Superluminous Supernovae in LSST: Rates, Detection Metrics, and Light Curve Modeling

V. Ashley Villar11affiliationmark: , Matt Nicholl11affiliationmark: , and Edo Berger11affiliationmark: Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, Massachusetts 02138, USA;

We explore and demonstrate the capabilities of the upcoming Large Synoptic Survey Telescope (LSST) to study Type I superluminous supernovae (SLSNe). We first fit the light curves of 58 known SLSNe at , using an analytical magnetar spin-down model implemented in MOSFiT. We then use the posterior distributions of the magnetar and ejecta parameters to generate thousands of synthetic SLSN light curves, and we inject those into the LSST Operations Simulator (OpSim) to generate realistic light curves. We define simple, measurable metrics to quantify the detectability and utility of the light curve, and to measure the efficiency of LSST in returning SLSN light curves satisfying these metrics. We combine the metric efficiencies with the volumetric rate of SLSNe to estimate the overall discovery rate of LSST, and we find that SLSNe per year with data points will be discovered in the Wide-Fast-Deep (WFD) survey at , while only SLSNe per year will be discovered in each Deep Drilling Field at . To evaluate the information content in the LSST data, we refit representative output light curves with the same model that was used to generate them. We correlate our ability to recover magnetar and ejecta parameters with the simple light curve metrics to evaluate the most important metrics. We find that we can recover physical parameters to within 30% of their true values from % of WFD light curves. Light curves with measurements of both the rise and decline in -bands, and those with at least fifty observations in all bands combined, are most information rich, with % of these light curves having recoverable physical parameters to % accuracy. WFD survey strategies which increase cadence in these bands and minimize seasonal gaps will maximize the number of scientifically useful SLSN light curves. Finally, although the Deep Drilling Fields will provide more densely sampled light curves, we expect only SLSNe with recoverable parameters in each field in the decade-long survey.

Subject headings:
supernovae: general

1. Introduction

Type I Superluminous supernovae (SLSNe) are an observationally-classified class of transients that typically reach a peak absolute magnitude of mag and display unique early-time spectra with O ii absorption superposed on a hydrogen-free blue continuum (Chomiuk et al., 2011; Quimby et al., 2011; Gal-Yam, 2012). These events also typically exhibit long durations, with a time to rise and decline by one magnitude of days, allowing them to radiate erg in the optical/UV, comparable to the kinetic energies of normal core-collapse SNe. Despite their high luminosities and long durations, SLSNe are a relatively recent discovery due to the advent of untargeted wide-field time-domain surveys. These surveys are essential due to the low volumetric rate and low-luminosity host galaxies of SLSNe (Neill et al., 2010; Lunnan et al., 2014; Chen et al., 2017a; Leloudas et al., 2015; Angus et al., 2016; Perley et al., 2016; Schulze et al., 2018).

There is ongoing debate about the energy source of SLSNe. Unlike hydrogen-rich Type II SLSNe which appear to be powered by interaction with a dense circumstellar medium (Chevalier and Irwin, 2011), such interaction is disfavored as the dominant heating source for Type I SLSNe, due to the exceptionally large CSM mass required to reproduce the bright observed light curves (Moriya et al., 2018), coupled with low-density environments suggested by X-ray (Margutti et al., 2017) and radio (Nicholl et al., 2016a; Coppejans et al., 2018) observations. Instead, a central engine model is preferred, and it appears to explain the light curve shapes and diversity (Nicholl et al., 2017a), early-time spectra (e.g., Dessart et al. 2012; Howell et al. 2013; Mazzali et al. 2016), and the velocity and density structures inferred from nebular spectra (Nicholl et al., 2016b; Jerkstrand et al., 2017; Nicholl et al., 2018).

Currently, the best central engine candidate to power SLSNe is a rapidly spinning magnetar, or a pulsar with a strong magnetic field ( G; Kasen and Bildsten 2010; Woosley 2010; Inserra et al. 2013; Chatzopoulos et al. 2013; Metzger et al. 2015; Nicholl et al. 2017a). The magnetar model can explain the diversity of SLSN light curves (Nicholl et al., 2017a; Villar et al., 2017), and the inferred velocities and temperatures (Moriya et al., 2018). Recently, Nicholl et al. 2017a fit a sample of 38 well-observed SLSNe with a semi-analytical magnetar model and found that this model is able to reproduce the observed light curves using a fraction of parameter space (see also, Nicholl et al. 2015a; Prajs et al. 2016; Yu et al. 2017; Liu et al. 2017).

Statistical population studies like these are essential for mapping the properties of SLSNe. Currently, about 10 SLSNe are discovered per year (Guillochon et al., 2017)111See, and this low rate allows for detailed spectroscopic follow-up of each event. However, future surveys will lead to a substantial increase in the discovery rate. For example, Tanaka et al. (2012) and Tanaka et al. (2013) explored several future optical and near-infrared (NIR) surveys, concluding that missions like WFIRST and LSST will find SLSNe per year. Due to limited spectroscopic resources, it is essential to explore what information can be obtained about these large samples from light curves alone; namely, their diverse observational properties (Nicholl et al., 2015a), progenitor populations (Lunnan et al., 2014), host galaxies (Berger et al., 2012; Schulze et al., 2018), and potentially cosmological parameters (Inserra and Smartt, 2014; Scovacricchi et al., 2015).

