Super Luminous Ic Supernovae: catching a magnetar by the tail

We report extensive observational data for five of the lowest redshift Super-Luminous Type Ic Supernovae (SL-SNe Ic) discovered to date, namely PTF10hgi, SN2011ke, PTF11rks, SN2011kf and SN2012il. Photometric imaging of the transients at +50 to +230 days after peak combined with host galaxy subtraction reveals a luminous tail phase for four of these SL-SNe. A high resolution, optical and near infrared spectrum from xshooter provides detection of a broad He I $\lambda$10830 emission line in the spectrum (+50d) of SN2012il, revealing that at least some SL-SNe Ic are not completely helium free. At first sight, the tail luminosity decline rates that we measure are consistent with the radioactive decay of \co, and would require 1-4M of \ni to produce the luminosity. These \ni masses cannot be made consistent with the short diffusion times at peak, and indeed are insufficient to power the peak luminosity. We instead favour energy deposition by newborn magnetars as the power source for these objects. A semi-analytical diffusion model with energy input from the spin-down of a magnetar reproduces the extensive lightcurve data well. The model predictions of ejecta velocities and temperatures which are required are in reasonable agreement with those determined from our observations. We derive magnetar energies of $0.4\lesssim E$($10^{51}$erg) $\lesssim6.9$ and ejecta masses of $2.3\lesssim M_{ej}$(\M) $\lesssim 8.6$. The sample of five SL-SNe Ic presented here, combined with SN 2010gx - the best sampled SL-SNe Ic so far - point toward an explosion driven by a magnetar as a viable explanation for all SL-SNe Ic.


INTRODUCTION
The discovery of unusually luminous optical transients by modern supernova (SN) surveys has dramatically expanded the observational and physical parameter space of known SN types. The Texas Supernova Search was a pioneer in this area, with one of the first searches of the local Universe without a galaxy bias (Quimby et al. 2005). This has been followed by deeper, wider surveys from the Palomar Transient Factory (PTF, Rau et al. 2009), the Panoramic Survey Telescope & Rapid Response System (Pan-STARRS, Kaiser et al. 2010), the Catalina Real-time Transient Survey (CRTS, Drake et al. 2009), and the La Silla QUEST survey (Hadjiyska et al. 2012), all of which have found unusually luminous transients which tend to be hosted in intrinsically faint galaxies. These Super-Luminous SNe (SL-SNe) show absolute magnitudes at maximum light of M AB < −21 mag and total radiated energies of order 10 51 erg. They are factors of 5 to 100 brighter than Type Ia SNe or normal corecollapse events. Gal-Yam (2012) proposed that three distinct physical groups of SL-SNe have emerged. The first group which was recognised was the luminous Type IIn SNe epitomised by SN 2006gy Smith & McCray 2007;Ofek et al. 2007;Agnoletto et al. 2009) which show signs of strong circumstellar interaction. The second group includes Type Ic SNe that have broad, bright lightcurves and the decay rates imply that they could be due to pair-instability explosions powered by large ejecta masses of 56 Ni (3-5 M ⊙ ). To date only one object of this type (SN 2007bi) has been published and studied in detail (Gal-Yam et al. 2009;Young et al. 2010). The third group was labelled by Gal-Yam (2012) as Super-Luminous Type I Supernovae, or "SLSN-I" and the two earliest examples are SCP-06F6 and SN 2005ap (Barbary et al. 2009;Quimby et al. 2007) which are characterized at early times by a blue continuum and a distinctive "W"-shaped spectral feature at ∼4200Å. In this paper we will call this type Super-Luminous Supernovae of Type Ic (or SL-SNe Ic), simply because they are Type Ic in the established supernova nomenclature and are extremely luminous.
The existence of this class of SL-SNe Ic was firmly established when secure redshifts were determined with the identification of narrow Mg ii λλ2796,2803 absorption from the host galaxies in the optical spectra of z > 0.2 transients by Quimby et al. (2011a). The spectra of four PTF transients, SCP-06F6 and SN 2005ap were then all linked together with these redshifts establishing a common type (Quimby et al. 2011a). Subsequently, the identification of host galaxy emission lines such as [O ii] λ3727, [O iii] λλ1959,5007, Hα and Hβ has confirmed the redshift derived from the Mg ii absorption in many SL-SNe Ic, such as in the case of SN 2010gx (Quimby et al. 2010;Mahabal & Drake 2010;Pastorello et al. 2010). These distances imply an incredible luminosity with u− and g−band absolute magnitudes reaching about −22. This luminosity allowed these SNe to be easily identified in the Pan-STARRS Medium Deep fields at z ∼ 1 (Chomiuk et al. 2011) and beyond (Berger et al. 2012).
The typical spectroscopic signature of the class of SL-SNe Ic is a blue continuum with broad absorption lines of intermediate mass elements such as C, O, Si, Mg with velocities 10000 < v < 20000 km s −1 . No clear evidence of H or He has been found so far in the spectra of SL-SNe Ic, whereas Fe, Mg and Si lines are typically prominent after maximum. The study of the well sampled SN 2010gx  showed an unexpected transformation from a SL-SN Ic spectrum to that of a normal Type Ic SN. A similar transformation was also observed in the late-time spectrum of PTF09cnd (Quimby et al. 2011a), which evolved to become consistent with a slowly evolving Type Ic SN.
