spectrum with a randomly drawn value from the distribution of residuals.

With 10,000 simulated spectra, we compute a test statistic that measures the strength of the absorption relative to the continuum. To estimate the continuum level, we calculate $\mathrm{median}({f}_{1.45-1.55})$, the median flux in the wavelength range 14500–15500 Å. We next calculate $\mathrm{median}({f}_{\,\mathrm{absorp}}^{{\rm{H}}\alpha })$, the median flux within ±150 Å of the absorption minimum which corresponds to the 2–3σ width of SN 1987A-like SN Hα absorption features (see Figure 10). The difference,

$$\begin{eqnarray}&&{{\rm{\Delta }}}_{\mathrm{absorp}}=\mathrm{median}({f}_{\,\mathrm{absorp}}^{{\rm{H}}\alpha })-\mathrm{median}({f}_{1.45-1.55}),\end{eqnarray} \tag{ 1 }$$

is used as the test statistic to compute a p value. For the grism spectrum, we measure ${{\rm{\Delta }}}_{\ \mathrm{absorp}}^{\mathrm{grism}}=(-2.5\pm 0.9)\times {10}^{-20}$ erg s⁻¹ cm⁻² Å⁻¹. We compute the probability of finding a lesser value ${{\rm{\Delta }}}_{\mathrm{absorp}}^{\mathrm{grism}}$ by random chance using the spectra we simulate. We compute p = 0.004, which provides statistically significant evidence against the hypothesis that the apparent Hα absorption in the grism spectrum is a random artifact.

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Given the width of the Hα absorption line and p = 0.004 significance, we would not expect any other similarly strong absorption feature, and none exists in the range 14000–16100 Å. If we instead extend the wavelength range used in the analysis blueward to 11500–15500 Å, then the p-value increases to ∼0.02. Simulating grism spectra by repeatedly randomly drawing from residuals does not model any covariance in the random noise, although we do not expect a strong covariance.

In the case of the X-shooter spectra, the wavelength of the absorption minimum is poorly constrained, so it is not possible to apply the same statistical test. For the purpose of completeness, however, we calculate the p value for an absorption feature located at 15983 Å, the median of the absorption minima measured from the bootstrapped spectra. The continuum is measured as the median of the spectral regions 15300–15600 Å and 16500–17000 Å. We calculate p = 0.800, but note that 15983 Å does not coincide with either peak of the bimodal distribution of minima measured from the bootstrapped spectra.

4.2. Hα Expansion Velocity Evolution

4.3. Models of the Hα Emission and Absorption Profiles

The Hα emission from SNe IIn generally exhibits a Lorentzian profile that arises from Thompson scattering of photons off of free electrons (Chugai 2001; Smith et al. 2010), while Doppler broadening of Hα emission from SN 1987A-like SNe instead produces approximately Gaussian profiles. Since the line shape contains information about the SN spectroscopic type, we examine which functional form better fits the grism and X-shooter spectra. As shown in Figures 10 and 12, we also model the grism spectrum with a P-Cygni profile including an absorption feature. Our simple model for the P-Cygni absorption consists of two Gaussians, where the difference between their respective centers is set to be equal to twice the sum of their standard deviations.

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The model fits provide strong evidence favoring a Gaussian profile over a Lorentzian profile, and very strong evidence for a P-Cygni model for the WFC3 grism spectrum. In Table 5, we list the differences in the AIC to interpret the differences in the χ² statistics. The AIC penalizes models having a greater number of parameters. A Gaussian model for the absorption feature in the grism spectrum yields a ∼4300 km s⁻¹ FWHM.