Here, we explore and study the characteristics of SLSNe observed by the upcoming Large Synoptic Survey Telescope (LSST), an 8.4-m diameter telescope with a 9.6 deg field-of-view that will conduct several 10-year wide-field surveys across the Southern hemisphere in the filters. The current LSST observing strategy spends the majority () of the time executing the Wide-Fast-Deep (WFD) survey, covering 18,000 deg with a cadence of roughly four days in any filter and ten days in a specific filter, and with a per-visit limiting magnitude of mag. About 5% of the observing time will focus on several Deep Drilling fields (DDFs), each comprised of a single pointing with five times more cumulative imaging than a typical field in the WFD survey and with a nightly stack limiting magnitude of mag. The remaining time will be split between the Galactic Plane and South Celestial Pole surveys. We focus on the WFD survey and DDFs in this study (see LSST Science Collaboration et al. 2009 for technical details).

The large survey area, cadence and depth make LSST a potential powerhouse for time-domain astronomy, particularly in the case of volumetrically-rare events like SLSNe. However, there are two key questions that must be addressed to maximize the potential of LSST. First, it is essential to quantify the number of SLSNe that LSST will discover, their redshift distribution, and their observational properties. Second, it is vital to predict the information content from LSST light curves alone to account for cases which will lack spectroscopic follow up. In this work we perform the first detailed study of SLSNe discovered with LSST using an observationally-motivated suite of SLSN models and a realistic observational simulator provided by the LSST collaboration.

The paper is structured as follows. In §2, we outline the simulations used to produce realistic SLSN light curves as they would appear in the LSST WFD survey and DDFs. In §3, we describe the characteristics of the SLSNe discovered by LSST based on our simulation results. In §4, we discuss the ability to recover physical parameters from the LSST light curves, and quantify the information content of the simulated light curves. We conclude in §5. All magnitudes are reported in the AB system, and we assume a standard cosmology, with km s Mpc, , and (Planck Collaboration et al., 2016).

Figure 1.— A subset of the model parameters for the SLSN magnetar model, showing the results for the observed sample (orange circles: Nicholl et al. 2017a; purple squares: Lunnan et al. 2018; green diamonds; De Cia et al. 2017), and our simulated population (blue circles). The simulated sample captures intrinsic correlations between parameters (including nuisance parameters) that are seen within the observed population.

2. Simulation Set-Up

To simulate the observable SLSN population in the LSST surveys we construct a sample of light curve models and inject these into the LSST Operations Simulator (OpSim). We describe these steps in the following subsections.

2.1. Constructing Simulated SLSN Light Curves

We construct a sample of simulated light curves based on known events from the literature. Several studies have previously aggregated SLSN light curves (e.g. Nicholl et al. 2015a; Prajs et al. 2017; Liu et al. 2017; De Cia et al. 2017; Lunnan et al. 2018). Recently, Nicholl et al. (2017a) uniformly modeled a sample of 38 SLSNe requiring the events to be spectroscopically classified and to have some photometric data near peak. As such, the sample spans a range of peak luminosities and light curve timescales. Here we combine the sample of Nicholl et al. (2017a) with 12 events discovered by the Palomar Transient Factory (PTF; De Cia et al. 2017) and 8 events discovered in the Pan-STARRS1 Medium Deep Survey (PS1-MDS; Lunnan et al. 2018), leading to 58 spectroscopically classified SLSNe spanning a wide range of observational properties (see Table 1).

We model the 21 PTF and PS1-MDS SLSNe with the same model described in Nicholl et al. (2017a). In short, we use the open-source code MOSFiT (Guillochon et al., 2018) to fit a magnetar spin-down model to the multi-band light curves. We assume a modified blackbody spectral energy distribution (SED) in which flux is linearly suppressed below a “cutoff” frequency of 3000Å. This SED shape is consistent with observed SEDs (Chomiuk et al. 2011; Nicholl et al. 2016c, but see also Yan et al. 2018 who argue that more UV variation is seen in SLSN SEDs). We remove data in which a pre-peak “bump” is observed (see Nicholl and Smartt 2016). Our best-fit parameters and their error bars are provided in Table 3.

We use the sample of 58 fitted events to generate our simulated SLSN light curves. Because drawing walkers directly from the model posteriors would lead to undersampling of the parameter space, we sample from a model of the underlying population distribution as follows. We draw one walker from the posterior of each event to create a distribution of the model parameters of the underlying population. We fit this distribution to a truncated multivariate log-Gaussian which allows us to capture the correlations between parameters observed in the sample events. We place physically-motivated limits on the parameters, as listed in Table 2. We then draw samples from the population distribution to generate 1,000 events per redshift bin of from to . Finally, from this sample we eliminate events with mag; although these magnetar-powered events may exist in nature, they are not necessarily distinguishable from the broader population of Type I SNe. The parameters for the modeled SLSNe and for our simulated events are shown in Figure 1.

