Hydrogen-poor Superluminous Supernovae from the Pan-STARRS1 Medium Deep Survey

The PS1 telescope on Haleakala is a high-etendue wide-field survey instrument with a 1.8 m diameter primary mirror and a 33 diameter field of view imaged by an array of sixty 4800 × 4800 pixel detectors with a pixel scale of 0258 (Tonry & Onaka 2009; Kaiser et al. 2010). Tonry et al. (2012) describes the photometric system and broadband filters in detail.

The Pan-STARRS1 system and its surveys are fully described in Chambers et al. (2016). The stacked 3π survey data are publicly available from the Space Telescope Science Institute archive.¹⁹ This paper describes the data taken from the Pan-STARRS1 Medium deep Survey (MDS) designed by the Pan-STARRS1 Science Consortium (PS1SC). The Pan-STARRS1 Medium Deep Survey (PS1 MDS) operated from late 2009 to early 2014. PS1 MDS consists of 10 fields, each with a single PS1 imager footprint. The fields were observed in ${g}_{{\rm{P}}1}$ ${r}_{{\rm{P}}1}$ ${i}_{{\rm{P}}1}$ ${z}_{{\rm{P}}1}$ with a typical cadence of 3 days in each filter, to a typical nightly depth of ~23.3 mag ($5\sigma$); ${y}_{{\rm{P}}1}$ was used near full moon with a typical depth of ~21.7 mag (AB magnitudes are used throughout this paper). The standard reduction, astrometric solution, and stacking of the nightly images were performed by the Pan-STARRS1 Image Processing Pipeline (IPP) system on a computer cluster originally based at the Maui High Performance Computer Center. The processing steps to reduce and stack the data are described in Magnier et al. (2016a) and in Waters et al. (2016), while the steps for astrometric calibration are in Magnier et al. (2016b). For the transients search, the nightly MDS stacks were transferred to the Harvard FAS Research Computing cluster, where they were processed through a frame subtraction analysis using the photpipe pipeline developed for the SuperMACHO and ESSENCE surveys (Rest et al. 2005; Garg et al. 2007; Miknaitis et al. 2007; Rest et al. 2014). An additional set of difference images was produced by the IPP in Hawaii, and the catalogs of the detections were ingested into a database at Queen's University Belfast (see McCrum et al. 2015). Cross-matches between the two end-to-end pipelines were made to mitigate the loss of transients through either.

A subset of targets was selected for spectroscopic follow-up, using the Blue Channel spectrograph on the 6.5 m MMT telescope (Schmidt et al. 1989), the Gemini Multi-Object Spectrograph (GMOS; Hook et al. 2004) on the 8 m Gemini telescopes, and the Low Dispersion Survey Spectrograph (LDSS3) and Inamori-Magellan Areal Camera and Spectrograph (IMACS; Dressler et al. 2006) on the 6.5 m Magellan telescopes. The SLSNe were generally targeted for spectroscopy based on a combination of blue observed color, long observed rise time, and being several magnitudes brighter than any apparent host in the PS1 deep stacks—for more details, see Section 5.1 of Lunnan et al. (2014), which discusses both the selection and possible biases introduced. We note that the combination of a modest survey area and deep photometry provides sensitivity primarily to SLSNe at higher redshifts: the sample spans $0.3\lesssim z\lesssim 1.6$. Table 1 lists the full sample.

Table 1.  SLSNe from PS1 MDS

Object	Redshift	R.A.	Decl.	Reference
PS1-12cil	0.32	08h40m56169	+45°24'4193	⋯
PS1-14bj	0.5125	10h02m08433	+03°39'1902	Lunnan et al. (2016)
PS1-12bqf	0.522	02h24m54621	−04°50'2272	⋯
PS1-11ap	0.524	10h48m27752	+57°09'0932	McCrum et al. (2014)
PS1-10bzj	0.650	03h31m39826	−27°47'4217	Lunnan et al. (2013)
PS1-11bdn	0.738	02h25m46292	−05°03'5657	⋯
PS1-13gt	0.884	12h18m02035	+47°34'4595	⋯
PS1-10awh	0.909	22h14m29831	−00°04'0362	Chomiuk et al. (2011)
PS1-10ky	0.956	22h13m37851	+01°14'2357	Chomiuk et al. (2011)
PS1-11aib	0.997	22h18m12217	+01°33'3201	⋯
PS1-10ahf	1.10	23h32m28311	−00°21'4346	McCrum et al. (2015)
PS1-10pm	1.206	12h12m42200	+46°59'2948	McCrum et al. (2015)
PS1-11tt	1.283	16h12m45778	+54°04'1696	⋯
PS1-11afv	1.407	12h15m37770	+48°10'4862	⋯
PS1-13or	1.52	09h54m40296	+02°11'4224	⋯
PS1-11bam	1.565	08h41m14192	+44°01'5695	Berger et al. (2012)
PS1-12bmy	1.572	03h34m13123	−26°31'1721	⋯