The SL-SNe Ic discovered to date appear to be associated with faint and metal poor galaxies at redshifts ranging between 0.23 − 1.19 (typically M g > −17 mag, Quimby et al. 2011a;Neill et al. 2011;Chomiuk et al. 2011;Chen et al. 2013), although the highest redshift SL-SNe Ic (PS1-12bam, z = 1.566) is in a galaxy which is more luminous and more massive than the lower redshift counterparts (Berger et al. 2012). An estimate of the metallicity of the faint host galaxy of SN 2010gx, from the detection of the auroral [O III] λ4363 line indicates a very low metallicity of 0.05 Z ⊙ (Chen et al. 2013). Research on SL-SNe Ic is progressing rapidly, with thirteen of these intriguing transients now identified since the discovery of SCP-06F6. To power the enormous peak luminosity of SL-SNe Ic with radioactive decay would require several solar masses of 56 Ni. However, this is inconsistent with the width of the lightcurves as shown by Chomiuk et al. (2011). The lightcurves cannot be reproduced with a physical model that has an ejecta mass significantly greater than the 56 Ni mass needed to power the peak. In the case of SN 2010gx, Chen et al. (2013) showed that the tail phase faded to levels which would imply an upper limit of around 0.4M ⊙ of 56 Ni.
Among the scenarios proposed to explain the remarkable peak luminosity are the spin down of a rapidly rotating young magnetar (Kasen & Bildsten 2010;Woosley 2010), that provides an additional reservoir of energy for the SN (Ostriker & Gunn 1971;Usov 1992;Wheeler et al. 2000; Thompson et al. 2004); the interaction of the SN ejecta with a massive (3-5 M ⊙ ) C/O-rich circumstellar medium (CSM, Blinnikov & Sorokina 2010) or with a dense wind (Chevalier & Irwin 2011;Ginzburg & Balberg 2012); or collisions between high velocity shells ejected by a pulsational pair instability, which would give rise to successive bright optical transients (Woosley et al. 2007). One of these SNe (SN 2006oz) was discovered 29 days before peak luminosity and showed a flat plateau in the restframe NUV before its rise to maximum, indicating that finding these objects early could give constraints on the explosion channel (Leloudas et al. 2012). In most cases to date however, the lightcurves and energy released at >100d is unexplored territory. Chen et al. (2013) quantified host of SN2010gx, but difference imaging showed no detection of SN flux at 250-300 days to deep limits. Quimby et al. (2011a) detected flux at the position of PTF09cnd at +138d after peak in a B-band image, but it's not clear if this flux is from the host or the SN. In this paper we present the detailed follow-up of five SL-SNe Ic at 0.100 < z < 0.245, namely PTF11rks, SN 2011ke, SN 2012il, PTF10hgi and SN 2011kf, and attempt to follow them for as long as possible to garner further evidence to probe the physical mechanism powering these intriguing events. A detailed analysis of their hosts will be part of a future paper (Chen et el. in prep).
The paper is organized as follows: in Sect. 2 we introduce the SNe, and report distances and reddening values. Photometric data, light and colour curves as well as the absolute light curves in the rest-frame are presented in Sect. 3. Sect. 4 is devoted to the analysis of bolometric and pseudo-bolometric light curves and the evaluation of possible ejected 56 Ni masses, while in Sect. 5 we describe and analyse the spectra. Finally, a discussion about the origin of these transients is presented in Sect. 6, followed by a short summary in Sect. 7.

DISCOVERY AND TARGET SAMPLE
2.1. Pan-STARRS1 data : discovery and recovery of the transients The strong tendency for these SL-SNe to be hosted in faint galaxies appears not to be a bias, which suggests a straightforward way of finding them in large volume, wide-field searches. With the Pan-STARRS1 survey, we have been running the "Faint Galaxy Supernova Survey" (FGSS) which is aimed at finding transients in faint galaxies originally identified in the Sloan Digital Sky Survey catalogue .
The Pan-STARRS1 optical system uses a 1.8m diameter aspheric primary mirror, a strongly aspheric 0.9m secondary and 3-lens corrector and has 8m focal length (Hodapp et al. 2004). The telescope illuminates a diameter of 3.3 degrees and the "GigaPixel Camera" (Tonry & Onaka 2009) comprises a total of 60 4800 × 4800 pixel detectors, with 10 µm pixels that subtend 0.258 arcsec (for more details see Magnier et al. 2013). The PS1 filter system is described in , and is similar to but not identical to the SDSS griz (York et al. 2000) filter system. However it is close enough that catalogued cross-matching between the surveys can identify high amplitude transients. In this paper we will convert all the PS1 filter magnitudes g P1 r P1 i P1 z P1 y P1 to the SDSS AB magnitude system as the bulk of the follow-up data were taken in SDSS-like filters (see Section 3 for more details). The PS1 telescope is operated by the PS1 Science Consortium (PS1SC) to undertake several surveys, with the two major ones being the "Medium Deep Field" survey (e.g Botticella et al. 2010;Gezari et al. 2012;Berger et al. 2012) which was optimised for transients (allocated around 25% of the total telescope time) and the wide-area 3π Survey, allocated around 56% of the available observing time. As described in Magnier et al. (2013), the goal of the 3π Survey is to observe the portion of the sky North of −30 deg declination, with a total of 20 exposures per year across all five filters for each field center. The 3π survey plan is