Name Redshift Reference Name Redshift Reference
PTF11hrq 0.057 De Cia et al. (2017) PTF09cwl* 0.350 Quimby et al. (2011)
PTF10hgi* 0.099 Inserra et al. (2013) De Cia et al. (2017)
De Cia et al. (2017) SN2006oz* 0.376 Leloudas et al. (2012)
Gaia16apd* 0.102 Yan et al. (2017a) PTF13cjq 0.396 De Cia et al. (2017)
Nicholl et al. (2017b) PTF13bdl 0.403 De Cia et al. (2017)
Kangas et al. (2017) iPTF13dcc* 0.431 Vreeswijk et al. (2017)
PTF12hni 0.106 De Cia et al. (2017) De Cia et al. (2017)
PTF12dam* 0.107 Nicholl et al. (2013) PTF10vqv 0.452 De Cia et al. (2017)
Chen et al. (2015) PTF09atu* 0.502 Quimby et al. (2011)
De Cia et al. (2017) De Cia et al. (2017)
Vreeswijk et al. (2017) PS1-14bj* 0.522 Lunnan et al. (2016)
SN2015bn* 0.114 Nicholl et al. (2016a) Lunnan et al. (2018)
Nicholl et al. (2016b) PS1-12bqf 0.522 Lunnan et al. (2018)
PTF10nmn 0.124 De Cia et al. (2017) PS1-11ap* 0.524 McCrum et al. (2013)
SN2007bi* 0.128 Gal-Yam et al. (2009) Lunnan et al. (2018)
SN2011ke* 0.143 Inserra et al. (2013) DES14X3taz* 0.608 Smith et al. (2016)
De Cia et al. (2017) PS1-10bzj* 0.650 Lunnan et al. (2013)
SSS120810* 0.156 Nicholl et al. (2014) Lunnan et al. (2018)
PTF10bfz 0.170 De Cia et al. (2017) DES13S2cmm* 0.663 Papadopoulos et al. (2015)
SN2012il* 0.175 Inserra et al. (2013) PS1-11bdn 0.738 Lunnan et al. (2018)
PTF12gty 0.177 De Cia et al. (2017) iPTF13ajg* 0.740 Vreeswijk et al. (2014)
PTF11rks* 0.192 Inserra et al. (2013) De Cia et al. (2017)
De Cia et al. (2017) PS1-13gt 0.884 Lunnan et al. (2018)
PTF10aagc 0.207 De Cia et al. (2017) PS1-10awh* 0.908 Chomiuk et al. (2011)
iPTF15esb* 0.224 Yan et al. (2017b) Lunnan et al. (2018)
SN2010gx* 0.230 Pastorello et al. (2010) PS1-10ky* 0.956 Chomiuk et al. (2011)
Quimby et al. (2011) Lunnan et al. (2018)
De Cia et al. (2017) PS1-11aib 0.997 Lunnan et al. (2018)
SN2011kf* 0.245 Inserra et al. (2013) PS1-10ahf* 1.1 McCrum et al. (2015)
iPTF16bad* 0.247 Yan et al. (2017b) Lunnan et al. (2018)
LSQ14mo* 0.253 Chen et al. (2017b) SCP-06F6* 1.190 Barbary et al. (2008)
LSQ12dlf* 0.255 Nicholl et al. (2014) PS1-10pm* 1.206 McCrum et al. (2015)
De Cia et al. (2017) Lunnan et al. (2018)
PTF09cnd* 0.258 Quimby et al. (2011) PS1-11tt 1.283 Lunnan et al. (2018)
SN2013dg* 0.265 Nicholl et al. (2014) PS1-11afv 1.407 Lunnan et al. (2018)
PTF13bjz 0.271 De Cia et al. (2017) SNLS-07D2bv* 1.50 Howell et al. (2013)
SN2005ap* 0.283 Quimby et al. (2007) PS1-13or 1.52 Lunnan et al. (2018)
PTF10uhf 0.288 De Cia et al. (2017) PS1-11bam* 1.565 Berger et al. (2012)
PTF12mxx 0.327 De Cia et al. (2017) PS1-12bmy 1.572 Lunnan et al. (2018)
iPTF13ehe* 0.343 Yan et al. (2015) Lunnan et al. (2018)
De Cia et al. (2017) SNLS-06D4eu* 1.588 Howell et al. (2013)
LSQ14bdq* 0.345 Nicholl et al. (2015b)

Note. – Best fit magnetar parameters presented in Nicholl et al. 2017a. Other magnetar parameters presented in Table 3.

Table 1Type I SLSNe Used in this Analysis

The resulting -band peak-luminosity function of our simulated events and the observed sample are shown in Figure 2. Our simulated luminosity function is consistent with that derived by Nicholl et al. 2017a. We do not attempt to correct for any potential observational biases within the various surveys, as we expect these effects to be small relative to the overall uncertainty in the volumetric rate (approximately a factor ; see Quimby et al. 2013; McCrum et al. 2015; Prajs et al. 2016 and §4). Similarly, we show the duration distribution of the known SLSNe and of our simulated events in Figure 3, finding a good agreement between the two.

Parameter Min Max
/ms 0.7 100
/M 1 100
km s 0.5 100
/ g cm 0.05 0.2
/ g cm
/M 1.4 2.2
K 0.1 50

Note. – Parameters described in detail in Nicholl et al. 2017a.
Indicates limits well within the tail of the Gaussian distribution.

