Issue 
A&A
Volume 609, January 2018



Article Number  A83  
Number of page(s)  12  
Section  Extragalactic astronomy  
DOI  https://doi.org/10.1051/00046361/201731758  
Published online  18 January 2018 
Euclid: Superluminous supernovae in the Deep Survey^{⋆}
^{1} Department of Physics and Astronomy, University of Southampton, Southampton SO17 1BJ, UK
email: C.Inserra@soton.ac.uk
^{2} Astrophysics Research Centre, School of Mathematics and Physics, Queen’s University Belfast, Belfast BT7 1NN, UK
^{3} Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth PO1 3FX, UK
^{4} IRFU, CEA, Université ParisSaclay, 91191 GifsurYvette Cedex, France
^{5} INAFCapodimonte Observatory, Salita Moiariello 16, 80131 Napoli, Italy
^{6} INAF, Istituto di Radioastronomia, via Piero Gobetti 101, 40129 Bologna, Italy
^{7} Dipartimento di Fisica e Scienze della Terra, Università degli Studi di Ferrara, via Giuseppe Saragat 1, 44122 Ferrara, Italy
^{8} INFN – Bologna, via Irnerio 46, 40126 Bologna, Italy
^{9} INAF–Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, 35122 Padova, Italy
^{10} Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, 1749016 Lisboa, Portugal
^{11} INFN section of Naples, via Cinthia 6, 80126 Napoli, Italy
^{12} Department of Physics “E. Pancini”, University Federico II, via Cinthia 6, 80126 Napoli, Italy
^{13} INAF – IASF Bologna, via Piero Gobetti 101, 40129 Bologna, Italy
^{14} Université Paris Diderot, AIM, Sorbonne Paris Cité, CEA, CNRS 91191 GifsurYvette Cedex, France
^{15} Observatoire de Paris, PSL Research University, 61 avenue de l’Observatoire, 75014 Paris, France
^{16} Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Edifício C8, Campo Grande, 1749016 Lisboa, Portugal
^{17} International Center for Relativistic Astrophysics, Piazzale della Repubblica 2, 65122 Pescara, Italy
^{18} Department of Physics, Lancaster University, Lancaster, LA1 4YB, UK
^{19} Institut d’Astrophysique de Paris, 98bis boulevard Arago, 75014 Paris, France
^{20} MaxPlanckInstitut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany
^{21} Mullard Space Science Laboratory, University College London, Holmbury St Mary, Dorking, Surrey RH5 6NT, UK
^{22} Department of Physics and Helsinki Institute of Physics, Gustaf Hällströmin katu 2, 00014 University of Helsinki, Finland
^{23} Institute of Space Sciences (IEECCSIC), c/Can Magrans s/n, 08193 Cerdanyola del Vallès, Barcelona, Spain
^{24} INAF–Osservatorio Astronomico di Trieste, via G. B. Tiepolo 11, 34131 Trieste Italy
^{25} NASA Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, MS 169237, CA 91109, USA
^{26} INAF–Osservatorio Astronomico di Roma, via Frascati 33, 00078 Monteporzio Catone, Italy
^{27} AixMarseille Univ., CNRS/IN2P3, CPPM, 13288 Marseille, France
^{28} Tsinghua Center for Asttrophysics, Tsinghua University, 100084 Beijing, PR China
^{29} Depto. de Electroónica y Tecnología de Computadoras Universidad Politécnica de Cartagena, 30202 Cartagena, Spain
^{30} Instituto de Astrofísica e Ciências do Espao, Universidade de Lisboa, Tapada da Ajuda, 1349018 Lisboa, Portugal
Received: 11 August 2017
Accepted: 3 October 2017
Context. In the last decade, astronomers have found a new type of supernova called superluminous supernovae (SLSNe) due to their high peak luminosity and long lightcurves. These hydrogenfree explosions (SLSNeI) can be seen to z ~ 4 and therefore, offer the possibility of probing the distant Universe.
Aims. We aim to investigate the possibility of detecting SLSNeI using ESA’s Euclid satellite, scheduled for launch in 2020. In particular, we study the Euclid Deep Survey (EDS) which will provide a unique combination of area, depth and cadence over the mission.
Methods. We estimated the redshift distribution of Euclid SLSNeI using the latest information on their rates and spectral energy distribution, as well as known Euclid instrument and survey parameters, including the cadence and depth of the EDS. To estimate the uncertainties, we calculated their distribution with two different setups, namely optimistic and pessimistic, adopting different star formation densities and rates. We also applied a standardization method to the peak magnitudes to create a simulated Hubble diagram to explore possible cosmological constraints.
Results. We show that Euclid should detect approximately 140 highquality SLSNeI to z ~ 3.5 over the first five years of the mission (with an additional 70 if we lower our photometric classification criteria). This sample could revolutionize the study of SLSNeI at z > 1 and open up their use as probes of starformation rates, galaxy populations, the interstellar and intergalactic medium. In addition, a sample of such SLSNeI could improve constraints on a timedependent dark energy equationofstate, namely w(a), when combined with local SLSNeI and the expected SN Ia sample from the Dark Energy Survey.
Conclusions. We show that Euclid will observe hundreds of SLSNeI for free. These luminous transients will be in the Euclid datastream and we should prepare now to identify them as they offer a new probe of the highredshift Universe for both astrophysics and cosmology.
Key words: surveys / supernovae: general / cosmology: observations
© ESO, 2018
1. Introduction
Over the last decade, new dedicated transient surveys of the Universe have discovered a multitude of new phenomena. One of the most surprising examples of such new transients is the discovery of superluminous supernovae (SLSNe; Quimby et al. 2011; GalYam 2012) which appear to be longlived explosions (hundreds of days) with peak magnitudes far in excess of normal supernovae (5–100 times the luminosity of Type Ia and corecollapse supernovae, GalYam 2012; Inserra et al. 2013).
Over the last five years, it has been established that SLSNe come in different types (GalYam 2012; Nicholl et al. 2015; Inserra et al. 2016b) and can be seen to high redshift (z ~ 1−4, Cooke et al. 2012; Howell et al. 2013). The power source for these events remains unclear but the most popular explanation is the rapid spindown of a magnetar (a highly magnetic neutron star) which can explain both the peak luminosities and the extended lightcurve of SLSNe (Kasen & Bildsten 2010; Woosley 2010). Alternatives include possible interactions between the supernova ejecta and the surrounding circumstellar material previously ejected from the massive central star (Chatzopoulos et al. 2013).
With forthcoming surveys like the Zwicky Transient Factory (ZTF; Kulkarni et al. 2012) and the Large Synoptic Survey Telescope (LSST; Ivezic et al. 2008; LSST Science Collaboration et al. 2009), the interest in SLSNe as possible highredshift cosmological probes has grown due to their high luminosity and possibly increased space density at high redshift (Howell et al. 2013). Recent studies (Inserra & Smartt 2014; Papadopoulos et al. 2015; Chen et al. 2017a) suggest Type Ic SLSNe (namely hydrogenpoor events with similar spectral features as normal Type Ic supernovae, Pastorello et al. 2010) could be standardized in their peak luminosities using empirical corrections similar in spirit to those used in the standardization of Type Ia supernova (Rust 1974; Pskovskii 1977; Phillips 1993; Hamuy et al. 1996; Riess et al. 1996, 1998; Perlmutter et al. 1997; Goldhaber et al. 2001; Guy et al. 2005, 2007; Mandel et al. 2009, 2011). Inserra & Smartt (2014) showed that a correction based on the colour of the SLSNIc (over 20 to 30 days past peak in the restframe) could reduce the scatter in the peak magnitudes to 0.26 (Table 3 in Inserra & Smartt 2014) thus raising the possibility that such SLSNe could be used as standard candles.