4.4. Measurements of the Hα Line Profile and Flux

In Figure 13, we compare the total Hα luminosity of SN Refsdal at −62 ± 8 days, −47 ± 8 days, and +16 ± 8 days with the Hα luminosity of SN 1987A-like SNe, as well as SN 2005cp. We measure an upper limit from the MOSFIRE spectrum by fitting for the total flux of a Gaussian profile with σ = 900 km s⁻¹ for bootstrapped samples using replacement. Before fitting, we remove the background level by fitting it with a linear function. To account for the effect of structure in the background, we shift the center of the Gaussian profile by a random number within 500 Å of the host-galaxy Hα emission. This yields a 3σ upper limit of $1.5\times {10}^{-17}$ erg s⁻¹ cm⁻², which is in approximate agreement with that expected given the MOSFIRE exposure-time calculator.²³

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Using bootstrap resampled spectra and fitting a Gaussian model, we measure ${1.1}_{-0.6}^{+0.6}\times {10}^{-17}$ erg s⁻¹ cm⁻² and 2.91 ${}_{-0.5}^{+0.5}\times {10}^{-17}$ erg s⁻¹ cm⁻² fluxes from the WFC3 grism and VLT X-shooter spectra, respectively. In these cases, we measure and subtract the background level in adjacent apertures.

The inferred strength and statistically significant change in the Hα emission are consistent with the characteristics of Hα emission from SN 1987A-like SNe. We adopt a fiducial magnification of μ = 15 when estimating the Hα luminosity. The plotted gray line shows the systematic shift in the inferred luminosity corresponding to a change in magnification from μ = 10 to μ = 20 (see Table 4).

4.5. Constraint on the SN Ejecta Mass

4.6.  Superfit Analysis of the Grism Spectrum

Since the progenitor of SN 1987A was identified as a blue supergiant star (Gilmozzi et al. 1987; Sonneborn et al. 1987), the precursors of SN 1987A-like SNe are believed to be similar—compact, short-lived, massive stars. The properties of the emitting gas near the explosion site of SN Refsdal measured from strong nebular lines should be similar to the properties of the gas that formed the massive progenitor of SN Refsdal. To measure the host-galaxy narrow-line emission, we reduce the spectra in "stare mode" where we do not subtract the off-target spectra. This allows us to avoid subtracting any narrow-line emission from sources in the off-target position which can have bright emission lines. We list the narrow-line measurements in Tables 8 and 9 and the inferred extinction and properties of the ionized gas in Table 10.

Table 10.  Host-galaxy Measurements

Measurement	Nuclear Region	SN Site	Instrument
12 + log(O/H) (PP04 N2)	...	8.3 ± 0.1 dex	MOSFIRE
12 + log(O/H) (PP04 N2)	8.6 ± 0.1 dex	8.4 dex (3σ upper limit)	X-shooter
$E(B-V)$	0.1 ± 0.2 mag	0.8 ± 0.4 mag	X-shooter
AHα	0.2 ± 0.3 mag	1.5 ± 0.9 mag	X-shooter
AV	0.3 ± 0.4 mag	2.0 ± 1.0 mag	X-shooter

Note. Properties of the ionized gas near the SN explosion site and in the host-galaxy nuclear region, as well as reddening along the line of sight from analysis of strong nebular emission lines.

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As Figure 14 shows, we detect strong nebular emission both near the SN explosion site and from the nuclear region of the host galaxy. The emission from the nuclear region has a significantly broader profile, which we attribute to the rotational motion of the gas. From the best-fit line centers, we measure redshifts of 1.48831 ± 0.00007 from the spectrum extracted around the SN position and 1.48837 ± 0.00007 for the nuclear region, where the uncertainties include contributions from both line fitting and the wavelength solution.

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To constrain the source of the ionizing radiation and properties of the emitting gas, we construct a Baldwin, Phillips, & Terlevich (BPT; Baldwin et al. 1981) diagram, plotted in Figure 15. The intensity ratios [O iii]λ5007/Hβ and [N ii]λ6584/Hα of the strong emission lines from near the SN site and the nuclear region are consistent with the ratios expected for gas ionized by radiation from massive stars, and the positions on the BPT diagram coincide with the Sloan Digital Sky Survey (SDSS; Thomas et al. 2013) star-forming galaxy population.