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As we are interested in the true luminosity range of SLSNe, we do not include a luminosity threshold in our definition and instead adopt a spectroscopy-based selection. We define our sample of SLSNe as SNe that are spectroscopically similar to either of the prototypes SN 2005ap/SCP06F6 (2005ap-like) or to SN 2007bi (2007bi-like). Although this is reminiscent of the division by Gal-Yam (2012) into "SLSN-I" and "SLSN-R," we do not include any light curve information or intend to imply anything regarding the power source by making this distinction; we simply wish to include all kinds of H-poor SLSNe. Indeed, there are examples of objects (e.g., PS1-11ap and PTF12dam; Nicholl et al. 2013; McCrum et al. 2014) that resembled SN 2005ap near peak but developed features similar to SN 2007bi on their decline; it has been suggested that the differences mainly arise due to temperature effects (Nicholl et al. 2017b). Here, we use the spectrum taken closest to peak light for classification, to make the selection as uniform as possible. Using peak spectra also minimizes confusion with SN Ib/c, as SLSN-I on the decline often develop features similar to SN Ib/c at peak, as the ejecta cool and the photosphere reaches comparable temperatures (e.g., Pastorello et al. 2010; Mazzali et al. 2016). With these criteria, we find 16 2005ap-like objects in the PS1 MDS spectroscopic sample, and one 2007bi-like (PS1-14bj, discussed in detail in Lunnan et al. 2016) object. All classification spectra are shown in Figure 1, and the details of the spectroscopic observations (if previously unpublished) are listed in Table 2.

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In practice, given the redshifts of our objects, the features most commonly used for classification of the 2005ap-like objects was the series of broad UV features bluewards of 2800 Å, marked on the spectrum of SCP06F6 in Figure 1. Despite many objects having limited wavelength coverage, all but two of our spectra go sufficiently blue to cover at least the broad Mg ii feature, which is the reddest of the series. In the optical, the series of characteristic O ii features (marked on the spectrum of PTF09cnd) are comparatively shallower and typically stronger during the rise of the light curve than at peak light. These features are convincingly present at peak in PS1-11ap, PS1-10bzj, and PS1-13gt, though PS1-13gt is the only object where the classification is based on the O ii absorption as opposed to the UV features. The fact that the redshift is unambiguously known from narrow host galaxy features in the majority of cases also aids classification, particularly in cases where there are just a few discernible features in the spectrum and/or the wavelength coverage is limited.

A few objects have been discussed in the literature as SLSNe from PS1 MDS but are not included in our sample here. One such object is PS1-12zn, which was included in the sample of H-poor SLSNe in the host galaxy study of Lunnan et al. (2014). Although we do not detect H lines in its spectrum and its luminosity places it firmly in the SLSN category, the spectrum shows a featureless blue continuum, lacking both the broad UV features and the O ii features we use here as our spectroscopic criteria. As our spectrum does not cover Hα, we cannot rule out that this object was a H-rich SLSN, and we therefore do not include it in our spectroscopically selected sample here. We also exclude PS1-10afx, presented as a possible SLSN in Chornock et al. (2013), as the discovery of a second galaxy along the line of sight has revealed this object to be a lensed SN Ia (Quimby et al. 2013a, 2014), and its spectrum is indeed better matched to a normal SN Ia than to SN 2005ap or SN 2007bi.

All but three objects in our sample have narrow-line host galaxy redshifts from either [O ii] λ3727 emission or Mg ii $\lambda \lambda$ 2796, 2803 absorption lines. For the three objects without any host galaxy absorption or emission lines, PS1-12cil, PS1-10ahf, and PS1-13or, we instead determine the redshift from the supernova spectra. The higher redshift objects were matched to the series of strong UV features seen in SCP06F6 and PS1-10ky (Barbary et al. 2009; Chomiuk et al. 2011). Owing to its lower redshift, only the first of these features is detected in PS1-12cil, but post-peak spectra of this object (R. Chornock et al. 2018, in preparation) develop features similar to SN Ib/c post-peak as the ejecta cool (similar to other SLSN-I). We use these later spectra, cross-correlated to SN Ib/c templates using SNID (Blondin & Tonry 2007), to determine the redshift of this object. We caution that redshifts derived from supernova features are degenerate with the expansion velocity, and therefore less precise than the narrow-line redshifts reported for the rest of the sample, and we only report the redshift to two decimal places for these objects.