This concept was explored in Scovacricchi et al. (2016) where we investigated the potential of SLSNeI^{1} for constraining cosmological parameters. Scovacricchi et al. (2016) found that even the addition of ≃ 100 SLSNeI to present supernova (SN) samples could significantly improve the cosmological constraints by extending the Hubble diagram into the deceleration epoch of the Universe (i.e. z > 1). Also, this work predicted that LSST could find ~10^{4} SLSNeI (over 10 yrs) which would constrain Ω_{m} (the density parameter of matter of the Universe) and w (a constant equationofstate of dark energy) to 2% and 4%, respectively. Such a sample of LSST SLSNI would also provide interesting constraints on Ω_{m} and w(z) (a varying equationofstate) that were comparable to that predicted for ESA’s Euclid mission (Laureijs et al. 2011).
Euclid is a 1.2 m optical and nearinfrared (NIR) satellite (Laureijs et al. 2011) designed to probe the dark Universe using measurements of weak gravitational lensing and galaxy clustering. Euclid is scheduled for launch in late 2020 and will spend the next six years performing two major surveys, namely a “wide” survey of 15 000 deg^{2} and a “deep” survey of 40 deg^{2} at both visual (photometry) and NIR (photometry and grism spectroscopy) wavelengths.
There are proposals to perform a highredshift Type Ia supernova (SNe Ia) survey with Euclid (see DESIRE by Astier et al. 2014) and WFIRST (Hounsell et al. 2017), which will complement groundbased searches for local and intermediate redshift SNe Ia. DESIRE would be a dedicated 6month NIR rolling search with Euclid and is predicted to measure distances to 1700 highredshift SNe Ia (to z ≃ 1.5) thus constraining w to an accuracy of 2%.
In this paper, we study an additional supernova search with Euclid that is different from DESIRE in two ways. First, we only consider using the already planned Euclid surveys, specifically the Euclid Deep Survey (EDS) as it has a planned observing cadence that could be wellsuited to the long SLSN lightcurves. Secondly, we study the possibility of using SLSNeI as an additional cosmological probe, which can be seen to higher redshift because of their high luminosities, especially at restframe UV wavelengths (although they are not as wellunderstood as SNe Ia). Therefore, these observations are essentially for free and will be complementary to DESIRE and other Euclid dark energy constraints.
In Sect. 2, we outline the rate of SLSNI as a function of redshift and what is possible with the EDS, while in Sect. 3 we give an overview of spectroscopic followup of Euclid SLSNe. In Sect. 4 we discuss astrophysical uses of the Euclid SLSNe, while in Sect. 5, we construct a mock Hubble diagram using these Euclid SLSNe and study the possible cosmological constraints. We discuss Euclid SLSNe in Sect. 6 and conclude in Sect. 7. Throughout this paper, we assume a fiducial flat ΛCDM cosmology with H_{0} = 68 km s^{1} Mpc^{1} and Ω_{m} = 0.3, which is consistent with recent cosmological measurements (e.g. Aubourg et al. 2015).
2. Modelling the rate of SLSNI
2.1. The observed SLSNI rate
Despite their intrinsic luminosity, there are only approximately 30 wellstudied SLSNeI presently available in the literature with both spectroscopy and multiband photometric lightcurves (e.g. see SLSNI collections presented in Inserra & Smartt 2014; Nicholl et al. 2015). However, with forthcoming widefield imaging surveys (e.g. ZTF, LSST, Euclid), targeting the distant Universe (z> 1), we expect the number of such wellstudied SLSNeI to increase significantly over the next decade.
We focus here on predictions for Euclid. To make such predictions, we need an estimate of the rate of SLSNI with redshift. Unfortunately there is still uncertainty in the rate of these rare objects especially at high redshift. For example, Quimby et al. (2013) estimates a SLSNI rate of 32$\begin{array}{c}\mathrm{+}\mathrm{77}\\ 26\end{array}$ yr^{1} Gpc^{3} with a weighted mean redshift of $\overline{)\mathit{z}}\mathrm{=}\mathrm{0.17}$. This corresponds to a fraction (~ 10^{4}) of the volumetric rate of corecollapse SNe (CCSNe) at the same redshift (consistent with the previous estimate from Quimby et al. 2011). The recent rate measurement of Prajs et al. (2017) using the first four years of the CanadaFrance Hawaii Telescope Supernova Legacy Survey (SNLS) finds 91$\begin{array}{c}\mathrm{+}\mathrm{76}\\ 36\end{array}$ yr^{1} Gpc^{3}, at a weighted mean redshift of $\overline{)\mathit{z}}\mathrm{=}\mathrm{1.13}$, thus consistent with Quimby et al. (2013). Between the two measurements there is an increase in the volumetric rate as a function of redshift that is a consequence of the observed star formation history.
However, McCrum et al. (2015) estimate that the SLSNI rate could be up to ten times lower, based on the PanSTARRS Medium Deep Survey over the redshift range 0.3 <z< 1.4, while Cooke et al. (2012) obtain an optimistic rate of ~ 200 yr^{1} Gpc^{3} based on only two SLSNeI at a weighted redshift of $\overline{)\mathit{z}}\mathrm{=}\mathrm{3.0}$. The large uncertainties on all these rate measurements allow them to be consistent with each other, demonstrating that further observations are needed to resolve any apparent discrepancies.
In addition, if we note that only one SN of the ≃ 50 gammaray burst (GRB) SNe appears to be close to superluminous magnitudes (Greiner et al. 2015; Kann et al. 2016), then the rate of SLSNI is likely to be smaller than the GRBSN rate by approximately two orders of magnitude. Assuming a ratio of ≃ 4% between GRBSN and SNIbc (Guetta & Della Valle 2007), and a rate of ≃ 2.5 × 10^{4} yr^{1} Gpc^{3} for SNIbc (from Asiago and Lick surveys, Cappellaro et al. 1999; Li et al. 2011, respectively), the expected rate of SLSNI would be approximately 10 to 100 objects yr^{1} Gpc^{3}, which provides an independent estimate consistent with Quimby et al. (2013) and Prajs et al. (2017).
Fig. 1 Summary of the EDS cadence over the fiveyear (1825 days) survey. Open symbols refer to the calibration epochs, which are ten per field excluding the Fornax field. Calibration epochs will have the same nominal depth of whole EDS. See Table 1 for further details. 
Sampling and coverage information of the three fields of the Euclid Deep Survey (EDS).
2.2. Euclid Deep Survey
To calculate the number of likely Euclid SLSNeI, we need to know the volume sampled by the EDS as a function of epoch. The current EDS will likely comprise of three separate areas (see Scaramella et al., in prep., for further information); one near the north ecliptic pole (EDSN), one near the south ecliptic pole (EDSS) and a third overlapping the Chandra Deep Fields South (EDSFornax).
EDSN is presently scheduled for 40 visits over a five year period. The sampling will not be homogeneous with time differences between consecutive visits ranging from 16 to 55 days (excluding the two 240day gaps at the beginning and ending of the nominal survey). Ten of these 40 visits will be devoted to calibration purposes (covering an area of 20 deg^{2}), while the remaining 30 visit of EDSN will scan a central 10 deg^{2}. We only consider this central region in this paper.
EDSS will also have 40 visits over a five year period, but will cover an area of 20 deg^{2}. These observations will be clustered in sixmonth blocks with an average cadence between visits of 28 days. Every 28 days two visits will be grouped in a threeday window. Discover astronomical transients in a field rich of foreground stars will not be a problem if algorithms using supervized machine learning techniques are employed as done by current transient surveys (e.g. Bloom et al. 2012; Goldstein et al. 2015; Wright et al. 2015).
EDSFornax (covering an area of 10 deg^{2}) will be observed 56 times, to compensate for the expected higher background, with a limited visibility. It will be observed every day for a week with gaps of six months between the week of visibility.
We present a summary of these three EDS fields in Fig. 1 and Table 1. For this work, we have ignored the EDSFornax because of its lowvisibility and therefore, the final areal coverage assumed is 30 deg^{2} over the first two fields (north central area plus the whole southern area).