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We next estimate the reddening along the line of sight to the emitting gas from the measured Balmer decrement. Making the assumption of Case B recombination, we apply the prescription from Domínguez et al. (2013) and adopt the R_V = 2.51 Reddy et al. (2015) extinction curve inferred from MOSFIRE Deep Evolution Field spectroscopy of galaxies at z ≈ 1.4–2.6. We estimate a color excess of $E(B-V)=0.1\pm 0.2$ mag (${A}_{V}=0.3\pm 0.4$ mag) for the nuclear region and $E(B-V)=0.8\pm 0.4$ mag (${A}_{V}=2.0\pm 1.0$ mag) near the SN site. In Table 10, we also list the extinction expected for Hα.

SN Refsdal occurred at an offset from its host galaxy's nucleus of ∼7 kpc, and Yuan et al. (2015) used OSIRIS (Larkin et al. 2006) integral-field-unit observations to constrain the oxygen abundance at ∼5–7 kpc to be 12 + log(O/H)${}_{\mathrm{PP}04{\rm{N}}2}\,\leqslant \,$ 8.11 dex by comparing an upper limit on the [N ii] emission to the measured Hα flux using the Pettini & Pagel (2004) abundance diagnostic. As in Yuan et al. (2015), we use the Pettini & Pagel (2004) N2 metallicity indicator based on the intensity ratio [N ii] λ6584/Hα. We find that the nuclear region has an oxygen abundance of 12 + log(O/H) = 8.6 ± 0.1 dex. From an upper limit on the [N ii] flux, we compute a 3σ upper limit of 8.4 dex near the SN site. The MOSFIRE spectrum yields a 3σ detection of [N ii] and an estimate for the oxygen abundance of 12+log(O/H) = 8.3 ± 0.1 dex. The presence of strong night-sky lines close to both [N ii] emission lines limits the sensitivity of the spectra to the metallicity. Since the ratio of nitrogen to oxygen and the ionization parameter substantially affect the N2 metallicity diagnostic, our estimates may have an accuracy of only ∼0.2 dex. The relatively large uncertainty in our measurement of Hβ implies that the R₂₃ diagnostic (Pagel et al. 1979) is not able to provide a useful constraint on the oxygen abundance.

Karman et al. (2016) have used the Multi Unit Spectroscopic Explorer on the VLT to take optical spectra of the three separate images of the host-galaxy environment of SN Refsdal. Within a 06-radius aperture surrounding the explosion site, they report a high [O ii]/Mg ii ratio of 10–20, consistent with low metallicity and a high ionization parameter. From the X-shooter spectra, we measure 3σ limits on the flux of Mg ii λ2796 to be ≤4.7 × 10⁻¹⁸ erg s⁻¹ cm⁻² and of Mg ii λ2803 to be ≤6.3 × 10⁻¹⁸ erg s⁻¹ cm⁻², consistent with the flux levels measured by Karman et al. (2016).

5.1. Comparison of Host-galaxy Environments

We have used HST WFC3 grism and VLT X-shooter NIR spectra and images to classify SN Refsdal, the first example of a resolved, strongly lensed SN. Its slowly rising broad-band HST light curve can be matched by those of SN 1987A-like SNe, a peculiar class of SNe II that may account for ∼1.5%–3% of nearby SNe (Smartt et al. 2009; Kleiser et al. 2011; Pastorello et al. 2012). The only other SNe having similar light curves and colors are SNe IIn, which erupt into dense CSM and whose light curves are heterogeneous. Detection of strong and wide Na I D absorption and Hα P-Cygni absorption in the SN Refsdal spectra, however, identifies it as a SN 1987A-like SN, and provides strong evidence against the possibility that SN Refsdal is a SN IIn with continuum emission arising primarily from circumstellar interaction near peak luminosity.

The specific properties of the Hα emission and absorption features are also consistent with measurements of low-redshift SN 1987A-like SNe. The Hα expansion velocity we measure from the grism spectrum agrees with the velocities of SN 1987A-like SNe at comparable pre-maximum phases. Similarly, the strength and evolution of the Hα luminosity are consistent with those of SN 1987A-like events, and may not have been as strong or evolved the same way as was observed for the Type IIn SN 2005cp. Finally, the Hα emission-line profile is Gaussian instead of Lorentzian.