to observe each field center 4 times in each of g P1 r P1 i P1 z P1 y P1 during a 12 month period, although this can be interrupted by bad weather. As described by Magnier et al. (2013), the 4 epochs in a calendar year are typically split into two pairs called Transient Time Interval (TTI) pairs which are single observations separated by 20-30 minutes to allow for the discovery of moving objects. The temporal distribution of the two sets of TTI pairs is not a well defined and straightforward schedule. The blue bands (g P1 , r P1 , i P1 ) are scheduled close to opposition to enhance asteroid discovery with g P1 and r P1 being constrained in dark time as far as possible. The z P1 and y P1 filters are scheduled far opposition to optimise for parallax measurements of faint red objects. Although a large area of sky is observed each night (typically 6000 square degrees), the moving object and parallax constraints mean the 3π survey is not optimised for finding young, extragalactic transients in a way that the Palomar Transient Factory and La Silla-QUEST projects are. The exposure times at each epoch (i.e. in each of the TTI exposures) are 43s, 40s, 45s, 30s and 30s in g P1 r P1 i P1 z P1 y P1 . These reach typical 5σ depths of roughly 22.0, 21.6, 21.7, 21.4. 19.3 as estimated from point sources with uncertainties of 0.2 m . (in the PS1 AB magnitude system described by . The PS1 images are processed by the Pan-STARRS1 Image Processing Pipeline (IPP), which performs automatic bias subtraction, flat fielding, astrometry (Magnier et al. 2008) and photometry (Magnier 2007). These photometrically and astrometrically calibrated catalogues produced in MHPCC are made available to the PS1SC on a nightly basis and are immediately ingested into a MySQL database at Queen's University Belfast. We apply a tested rejection algorithm and cross match the PS1 objects with SDSS objects in the DR7 catalogue 14 (Abazajian et al. 2009). We apply the following selection filters to the PS1 data (all criteria must be simultaneously fulfilled) • PS1 source must have 15 <g P1 < 20 or 15 <r P1 < 20 or 15 <i P1 < 20 or 15 <z P1 < 20 • SDSS counterpart must have 18 < r SDSS < 23 • Distance between PS1 source and SDSS source < 3 arcsec • PS1 mag must be 1.5 mag brighter than SDSS (in the corresponding filter) • The PS1 object must be present in both TTI pairs and the astrometric recurrences < 0.3 ′′ . Objects with multiple detections must have RMS scatter < 0.1 ′′ • The PS1 object must not be in the galactic plane (|b| > 5 • ).
All objects are then displayed through a Django-based interface to a set of interactive webpages, and human eyeballing and checking takes place. We use the stargalaxy separation in SDSS to guide us in what may be variable stars (i.e. stellar sources in SDSS which increase their luminosity) or extragalactic transients (i.e. QSOs, AGNs and SNe). While the cadence of the PS1 observations is not ideal for detections of young SNe we have found many SNe in intrinsically faint galaxies. As of January 2013, spectroscopically confirmed objects include 34 QSOs or AGNs and 41 SNe. Several of these have been confirmed as SL-SNe. Pastorello et al. (2010) presented the data of SN 2010gx recovered in 3π images, and in many cases the same object is detected by the Catalina Real-Time Transient Survey (CSS/MSS) and PTF. As we are not doing difference imaging and only comparing to objects in the SDSS footprint, there are some cases where objects are reported by PTF or CRTS and interesting pre-discovery epochs are available in PS1. As 3π difference imaging is not being carried out routinely, we often use the PTF and CRTS announcements to inform a retrospective search. In this paper, we present five SL-SNe Ic which were either detected through the PS1 Faint Galaxy Supernova Survey, or were announced in the public domain. A sixth object (PTF12dam≡PS1-12arh) is discussed in a companion paper (Nicholl et al. in prep.). In all five cases follow-up imaging and spectroscopy was carried out as discussed below.
For all the SNe listed here (and throughout this paper) we adopt a standard cosmology with H 0 = 72 km s −1 , Ω M = 0.27 and Ω λ = 0.73. There is no detection of Na i interstellar medium (ISM) features from the host galaxies, nor do we have any evidence of significant extinction in the hosts from the SNe themselves. This suggests that the absorption in host is low and we assume that extinction from the host galaxies is negligible. Although we do detect Mg ii ISM lines from the hosts in some cases, there is no clear correlation with these line strengths and line of sight extinction. In all cases only the Milky Way foreground extinction was adopted.

PTF10hgi
PTF10hgi was first discovered by PTF on 2010 May 15.5 and announced on 2010 July 15 (Quimby et al. 2010). The spectra taken by PTF on May 21.0 UT and June 11.0 UT were reported as a blue continuum with faint features typical of SL-SNe Ic. Another spectrum obtained by PTF on July 7.0 UT was similar to PTF09cnd at 3 weeks past peak brightness. Initiated by Quimby et al. (2010), UV observations were obtained with Swift+UVOT in July 2010, and we analyse those independently later in Sect.3. PTF10hgi lies outside the SDSS DR9 15 area (Ahn et al. 2012), hence was not discovered by our PS1 FGSS software. However after the announcement (Quimby et al. 2010), we recovered it in PS1 images taken (in band r P1 ) on 2010 May 18 and on 4 other epochs around peak magnitude (in bands g P1 r P1 i P1 ), listed in Table 5.