Fig. 2 Normalized filter transmission of VIS and Y, J, H (NISP). 
We assumed a 5σ limiting magnitude of 25.5 for each of the individual EDS visual visits (VIS passband is equivalent to r + i + z passbands, see Fig. 2 and Table 2), while we assumed Y = J = H = 24.05 mag for each Near Infrared Spectrometer and Photometer (NISP) visit of the EDS. These point source values are slightly different from those reported in Astier et al. (2014), but are in agreement with the Euclid science requirements (Laureijs et al. 2011) and the latest estimates of the Euclid performance. We assumed the latest filter transmission curves and quantum efficiencies for VIS (Cropper et al. 2014) and NISP. The filter transmission functions are shown in Fig. 2, and have been implemented in the S3 software package (see Inserra et al. 2016b, for further details on the programmes) for kcorrections. We note that with such a steady cadence, and consistent limit magnitudes per visit, there will always be at least ten epochs for each detected supernova (at any redshift) that can be used as a reference image (e.g. without SN light) for difference imaging.
Euclid filters specifications.
2.3. Luminosity function
We adopted a luminosity function with an average lightcurve peak of −21.60 ± 0.26rband magnitude, rising for 25 ± 5 days and declining 1.5 ± 0.3 mag in 30 days (Inserra & Smartt 2014; Nicholl et al. 2015). This has been built fitting literature data (e.g. Inserra et al. 2013; Nicholl et al. 2015) with loworder polynomials (as done in Nicholl et al. 2016) and the magnetar model (Inserra et al. 2013), allowing a reduced χ^{2} ≲ 5. Such a luminosity function is in agreement, within the uncertainties, with the recent findings of De Cia et al. (2017) and Lunnan et al. (2017). We utilized an empirical template for the spectral energy distribution (SED) of SLSNI based on 110 restframe spectra taken for 20 SLSNeI spanning a redshift range of 0.1 <z< 1.2 (from 1800 Å to 8700 Å) and covering approximately −20 to 250 days (with respect to peak luminosity) in their lightcurve evolution (GalYam et al. 2009; Pastorello et al. 2010; Quimby et al. 2011; Inserra et al. 2013; Nicholl et al. 2013, 2014, 2016; Vreeswijk et al. 2014).
Fig. 3 Left: simulated observerframe lightcurve for a z = 2.0 SLSNI in the four Euclid passbands. The horizontal (dashed) lines represent the assumed 5σ point source limiting magnitudes for each filter as discussed in the text. J and H limiting magnitudes are shifted of 0.05 and 0.10 mag to facilitate the reading. The cross symbols at the top of the panel represent a typical observing cadence for the southern EDS away from the six months gap (including two consecutive observations per passage that are not considered in the rate simulations), which would detect this SLSN four times in three bands. Similarly, the short lines at the top of the panel represent a typical observing cadence for the northern EDS, with four detections in three bands. Right: the same as the left panel but at z = 3.5. In this case both the southern and northern EDS would detect this SLSN three separate times (again excluding double observations within three days of each other). Observed phase is with respect to the observer frame Jband peak. 
This template was implemented in the snake software package (Inserra et al. 2016b) to calculate the necessary kcorrections between the assumed Euclid visual and NIR filters and the standard optical restframe passbands, namely the SDSS rband and the two narrow passbands used in Inserra & Smartt (2014) to standardize SLSNeI (namely, their 4000 and 5200 Å synthetic filters). We use the SDSS r filter as our main reference restframe filter for our calculation. Uncertainties on the kcorrections have been evaluated as RMS of the uncertainties on redshift, spectral template and different standard passbands following the methodology of Inserra et al. (2016b). Usually such uncertainties are smaller than 0.05 mag (Kim et al. 1996; Blanton & Roweis 2007; Hsiao et al. 2007; Inserra et al. 2016b). Assuming that the terms leading to the definition of our observed magnitude (m) are uncorrelated, and the uncertainties deriving from the cosmology adopted are negligible, these uncertainties are given by $\begin{array}{ccc}& & \mathit{\sigma}\mathrm{(}\mathit{m}{\mathrm{)}}^{\mathrm{2}}\mathrm{=}\mathit{\sigma}\mathrm{(}\mathit{M}{\mathrm{)}}^{\mathrm{2}}\mathrm{}\mathrm{4.7}{\left(\frac{\mathit{\sigma}\mathrm{\left(}{\mathit{D}}_{\mathrm{L}}\mathrm{\right)}}{{\mathit{D}}_{\mathrm{L}}}\right)}^{\mathrm{2}}\mathrm{}\mathit{\sigma}\mathrm{(}\mathit{A}{\mathrm{)}}^{\mathrm{2}}\mathrm{}\mathrm{1.2}\\ & & \mathrm{\times}\left[{\left(\frac{\mathit{\sigma}\mathrm{\left(}\mathit{z}\mathrm{\right)}}{\mathit{z}}\right)}^{\mathrm{2}}\mathrm{+}{\left(\frac{\mathit{\sigma}\mathrm{\left(}{\mathit{L}}_{{\mathit{\lambda}}_{\mathrm{o}}}\mathrm{\right)}}{{\mathit{L}}_{{\mathit{\lambda}}_{\mathrm{o}}}}\right)}^{\mathrm{2}}\mathrm{+}{\left(\frac{\mathit{\sigma}\mathrm{\left(}{\mathit{L}}_{{\mathit{\lambda}}_{\mathrm{r}}}\mathrm{\right)}}{{\mathit{L}}_{{\mathit{\lambda}}_{\mathrm{r}}}}\right)}^{\mathrm{2}}\mathrm{+}{\left(\frac{\mathit{\sigma}\mathrm{\left(}\mathit{Z}{\mathit{P}}_{{\mathit{\lambda}}_{\mathrm{o}}}\mathrm{\right)}}{\mathit{Z}{\mathit{P}}_{{\mathit{\lambda}}_{\mathrm{o}}}}\right)}^{\mathrm{2}}\mathrm{+}{\left(\frac{\mathit{\sigma}\mathrm{\left(}\mathit{Z}{\mathit{P}}_{{\mathit{\lambda}}_{\mathrm{r}}}\mathrm{\right)}}{\mathit{Z}{\mathit{P}}_{{\mathit{\lambda}}_{\mathrm{r}}}}\right)}^{\mathrm{2}}\right]\mathit{,}\end{array}$(1)where M refers to the absolute magnitude, D_{L} is the luminosity distance, A is the extinction coefficient, L_{λ} is the luminosity function in that filter, z the redshift, ZP are the filter zeropoints, and o and r refer to the observer and restframes, respectively (see Inserra & Smartt 2014; Inserra et al. 2016b). All these uncertainties are included in the uncertainties estimate, with the exception of the uncertainties on the host galaxy extinction, which are usually negligible for SLSNeI (Inserra & Smartt 2014; Nicholl et al. 2015; Leloudas et al. 2015).
Fig. 4 Number of SLSNeI detected, per redshift bin (Δz = 0.5), during the five years of the EDS (combining both the northern and southern EDS observations). Gold stars denote the “gold sample” (three filter detections for each of three epochs, or 3e3f in legend), while the silver circles are the “silver sample” (two filter detections for each of three epochs, or 3e2f). The error bars are Poisson uncertainties based on the number of SLSNeI in each bin (Gehrels 1986), while the rates assumed are for our optimistic model (see text). Both gold and silver points are offset of Δz = 0.05 to facilitate the reading. 