Thanks to the multiband data from PS1 MDS, ${g}_{{\rm{P}}1}$ ${r}_{{\rm{P}}1}$ ${i}_{{\rm{P}}1}$ ${z}_{{\rm{P}}1}$ light curves are available for all objects. Most objects are undetected in the shallower ${y}_{{\rm{P}}1}$ band, and we find that the upper limits do not provide meaningful constraints—we therefore only report ${y}_{{\rm{P}}1}$ photometry for the three objects that are actually detected: PS1-12cil, PS1-12bqf, and PS1-11ap. The final photometric pipeline is described in Scolnic et al. (2017). In addition to the PS1 photometry, some objects have additional follow-up imaging acquired with GMOS, LDSS, and IMACS; we reduced these images and extracted magnitudes by aperture photometry using standard routines in IRAF. PS1-11bdn was also observed with the Swift Ultra-Violet/Optical Telescope (UVOT); magnitudes in a 3'' aperture were extracted following the procedure in Brown et al. (2009). All photometry is listed in Table 4. The light curves of the 17 objects in our sample are shown in Figure 2. Due to the large redshift range of our sample, the effective wavelengths of each filter vary significantly; Table 3 lists these effective wavelengths at the redshift of each supernova.

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Table 3.  Effective Wavelengths of PS1 Bandpasses

Object	${g}_{{\rm{P}}1}$	${r}_{{\rm{P}}1}$	${i}_{{\rm{P}}1}$	${z}_{{\rm{P}}1}$	${y}_{{\rm{P}}1}$
	(Å)	(Å)	(Å)	(Å)	(Å)
PS1-12cil	3647	4677	5693	6563	7285
PS1-12bqf	3163	4056	4938	5692	6318
PS1-11ap	3158	4051	4931	5684	6310
PS1-14bj	3164	4058	4939	5694	6320
PS1-10bzj	2917	3742	4555	5250	5828
PS1-11bdn	2770	3552	4324	4984	5533
PS1-13gt	2555	3277	3989	4598	5104
PS1-10awh	2521	3234	3937	4538	5037
PS1-10ky	2461	3156	3842	4429	4916
PS1-11aib	2410	3091	3763	4338	4815
PS1-10ahf	2230	2861	3482	4014	4456
PS1-10pm	2182	2798	3406	3927	4359
PS1-11tt	2108	2704	3292	3794	4212
PS1-11afv	2000	2565	3122	3599	3995
PS1-13or	1910	2450	2982	3437	3816
PS1-11bam	1876	2407	2930	3377	3749
PS1-12bmy	1871	2400	2922	3368	3739

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Table 4.  Photometry of PS1 SLSNe

Object	MJD	Rest-frame Phase	Filter	AB Mag	Instrument
	(days)	(days)
PS1-12bqf	56206.6	−26.8	${g}_{{\rm{P}}1}$	22.48 ± 0.14	PS1
PS1-12bqf	56209.6	−24.8	${g}_{{\rm{P}}1}$	22.22 ± 0.09	PS1
PS1-12bqf	56214.4	−21.7	${g}_{{\rm{P}}1}$	22.09 ± 0.11	PS1
PS1-12bqf	56217.5	−19.6	${g}_{{\rm{P}}1}$	21.85 ± 0.07	PS1
PS1-12bqf	56220.5	−17.6	${g}_{{\rm{P}}1}$	22.11 ± 0.12	PS1
PS1-12bqf	56235.5	−7.8	${g}_{{\rm{P}}1}$	21.76 ± 0.08	PS1
PS1-12bqf	56238.3	−5.9	${g}_{{\rm{P}}1}$	21.56 ± 0.11	PS1
PS1-12bqf	56241.4	−3.9	${g}_{{\rm{P}}1}$	21.73 ± 0.12	PS1
PS1-12bqf	56268.3	13.8	${g}_{{\rm{P}}1}$	22.38 ± 0.12	PS1
PS1-12bqf	56271.3	15.8	${g}_{{\rm{P}}1}$	22.17 ± 0.08	PS1