We detect a faint host galaxy in deep griz-band images taken with the William Herschel Telescope on 2012 May 26 and the Telescopio Nazionale Galileo on 2012 May 28. At a magnitude r = 22.01 ± 0.07, this is too faint to affect the measurements of the SN flux up to +90 days. There are no host galaxy emission lines detected in our spectra, hence the redshift is determined through cross-correlation of the spectra of PTF10hgi with other SNe at confirmed redshift indicating a redshift of z = 0.100 ± 0.014, corresponding to a luminosity distance of d L ∼ 448 Mpc. The Galactic reddening toward the SN line of sight is E(B − V ) = 0.09 mag (Schlegel et al. 1998 (Drake et al. 2011;Quimby et al. 2011c). We also independently detected this transient in the PS1 FGSS (PS1-11xk) on images taken on 2011 April 15 (Smartt et al. 2011). However earlier PS1 data show that we can determine the epoch of explosion to around one day, at least as 15 http://www.sdss3.org/dr9/ far as the sensitivity of the images allow. On MJD 55649.55 (2011 March 29.55 UT) a PS1 image (r P1 = 40s) shows no detection of the transient to r ≃ 21.17 mag. Quimby et al. (2011c) report the PTF detection on 2011 March 30 (MJD=55650) the night after the PS1 non-detection at g ≃ 21. PS1 detections then occurred 1 and 3 days after this on 55651.6 and 55653.6 (in i P1 and r P1 ) respectively. The photometry is given in Table 6. This is the best constraint on the explosion epoch of an SL-SNe to date, allowing the rise time and light curve shape to be confidently measured. The object brightened rapidly, by ∼ 3 mag in g−band in the first 15 days and 1.7 mag in the subsequent 20 days. It was classified as an SL-SNe Ic by both Drake et al. (2011) and Quimby et al. (2011c); their spectra obtained on May 8.0 and 11.0 UT, respectively, showed a blue continuum with faint features, similar to PTF09cnd about 1 week past maximum light (Quimby et al. 2011c).
We found a nearby source in the SDSS DR9 catalog (g = 21.10 ± 0.08, r = 20.71 ± 0.08), which is the host galaxy as confirmed by deep griz images taken with the William Herschel Telescope on the 26th of May 2012 at a magnitude g = 21.18 ± 0.05, r = 20.72 ± 0.04 . The host emission lines set the SN at z = 0.143, equivalent to a luminosity distance of d L = 660 Mpc. The Galactic reddening toward the position of the SN is E(B − V ) = 0.01 mag (Schlegel et al. 1998).

PTF11rks
PTF11rks was first detected by PTF on 2011 December 21.0 UT (Quimby et al. 2011b). Spectra acquired on December 27.0 UT and 31.0 UT showed a blue continuum with broad features similar to PTF09cnd at maximum light, confirming it as a SL-SN Ic. A non-detection in the r-band on Dec. 11 UT prior to discovery is also reported, setting a limit of >20.6 mag at this epoch. Quimby et al. (2011b) detailed a brightening of 0.8 mag in r-band in the first 6 days after the discovery. Prompt observations with Swift revealed an ultraviolet (UV) source at the optical position of the SN, but no source was detected in X-rays at the same epochs. There are no useful early data from PS1 for this object.
The host galaxy is listed in the SDSS DR9 catalogue with g = 21.59±0.11 mag and r = 20.88±0.10 mag. Confirmation of these host magnitudes as achieved with our deep gr-band images taken with the William Herschel Telescope on the 22nd of September 2012 at a magnitude g = 21.67 ± 0.07 and r = 20.83 ± 0.05. The emission lines of the host and narrow absorptions consistent with Mg ii λλ2796,2803 doublet locate the transient at z = 0.19, corresponding to a luminosity distance of d L = 904 Mpc. The Galactic reddening toward the position of the SNe is E(B − V ) = 0.04 mag (Schlegel et al. 1998  ). The spectra taken by Prieto et al. (2012) on 2012 January 2.5 UT and 17.5 UT reveal a blue continuum with absorption feature typical of a luminous Type Ic SN.
The closest galaxy is ∼ 23 ′′ S/W of the object position and is hence too far to be the host. There is no obvious host coincident with the position of this SN in SDSS DR9. We detect a faint host galaxy in deep gri-band images taken with the William Herschel Telescope on 20 July 2012. At a magnitude r = 23.94 ± 0.20, this is too faint to affect the measurements of the SN flux out to +120 days. The redshift of the object has been determined to be z=0.245 from narrow Hα and [O iii], equivalent to a luminosity distance of d L = 1204 Mpc. The foreground reddening is E(B − V ) = 0.02 mag from Schlegel et al. (1998).
2.6. SN 2012il SN 2012il was first detected in the PS1 FGSS on 2012 January 19.9 UT (Smartt et al. 2012) and also independently discovered by CRTS on the 21st of January 2012 (CSS120121: 094613+195028 Drake et al. 2012). On January 29 UT we obtained a spectrum of the SN, which resembled SN 2010gx 4d after maximum light. The merged PS1 and CRTS data suggest a rise time of more than 2 weeks, different from that of SN 2010gx ) but similar to PS1-11ky (Chomiuk et al. 2011). An initial analysis of observations from Swift revealed a marginal detection in the u, b, v and uvm2 filters, with no detection in the uvw1 and uvw2 filters, or in X-rays ). However our re-analysis of the Swift data reveals a detection above the 3σ level in the uvw1 and uvw2 filters (see Tab. 11). No radio continuum emission from the SN was detected by the EVLA .

FOLLOW-UP IMAGING AND PHOTOMETRY
Optical and near infrared (NIR) photometric monitoring of the five SNe was carried out using the telescopes and instruments listed in Appendix A. The main sources of our photometric follow-up were the SDSSlike griz filters in the cameras at the Liverpool Telescope (RATCam), William Herschel Telescope (ACAM), and the Faulkes North Telescope (MEROPE). Further data in BV and JHK filters were taken for some of the SNe with the EKAR 1.8m Telescope (AFOSC), the ESO NTT (EFOSC2) and the Nordic Optical Telescope (NOTCam). Swift+UVOT observations have been taken for four out of five SNe in the UV filters uvw2, uvm2 and uvw1 (and for three SNe in the Swift u filter) and we analysed these publicly available data independently. Aside from SN 2011ke, ground based SDSS-like u observations were sparse, and for two SNe of our sample nonexistent.