2.4. Euclid SLSNI rate
In order to estimate the volumetric rate of SLSNI in the EDS, we used a model for the evolution of the starformation rate (SFR) density with redshift (see Hopkins & Beacom 2006), based on the Salpeter initial mass function (IMF) published by Cole et al. (2001), and using the methodology of Botticella et al. (2008). Adopting an IMF and SFR at any redshift then allowed a calculation of the volumetric rate of corecollapse supernova, assuming that all stars above 8 M_{⊙} produce a SN (the upper mass limit is not important as long as its ≳ 50 M_{⊙}). We then assumed that the ratio between the SLSNI and CCSN rate is 10^{4} (Quimby et al. 2013; Prajs et al. 2017), which provides a rate per comoving volume element. We will refer to this rate as the “optimistic” model.
To estimate the systematic uncertainty on this rate, we also recalculate it adopting a slightly different evolution for the SFR density (Bouwens et al. 2011) as well as the lower ratio of 10^{5} between the SLSNI to CCSN rates (McCrum et al. 2015). This will be our “pessimistic” model. This approach gives more freedom and allowed us to have better uncertainties in case SLSNe do not follow the SFR of the bulk of the Universe. In fact lowmetallicity, faint, galaxies appear to have a much flatter SFR with redshift than the nominal SFR of the Universe (see Heavens et al. 2004). We assume Poisson statistical uncertainties on both estimates. We note that the optimistic setup is the one consistent with other SLSNI rate estimates up to redshift z ~ 1 (see Fig. 9 of Prajs et al. 2017, for a comparison) and those at higher redshift (Tanaka et al. 2012, 2013). SLSNeI host galaxies properties, such as metallicity, star formation rate and stellar mass, do not show any obvious redshift dependence (Lunnan et al. 2014; Leloudas et al. 2015; Chen et al. 2017a) but only a general metallicity threshold (12 + log(O/H)_{N2}< 8.5), which however strongly depends on the diagnostic used (see Chen et al. 2017b, for an indepth discussion). Hence, we do not expect any significant quantitative change in our assumptions (SFR density and SLSNI to CCSN rate) with redshift.
These two models are then used to calculate the number of SLSNeI, in bins of Δz = 0.5 width, centred on multiples of z = 0.5 up to z = 3.5 which is consistent with the highest SLSNI redshift observed to date, and likely achievable with Euclid (see Inserra & Smartt 2014).
We then performed 10^{5} Monte Carlo simulations^{2} of Euclid SLSNI lightcurves for each bin of Δz = 0.5 and placing them at random explosion epochs relative to the EDS observing strategy that is, the survey time, depth, cadence and volume as discussed above. We show in Fig. 3 two examples of such simulated lightcurves at z = 2.0 and z = 3.5. During these simulations, we also assumed an average foreground extinction of E(B−V) = 0.02 (see Inserra & Smartt 2014).
Using these simulated lightcurves, we then determined which SLSNeI would be useful for any meaningful astrophysical and cosmological analysis. We therefore defined two subsets of SLSNI using the following selection criteria. First, we defined a “silver sample” that requires each SLSN to be detected (5σ point source) for at least three epochs (3e) in their lightcurves in at least two Euclid filters (2f) per epoch (or 3e2f). Second, we defined a “gold sample” which requires a detection (5σ point source) in at least three Euclid filters, each for at least three epoch (3e3f). In all cases, we required at least one of these detections to be before peak brightness. In addition, we only considered epochs that are separated by at least three days to ensure reasonable coverage of the whole lightcurve (Fig. 3). We simply ignored all but one epoch of those more closely separated by less than three days. These extra (close) epochs would not provide any additional information in terms of the light curve sampling, and colour evolution at z ≳ 2, but in reality they could be helpful for SN detection (e.g. removing bogus artifacts, asteroids, and cataclysmic variables) and increased signal to noise ratio (S/N).
Moreover, these close epochs (Δt< 3 days) in both EDSS and EDSN would be excellent for discovering fast transients such as rapidly evolving SNe (Drout et al. 2014) or observe red kilonovae (e.g. Kasen et al. 2015; Metzger et al. 2015a). The latter are fast transients visible for approximately two weeks as a result of two neutron stars merging and likely producing gravitational waves in the sensitivity region of the LIGO interferometers (strain noise amplitudes below 10^{23} Hz^{−1/2} in the frequency regime 10^{2}–10^{3} Hz; Berry et al. 2015; LIGO Scientific Collaboration et al. 2015).
These criteria should be sufficient to efficiently separate SLSNeI from other transients^{3}, such as active galactic nuclei and high−z lensed SNe Ia because of their characteristic photometric colour evolution (see the colour evolution shown by Inserra et al. 2013; Inserra & Smartt 2014; Nicholl et al. 2015). Also, recent work has shown that the evolution of the luminosity and colour of SLSNe trace a distinctive path through parameter space (see Inserra et al. 2017b), while targeting apparently “hostless” SLSN candidates can also improve the success rate of any spectroscopic followup (e.g. McCrum et al. 2015). Finally, SLSNe have been shown to possess similar spectrophotometric evolution up to z ~ 2 (Pan et al. 2017; Smith et al. 2017), which supports our assumption on the luminosity function and our analysis in Sect. 5. Furthermore, requiring a detection in at least two passbands will provide at least one colour measurement which is essential for using the relationship between peak magnitude and colour evolution as discussed in Inserra & Smartt (2014) for standardization. Having three passbands would provide a better estimate of the bolometric lightcurve which could further be used to standardize SLSNeI, for example correlating the spin period of the bestfit magnetar model to the host galaxies metallicity (see Chen et al. 2017a).
In Fig. 4, we show the results of our simulation. When determining the number of SLSNeI expected from the EDS, we assume that only the northern and southern areas of the EDS (total of 30 deg^{2}) are observed as shown in Fig. 1. In the case of our optimistic model, this provides a yearly volumetric rate of $\mathrm{4}{\mathrm{1}}_{6}^{\mathrm{+}\mathrm{11}}$ yr^{1} Gpc^{3} for the silver sample (3e2f) and $\mathrm{2}{\mathrm{7}}_{4}^{\mathrm{+}\mathrm{9}}$ yr^{1} Gpc^{3} for the gold sample (3e3f). Uncertainties are Poisson and have been estimated using Gehrels (1986) for small numbers of events in astrophysics. In addition, uncertainties on the yearly rates at 0.5 <z< 3.5 have been estimated with the same formalism applied to the sum of each bin since the sum of each independent Poisson random variable is Poisson.
We present in Table 3 the expected number of SLSNeI as a function of redshift for both rates models, while in Fig. 4 we only plot the results of the optimistic model. In total, we predict Euclid will detect ≃ 140 highquality (gold sample) SLSNeI up to z ~ 3.5 over the five years of the EDS. On the other hand, the silver sample could deliver an extra 70 SLSNeI, with respect to the gold, over the same five years. Extending the EDS beyond the nominal fiveyear duration could add approximately 40 SLSNeI per year to the sample. If in our optimistic model we increase the detection level from 5σ to 10σ, then the predicted rates would be similar to those for the 5σ pessimistic model. Furthermore, if the limiting magnitude of the VIS filter was less efficient than assumed here, and closer to the initial 24.5 mag limit originally expected, we would see a drop of ~ 7% in our rate.
Number of SLSNeI per year for both samples (silver and gold) and with both rate models (see text).
3. SLSN spectroscopy
Throughout this analysis, we have assumed we know accurately the redshift and identification of the detected SLSNI events. Such information could be achieved through fitting models of SLSN to the Euclid photometric data as previously done with SNe Ia (e.g. Jha et al. 2007; Guy et al. 2010; Sullivan et al. 2011) or fitting the magnetar model to the multicolour lightcurve (e.g. Prajs et al. 2017). However, these approaches are modeldependent and there are degeneracies in such fitting techniques leading to systematic biases.