SN 1987A was the nearest detected SN of the modern era and is the best-studied event. Its progenitor star (Sk −69°202) in the LMC was a compact blue supergiant (B3 I; Gilmozzi et al. 1987; Sonneborn et al. 1987) inferred to have a mass close to 20 M_⊙ (see Arnett et al. 1989 for a review). The size of the progenitor (≲100 R_⊙) was significantly smaller than those of average red supergiants (500–1000 R_⊙), and accounts for the slowly rising light curve. Pastorello et al. (2012) suggest that all known SN 1987A-like SNe are consistent with explosions of blue supergiant progenitors with radii between 35 and 90 R_⊙ and masses at explosion of ∼20 M_⊙, which would be higher, on average, than those identified for SN IIP progenitors (Smartt et al. 2009).

For assumed values of the magnification, SN Refsdal had comparatively luminous M_B and M_V absolute magnitudes relative to well-studied low-redshift SN 1987A-like SNe (Pastorello et al. 2005; Kleiser et al. 2011; Pastorello et al. 2012; Taddia et al. 2012). While the K-corrections and photometric errors introduce some uncertainty, we find that the V − R color of SN Refsdal may be similar to those of blue low-redshift SN 1987A-like SNe, but that it may have an exceptionally blue B − V color, especially near maximum light. Scaling from a model of SN 1987A and using the fact that SN 1987A-like SNe exhibit a relatively small range of rise times, we estimate an ejecta mass of 20 ± 5 M_⊙ for the explosion.

We note that circumstellar interaction can range in intensity from very weak to very strong depending on the distribution, mass, and composition of any material surrounding the star. In the case of PTF 11iqb, for example, the CSM was overtaken quickly by the expanding ejecta and early-time narrow lines disappeared (Smith et al. 2015). Despite the lack of narrow lines near maximum light in spectra of PTF 11iqb, the CSM likely caused the SN to have a bluer color and higher luminosity. Indeed, SN 1987A is surrounded by a ring thought to have been ejected ∼10⁴ years before the explosion (Meaburn et al. 1995; Crotts & Heathcote 2000). Smith et al. (2014) have found that the light curves and spectra of the Type IIn SN 2009ip and SN 2010mc could be explained by the faint SN 1987A-like explosions of blue supergiant progenitors into dense CSM. However, deep and broad observed Na I D and Hα absorption features, the measured Hα evolution and strength, and the SN luminosity indicate that circumstellar interaction is not responsible for a substantial fraction of the SN Refsdal's luminosity during its photospheric phase.

Ongoing late-time HST imaging of the four images of SN Refsdal (PI P. Kelly; GO-14199) will continue to improve our understanding of the SN. As predicted (Diego et al. 2015; Grillo et al. 2016; Jauzac et al. 2015; Kawamata et al. 2015; Kelly et al. 2015b; Oguri 2015; Sharon & Johnson 2015; Treu et al. 2016), SN Refsdal has reappeared in a different image of its spiral host galaxy (Kelly et al. 2015a). While other faded SNe depart forever, we will have a second opportunity to study SN Refsdal and to learn about its early evolution.

We would like to thank Space Telescope Science Institute (STScI) director Matt Mountain for making it possible to obtain the HST WFC3 grism spectra of SN Refsdal. We express our appreciation for the efforts of HST Program Coordinator Beth Periello and Contact Scientist Norbert Pirzkal, as well as Claus Leitherer, Andrew Fox, Ken Sembach, and Miranda Link for scheduling the grism observations. Based in part on observations made with ESO telescopes at the La Silla Paranal Observatory under program ID 295.D-5014. We thank Ori Fox for helpful discussions about the Type IIn SN 2005cp, and Nathan Smith for useful comments about CSM interaction and SN 1987A-like SNe.