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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Note the long observed timescales in many cases, due both to intrinsically longer timescales of SLSNe and to time dilation. The long timescales also mean that depending on when an object was discovered during an observing season, we may not have a complete light curve. Particularly among the higher redshift objects, we tend to sample either the rise or the decline, although we do observe either a turnover or flattening of the flux, suggesting we are capturing the peak in most cases. Exceptions to this, where the time of peak is uncertain, include PS1-13gt (which is declining in all filters), PS1-11bdn (which has a very sparsely sampled light curve), and to a lesser extent, PS1-10ahf and PS1-13or.

The multiband nature and large redshift range of the PS1 MDS SLSN sample allow us to probe the light curves and colors of SLSNe in the rest-frame UV. The observed colors at peak are shown in Figure 3. The strongest trend with redshift is seen in ${g}_{{\rm{P}}1}$−${r}_{{\rm{P}}1}$, as the peak of the SED moves through the observed ${g}_{{\rm{P}}1}$ band; this is also illustrated in Figure 4, which shows the PS1 filter curves at different redshifts compared with typical SLSN-I spectra. ${g}_{{\rm{P}}1}$−${r}_{{\rm{P}}1}$ also shows the largest scatter at a given redshift, reflecting the corresponding spread in UV luminosities. Such a spread is also seen among well-studied low-redshift SLSNe with good UV coverage; see, e.g., the very UV-luminous SLSN Gaia16apd (Kangas et al. 2017; Nicholl et al. 2017a; Yan et al. 2017b). This illustrates a challenge in using colors in identifying high-redshift SLSNe. ${r}_{{\rm{P}}1}$ −${i}_{{\rm{P}}1}$ and ${i}_{{\rm{P}}1}$−${z}_{{\rm{P}}1}$ are flatter with redshift and have less scatter.

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We correct the photometry for foreground extinction following Schlafly & Finkbeiner (2011), but are not able to correct for the (unknown) host galaxy extinction. This could also be contributing to the spread in observed colors, although the host galaxies of most of the SLSNe in this sample were studied in Lunnan et al. (2014) and found to have little inferred dust extinction; the same result is found in other studies and appears to be true for SLSN host galaxies in general (e.g., Leloudas et al. 2015; Perley et al. 2016). Therefore, we do not generally expect a large contribution from the host galaxies; this is also supported by the low average extinction found in the modeling by Nicholl et al. (2017b). In individual cases, host galaxy reddening may still be important, however. Another uncertainty is reddening by dust associated with circumstellar material lost by the progenitor star—some models of SLSNe predict eruptive mass loss prior to explosion (e.g., Woosley 2017), and late-time interaction signatures in some H-poor SLSNe also support the idea of a complex circumstellar environment (Yan et al. 2015, 2017a). Depending on the distance to the CSM, dust is likely destroyed by the supernova radiation, however, so this may not be an important effect.

One SLSN in our sample with signs of possible reddening is PS1-13gt, which shows a comparatively red continuum despite also showing the characteristic O ii features in its spectrum that require high temperatures (Figure 1; e.g., Mazzali et al. 2016). This suggests that the temperature is higher than one would infer from the shape of the continuum. When correcting the spectrum to rest-frame wavelengths and dereddening by E(B − V)  0.3 mag, the spectrum of PS1-13gt is an excellent match to PTF09cnd (Quimby et al. 2011). This SLSN is also one of the faintest found in the sample, which supports the possibility of higher extinction.

We measure temperature as a function of time from the light curves by fitting blackbody curves to the observed photometry. Typically, PS1 observed ${g}_{{\rm{P}}1}$ and ${r}_{{\rm{P}}1}$ on the same night, so we generally use ${r}_{{\rm{P}}1}$ as the baseline for these calculations. If there is photometry from the other bands from the same night or ±1 day, we use those measurements without corrections. If not, we use a polynomial fit to the light curve in that filter and interpolate to the date of the ${r}_{{\rm{P}}1}$ observation. We only fit SEDs to epochs where the object was observed in at least three filters. Figure 5 shows the res-ulting blackbody temperatures derived from the photometry.