Fig. 5 Example of an observed spectrum with S ! N ~ 20, R ≃ 350 of a SLSNI at various redshifts (0.5 <z< 2.5). The spectrum is that of iPTF13ajg at peak epoch (Vreeswijk et al. 2014) with a flux of ~ 10^{16} erg s^{1} cm^{2} Å^{1} at Yband wavelength and at redshift z = 0.5, which should be feasible for the Euclid “blue” grism (see text). The cyan, yellow and red solid lines represent the wavelength regions covered by Euclid VIS, Y and J filters, respectively (we note that VIS and Y are superimposed for 600 Å). The blue region shows the Euclid “blue” grism covering 0.92 to 1.25 microns. The spectra at z> 0.5 show the potential of future facilities (e.g. JWST, EELT) and their use in identifying SN features, since they will go deeper and with a better resolution than the Euclid spectrograph. 
The logical next step is to secure a spectrum, especially after peak (see Inserra et al. 2017b) for as many of these SLSNeI as possible to determine both their redshift and classification. This has traditionally been the approach for SNe Ia, but recently the number of detected SN Ia candidates is far beyond our capability to perform realtime spectroscopic followup of all these events (see Campbell et al. 2013). For example, the Dark Energy Survey (DES) is now focussed on gaining spectroscopic followup for all SN host galaxies which is easier given large multiobject spectrograph (see Yuan et al. 2015). However, such an approach may not work for all SLSNeI as many of these events happen in lowmass, compact dwarf galaxies (Lunnan et al. 2014).
Fortunately, the rate of new Euclid SLSN detections should be approximately once a week, and each supernova will last for several months in the observerframe (see Fig. 3). Therefore, it should be feasible to obtain realtime spectroscopic followup of these Euclid SLSNe, unlike the LSST SLSN sample where we may find ~ 25 new SLSNeI per week (Scovacricchi et al. 2016) over the ten years of operations. Also, the intrinsic rate of SLSNI events should be far in excess of the expected SLSNII rate, meaning the expected contamination from such events (e.g. for our cosmological analysis) will be minimal, although we note the discovery of more highredshift SLSNeII would be of great interest for astrophysical studies.
To assess the feasibility of obtaining spectra of these Euclid SLSNeI, we use the exposure time simulator of the nearinfrared integralfield spectrograph HARMONI (Zieleniewski et al. 2015) planned for the European Extremely Large Telescope (EELT). We estimate that an effective exposure time of 900 s would give a S/N of ~20 for an average SLSNI at z = 2. Such S/N is sufficient to identify a transient as shown in Fig. 5 and by the Public ESO Spectroscopic Survey of Transient Objects (PESSTO; Smartt et al. 2015). Alternatively, it would only require 300 s to achieve a similar S/N for the same SLSNI using the lowresolution grating on the NearInfrared Spectrograph (NIRSpec) on the James Webb Space Telescope (JWST). We anticipate similar exposure times for the Wide Field Infrared Survey Telescope (WFIRST), as well as the 30 m Thirty Meter Telescope (TMT) and the 23 m Giant Magellan Telescope (GMT).
On the other hand, it may be more challenging with existing groundbased eightmeter telescopes. For example, we would require a twohour integration using the NearInfrared Integral Field Spectrometer (NIFS) on the Gemini telescope, to achieve S/N ~ 5, which is a lower limit for identifying transients object with broad feature like SLSNeI and secure a redshift.
It may also be possible to obtain some spectral information for these SLSNeI from the lowresolution (R ≃ 350) Euclid NIR slitless spectroscopy that is planned for the EDS in parallel to the imaging data. The information on the NIR slitless spectroscopy here reported is the latest available to the Euclid consortium and likely to be the final, even though we warn the readers that later changes could always happen. The Euclid NISP instrument has two NIR grisms, namely a “blue” grism covering 0.92 to 1.25 microns and a “red” grism covering wavelengths of 1.25 to 1.85 microns. The EDS slitless spectroscopy strategy may focus primarily on observations with the blue grism with approximately threequarters of the deep field visits (each of 4 dithers) dedicated to this grism. We expect each visit to reach a limiting flux of 2 × 10^{16} erg s^{1} cm^{2} Å^{1} (3.5σ) to match the depth of the Euclid wide survey (for calibration purposes). We estimate that such data may provide spectroscopic information on a live SLSN (as detected in the imaging) to z ≤ 0.5. Better performance could be obtained by rebinning the spectrum as the SLSNI features are broad and optimally extracting the spectral data using our prior knowledge of a candidate SLSN at that location. In addition, in case of nearby SLSNe, a spectrum observed after peak should contain more information as both the O i and Ca NIR lines will be present in the observed region of a blue NIR grism configuration.
We may also obtain the redshift of a SLSNI host galaxy through the coaddition of multiple NISP grism spectra, at the known location of the SLSN, to achieve a possible flux limit of 3 × 10^{17} erg s^{1} cm^{2} Å^{1} (over a one arcsecond aperture). Many SLSNeI are located in starforming dwarf galaxies with strong oxygen nebular emission lines that means we should detect [O iii] to z = 1 in the blue grism for several of the SLSNI host galaxies (e.g. Leloudas et al. 2015; Perley et al. 2016).
4. Astrophysics from highredshift SLSNe
The discovery of hundreds of SLSNeI in the EDS will improve several areas of astrophysics. For example, Euclid photometry and spectroscopy of nearby SLSNeI will improve our knowledge of their SEDs in the NIR (only up to z = 0.5 objects), where the uncertainties due to extinction are minimized. This would then allow us to compare SLSNeI with similar photospheric spectra, but different observed colours and continuum slopes, to gain insights into the host galaxy extinction. On the other hand, Euclid will deliver hundreds of SLSNe over a longer redshift baseline than those currently available. This will increase the statistical power providing for a more principled approach in the spectrophotometric analysis. Consequently, it could lead to a better understanding of the mechanism responsible for the luminosity of SLSNeI, which has been narrowed to an inner engine, spin down of a rapidly rotating magnetar (e.g. Kasen & Bildsten 2010; Woosley 2010; Dessart et al. 2012) or a black hole (Dexter & Kasen 2013) and/or interaction of the SN ejecta with a massive (3−5M_{⊙}) C/Orich circumstellar medium (e.g. Woosley et al. 2007; Chatzopoulos et al. 2013). We also note that a pair instability explosion (e.g. Kozyreva & Blinnikov 2015) could still be a viable alternative at high redshift after having been disfavoured for SLSNeI at z ≲ 1.5 (e.g. Nicholl et al. 2013; Smith et al. 2016; Inserra et al. 2016a, 2017a).
Due to their high luminosity, SLSNeI are also excellent probes of the physical conditions of the gas surrounding the SN, as well as the interstellar medium within the host galaxy interstellar medium. This is possible through the detection of broad UVabsorption lines, which will be redshifted into the NIR wavelength range. For example, elements like Mg, Si, Fe, and Zn can be detected, via narrow absorption lines in the followup spectra of SLSNI, thus allowing us to measure the metal column densities, relative abundances, dust content, ionization state, and kinematics of the gas. First attempts to detect such metal lines in the restframe UV of such SLSNeI have been successful (e.g. Berger et al. 2012; Vreeswijk et al. 2014). Furthermore, any Fe and Ni within 100 parsecs of the SN should be excited via “UVpumping”, thus providing an estimate of the distance between the SN and any absorbing gas (as achieved for GRBs, e.g. Vreeswijk et al. 2013). This, combined with the velocity information, would provide a novel constraint on the immediate environment, and progenitors, of these SLSNeI.
In Sect. 2, we estimated the number of SLSNeI observed by Euclid by assuming they follow the cosmic starformation history, since these events are proposed to originate from massive stars (e.g. Jerkstrand et al. 2017). Such an assumption will be tested via these Euclid SLSNeI, especially with those objects beyond z> 1.5, which is currently the limit of the reliability of rate estimates (Prajs et al. 2017). SLSNeI are associated with lowmetallicity, high starforming galaxies (e.g. Lunnan et al. 2014; Leloudas et al. 2015; Chen et al. 2017a) at all observed redshifts (z< 4; Cooke et al. 2012), hence we do not expect that to change at Euclid SLSNeI redshifts. This implies that Euclid SLSNeI will also trace the cosmic chemical enrichment as previously done with CCSNe (e.g. Strolger et al. 2015).