Support for the preparation of the paper is from HST grants GO-14041 and GO-14199. The GLASS program was supported by GO-13459, and the FrontierSN photometric follow-up program has funding through GO-13386. A.Z. is supported by a Hubble Fellowship (HF2-51334.001-A) awarded by STScI, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS 5-26555. R.J.F. gratefully acknowledges support from National Science Foundation (NSF) grant AST-1518052 and the Alfred P. Sloan Foundation. Supernova research at Rutgers University (S.W.J.) is supported by NSF CAREER award AST-0847157, and NASA/Keck JPL RSA 1508337 and 1520634. C.M. is supported through NSF grant AST-1313484. The DNRF provided funding for the Dark Cosmology Centre. JMS is supported by an NSF Astronomy and Astrophysics Postdoctoral Fellowship under award AST-1302771. A.V.F.'s group at UC Berkeley has received generous financial assistance from the Christopher R. Redlich Fund, the TABASGO Foundation, Gary & Cynthia Bengier, and NSF grant AST-1211916. The work of A.V.F. was completed at the Aspen Center for Physics, which is supported by NSF grant PHY-1066293; he thanks the Center for its hospitality during the black holes workshop in 2016 June and July.

This research uses services or data provided by the NOAO Science Archive. NOAO is operated by the Association of Universities for Research in Astronomy (AURA), Inc., under a cooperative agreement with the NSF. 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 NASA; the observatory was made possible by the generous financial support of the W. M. Keck Foundation. We recognize the Hawaiian community for the opportunity to conduct these observations from the summit of Mauna Kea.

A.1. Phases of the MOSFIRE, WFC3, and X-shooter Spectra Relative to Time of Maximum Light

A.2. HST WFC3-IR G141 Grism Data

A.2.1. Processing

We processed the WFC3/IR FLT images obtained from the HST archive using the software pipeline developed for the 3D-HST project²⁵ (Brammer et al. 2012b). This pipeline employs the DrizzlePac package (Gonzaga 2012)²⁶ to align the WFC3 images, and a custom software package to extract and model the grism spectra (Brammer et al. 2012a; Momcheva et al. 2015).^{27 ,28}

A.2.2. Modeling Contaminant Spectroscopic Traces

In a grism spectral element, light passes first through a prism and then a diffraction grating. The light from all objects in the field is dispersed in a common direction, making efficient spectroscopy of a large number of objects possible. The Einstein cross, however, presents a challenge for grism spectroscopy, because the SN images are embedded in light from both the spiral host galaxy and the early-type galaxy lens. In Figure 16, we show a coaddition of all F125W and $F160W$ direct exposures of the SN images S1–S4, adjacent sources, and the dimensions of the first-order and second-order grism traces. The traces of nearby, bright cluster members create additional strong contamination, and a nearby bright star with r = 15.1 mag AB produces strong diffraction spikes.

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The roll angle of the spacecraft determines the dispersion axis of the WFC3 G141 grism. Acquiring spectra at more than one roll angle makes possible a more robust extraction, because the trace at each roll angle is contaminated by different sources. To identify the two combinations of roll angles and SN images that would yield the least contamination, we simulated the expected grism spectra at all roll angles available at the time of the observation, and predicted that image S2 observed at angles 111° and 119° would be least contaminated.

Even after configuring the observations to obtain the cleanest possible SN spectra, light from other sources accounts for 85%–90% of the light along the traces of image S2 of SN Refsdal. To recover the SN spectrum, we constructed and subtracted models of overlapping traces. We used the wide-band $F125W-F160W$ color and the $F160W$ flux to model the continuum of the spiral host galaxy, the z = 0.54 elliptical cluster-member lens, and the two adjacent red-sequence cluster members. We used the $F160W$ flux to model the Hα and [O iii] narrow-line emission from the z = 1.49 spiral host galaxy. Figure 17 shows the two-dimensional models for the contaminating sources. Finally, we subtracted the residual background measured within a parallel adjacent aperture. Figure 18 shows the successive removal of the modeled sources and the parallel background measurement for the grism spectrum taken in the 111° telescope orientation. In Figure 19, we plot the extracted spectra of image S2 in orients 111° and 119°, and, for comparison, that of SN 1987A at the same epoch.