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Early measurements in particular are noisy, because the peak of the blackbody can be bluewards of the observed bands, even for the high-redshift PS1 MDS sample. To the extent that we can measure it, we find that the color temperatures prior to peak are either constant or slowly cooling, with temperatures in the range 10,000–25,000 K. This highlights the need for UV follow-up of SLSNe, particularly at early epochs. Post-peak, the color temperatures decrease as the SN ejecta expand and cool, and also seem to plateau around 6000–7000 K.

PS1-14bj deviates from this general trend, having redder colors and cooler temperatures over the entire observed time period, and an overall flat color evolution. PS1-13gt shows the reddest color temperature at peak, which would be consistent with this supernova being reddened by dust as discussed above.

We measure velocities from the spectra by fitting Gaussians to the absorption features and determining the locations of the minima. The identification of the strong UV features is debated—Quimby et al. (2011) identified them with C ii, Si iii, and Mg ii, whereas Howell et al. (2013) favor Fe III, C ii/iii, and Mg ii; see also Mazzali et al. (2016). We do not attempt to model the spectra given the spread in quality and wavelength coverage for our objects. However, in all but one of our SLSNe that are classified as 2005ap-like, our spectra cover the broad Mg ii feature, and we use this to estimate the velocity at peak and to calculate the associated velocity from the blueshift relative to the narrow Mg ii lines from the host galaxy. Table 5 lists the expansion velocities derived in this fashion. They range from 10,000 to 18,000 km s⁻¹, with typical values of about 15,000 km s⁻¹. This is similar to what has been seen in other SLSNe around peak light (e.g., Quimby et al. 2011; Inserra et al. 2013; Nicholl et al. 2014; Liu et al. 2017b).

Table 5.  Derived Properties

Object	${T}_{{\rm{B}}{\rm{B}}}$ at Peak	Peak Lum.	Rad. Energya	${\tau }_{r}$	${\tau }_{d}$	Velocity at Peakb	M400	M260
	(K)	(${10}^{44}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$)	(${10}^{51}\,\mathrm{erg}$)	(days)	(days)	(km s−1)	(AB mag)	(AB mag)
PS1-12cil	13,000	0.50	0.22	20.1	50.9	⋯	−20.69 ± 0.05	−20.54 ± 0.05
PS1-14bj	7000	0.46	0.78	97.6	122.0	5000c	−20.47 ± 0.04	−18.91 ± 0.06
PS1-12bqf	11,000	0.47	0.28	28.4	70.6	14,000	−20.53 ± 0.11	−19.90 ± 0.14
PS1-11ap	10,000	1.63	1.04	35.2	72.6	16,000	−21.86 ± 0.05	−21.06 ± 0.10
PS1-10bzj	17,000	1.17	0.37	15.2	36.1	14,000	−21.11 ± 0.13	−21.41 ± 0.17
PS1-11bdn	12,000	4.70	0.61	19.8	⋯	16,000	−21.76 ± 0.03	−22.31 ± 0.07
PS1-13gt	6000	1.25	0.40	⋯	41.0	⋯	−20.99 ± 0.09	⋯
PS1-10awh	16,000	2.16	0.59	22.5	⋯	13,000	−21.77 ± 0.03	−21.97 ± 0.10
PS1-10ky	16,000	2.75	0.58	⋯	28.2	18,000	−21.92 ± 0.08	−22.28 ± 0.13
PS1-11aib	10,000	2.24	2.02	56.5	79.8	16,000	−22.01 ± 0.05	−22.02 ± 0.17
PS1-10pm	8000	2.56	0.77	⋯	⋯	16,000	−22.22 ± 0.33	−21.42 ± 0.10
PS1-11tt	9000	2.61	1.19	45.2	45.1	9000	−22.16 ± 0.17	−21.10 ± 0.15
PS1-11afv	12,000	2.32	0.41	⋯	⋯	9000	−22.07 ± 0.13	−22.08 ± 0.16
PS1-13or	11,000	5.20	1.12	29.5	⋯	⋯	−22.61 ± 0.14	−22.77 ± 0.20
PS1-11bam	12,000	4.13	0.94	⋯	29.8	17,000	−22.46 ± 0.23	−22.54 ± 0.10
PS1-12bmy	9000	3.51	1.04	⋯	30.5	16,000	−22.61 ± 0.18	−21.90 ± 0.18

Notes.

^aLower limits. ^bMeasured from the minimum of the Mg ii feature, unless stated otherwise. ^cFrom the SYNOW fit presented in Lunnan et al. (2016).