Furthermore, this large number of Euclid SLSNeI discovered over a wide redshift range will improve our understanding of stellar explosions and transient events, for example, Euclid could discover interesting objects similar to SN 2011kl (Greiner et al. 2015; Kann et al. 2016; Bersten et al. 2016) and ASASSN15lh (e.g. Dong et al. 2016; Leloudas et al. 2016; van Putten & Della Valle 2017; Margutti et al. 2017) which achieve similar luminosities as SLSNe, but show different spectrophotometric evolution.
5. SLSN cosmology
5.1. Methodology
Following the work of Scovacricchi et al. (2016), we can also consider the cosmological usefulness of the Euclid SLSNeI. For this analysis we explored what could be achieved if we were to obtain a sample of 300 Euclid SLSNeI with the redshift distribution given in Fig. 4. Such an optimistic sample may be possible if we can utilize the additional silver sample (140 + 70) and obtain an extension to the EDS beyond the nominal fiveyear duration of the Euclid mission, for example like DESIRE. Moreover, we may find even more SLSNeI given the present uncertainties in the highredshift SLSN rate, and our assumed luminosity function (which is quite conservative).
We note that, despite such SLSNeI showing a luminosity function with a gaussianlike distribution (e.g. Inserra & Smartt 2014; Nicholl et al. 2015; Inserra et al. 2017b; Lunnan et al. 2017), current surveys are starting to populate the lower luminosity end creating a continuum in luminosity between normal and superluminous SNe (see De Cia et al. 2017).
We followed the methodology outlined in Scovacricchi et al. (2016) to construct a mock Hubble diagram (redshiftdistance relationship) for such a sample. As in Scovacricchi et al. (2016), we include the additional magnitude dispersion of weak gravitational lensing, which will be important for highredshift objects for example beyond z ≃ 2 (Marra et al. 2013). We also assume that all the SLSNeI have been successfully classified (see Sect. 3 for discussion of spectroscopic followup of these events) and our sample contains negligible contamination (e.g. outliers on the Hubble diagram).
In addition to the highredshift SLSNeI, we need to include a low redshift sample to help anchor the Hubble diagram. Therefore, we assumed 50 SLSNeI, homogeneously distributed over the redshift range 0.1 <z< 0.5 for this local sample. This choice is consistent with Scovacricchi et al. (2016) and is rather conservative given existing samples of lowredshift SLSNI in the literature and expectations from planned, and ongoing, transient searches like ASASSN (Shappee et al. 2014) and ZTF, and spectroscopic followup programmes like PESSTO & ePESSTO (Smartt et al. 2015). Within each redshift bin, we assigned the redshift value at random for the number of supernovae given in Table 3.
We combined the SLSN mock Hubble diagram with a DES (see Bernstein et al. 2012) mock sample for SN Ia^{4}. It is composed of 3500 SNe Ia (distributed according to the hybrid10 strategy in Bernstein et al. 2012) and 300 lowredshift SNe Ia (uniformly distributed for z< 0.1).
We fitted our mock Hubble diagram using the publicly available code cosmomc (July 2014 version, Lewis & Bridle 2002), run as a generic Markov chain Monte Carlo sampler. This allows us to include a custommade likelihood in the software, $\mathrm{\mathcal{L}}\mathrm{=}{\mathrm{\mathcal{L}}}_{\mathrm{SLSN}}\mathrm{\times}{\mathrm{\mathcal{L}}}_{\mathrm{SNIa}}\mathit{,}$(2)defined as the product of two likelihoods, one for each of the data samples considered here (“SLSN” and “SNIa” hereafter).
Our onesigma predicted cosmological constraints for one parameter (ϵ = Δp/p_{fid}) for various combinations of likely Euclid and DES samples and priors (see text for details).
Both of these likelihoods have the same functional form, $\mathrm{\mathcal{L}}\mathrm{=}\frac{\mathrm{1}}{\mathrm{(}\mathrm{2}\mathit{\pi}{\mathrm{)}}^{\mathit{n}\mathit{/}\mathrm{2}}\sqrt{\mathrm{det}\mathit{C}}}\mathrm{exp}\left[\mathrm{}\frac{\mathrm{1}}{\mathrm{2}}\mathrm{(}{{\Delta}{\mu}}^{\mathit{T}}{\mathit{C}}^{1}{{\Delta}{\mu}}^{\mathrm{)}}\right]\mathit{,}$(3)where Δμ is the ndimensional vector containing the Hubble residuals (see below) and n is the number of supernovae in that sample. As discussed in Scovacricchi et al. (2016), we neglect the covariance between supernovae (i.e. all the nondiagonal terms are set to be zero) as we expect these to be small compared to the statistical noise of the limited sample sizes and gravitational lensing (see below). We also do not yet have a good understanding of possible systematic uncertainties (e.g. the photometric calibration) but assume they will be subdominant given present expertise in calibrating such photometric surveys. Also, the science requirement on the Euclid relative photometry is 0.002 mag, which exceeds the calibration uncertainties with present groundbased largearea surveys.
Hence, each covariance matrix C would reduce to diagonal elements only, giving ${\mathit{C}}_{\mathit{ij}}\mathrm{=}\mathrm{\u27e8}\mathrm{\Delta}{\mathit{\mu}}_{\mathit{i}}\mathrm{\Delta}{\mathit{\mu}}_{\mathit{j}}\mathrm{\u27e9}\mathrm{=}{\mathit{\sigma}}_{\mathit{ij}}^{\mathrm{2}}{\mathit{\delta}}_{\mathit{ij}}\mathrm{=}{\mathit{\sigma}}_{\mathit{err}}^{\mathrm{2}}{\mathit{\delta}}_{\mathit{ij}}\mathrm{+}{\mathit{\sigma}}_{\mathrm{len}}^{\mathrm{2}}\mathrm{\left(}{\mathit{z}}_{\mathit{i}}\mathrm{\right)}{\mathit{\delta}}_{\mathit{ij}}\mathit{.}$(4)Each measurement then has an uncertainty equal to the sum in quadrature of the data and lensing uncertainties (respectively σ_{err} and σ_{len}(z_{i}), see Sect. 3.2 of Scovacricchi et al. 2016). We assumed that the magnitudes of the SLSNI population will be standardized using techniques like those outlined in Inserra & Smartt (2014), or more advanced future techniques similar to those now used for SNe Ia (e.g. SALT and BayeSN; Guy et al. 2010; Mandel et al. 2011). To be conservative, for our SLSNI mock samples, we assumed a dispersion σ_{err} = 0.26 mag, based on the findings of Inserra & Smartt (2014) and following the previous work of Scovacricchi et al. (2016). Specifically, we select this value for σ_{err} from Table 3 of Inserra & Smartt (2014) based on their Δ(400−520) extended SLSNI sample as this is the most appropriate representation of the corrected peak magnitude rootmeansquare that will be available in the future.
For our DES SN Ia mock Hubble diagram we replicated the approach of Scovacricchi et al. (2016), who assumed a redshift dependent σ_{err}, equal to the values published in Bernstein et al. (2012) and reported in Fig. 2 of Scovacricchi et al. (2016). For DES SNe Ia only, we also included σ_{sys} = 0.1 mag to reproduce the possible overall effects of systematic uncertainties (see Scovacricchi et al. 2016, for further details).