Observations were reduced using standard procedures in the IRAF 16 environment. The magnitudes of the SNe, obtained through a point spread function (PSF) fitting, were measured on the final images after overscan correction, bias subtraction, flat field correction and trimming. When necessary we applied a template subtraction technique on later epochs (through the HOT-PANTS 17 package based on the algorithm presented in Alard 2000). The instruments used to obtain reference images were the William Herschel Telescope and the Telescopio Nazionale Galileo. The same images were used to measure the host magnitudes and listed in Appendix A (Tabs. 5,6,7,9 & 10) and labelled as "Host". When we did not have template images, we used SDSS images as template to remove the flux of the host. The magnitudes of SDSS stars in the fields of the transients were used to calibrate the observed light curves (Fig. 2). All Sloan magnitudes -as well as the NTT U and R magnitudes -were converted to the SDSS AB magnitude system and colour corrections were applied. PS1 magnitudes were also converted to SDSS magnitudes following the prescription in . B and V magnitudes are reported in the Vega system. The PTF10hgi field was not covered by SDSS, so the average magnitudes of local sequence stars were determined on photometric nights, and subsequently used to calibrate the zero points for the non-photometric nights. Magnitudes of the local sequence stars are reported in Appendix B (Tab. 12) along with their rms (in parentheses).
For the Swift u band data, we determined magnitudes in the UVOT instrumental system (Poole et al. 2008) and subsequently converted to Sloan u by applying a shift of ∆u ≈ 0.2 mag. The shift has been computed for each SN from a comparison of the magnitudes of the reference stars in the SNe fields in the UVOT and Sloan photometric systems. The only exception is PTF10hgi, where due to the absence of ground-based u images, we applied the average shift of the other SNe. The UV magnitudes are reported in Appendix A (Tab. 11).
NIR observations are not shown in Fig. 2 as these were only obtained for PTF11rks. The JHK photometry was calibrated to the 2MASS system (Vega based), using the same local sequence stars as for the optical calibration.
Thus the values reported are Vega magnitudes. Pre-peak observations are available only in the r−band, suggesting a rise time comparable to SN 2011ke. PTF10hgi shows a bell-like shaped light curve around peak. The post maximum lightcurve shows a constant decline in all the bands until 40d. After 40d, the decline rate of PTF10hgi changes to have a slope similar to the decays shown by the other SNe. The change in the i−band slope is not as evident, while the z−band light curve is also dissimilar to the other bands. The magnitudes beyond 90d are evaluated using the template subtraction with 646-648d epochs as template images.

SN 2011ke
SN 2011ke was detected during the rise phase, and we continued to observe the SN until it disappeared behind the Sun in late August 2011. The non-detection of the  Appendix A,in Tabs. 5,6,7,9 and 10. transient the day before the discovery gives us the best constraint on the explosion epoch of any SL-SN to date, allowing the rise time and light curve shape to be confidently measured. The light curve is bell shaped around peak in the observed-frame g−band, and more similar to the light curve of SCP-06F6 (Barbary et al. 2009). The post maximum light decrease is slower at redder wavelengths, as in the previous object. It follows a constant slope until 50d, when the slope changes to a slower decline. SN 2011ke then continued to fade at the same rate until the last available photometric point at ∼ 200d post maximum. The reference template (339d) was used to retrieve the magnitudes after 51d.

PTF11rks
The transient was discovered just before the g−band peak.
The pre-discovery limit of December 11 (Quimby et al. 2011b) indicates a rise time on the order of 20 d, followed by a slower decline post-maximum. The r−band light curve shows an asymmetric peak as for SNe 2005ap and 2010gx (Quimby et al. 2007;Pastorello et al. 2010), in contrast to the rounded peaks of the light curves of PS1-10awh and PS1-10ky (Chomiuk et al. 2011). The SN fades by ∼ 2.1 mag over the first 30d in rest frame g band, with a slower decline in the redder bands. The decrease is faster than that of the other SL-SNe Ic, although a more rapid decline at redder wavelengths is common in SNe (see Fig. 1 in Pastorello et al. 2010). After 50 days the SN faded below our detection limit, even in deep imaging. A small, but non-negligible, flux contribution from the host has been found after 28d and was removed using template subtraction with the reference images at 218d. While for the i and z bands we used the SDSS images as template.

SN 2011kf
The light curve of SN 2011kf is the least well sampled as our monitoring started some 20 days after the ATel discovery announcement. We assume that the reported point of Drake et al. (2012) is at peak which is supported by the spectral and colour evolution of the SL-SN during its subsequent evolution. During the first 50d, the decline in the g−band resembles those of the other SL-SNe Ic. But between 50-150d the decline rate changes markedly and the fading is slower. The reference template (164d) was used to retrieve the magnitudes after 71d. Because of the proximity of the template epoch and last SN epoch, we also used SDSS images as secondary template. The values retrieved with the two different templates were in agreement, strengthening simultaneously the lack of the SN at 145d and the detection of the faint host in the deep images of 164d.
3.1.5. SN 2012il SN 2012il was discovered before it peaked in the g− and r−bands. The first two epochs available are in the PS1 z P1 band and the CSS unfiltered system Drake et al. (2012). We can not set a robust constraint on the rise time for SN 2012il, but it is likely at least two weeks. The shape of the light curve around peak in r−band is possibly asymmetric as in PTF11rks and SN 2010gx, although we are somewhat constrained in this statement due to the uncertainty of the peak epoch. As for SN 2011ke, we see a clear change in the decline rate after 50 days, when SN 2012il has a slower decline (shown in Fig. 2. This change in decline to a slower fading rate is illustrated with the latest detection in all three filters riz at ∼113d after peak. The reference template (327d) was used to retrieve the magnitudes at 113d and the g magnitudes after 58d.