Table 2Model Parameters and Imposed Limits
Figure 2.— Observed (orange) and simulated (blue) -band peak luminosity function for SLSNe. The luminosity functions are in good agreement, with only % of our models extending to brighter -band peak luminosities () than currently observed.
Figure 3.— Same as Figure 2 but for the -band duration () of the observed (orange) and simulated (blue) SLSNe. The duration distributions are in good agreement, with only % of our models extending to durations longer than those in our observed sample.
Figure 4.— Sample LSST light curves from OpSim at four representative redshifts. For each redshift, the light curves are ordered by the number of observations, with the left-most representing the bottom 10th percentile, the two middle panels representing the 50th percentile, and the right-most panel representing the 90th percentile.
(ms) G M km s-1 erg cm2g-1 cm2g-1 M K mag mag
PS1-11afv 1.41 1.63 0.20 4.36 11.21 8.25 0.14 0.97 1.87 6.15 0.26 0.01 34
PS1-11aib 1.00 1.24 0.60 28.78 5.44 12.47 0.11 1.48 1.83 6.71 0.44 0.09 137
PS1-11bdn 0.52 3.47 0.90 1.09 8.07 1.10 0.10 21.65 1.82 6.77 0.13 0.07 15
PS1-11tt 1.28 1.11 0.06 9.24 13.77 28.70 0.16 0.03 1.85 6.07 0.20 0.01 80
PS1-12bmy 1.57 2.31 0.52 2.93 13.10 7.79 0.14 1.05 1.90 5.87 0.36 0.01 47
PS1-12bqf 0.52 5.15 0.83 2.82 5.98 1.51 0.09 4.21 1.81 6.06 0.19 0.01 108
PS1-13gt 0.88 1.03 0.04 7.04 17.90 35.96 0.16 0.02 1.75 6.79 0.27 0.01 76
PS1-13or 1.52 1.82 0.56 8.43 8.84 9.37 0.14 0.48 1.78 5.99 0.02 0.10 69
PTF10aagc 0.21 4.48 7.81 1.62 8.16 1.63 0.07 7.34 1.84 5.98 0.14 0.19 50
PTF10bfz 0.17 1.21 4.48 10.23 9.84 17.29 0.13 0.88 1.88 5.23 0.20 0.09 82
PTF10nmn 0.12 2.21 1.03 5.12 10.38 7.06 0.13 0.43 1.87 7.22 0.19 0.13 35
PTF10uhf 0.29 4.35 3.19 2.39 10.54 3.69 0.15 1.56 1.84 5.94 0.35 0.14 27
PTF10vqv 0.45 3.12 1.43 2.71 9.30 3.59 0.11 3.44 1.87 8.72 0.05 0.01 35
PTF11hrq 0.06 7.68 1.15 1.73 11.36 3.30 0.16 0.38 1.89 5.31 0.19 0.06 170
PTF12gty 0.18 6.38 1.56 7.92 5.67 3.95 0.17 1.85 1.84 5.71 0.27 0.13 97
PTF12hni 0.11 6.85 3.21 3.77 6.67 2.56 0.13 3.23 1.84 5.22 0.15 0.33 39
PTF12mxx 0.33 2.24 0.95 6.71 8.16 6.78 0.16 0.03 1.85 6.04 0.26 0.05 197
PTF13bdl 0.40 1.09 1.40 68.80 5.76 35.18 0.18 0.90 1.84 5.97 0.36 0.01 59
PTF13bjz 0.27 2.98 5.51 2.07 11.09 3.90 0.13 0.66 1.75 5.88 0.21 0.18 19
PTF13cjq 0.40 1.75 1.49 7.75 8.33 6.96 0.12 10.02 1.86 6.83 0.10 0.22 63

Note. – The Watanabe-Akaike information criteria (or “widely applicable Bayesian criteria”; Watanabe 2010; Gelman et al. 2014

Table 3SLSNe Parameters for Events Modeled in this Paper

2.2. Description of the LSST Simulation

After generating the sample of SLSN models, we inject the simulated events into OpSim, a publicly available application that simulates LSST’s scheduler and image acquisition process over its 10-year survey. OpSim realistically accounts for the science program requirements, mechanics of the telescope design and potential environmental conditions to produce a database of observations. We use OpSim to calculate the estimated signal-to-noise ratios and limiting magnitudes of each observation, using the formulae outlined in the Appendix. OpSim offers a number of unique schedulers, each designed to optimize distinct scientific goals; we use the most recent simulation, dubbed minion_1016 (Delgado et al., 2014).

For both the WFD survey and DDFs, we inject our simulated models uniformly at in bins of . In each bin, a sample of 1,000 models are randomly injected uniformly across the sky and in time to calculate the “discovery efficiency” (see §3.1) of the LSST observing strategy as a function of redshift. We resample the simulated models to the observed times and add white noise corresponding to the estimated signal-to-noise ratio reported by OpSim. Additionally, we add Milky Way extinction based on the injected sky positions. We disregard host galaxy extinction since most known SLSN host galaxies appear to have negligible extinction (e.g., Chen et al. 2015; Leloudas et al. 2015; Nicholl et al. 2017a; Lunnan et al. 2014). Example light curves at representative redshifts are shown in Figure 4; featured light curves are selected to highlight a combination of best, typical and worst cases in the WFD survey. The luminosity-duration phase space of our simulated SLSNe are shown in Figure 5.