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To construct bolometric light curves, we start with the observed photometry at each multifilter epoch (i.e., flux and effective wavelength for each filter) and sum up the observed flux using trapezoidal integration. We linearly extrapolate the flux from the effective wavelength to the blue edge of the bluest filter (typically ${g}_{{\rm{P}}1}$) and to the red edge of the reddest filter (typically ${z}_{{\rm{P}}1}$). To be explicit, for a series of fluxes $\{{f}_{0},{f}_{1},\,\ldots ,\,{f}_{n}\}$ with corresponding effective wavelengths $\{{\lambda }_{0},{\lambda }_{1},\,\ldots ,\,{\lambda }_{n}\}$, and the blue edge of the bluest filter ${\lambda }_{b}$ and the red edge of reddest filter ${\lambda }_{r}$, we calculate

$$\begin{eqnarray}{L}_{\mathrm{trap}} & = & \displaystyle \sum _{k=1}^{n}\displaystyle \frac{{f}_{k}+{f}_{k-1}}{2}({\lambda }_{k}-{\lambda }_{k-1})+\displaystyle {f}_{0}({\lambda }_{0}-{\lambda }_{b})\\ & & +\,\displaystyle {f}_{\mathrm{n}}({\lambda }_{r}-{\lambda }_{n})-\displaystyle \frac{{f}_{1}-{f}_{0}}{2}\displaystyle \frac{{({\lambda }_{0}-{\lambda }_{b})}^{2}}{({\lambda }_{1}-{\lambda }_{0})}\\ & & +\,\displaystyle \frac{{f}_{n}-{f}_{n-1}}{2}\displaystyle \frac{{({\lambda }_{r}-{\lambda }_{n})}^{2}}{({\lambda }_{n}-{\lambda }_{n-1})}.\end{eqnarray} \tag{ 1 }$$

Since this only takes into account the flux in the observed bands, it is a strict lower limit on the emitted flux. Given the large redshift range of our sample, the rest-frame wavelengths covered in this estimate also varies considerably; see Table 3 for the actual rest-frame wavelengths covered at the redshift of each object.

For a better estimate of the bolometric luminosities, we add a correction to the observed flux based on the estimated blackbody temperatures. While the spectrum clearly deviates from a blackbody at UV wavelengths (bluewards of the observed bands; Figure 1), it is reasonably well approximated by a blackbody at redder wavelengths. We therefore integrate a blackbody curve redwards of the observed bands, with the observed color temperature and scaled to match the flux in the reddest observed filter and add this to the observed flux. The size of this correction is small (10%–20%) at early times, but can be substantial at later times as the SNe cool and the blackbody peak shifts to the red. Similarly, the correction is larger for the higher redshift objects, as the observed filters cover bluer rest-frame wavelengths. We explore the luminosity function in a standardized bandpass in Section 6.

Figure 6 shows the pseudo-bolometric light curves calculated in this fashion. Although only a handful of light curves are well sampled both before and after peak, the diversity in light curve shapes is still apparent. We explore this in a more quantitative way in Section 4.

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Figure 7 shows the peak luminosities in erg s⁻¹, plotted as a function of redshift. The typical uncertainties, which can also be gleaned from Figure 6, are of order 10%—we caution, however, that systematic uncertainties due to not capturing the full bolometric flux likely dominate the statistical uncertainty. We see a clear spread of luminosities at redshifts $z\lesssim 1$, where we are also sensitive to lower luminosity objects. This illustrates the need to take into account the impact of survey and follow-up limits on the resulting luminosity distribution of SLSNe. At redshifts $z\gtrsim 1$, we are dominated by the higher luminosity objects, as one might expect due to Malmquist bias. Note that the low- and high-redshift luminosities are not directly comparable since our pseudo-bolometric light curves capture more of the UV light at higher redshifts—given that the overall trend toward higher luminosities at higher redshifts also holds when comparing K-corrected peak magnitudes (Section 6, Figure 13), this is unlikely to be a dominant effect, however. With the exception of the lowest luminosity objects PS1-12cil, PS1-12bqf, and PS1-14bj, all of the PS1 H-poor SLSNe peak at $(1\mbox{--}5)\times {10}^{44}\,\mathrm{erg}\ {{\rm{s}}}^{-1}$.