Absolute Magnitudes
In calculating absolute magnitudes (and subsequently bolometric magnitudes), we have assumed negligible internal host galaxy reddening for all the objects, and applied only foreground reddening, with the values reported in Sect. 2. No Na ID absorption features due to gas in the hosts were observed. However, we can not exclude possible dust extinction from the hosts, therefore the absolute magnitudes reported here are technically lower limits. Given that the hosts are all dwarf galaxies, and the transients have quite blue spectra around peak it appears that any correction would be small. We computed k-corrections for each SN using the spectral sequence we have gathered. For photometric epochs for which no spectra were available, we determined a spectral energy distribution (SED) using the multi-color photometric measurements available. This SED was then used as a spectrum template to compute the K-corrections. Comparisons between the two methods (K-correction directly from spectra, or with the photometric colours) showed no significant differences. We also determined Kcorrections for SN2010gx using the spectral method and using photometric colours. Again we found consistency between the two methods. After applying foreground reddening corrections and K-corrections we estimated absolute rest-frame peak magnitudes (cfr. Tab. 1).
In Fig. 3, we compare the rest frame g−band absolute light curves (in the AB system) of the SNe studied here with those of other low-z super-luminous events and the well studied Type Ic SN 1998bw (Galama et al. 1998;McKenzie & Schaefer 1999;Sollerman et al. 2000;Patat et al. 2001). The epochs of the maxima were computed with low-order polynomial fits and by comparison of the light curves and their colour evolution with those of other SL-SNe, and are listed in Tab. 1. The absolute peak magnitudes of PTF11rks and PTF10hgi are fainter than the bulk of SL-SNe, although they are still ∼ 2 mag brighter than SN 1998bw. Interestingly, the two faintest SL-SNe Ic display different decline rates to each other, PTF11rks is similar to SN 2010gx whereas PTF10hgi decreases at a slower rate. The other three objects have peak magnitudes comparable with that of SN 2010gx (M g ≈ −21.67) and show a similar decline. The decline slope changes in four of the five objects after 50 days in the rest frame (while for the other, SN 2011ke, our data do not constrain it). The light curves then settle on a tail resembling the decay of 56 Co. This is apparent in Fig. 3 as the tails of the SL-SNe are similar to that of SN 1998bw which is known to be powered by 56 Ni. The light curves follow the 56 Co decay within errors of 10%, the biggest discrepancy is for SN 2011kf which falls more rapidly between 100-200 days. SN 2007bi (Gal-Yam et al. 2009;Young et al. 2010) also followed the 56 Co decay at late times, but with a tail that is ∼ 2 mag brighter than the SL-SNe Ic, and with a and SN 2012il and a number of super-luminous events as well as the stripped envelope SN 1998bw. The light curves for each SN have been derived by correcting the observed broadband photometry for time dilation, distance modulus, foreground extinction, and differences in effective rest-frame bandpass (K-correction). The last PTF10hgi and SN 2012il points were converted from the r mag applying a colour correction derived from SN 2011ke and SN 2011kf at similar epochs. much slower overall evolution. We also note that the light curves of our objects flatten at slightly different epochs, with the tail for SN 2011ke commencing ∼ 10 days after the last point in the lightcurve for SN 2010gx.

Colour Evolution
We computed rest-frame colour curves, after accounting for the reddening and redshift effects of time-dilation and K−correction. The colour curves are useful probes of the temperature evolution of the SNe. We also calculated rest-frame colour evolution of SN 2010gx, the only other SL-SN Ic with a good coverage in SDSS filters at a similar redshift. In Fig. 4 the SL-SNe show a constant colour close to g − r = 0 from the pre-peak phase to ∼ 15d. This evolution is similar to the colour evolution of the higher redshift PS1-10ky in the observed bands i P1 − z P1 Chomiuk et al. (2011).
The constant colour until 15 d implies that the SED does not evolve over these epochs.
Up to maximum light, the spectra of these SL-SNe appear to be blue, with the only strong features being the O ii lines in this range covered by the gr filters ( Chomiuk et al. 2011;Leloudas et al. 2012). Hence this could be due to an approximately constant temperature. This is also illustrated in Fig. 8   (2011) for the higher redshift PS1-10ky. Close to peak the O ii lines disappear, leaving the spectra featureless for ∼ 10 days, while after peak the temperature begins to decrease (see Sect. 5.1). A monotonic temperature decline between 14000 K and 12000 K (blackbody peak 2100Å λ 2500Å) in objects with featureless spectra does not strongly affect the colour evolution for λ λ peak , as the slopes of blackbodies at these two temperatures are quite similar. To detect differences in temperature between a 12000 K and a 14000 K blackbody requires colour curves which sample rest wavelengths below 3800Å, such as the g − z colour of PS1-10ky. And indeed this object did show an increase in g − z.
After this early period of constant colour, the g − r colour increases, reaching another phase of almost constant value at ∼ 40d, perhaps indicating a decrease in the cooling rate. There are some exceptions to this behaviour, as seen for PTF11rks and PTF10hgi. The g − r colour of PTF11rks increases earlier and with a steeper slope than the other SNe, but unfortunately our data stop before the possible second period of constant colour. In contrast, the g −r colour for PTF10hgi increases much more slowly, and only reaches the possible late constant phase at ∼ 80d.
The r−z colours of the sample show a roughly constant increase from peak to ∼ 50 − 60d, when the colour evolution appears to flatten. The two exceptions are again PTF11rks and PTF10hgi; the former increases in r − z more rapidly than the other objects, whereas the latter does not become as red, and experiences a clear decrease in r − z after 80d. The r − z colour evolution of SN 2010gx is similar to that of SN 2011ke and PTF10hgi.