3. Characteristics of SLSNe discovered by LSST

The thousands of injected simulated light curves reflect the wide range of observed SLSN properties expected from LSST. Here we summarize these properties, define our criteria for detection, and determine the rate of detected SLSNe as a function of redshift for both the WFD survey and DDFs.

We calculate the expected number of SLSNe within each redshift bin by multiplying the sample recovered from OpSim by the estimated volumetric rate from Quimby et al. (2013) normalized to the cosmic star formation history (Madau and Dickinson, 2014):


where is the normalized SLSNe rate at with an uncertainty range of Gpc (Quimby et al., 2013; Prajs et al., 2016). Using this prescription, the volumetric SLSN rate peaks at .

We first focus on the -band light curves to provide an overview of the broad observational properties. In Figure 5, we show the observed duration-luminosity phase space for our injected light curves (weighted by their volumetric rate) using a kernel density estimate. For the WFD survey, peak observed magnitudes span mag, with the distribution peaking at mag. We also find that the observed durations of the SLSNe span days. This timescale is comparable to the expected LSST season length ( months), implying that for a substantial fraction of events the rise or decline will be missed in seasonal gaps. We find that a typical SLSN is tracked for days ( uncertainty range). For the DDFs, we find that average peak magnitudes are slightly dimmer, with the distribution peaking at mag. The observed durations are similar to those in the WFD survey.

The total number of observed light curve data points (combined in all filters) rapidly decreases with redshift; see Figure 6. For the WFD survey, SLSNe at will have data points, while the majority of SLSNe have light curves with data points. The number of observed data points roughly doubles for the SLSNe in the DDFs due to both their higher cadence and deeper limits, enabling a longer temporal baseline.

Figure 5.— Duration-luminosity phase space for a representative sample of our simulated SLSNe as observed with LSST in the WFD survey (orange) and DDFs (blue). Contours are a kernel density estimate of the two populations, while points represent outliers. The majority of objects have a peak magnitude of mag and durations of days. The events in the DDFs extend to lower peak magnitudes and longer durations.
Figure 6.— Number of observed data points per event as a function of redshift. Bold lines show the mean in each redshift bin, with the shaded regions representing ranges due to event-to-event variations. The number of observed points drops to (our minimum criterion for a detection) at in the WFD survey, while it typically remains at in the DDFs even to .
Metric Limiting Discovered Useful Useful Limiting z Discovered Useful Useful
(yr) (lenient) (strict) (yr) (lenient) (strict)
detections 2.9 9600 4810 (0.50) 1680 (0.18) 3.9 13 5 (0.40) 1 (0.13)
detections 2.3 3320 2170 (0.65) 900 (0.27) 3.5 9 4 (0.50) 1 (0.17)
detections 2.0 590 416 (0.71) 216 (0.37) 2.7 3 2 (0.62) 0 (0.24)
detections in 2.5 50 30 (0.65) 20 (0.37) 2.4 4 2 (0.61) 0 (0.22)
detections in 2.3 1090 720 (0.66) 320 (0.29) 3.1 6 3 (0.55) 1 (0.20)
detections in 2.8 6600 3190 (0.48) 1170 (0.18) 3.7 10 4 (0.40) 1 (0.13)
detections in 2.7 6120 3170 (0.52) 1170 (0.19) 3.8 10 4 (0.41) 1 (0.13)
detections in 2.3 2770 1730 (0.63) 730 (0.27) 3.8 10 4 (0.45) 1 (0.15)
detections in 2.0 1300 890 (0.69) 420 (0.33) 3.2 6 3 (0.53) 1 (0.19)
observations in rise 3.6 2240 577 (0.26) 131 (0.06) 4.0 8 2 (0.35) 0 (0.10)
during peak 2.2 2690 1740 (0.65) 780 (0.29) 3.4 9 4 (0.49) 1 (0.17)
Detected days after explosion 2.9 100 36 (0.36) 13 (0.14) 3.7 2 0 (0.31) 0 (0.10)
Detected days after explosion 3.2 350 119 (0.34) 42 (0.12) 3.9 5 1 (0.28) 0 (0.09)
Measurable duration in 1.2 50 39 (0.77) 23 (0.46) 1.8 0 0 (0.71) 0 (0.34)
Measurable duration in 2.1 280 185 (0.66) 78 (0.28) 2.2 1 0 (0.65) 0 (0.27)
Measurable duration in 2.2 960 618 (0.65) 261 (0.27) 2.7 2 1 (0.59) 0 (0.22)
Measurable duration in 2.0 770 514 (0.67) 221 (0.29) 3.1 2 1 (0.60) 0 (0.22)
Measurable duration in 2.1 310 215 (0.70) 108 (0.35) 3.2 2 1 (0.57) 0 (0.22)
Measurable duration in 2.0 90 64 (0.69) 41 (0.44) 2.0 0 0 (0.63) 0 (0.26)

Note. – Cumulative redshift at which 90% of SLSNe are discovered.
Total number of discovered SLSNe satisfying given metric.
Total Number of discovered SLSNe satisfying given metric with recoverable parameters to within a factor of two.
Total Number of discovered SLSNe satisfying given metric with recoverable parameters to within 30%.
Here we define “peak” as within one magnitude of peak brightness.