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We determine a lower limit on the total radiated energy by integrating the estimated bolometric light curves; the results are plotted in Figure 8. Filled symbols correspond to objects for which we sample both the rise and the decline; the results span close to an order of magnitude. Both light curve shape and overall luminosity contribute to this scatter—while PS1-14bj and PS1-12bqf are the lowest luminosity objects in the sample, the total radiated energy of PS1-14bj is comparable to that of the higher luminosity objects, thanks to the exceptionally broad light curve. By contrast, the radiated energies of PS1-12cil and PS1-12bqf are the lowest of all in the sample, despite incomplete light curves for several other SLSNe.

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We measure the time of peak, and the rise and decline times by fitting low-order polynomials to our pseudo-bolometric light curves. For estimates of the rise and decline times, we follow Nicholl et al. (2015a) and define these timescales as the time between peak and the luminosity being $1/e$ of the value at peak; we will refer to them as ${\tau }_{r}$ and ${\tau }_{d}$, respectively.

The rise and decline timescales are plotted as a function of redshift in Figure 9, along with the data from Nicholl et al. (2015a). Our pseudo-bolometric light curves differ from those of Nicholl et al. (2015a), who constructed theirs by summing up the rest-frame (K-corrected) griz photometry. This choice would not have been practical for our purposes, since the higher redshifts of our sample mean we lack both sufficiently red spectral coverage as well as the temporal spectral coverage to calculate K-corrections to these filters. In addition, restricting to the rest-frame optical would ignore the fact that we do cover the rest-frame UV where the SED peaks, which is one of the unique aspects of our sample. However, this difference means that the timescales derived may also differ somewhat, since the bluest flux also fades the fastest given the temperature evolution (Figure 5). In the two objects overlapping between the samples, PS1-10bzj and PS1-11ap, we recover similar values to within 10%, however, so this is unlikely to be a significant effect. Typical (statistical) error bars for the rise and decline timescales are two to five days, but as with the peak luminosity, this does not capture any systematic effects from our light curves not including the full bolometric light. Generally, we find timescales in the PS1 sample similar to those in the low-redshift sample, with a few interesting exceptions: PS1-14bj is a clear outlier in both plots, with both the rise and decline being significantly slower than the rest of the sample. PS1-11aib, PS1-11tt, and PS1-10ahf show longer rise times than any of the low-redshift objects, though they are not nearly as extreme as that in PS1-14bj; in the case of PS1-11aib, the measured rise time is also affected by a possible "precursor" bump (Section 4.2). We also note that PS1-14bj and PS1-11aib do not fall on the ${\tau }_{d}\simeq 2\times {\tau }_{r}$ correlation found in Nicholl et al. (2014), with light curves closer to symmetric in both cases.

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Another interesting feature in Figure 9 is the apparent clustering of decay times into two groups: one fast-declining group with a typical timescale of 30–40 days, and a slow-declining group with a typical timescale of about 70 days. Whether this is a double-peaked distribution or simply a single-peak distribution with a long tail cannot be determined from the PS1 sample alone, however. We note that PS1-12cil's decline time is intermediate between the groups, and that PS1-14bj has a significantly longer decline time than any of the other objects in the "slowly declining" group, indicating a continuum; this is also supported by other recent compilation studies (De Cia et al. 2017; Nicholl et al. 2017b).

Many SLSN light curves show a double-peaked structure on the rise, with a precursor "bump" preceding the main rise. This was first seen in SN 2006oz (Leloudas et al. 2012) and LSQ14bdq (Nicholl et al. 2015b) and was suggested to be a ubiquitous feature of H-poor SLSNe by Nicholl & Smartt (2016). In our sample, there are no clear examples of distinct bumps like that seen in LSQ14bdq, but PS1-11aib and PS1-13or do show a flattening in their early light curves. The early, marginal ${r}_{{\rm{P}}1}$ detection of PS1-11tt could also be indicative of a precursor (Figure 2), but given the sparsely covered rise for this object, the nature of the early detection is unclear.

Figure 10 shows the rising ${i}_{{\rm{P}}1}$ and ${z}_{{\rm{P}}1}$ light curves of PS1-11aib and PS1-13or. Both objects show structure in their early light curves, in the form of a flattening before rising to the main peak. Compared to the precursor peak seen in LSQ14bdq, these are significantly brighter, with the contrast between the light curve peak and the "precursor" less than 1 mag, whereas in LSQ14bdq the contrast was ~2 mag (Nicholl et al. 2015b). In fact, precursors like the one in LSQ14bdq would only be detectable in our lowest redshift data: our typical SLSN peaks at around 22 mag, so a precursor peak as in LSQ14bdq would be $\gt 24\,\mathrm{mag}$ and thus too faint to be detected. We note that the magnetar shock breakout model of Kasen et al. (2016) predicted lower contrast between the peaks than was seen in LSQ14bdq; this mechanism might be relevant for PS1-11aib and PS1-13or.