3.4. Temperature evolution In Fig. 5 the evolution of the temperature is plotted. This is derived from a blackbody fit to the continuum of our spectra (see Sect. 5), and compared to those of SN 2010gx and SN 2007gr. We also fit colour temperatures at rest-frame with a blackbody and the measurements are in good agreement with those from spectra.
Only PTF11rks has a good temperature coverage around peak, whereas our spectroscopic data are not well sampled at that phase. While we can not clearly confirm the apparent constant temperature seen in SN 2010gx until ∼ 10d, the epochs either side at ±10d are suggestive of a roughly constant temperature phase. After ∼ 10d a clear decline in temperature is seen, with a rate of decline of ∼2500 K over 10d. This decline continues until the SN reaches a constant temperature of ∼ 6000 K prior to, and during, the pseudo nebular phase.

BOLOMETRIC LUMINOSITY
Simultaneous UV-optical-NIR photometry at all epochs is required to obtain a direct measurement of the bolometric luminosity. This is typically difficult to attain at all epochs during a SN lightcurve, and we do not have complete wavelength coverage for the five SL-SNe. Nevertheless, valid corrections can be applied to the observed photometric bands to compute the bolometric flux.
The effective temperatures of the photospheres of SL-SNe Ic during their first 30-50 days after explosion are between T bb ∼ 13000 − 19000 K (see Table 10 and Pastorello et al. 2010;Chomiuk et al. 2012). This means that their fluxes peak in the UV (λ < 3000Å) during this period while our griz bands typically cover from restframe 3800Å redwards. Thus a significant fraction of the flux is not covered by the optical griz imaging. At around 20d after peak, the effective temperatures tend to drop below 10000 K, hence the SEDs peak between 3000Å and 4000Å. Although the peak of the SED moves redward, a significant amount of the bolometric flux is radiated in the UV even during these late stages. In the following, we will use the term "griz-bolometric lightcurve" to refer to a bolometric lightcurve determined using only the specified filters (in this example, griz) with the flux set to zero outside the observed bands.
Initially, the broad band magnitudes in griz were converted into fluxes at the effective filter wavelengths, then were corrected for the adopted extinctions (cfr. Sect. 2). A SED was then computed over the wavelengths covered and the flux under the SED was integrated assuming there was zero flux beyond the integration limits. Fluxes were then converted to luminosities using the distances previously adopted. We initially determined the points on the griz-bolometric lightcurves at epochs when griz were available simultaneously (or very close in time). For epochs with coverage in less than the four filters we were able to estimate the griz-bolometric lightcuves. Magnitudes from the missing bands were generally estimated by interpolating the light curves using low-order polynomials between the nearest points in time. For some points this interpolation was not possible and we used one of two methods. The first was an extrapolation assuming constant colours from neighbouring epochs, the second was using colours from the other SL-SNe at similar epochs. For example, we used the latter method for the last point on the lightcurve for PTF10hgi. The grizbolometric light curves estimated using this technique are plotted in the left panel of Fig. 6.
Useful Swift photometry for UV flux measurements exists for PTF11rks and SN 2011ke (see Table 11). Which allow us to compare the griz-bolometric light curves and the U V griz-bolometric lightcurves (pseudo-bolometric hereafter), where the U V component is determined from the uvw2, uvm2 and uvw1 filters covering 1800-3000Å. The difference between these two bolometric light curves, with and without the radiated energy below 3500Å is shown in the right panel of Fig. 6.
Inclusion of the Swift photometry results in maximum luminosities for PTF11rks and SN 2011ke of L≈ 4.27 × 10 43 erg s −1 and L≈ 7.08 × 10 43 erg s −1 respectively. Hence the griz-bolometric fluxes, are a factor 1.5 lower than when including the 1800-3000Å range covered by uvw1 − uvw2 filters. While one could fit a black-body curve to the observed griz SEDs (or the spectra) and integrate under the curve to determine the emitted total flux across all wavelengths, this would not account for the strong line absorption shown in the rest-frame UV spectra (for example, clearly seen in the high-z objects of Chomiuk et al. 2011). Hence from here on we will use griz-bolometric lightcurves for consistency on all objects, but we should bear in mind the additional contribution from the restframe UV that we have quantified in the right-hand panel of Fig. 6. The maximum luminosities reached by our computed griz-bolometric light curves are L PTF11rks ≈ 3.24 × 10 43 erg s −1 , L SN2011ke ≈ 4.47 × 10 43 erg s −1 , L SN2011kf ≈ 6.45 × 10 43 erg s −1 , L SN2012il 4.47 × 10 43 erg s −1 and L PTF10hgi ≈ 2.09 × 10 43 erg s −1 . As expected, these are lower than those reported by Chomiuk et al. (2011) for the z ≃ 0.9 objects PS1-10ky and PS1-10awh due to the lack of restrframe UV coverage for our low redshift sample.
The comparison in Fig. 6 further quantifies the large bolometric luminosities of these SL-SNe Ic -as discussed by Pastorello et al. (2010), Quimby et al. (2011a), Chomiuk et al. (2011) and Leloudas et al. (2012). There is clearly some diversity in the lightcurve peaks and widths. The low redshift of these objects makes it possible to follow the evolution beyond 100d after peak for the first time. Only one other object (SN 2010gx) has been investigated in this phase Chen et al. 2013) and no detection was found at greater than 100 days. Quantifying the host contribution and using image subtraction to recover the SL-SN flux in these late phases is essential (as discussed in Sect. 3). It transpires that SL-SNe Ic show a large diversity in this phase, quite different to the relatively homogenous behaviour around peak. After 50d post maximum, all four of the SL-SNe Ic for which we have data (SN 2011ke, SN 2012il, SN 2011kf and PTF10hgi) show an abrupt change in the slope of the griz-bolometric lightcurve. The slope flattens and is quite similar to that of the decay of 56 Co to 56 Fe. SN 2011ke and PTF10hgi appear to decline even slower than the 56 Co slope.