Table 4Observational Metrics

3.1. Efficiency and Metrics for Detectability

We now focus on more quantitative measures of “detectability” for the simulated light curves. There can be many definitions of a detection of a transient. We are most interested in the ability to: (1) accurately estimate the physical parameters from the light curve, and (2) discover events sufficiently early to enable follow up with other instruments. To address these points, we quantify the information content of the observed light curves by defining several properties that can be easily measured directly from the light curve. We focus on 19 representative properties, summarized in Table 4.

Figure 7.— WFD survey and DDFs efficiencies as a function of redshift. The left-hand y-axis shows the efficiency of SLSN detection, assuming the SLSNe are within the survey footprint (i.e., a SLSN may be in the footprint but too dim to detect). The right-hand y-axis shows the total efficiency, , including the effect of survey area. The shaded region represents the error bars from bootstrap analysis.

Using each property as an independent criterion of detection, we calculate the total detection efficiency for SLSNe in LSST. The efficiency can be divided into two multiplicative parts. The first is the survey efficiency, , arising from the survey footprint and cadence. We calculate this by injecting events uniformly across the complete survey duration and the sky. We then calculate the fraction of events that are in the LSST footprint during at least one observation. This efficiency is effectively the area covered by the survey, given the long duration of SLSNe compared to the cadence of LSST. The second efficiency, , is the fraction of simulated events that satisfy the metrics listed in Table 4.

The total efficiency, , as a function of redshift is shown in Figure 7 for light curves with observations (one of our 19 metrics). For both the WFD survey and DDFs, the efficiencies decline monotonically as a function of redshift; however, the decline is shallower in the case of the deeper DDFs. Within the WFD survey footprint, the efficiency peaks at % at low redshift; in the DDF fields, the efficiency peaks at %. The WFD survey peaks at a lower efficiency due to the fact that SLSNe (particularly if they explode outside of the observing season for their part of the sky) can be discovered well beyond peak, at which point they may already be below the LSST detection limit. The WFD survey efficiency reaches at and declines to at . For the DDFs, the efficiency reaches at and declines to at .

We combine the efficiency and the estimated volumetric rate to calculate the total expected number of SLSNe, the integral of the observed rate over the comoving volume, corrected for time dilation:


We estimate the statistical uncertainty in the number of detections due to the uncertainty in using a bootstrap analysis; namely, we resample the properties of the observed light curves repeatedly, recalculating the efficiencies each time. There is an overall scaling uncertainty due to the systematic uncertainty in the volumetric rate, but we expect this to be improved with new rate measurements from DES (The Dark Energy Survey Collaboration, 2005) and ZTF (Kulkarni, 2018). Therefore, in Figures 79 we show only the statistical uncertainties.

Figure 8.— First and third rows: The WFD survey annual detection rate of SLSNe as a function of redshift (black lines) for various metrics. The green shaded regions represent errors from our bootstrap analysis. Also shown are the rates for SLSNe with (strict) recoverable parameters (purple line and shaded area); note that the purple line is calculated assuming the same information efficiency for each metric. Second and fourth rows: Cumulative distributions of SLSNe that satisfy each metric (black) and those that have lenient recoverable parameters (purple).
Figure 9.— Same as Figure 8 but for each DDF.

The number of SLSNe discovered per year as a function of redshift is shown in Figures 8 and 9. For our most lenient definition of a detection (at least 10 light curve points), we find that LSST will discover SLSNe per year. This is in agreement with the rate reported in the Scientific Handbook (LSST Science Collaboration et al., 2009) and previous studies (Tanaka et al., 2013; Scovacricchi et al., 2015). The distribution roughly traces the cosmic star formation history to , at which point the observed distribution drops more rapidly due to the declining detection efficiency. The distribution extends to in the WFD survey and to in the DDFs.

Measuring both the peak brightness and duration can lead to robust measurements of the SLSN properties. About 2,700 SLSNe per year will have more than 20 observations within one magnitude of their peak brightness. We find that the duration is most readily measurable in -band, and that for about 950 SLSNe per year (as defined above) will be measured; we note that this represents only 10% of the overall SLSN sample.

Capturing the light curve rise can be especially important for constraining the underlying power source in SLSNe and to search for early bumps in the light curve. We find that SLSNe per year will be discovered within ten days (in the rest frame) of their explosion time, comparable to the typical time frame of the early pre-peak bumps seen to date (Nicholl and Smartt, 2016; Leloudas et al., 2012; Nicholl et al., 2015b; Smith et al., 2016). About SLSNe per year will be discovered within five days of explosion, most being located at . About SLSNe will be detected with at least ten observations during the rising phase; however, fewer than 10 SLSNe with this property will be found annually in each DDF, due to their small areal footprint.

4. Recovering the SLSN Parameters

In the previous section we explored the overall detection rates and the redshift distributions for a range of observational light curve metrics. Here we fit the simulated LSST light curves with the same model used to generate them to determine how well we can recover the injected model parameters. Our goals are to understand how well we can determine the model parameters from LSST data, and to correlate our simple light curve metrics to the information content of the light curves. The latter goal is important because the final survey strategies of LSST will be determined by providing a simple, measurable metric that can be optimized for a specific science goal.