One systematic uncertainty we must consider is the relative photometric calibration between the local SNe Ia and the more distant SLSN population. Similar to Scovacricchi et al. (2016), we therefore allowed for an unknown offset between the two samples by including a free parameter ξ in each of the two likelihoods. Therefore, the Hubble residual for the generic ith SN is $\mathrm{\Delta}{\mathit{\mu}}_{\mathit{i}}\mathrm{=}{\mathit{\mu}}_{\mathrm{obs}\mathit{,i}}\mathrm{}{\mathit{\mu}}_{\mathrm{cos}\mathit{,i}}\mathrm{+}\mathit{\xi ,}$(5)where μ_{obs,i} is the simulated distance modulus and μ_{cos,i} is the theoretical distance modulus using our assumed cosmology.
We then numerically marginalize over this calibration parameter (by doing so, we also reabsorb any difference in H_{0} with respect to its fiducial value). This approach is not ideal as it treats a possible systematic uncertainty as an additional statistical noise, but given we are still unclear about the accuracy of any crosscalibration of these samples, it is difficult to model otherwise.
5.2. Possible cosmological constraints
We report the cosmological results for our (optimistic) SLSNI sample in Table 4. We quote the value of the 1σ uncertainties for the free parameters in our fitting (Δp in the table, for a generic parameter p) which are computed by fitting a Gaussian distribution from the onedimensional posterior distributions. We do not quote the best fit values as they are all consistent with our fiducial cosmology within 2σ. In the same table, we also quote the relative uncertainties ϵ = Δp/p_{fid}, for a generic parameter p with fiducial value p_{fid}. Parameters with a dash symbol (“–”) in Table 3 are considered constant within that fit, and fixed to their fiducial values.
In Table 4, we present results for both a flat ΛCDM model (assuming w = −1) as well as exploring nonzero time derivative of the dark energy equationofstate parameter, namely w(a) = w_{0} + w_{a}(1−a) (Chevallier & Polarski 2001), which has traditionally been used to quantify possible evolving DE models (e.g. see Solà et al. 2017; Zhao et al. 2017). Such work should show the importance of obtaining highredshift distance measurements like those discussed here.
Due to the strong degeneracy between these two dark energy parameters, we therefore include Gaussian priors on Ω_{m} and w_{0} of width 0.015 and 0.25, consistent with the current uncertainties found by Planck. The use of these priors is indicated in Table 4 with P[Ω_{m}] and P[w_{0}].
In Table 4, we only show our results in combination with the expected DES SN Ia mock sample as the Euclid SLSNI results on their own are not competitive (due to their relatively small numbers and intrinsic scatter presently assumed). For example, in the case of flat ΛCDM, the Euclid SLSNeI alone (plus the lowz SLSNI sample) would constrain Ω_{m} to an accuracy of ~ 15%. This is not competitive with existing SNonly constraints (e.g. Betoule et al. 2014), nor are the results in Table 4 when combined with DES for example 3% uncertainty on Ω_{m}. Again, this is not surprising given the assumed fiducial model, the size of the SLSNI sample and the assumed uncertainties.
The cosmological constraints get more interesting when we allow w to vary as the importance of the highredshift SNe come more pronounced. In Table 4, we see that it is possible to improve on the uncertainty of Δw_{a} by adding our 300 SLSNeI to the existing DES sample (and possible priors from other observations). For example, our overall constraints on the flat w_{0}w_{a}CDM model (bottom line of Table 4) are better than the best SNonly constraints available in the literature today (e.g. Table 15 of Betoule et al. 2014), which show an uncertainty of order one for w_{a} using Planck+JLA (and assuming similar weak priors).
We also investigated the possible systematic uncertainty caused by changes in the absolute magnitude of SLSNeI with redshift due to uncertainties in the kcorrections. We repeated the approach in Scovacricchi et al. (2016) of splitting the Euclid SLSNI sample into two subsamples with different normalisation parameters (e.g. different absolute magnitudes). We chose to split the sample at z = 2.5 as this corresponds to the redshift where the broad UV spectral features in the SLSNI spectrum shift from the Euclid VIS band into the IR bands (see Fig. 5). We then analyzed these two subsamples together with the lowredshift SLSNeI and the DES SN Ia mock sample, which also has a free normalization parameter, giving a total of three nuisance parameters in our fitting. We find that both the uncertainties on Ω_{m} and w increase to 10% compared to the values given in Table 4.
The cosmological results in Table 4 could improve in several ways. First, our analysis assumes σ_{err} = 0.26 for the dispersion in peak magnitude for our Euclid SLSNeI. This is the value obtained by Inserra & Smartt (2014) based on only 14 SLSNeI available in the literature at the time. If SLSNeI are standardizable candles, we would expect their standardization to improve in the coming years with ongoing surveys and higher quality data on the individual events. In fact, the Euclid SLSNI sample should provide an important data set for revisiting the standardization of these events, and one may wish to include the standardization parameters in the cosmological fitting as presently performed for SN Ia cosmology.
Secondly, we have modeled several possible systematic uncertainties (e.g. lensing, calibration) as additional statistical noise. If these uncertainties could be measured, and corrected for, then we would expect the cosmological constraints to again improve compared to those presented in Table 4.
6. Discussion
We present predictions for the rate of SLSNI detected by the Euclid mission. In Fig. 4, we present the expected number of SLSNeI in the EDS, as a function of redshift, over the nominal five year mission. It is worth stressing that we predict to find a couple of hundred new SLSNeI to z ~ 3.5 which will revolutionize our understanding of these enigmatic objects, while providing a new window on the distant Universe. This is possible because of the unique combination of instrumentation available on the Euclid satellite (a widefield optical and NIR imager) as well as the EDS observing strategy, for example the continuous monitoring of the same field, which minimizes temporal edge effects that may affect groundbased searches. As demonstrated in the large uncertainty on our predictions, these Euclid data will immediately provide a precise determination of the SLSNI rate (with redshift), thus helping constraint the starformation history of the Universe at these early epochs. There is no other experiment prior to Euclid that will provide such information on highredshift SLSNeI, and therefore it is important to use these unique data to the best of our ability (especially if observed contemporaneously with other facilities like LSST).
In addition to improving our understanding of the astrophysics of these objects, the Euclid SLSNI sample provides additional cosmological constraints as discussed in Sect. 5. These constraints will be complementary to those planned from Euclid weak gravitational lensing, galaxy clustering and SNe Ia (e.g. DESIRE), as well as probing to higher redshift than SLSNI samples from LSST. For example, in Scovacricchi et al. (2016), we presented cosmological constraints from an idealised sample of LSST SLSNeI, but the unavailability of deep NIR imaging over the LSST area will limit the detection of SLSNe beyond z ~ 2. These Euclid SLSNeI will therefore be unique in allowing us to extend the overall cosmological constraints to z ~ 3.5 thus improving our constraints on possible dynamical DE models (Solà et al. 2017; Zhao et al. 2017). Any additional highredshift measurements of the expansion history of the Universe are welcome, especially if they come for free from data already planned.
The results of this paper depend on obtaining spectra for as many Euclid SLSNeI as possible (see Sect. 4). This implies the need for an effective (in terms of purity and completeness) method for identifying as many as “true” SLNSeI from other types of transients. In the case of objects not matching the conservative selection criteria used to define the golden and silver samples, other methods may be effective such as that presented by D’Isanto et al. (2016). In this case, lightcurves are first compressed to a reduced, but extensive, set of statistical features and then classified using the MLPQNA method (Brescia et al. 2014). While this approach has never been applied to the classification of SLSNeI, it has achieved 96% completeness and 85% purity in classifying SNe Ia in the Catalina RealTime Transient Survey.
Finally, we raise the possibility of measuring the gravitational lensing of these highredshift SLSNeI as we did include it as a likely “noise” term in our analysis above. While the probability of witnessing a strongly lensed SLSNI (Kelly et al. 2015) will be small, it may be possible to measure the crosscorrelation function between the peak, corrected magnitudes of these distant SLSNI with the foreground largescale structure as traced by galaxies (Scovacricchi et al. 2017), especially as these Euclid deep fields will become the focus of significant additional observations for example there will likely be overlap with LSST deep drill fields, and possibly WFIRST (Hounsell et al. 2017).