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A.2.3. Rejecting Outlying Flux Measurements

We compute a smoothed spectrum at the wavelength of each measurement with a weight proportional to a Gaussian density with σ = 3000 km s⁻¹ in the rest frame and inversely proportional to the square of the uncertainty of the flux measurement (Tonry & Davis 1979). The narrow lines have already been removed during an earlier processing step.

A.2.4. Comparison Between Direct Imaging Magnitudes and Grism Spectra

Given the fact that the SN flux was only a small fraction of the contaminating flux along the trace, a useful consistency check is to assess how well synthetic magnitudes calculated from the grism SN spectrum agree with direct photometry of the SN. We compute synthetic AB magnitudes using the $F125W$ and $F160W$ filter functions, and calculate a synthetic $F125W-F160W$ color.

The grism spectra were taken from 2014 December 23 through 2015 January 5, but all of the 202.9 s post-imaging exposures were taken with the $F160W$ wide-band filter from December 23–28, while all post-imaging exposures from 2014 December 30 through 2015 January 4 were taken with the $F125W$ wide-band filter. To estimate the average color of SN Refsdal during the period of grism observations, we have coadded post-imaging exposures acquired on 2014 December 28–31, when coverage spans approximately the same epochs. These dates bracket the midpoint of the grism observations on 2014 December 29.

We measure direct magnitudes of $F125W=25.01\pm 0.05$ mag AB and $F160W=25.06\pm 0.05$ mag, or a color of $F125W-F160W=-0.05\pm 0.07$ mag AB. Then we calculate a synthetic color of $F125W-F160W=0.14$ mag AB.

A.3. VLT X-shooter Spectroscopy

A.4. Estimating the Luminosity of the SN Hα Emission

A.5. K-corrections

For the purpose of computing the absolute magnitudes and colors of SN Refsdal at peak that are plotted in Figure 5, we adopt peak magnitudes of F105W = 24.90 mag AB, F125W = 24.55 mag AB and F160W = 24.2 mag AB representative of the light curves of S1–S3. Since the WFC3 grism spectrum covers only 11000–17000 Å (∼4400–6800 Å in the rest frame) and the continuum is difficult to extract from the VLT spectrum, we use spectra of low-redshift SN 1987A-like SNe as well as SN 2005cp to compute K-corrections between the observer-frame WFC3 F105W, F125W, and F160W magnitudes and the rest-frame B, V, and R filters. We define these color K-corrections as follows,

$$\begin{eqnarray}&&B-V={m}_{{\rm{F}}105{\rm{W}},\mathrm{syn}}^{\mathrm{AB}}-{m}_{{\rm{F}}125{\rm{W}},\mathrm{syn}}^{\mathrm{AB}}+{K}_{B-V},\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&V-R={m}_{{\rm{F}}125{\rm{W}},\mathrm{syn}}^{\mathrm{AB}}-{m}_{{\rm{F}}160{\rm{W}},\mathrm{syn}}^{\mathrm{AB}}+{K}_{V-R},\end{eqnarray} \tag{ 3 }$$

and

$$\begin{eqnarray}&&V-r={m}_{{\rm{F}}125{\rm{W}},\mathrm{syn}}^{\mathrm{AB}}-{m}_{{\rm{F}}160{\rm{W}},\mathrm{syn}}^{\mathrm{AB}}+{K}_{V-r}.\end{eqnarray} \tag{ 4 }$$

Here the K-correction is defined following Kim et al. (1996),

$$\begin{eqnarray}&&{m}_{y}={M}_{x}+\mu (z)+{K}_{{xy}}\end{eqnarray} \tag{ 5 }$$

where m_y is the apparent magnitude in the y band, M_x is the absolute magnitude in the x band, and μ(z) is the distance modulus.