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The bottom panels of Figure 10 show the evolution of the blackbody temperature of each event during the rise as calculated in Section 3.1. The temperature evolution is best constrained for PS1-11aib and shows an initial cooling at the beginning of the plateau followed by a flattening out. We note that in the only other SLSN-I with multicolor data available during any kind of precursor event, DES14X3taz, the color and temperature evolution during the precursor was consistent with rapid cooling, and it is interpreted as shock cooling in extended material (Smith et al. 2016).

PS1-12cil is another object with a complex structure in its light curve, but with a second, late-time peak or plateau seen in all filters about 40 days after maximum light. The nature of this secondary maximum and its physical interpretation will be discussed in detail in R. Chornock et al. (2018, in preparation), and we therefore do not investigate it further here.

As discussed in Section 4.2, the early points on the light curve of PS1-11aib might be part of an early precursor peak similar to what was seen in LSQ14bdq and DES14X3taz (Nicholl et al. 2015a; Smith et al. 2016). Thus, the best fit will depend on whether we attempt to fit the early points as part of a magnetar-powered light curve or not. Figure 11 shows several different magnetar fits to the light curve of PS1-11aib. The best three-parameter fit to the full light curve has ${M}_{\mathrm{ej}}\approx 9.8\,{M}_{\odot }$, $P\approx 1.9\,\mathrm{ms}$, and $B\approx 6\times {10}^{13}\,{\rm{G}}$. This model fits the rise and peak well, but overpredicts the late-time luminosity, which is a common problem with magnetar models. Wang et al. (2015) suggested this could be overcome by accounting for hard emission leakage as the ejecta become transparent to γ-rays. This is parameterized by adding a term $(1-{e}^{-{{At}}^{-2}})$ in Equation (2), where $A=9{\kappa }_{\gamma }{M}_{\mathrm{ej}}^{2}/40\pi {E}_{{\rm{K}}}$ describes the optical depth of the ejecta to gamma-rays as ${\tau }_{\gamma }={{At}}^{-2}$. Larger values of A correspond to a larger trapping rate and lower leakage rate; the original magnetar model has $A=\infty$. When adding a hard emission leakage term of $A=2\times {10}^{14}\,{{\rm{s}}}^{2}$, our best-fit model can also account for the late-time data point.

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If we interpret the early light curve as a precursor peak and powered by a different mechanism from the main light curve, then the effective rise time of the magnetar-powered light curve is shorter. The best fit when excluding the early data ($\gt 35$ days prior to peak) has a higher magnetic field ($B={10}^{14}\,{\rm{G}}$) and a slightly lower ejecta mass (${M}_{\mathrm{ej}}=8\,{M}_{\odot }$) compared to the model above, both of which contribute to making the light curve narrower; the initial spin is similar ($P=2.0\,\mathrm{ms}$). In this case, it is not necessary to invoke late-time leakage to fit the data point at +100 days.

Figure 12 shows the best-fit magnetar model to the light curve of PS1-12bqf. Unlike PS1-11aib, we do not need to invoke hard emission leakage, and the light curve is well fit with a simple model with ${M}_{\mathrm{ej}}=3\,{M}_{\odot }$, $P=4.8\,\mathrm{ms}$, and $B=1\times {10}^{14}\,{\rm{G}}$. Given the noise in the light curve, we can find adequate fits with a range of parameters; faster initial spin periods also require higher magnetic fields to reproduce the peak luminosity and rise time. Although PS1-12bqf has a lower luminosity than most H-poor SLSNe, the fact that it can be well fit with a magnetar should not be surprising: magnetar models have a large parameter space and can naturally produce light curves with a range of luminosities. We note that the values we derive for PS1-12bqf are within the distribution of parameters found by Nicholl et al. (2017b) and similar to what they derive for the SLSNe PTF10hgi and LSQ14mo. Our code is not set up to do a full parameter exploration and calculate confidence intervals; we refer the reader to recent Markov Chain Monte Carlo (MCMC) efforts to model H-poor SLSNe for typical parameter ranges (Guillochon et al. 2017; Liu et al. 2017a; Nicholl et al. 2017b). Such MCMC efforts are also better suited to explore degeneracies and covariances between the different parameters.

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