7. Conclusions
We present an analysis of the possible number of superluminous supernovae detected in the Euclid Deep Survey. We show that Euclid should find ≃ 140 highquality SLSNeI to z ~ 3.5 over a five year period. An extra ≃ 70 SLSNeI are possible depending on the quality cuts, while present uncertainties in the rates, luminosity functions, and instrument detection efficiencies may allow many more to be found. These data, especially if also spectroscopically targeted to secure their nature and redshift, will revolutionize the study of SLSNeI, increasing present samples of highredshift (z> 2) SLSNI by two orders of magnitude.
We stress the importance of these Euclid SLSNeI for the study of supernova astrophysics and the starformation history of the Universe. Such investigations will be enhanced by followup observations by the next generation of large space and ground–based telescopes (EELT, LSST, and JWST) and provide excellent targets for these observatories. Euclid will also provide lowresolution NIR grism spectroscopy for some lowredshift SLSNeI.
We also investigated the possibility of constraining cosmology using these SLSNeI, when combined with a lowredshift sample of 50 SLSNeI (from the literature), and the expected cosmological results from DES. In the case of a flat w_{0}w_{a}CDM model, our analysis suggests we could obtain an uncertainty of Δw_{a} ~ 0.9 which is an improvement on DES alone result, and the present constraints on this parameterization. Any additional measurements of the highredshift expansion history of the Universe are invaluable as present baryonic acoustic oscillations observations suggest a possible tension with the standard ΛCDM model (Zhao et al. 2017), either indicating unrecognized systematic uncertainties or dynamical dark energy.
We finish by noting that these Euclid SLSNeI come “for free” as we have just assumed the latest survey design of the EDS. It is therefore important to prepare the Euclid analysis software pipelines to detect such transients as they will be present in the data. This is a major motivation for this paper, that is, to highlight the urgent need to prepare for such longlived transients in the Euclid datastream and be ready to detect them in “realtime” (within days hopefully, but see Inserra et al. 2017b, about SLSN classification in real time) to trigger followup observations, for example using JWST which also has a finite lifetime.
Throughout this paper, we will use “SLSNeI” to refer to Type Ic SLSNe as discussed by Inserra et al. (2013). We do not refer further to Type II SLSNe which appear to have a significantly lower rate than SLSNeI.
This level of simulations has been used in previous literature studies (e.g. Prajs et al. 2017) and found to be adequate.
Details of this mock sample can be found in Sect. 3.2 of Scovacricchi et al. (2016).
Acknowledgments
We thank the internal EC referees (P. Nugent and J. Brichmann) as well as the many comments from our EC colleagues and friends. C.I. thanks Chris Frohmaier and Szymon Prajs for useful discussions about supernova rates. C.I. and R.C.N. thank Mark Cropper for helpful information about the VIS instrument. C.I. thanks the organisers and participants of the Munich Institute for Astro and Particle Physics (MIAPP) workshop “Superluminous supernovae in the next decade” for stimulating discussions and the provided online material. The Euclid Consortium acknowledges the European Space Agency and the support of a number of agencies and institutes that have supported the development of Euclid. A detailed complete list is available on the Euclid web site (http://www.euclidec.org). In particular the Agenzia Spaziale Italiana, the Centre National dEtudes Spatiales, the Deutsches Zentrum für Luft and Raumfahrt, the Danish Space Research Institute, the Fundação para a Ciênca e a Tecnologia, the Ministerio de Economia y Competitividad, the National Aeronautics and Space Administration, The Netherlandse Onderzoekschool Voor Astronomie, the Norvegian Space Center, the Romanian Space Agency, the State Secretariat for Education, Research and Innovation (SERI) at the Swiss Space Office (SSO), the United Kingdom Space Agency, and the University of Helsinki. R.C.N. acknowledges partial support from the UK Space Agency. D.S. acknowledges the Faculty of Technology of the University of Portsmouth for support during his PhD studies. C.I. and S.J.S. acknowledge funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/20072013)/ERC Grant agreement No. [291222]. C.I. and M.S. acknowledge support from EU/FP7ERC grant No. [615929]. E.C. acknowledge financial contribution from the agreement ASI/INAF/I/023/12/0. The work by KJ and others at MPIA on NISP was supported by the Deutsches Zentrum für Luft und Raumfahrt e.V. (DLR) under grant 50QE1202. M.B. and S.C. acknowledge financial contribution from the agreement ASI/INAF I/023/12/1. R.T. acknowledges funding from the Spanish Ministerio de Economía y Competitividad under the grant ESP201569020C22R. I.T. acknowledges support from Fundação para a Ciência e a Tecnologia (FCT) through the research grant UID/FIS/04434/2013 and IF/01518/2014. J.R. was supported by JPL, which is run under a contract for NASA by Caltech and by NASA ROSES grant 12EUCLID120004.
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All Tables
Sampling and coverage information of the three fields of the Euclid Deep Survey (EDS).
Number of SLSNeI per year for both samples (silver and gold) and with both rate models (see text).
Our onesigma predicted cosmological constraints for one parameter (ϵ = Δp/p_{fid}) for various combinations of likely Euclid and DES samples and priors (see text for details).
All Figures
Fig. 1 Summary of the EDS cadence over the fiveyear (1825 days) survey. Open symbols refer to the calibration epochs, which are ten per field excluding the Fornax field. Calibration epochs will have the same nominal depth of whole EDS. See Table 1 for further details. 

In the text 
Fig. 2 Normalized filter transmission of VIS and Y, J, H (NISP). 

In the text 
Fig. 3 Left: simulated observerframe lightcurve for a z = 2.0 SLSNI in the four Euclid passbands. The horizontal (dashed) lines represent the assumed 5σ point source limiting magnitudes for each filter as discussed in the text. J and H limiting magnitudes are shifted of 0.05 and 0.10 mag to facilitate the reading. The cross symbols at the top of the panel represent a typical observing cadence for the southern EDS away from the six months gap (including two consecutive observations per passage that are not considered in the rate simulations), which would detect this SLSN four times in three bands. Similarly, the short lines at the top of the panel represent a typical observing cadence for the northern EDS, with four detections in three bands. Right: the same as the left panel but at z = 3.5. In this case both the southern and northern EDS would detect this SLSN three separate times (again excluding double observations within three days of each other). Observed phase is with respect to the observer frame Jband peak. 

In the text 
Fig. 4 Number of SLSNeI detected, per redshift bin (Δz = 0.5), during the five years of the EDS (combining both the northern and southern EDS observations). Gold stars denote the “gold sample” (three filter detections for each of three epochs, or 3e3f in legend), while the silver circles are the “silver sample” (two filter detections for each of three epochs, or 3e2f). The error bars are Poisson uncertainties based on the number of SLSNeI in each bin (Gehrels 1986), while the rates assumed are for our optimistic model (see text). Both gold and silver points are offset of Δz = 0.05 to facilitate the reading. 

In the text 
Fig. 5 Example of an observed spectrum with S ! N ~ 20, R ≃ 350 of a SLSNI at various redshifts (0.5 <z< 2.5). The spectrum is that of iPTF13ajg at peak epoch (Vreeswijk et al. 2014) with a flux of ~ 10^{16} erg s^{1} cm^{2} Å^{1} at Yband wavelength and at redshift z = 0.5, which should be feasible for the Euclid “blue” grism (see text). The cyan, yellow and red solid lines represent the wavelength regions covered by Euclid VIS, Y and J filters, respectively (we note that VIS and Y are superimposed for 600 Å). The blue region shows the Euclid “blue” grism covering 0.92 to 1.25 microns. The spectra at z> 0.5 show the potential of future facilities (e.g. JWST, EELT) and their use in identifying SN features, since they will go deeper and with a better resolution than the Euclid spectrograph. 

In the text 
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