We calculate K-corrections using spectra of SN 2006V (+6 days; $B-V=0.21$ mag; $V-r=-0.17$ mag; $V-R=0.0$ mag), SN 2006au (−16 days; $B-V=0.063$ mag; $V-r=-0.18$ mag; $V-R=-0.04$ mag), SN 2005cp (+14 days; $B-V=0.21$ mag; $V-r=0.0$ mag; $V-R=0.0$ mag), and PTF 12gcx (+1 day; $B-V=0.306$ mag; $V-r=-0.37$ mag; $V-R=-0.01$ mag). All spectra were obtained within several weeks of maximum. In Figure 5, we adopt the representative values ${K}_{B-V}=0.2$ mag, and ${K}_{V-R}=0.0$ mag to compute the rest-frame B–V and V–R colors of SN Refsdal near maximum.

In Figure 5, we show inferred absolute B and V rest-frame magnitudes of SN Refsdal, and, to compute these values, we next calculate the following K-corrections,

$$\begin{eqnarray}&&{K}_{{\rm{F}}105{\rm{W}}B}=2.5\times \,{\mathrm{log}}_{10}(1+z)+{m}_{{\rm{F}}105{\rm{W}},\mathrm{syn}}^{\mathrm{AB}}-{m}_{{\rm{B}},\mathrm{syn}}^{\mathrm{Vega}}\end{eqnarray} \tag{ 6 }$$

and

$$\begin{eqnarray}&&{K}_{{\rm{F}}125{\rm{W}}V}=2.5\times \,{\mathrm{log}}_{10}(1+z)+{m}_{{\rm{F}}125{\rm{W}},\mathrm{syn}}^{\mathrm{AB}}-{m}_{{\rm{V}},\mathrm{syn}}^{\mathrm{Vega}}.\end{eqnarray} \tag{ 7 }$$

We calculate these K-corrections for SN 2006V (+6 days; ${\rm{F}}105{\rm{W}}B=-0.86$ mag; ${\rm{F}}125{\rm{W}}V=-0.80$ mag), SN 2006au (−16 days; ${\rm{F}}105{\rm{W}}B=-0.85$ mag; ${\rm{F}}125{\rm{W}}V=-0.788$ mag), SN 2005cp (+14 days; ${\rm{F}}105{\rm{W}}B=-1.01$ mag; ${\rm{F}}125{\rm{W}}V=-0.80$ mag), and PTF 12gcx (+1 day ${\rm{F}}105{\rm{W}}B=-0.91$ mag; ${\rm{F}}125{\rm{W}}V=-0.69$ mag). We adopt the representative values ${K}_{{\rm{F}}105{\rm{W}}B}=-0.9$ mag, and ${K}_{{\rm{F}}125{\rm{W}}V}=-0.8$ mag to compute the absolute B and V magnitudes of SN Refsdal near maximum plotted in Figure 5.

In Figure 4, we have instead transformed the B − V and V − R colors of the low-redshift SN to F105W−F125W and F125W−F160W at redshift z = 1.49. While Figure 5 presents a comparison of colors and absolute magnitudes at maximum light, Figure 4 shows the evolution of colors with SN phase. Since K-corrections are needed across a wide range of phase, we therefore use the spectra of the extremely well-sampled SN 1987A as a model. Using spectra of SN 1987A instead of the average of the SN samples used to compute K-corrections for Figure 5 above leads to a small, ∼0.2 mag, difference in the K-correction at maximum light.

A.6. Comparison with the Spectra of H-rich Superluminous Supernovae

In Figure 21, we show a comparison between the WFC3 G141 grism spectrum of SN Refsdal and the spectra of four SLSNe. The Hα emission from SN Refsdal has a significantly higher equivalent width (EW) than those of the Hα emission features of the SLSNe. The spectra of the superluminous comparison objects are drawn from the literature (SN 2006gy: Smith et al. 2007; SN 2008am: Chatzopoulos et al. 2011; SN 2008es: Gezari et al. 2009; SN 2013hx: Inserra et al. 2016).

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