4.1. Injection and Recovery of Representative SLSNe

We fit the output light curves using MOSFiT in the same manner that was used to generate them (§2). We focus on three SLSNe representative of the larger population: SN2013dg ( days), LSQ12dlf ( days), and SN2015bn ( days). All three have roughly the same peak luminosity, erg s. We inject and recover about 100 iterations of these SLSNe at .

We fix the redshift to its input value when fitting, finding that without doing so it is nearly impossible to constrain the explosion parameters. In reality, it is unclear how well we will know the redshift a priori through photometry or (in some cases) spectroscopic measurements of their host galaxies. SLSNe are typically found in low-luminosity ( mag) host galaxies (Lunnan et al., 2014). For , most of these hosts will fall in the so-called LSST “gold” galaxy sample (defined as galaxies with mag), which will have a root-mean-square scatter in the photometric redshifts of (see LSST Science Collaboration et al. 2009). We additionally fix the host reddening to be negligible.

We are interested in our ability to recover four key parameters: the ejecta mass, the ejecta velocity, the initial magnetar spin period, and the magnetic field. In our model, the spin period and magnetic field have strong degeneracies with several nuisance parameters, making them difficult to directly measure. We therefore recover the following variables, which directly correlate with the rotational energy and spindown timescales of the magnetar (Nicholl et al., 2017a; Villar et al., 2017):

, where is the angle between the rotational axis and magnetic dipole, and is the neutron star mass.

How well we need to recover the SLSN parameters depends on the scientific goal. For cosmological studies, determining the average distance modulus (assuming SLSNe are standardizable; see Inserra and Smartt 2014) to mag is sufficient to constrain, for example, to within 2% (Scovacricchi et al., 2015). In Nicholl et al. (2017a), constraining parameters to an average of % was sufficient to probe the underlying population with a sample of events. We track our ability to recover the four key parameters to (1) % of their input values and with error bars of % (“strict”), and (2) within a factor of two of their input values with error bars of % (“lenient”).

Example light curves and their best-fit models are shown in Figure 10. At low redshifts, many of the light curves are well-sampled both near and post peak, leading to better recovery of the input parameters. At higher redshifts, the majority of light curves are caught near peak and quickly drop below the detection limit, leading to typically poorer recovery. Additionally, due to the much deeper limits available in -bands, the light curves of higher redshift events are typically limited to these filters. Thus our ability to recover the input parameters significantly drops with redshift. At , our strict recovery rate is and our lenient recovery rate is for light curves with data points. By , the strict recovery rate drops to zero, while the lenient recovery rate is %. By , the lenient recovery rate also drops to zero.

Figure 10.— Light curves fits from MOSFiT to a sample of simulated LSST light curves at representative redshifts. For each event we list the ratio of the injected to fitted values for the four key model parameters. The light curves are ordered by the quality of parameter recovery from left (worst) to right (best).
Figure 11.— Average parameter residuals (for ) as a function of number of observations per light curve. The blue points show total number of observations per light curve, while the oranges points show the number of observations within 100 days of explosion (in the event’s rest frame). The solid lines are fits to exponential functions to guide the eye. Dotted lines show both the lenient and strict information criteria. There is little gain beyond observations per light curve, and almost no light curves have more than 50 observations within days post-explosion.

The parameter recovery rate is a function of both redshift and luminosity. The above calculations used a peak luminosity of erg s. We now consider the full luminosity function of our simulated SLSNe (Figure 2) to capture the overall recovery rate. For any luminosity, the recovery curve as a function of redshift, , is set to 1 at and to zero at , where is the limiting redshift for a given luminosity. For SLSNe with peak luminosity , the limiting redshift is . We assume that for all other peak luminosities, the recovery rate can be described as . This allows brighter events to be captured at higher redshifts, and all events will be capped to their limiting redshifts. After reweighting the recovery rate through this process with our simulated luminosity function, we find that the overall efficiencies decline more rapidly with redshift. For example, the lenient recovery rate drops to % at , rather than to % when we used just a single peak luminosity.

Multiplying our corrected recovery rates by the overall discovery efficiency from §3, we find that (about 1,700 out of 9,600 discovered annually) of SLSNe discovered in the WFD survey will have light curves that satisfy our strict criterion, and will satisfy the lenient criterion. Even at the high redshift end (), SLSNe per year will satisfy the lenient criterion.

For the DDFs, we find that the fraction of useful light curves is slightly smaller than that of the WFD survey. This is likely due to the fact that the overall efficiency reaches to higher redshifts, although fewer of the high-redshift light curves are useful due to their lower luminosities.

4.2. Correlating SLSN Properties to Parameter Recovery

Finally, we turn to the question of what properties of a SLSN light curve allow us to best recover key physical parameters. Unsurprisingly, the number of observations strongly correlates with our ability to recover parameters. This is demonstrated in Figure 11, in which we show the average parameter residual for each of the four important physical parameters (e.g., ) as a function of the number of observations for a sample of light curves spanning from to . We consider both the total number of observations (taken at any point during the event) and observations taken within the first days in the rest-frame (i.e., near-peak). In both cases, light curves with points are significantly more likely to have recoverable physical parameters compared to the average light curve with observations (% compared to % recovery rate). Light curves with observations are only somewhat more useful than those with observations when using the lenient definition (% vs %); however, they are more useful when using the strict criterion, with % compared to %.

Additionally, having a measurable duration in any filter is a good indicator of an information-rich light curve, with % compared to % recovery rate for the typical light curve. This is likely due to the fact that the light curve peak and width greatly constrain the model parameter space. For example, a bright and broad light curve cannot be produced by a small ejecta mass or weak magnetic field. The most “useful” filter for measuring duration appears to be -band, although this is likely due to the fact that light curves which are well-sampled in -band tend to be at low redshifts (i.e., the limiting redshift for this metric is only ). In contrast, light curves with a measurable -band duration can occur at higher redshift (). Again, this suggests that well-sampled light curves near peak are more scientifically useful.

These findings indicate that a survey strategy which optimizes a higher cadence in the most sensitive bands, , will provide the greatest return on scientifically useful light curves even at high redshift. Given the average SLSN duration of days (Figure 5), a cadence of roughly two to four days (similar to the nominal cadence) in any filter would be sufficient to recover magnetar parameters directly from most SLSN light curves at . Perhaps more importantly, the current WFD observing strategy has large seasonal gaps every months which interrupt many SLSN light curves. This is due to the fact that the WFD survey observes fields with airmass (LSST Science Collaboration et al., 2009). Reducing these gaps with even a few observations at higher airmass would be beneficial to provide more comprehensive temporal coverage and greater opportunity to recover SLSN properties. In a similar vein, stacking late-time observations can significantly extend our light curve coverage accross seasons.

5. Summary and Conclusions

We presented detailed simulations of Type-I SLSNe in the upcoming LSST survey. We constructed a realistic distribution of magnetar and explosion parameters from an existing sample of 58 SLSNe spanning and used this to simulate thousands of SLSNe at in the LSST Operations Simulator.

We define a number of measurable light curve metrics which we use to define a “detection”. For our loosest definition of a detection (observing data points in all filters combined), we find that the detection efficiency of the WFD survey quickly declines from % at to % at , while for the DDFs, the efficiency declines from % at to % at and at . We combine this detection efficiency with an estimate for the cosmic SLSN rate to find that LSST will discover SLSNe per year within the WFD survey and per year in each DDF. Most (%) of the discovered SLSNe are found at , although SLSN per year should be discovered at .

We refit the light curves of representative SLSNe injected into the LSST WFD survey and DDFs, and test how well we can recover four key physical parameters (initial magnetar spin period, magnetic field strength, ejecta velocity and ejecta mass). We find that we can successfully recover the four parameters in % of all SLSNe to within with error bars of % of the parameter values. We can recover the parameters to within a factor of two for % of all SLSNe. The majority of SLSNe with recoverable parameters will be found at low redshift (). Parameter recovery relies on having accurate redshifts; while LSST will provide photometric redshifts for many host galaxies this may become a challenge at the high redshift end.

We correlate our ability to recover physical parameters with the defined light curve metrics. In both the WFD survey and DDFs, light curves with observations, especially concentrated near-peak, are typically those with recoverable parameters. LSST survey strategies which maintain a rapid cadence ( day) in the most sensitive bands will provide the most scientifically useful SLSN light curves. Similarly, strategies which minimize seasonal gaps with some high airmass observations will increase our chance of covering the light curves peak and duration, and therefore provide more scientifically useful light curves. Finally, stacking observations at late times may allow us to probe more SLSNe across multiple seasons and better anchor our models.

Compared to the WFD survey, we find that the DDFs (in their current form) will not provide higher quality SLSNe, or SLSNe at significantly higher redshifts in large quantities due to the small area covered by these fields. It is therefore imperative to maximize the scientific return from events in the WFD survey, rather than relying on a small number of events from the DDFs.

Overall, our simulations indicate that LSST will be a powerhouse for discovering SLSNe. About 1,700 SLSNe per year will have sufficient photometry to extract key physical parameters directly from the light curves (given an accurate redshift estimate) to within 30%, significantly increasing our current sample by at least two orders of magnitude.

We thank J. Guillochon and P. Cowperthwaite for useful discussions. The computations presented in this work were performed on Harvard University’s Odyssey computer cluster, which is maintained by the Research Computing Group within the Faculty of Arts and Sciences. The Berger Time Domain group is supported in part by NSF grant AST-1714498 and NASA ADA grant NNX15AE50G. Using information provided by OpSim, we can calculate the signal-to-noise ratio () of our injected observations 222See

where is the source counts in ADU, is the background count per pixel in ADU, e is the instrumental noise in ADU, e/ADU is the gain, and is the effective number of source pixels. Both and are provided by OpSim. The source counts are calculated using:


where is source spectrum, and is the filter throughput, s is the integration time, cm is the effective collecting area and is Plank’s constant. The effective number of pixels can be calculated as:


where is the effective full-width-at-half-max of the source PSF as reported by OpSim and px ”/pixel is the pixel scale.

For the DDFs, the exposure time is increased according to the number of exposures taken in a single night in each filter, allowing us to probe deeper limiting magnitudes.


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