Additionally, at these later phases we know from detailed coverage of CCSNe that a significant amount of radiation will be emitted in the near-infrared when the photospheric temperature drops below 10000 K. This flux can be, mostly, captured by JHK photometric observations. As we lack this complete wavelength coverage for our SL-SNe, we employed an SED method to deter-   ) in black. The phase of each spectrum relative to light curve peak in the rest frame is shown on the right. The spectra are corrected for Galactic extinction and reported in the rest frames. The ⊕ symbols mark the positions of the strongest telluric absorptions. The most prominent features are labelled. mine the correction. We use the photospheric temperatures (derived in Sec. 3.4) to derive simple blackbody SEDs and integrate the flux redwards of the rest-frame zband. The flux missed in the NIR by our griz-bolometric measurements typically increases with time, and reaches roughly 50% after ∼ 60d post maximum. We plot the rest-frame NIR contributions as an average of all the SL-SNe presented here, for a representative redshift of z < 0.25, in the the bottom panel of Fig. 7. The optical component refers to the griz bands (green line), and the NIR contribution beyond the z-band is denoted with the red line. We also used this method to have a secondary estimate of the UV contribution (blue line). In this case we integrated the flux under the black body spectra below the g-band. We compared the UV flux contribution with those evaluated from the two SNe which have Swift UV photometry and find the two are consistent within the errors. Fig. 7 summarises the flux contributions from the different wavelength regimes and allows the griz-bolometric lightcurves to be corrected when required.
If these tail phase luminosities were powered by 56 Co then it would require that there is full γ-ray trapping in the ejecta. This is not typically seen in Type Ic SNe. For example, the BV RI bolometric lightcurve of SN 1998bw is shown for comparison which decays faster than the nominal 56 Co half-life. Sollerman et al. (2000) showed that if one assumes a fixed energy source (i.e. some mass of 56 Co), then the trapping efficiency decreases with time (∝ t −2 ). Hence at the epochs of these SL-SNe (100-200 days) only around ∼ 45% of the γ-rays would be trapped if they had similar ejecta mass and density profiles to other Type Ic SNe. This seems to be in contradiction to the measured slopes which appear either to follow the 56 Co decay timescale or even be slightly shallower. Despite this issue, we shall initially assume (for illustrative purposes) that the tail phases are actually powered solely by radioactive decay. This allows a corresponding mass of 56 Ni to be determined. Later in this paper we shall show that the tail phase luminosity may be powered by magnetar energy injection rather than 56 Co decay. Although four of the SL-SNe do show a flattening in their luminosity, it appears SN 2010gx does not, at least not at the detectability level of Chen et al. (2013). The data we have for PTF11rks does not allow a conclusion.
We initially make the assumption that γ-rays from 56 Co decay are fully thermalized during the full durations of the lightcurves we measure. We know that for typical SN Ic ejecta this is not the case, but it allows us to derive illustrative masses for 56 Co powering. The 56 Ni masses can thus be estimated using the formula 1.9 M ⊙ . The measured de-cline for SN 2011kf was slightly steeper than the fully trapped 56 Ni tail. We also estimated an upper limit M( 56 Ni) PTF11rks ∼ 1.3 M ⊙ , for PTF11rks based on the last epoch in which the SN was detected. These values should be considered as lower limits because of our limited rest frame wavelength coverage. At this phase, the contribution from the NIR plays an important role in the bolometric luminosity of SNe, as described above. Indeed, the SED of SN 1987A (data from Hamuy et al. 1988;Bouchet et al. 1989), also suggests that as much as 50% of the total flux for our transients could be outside the griz bolometric lightcurves (at these epochs SN 1987A has already reached a constant temperature in the tail phase). Thus, to obtain a truer idea of the 56 Ni mass required to power these tail phases, the measured luminosities should be increased by roughly a factor two. In summary, we find that if the luminosity in the tail phase is powered by As we discuss below, we consider that the luminosity we detect in this phase is not necessarily due to radioactive 56 Co decay energy injection.

SPECTROSCOPY
All spectra were reduced (including trimming, overscan, bias correction and flat-fielding) using standard routines within IRAF. Optimal extraction of the spectra was adopted to improve the final signal-to-noise (S/N) ratio. Wavelength calibration was performed using spectra of comparison lamps acquired with the same configurations as the SN observations. Atmospheric extinction correction was based on tabulated extinction coefficients for each telescope site. Flux calibration was performed using spectro-photometric standard stars observed on the same nights with the same set-up as the SNe. The flux calibration was checked by comparison with the photometry, integrating the spectral flux transmitted by standard griz filters and adjusted by a multiplicative factor when necessary. The resulting flux calibration is accurate to within 0.1 mag.
The collected spectra are shown in Fig. 8 together with spectra of SN 2010gx ) for comparison. A version with all the spectra convolved to the same resolution and binned to the same pixel scale is shown in Appendix C. In our spectroscopic sample we do not have pre-peak spectral coverage, which typically shows C ii, Si iii and Mg ii at UV wavelengths (< 3000Å) and O ii in the optical region (Quimby et al. 2011a). The only lines which we may expect to be visible in our wavelength regions (namely O ii) have already disappeared by ∼ 3 − 12 days. At those epochs the SL-SNe spectra are featureless with the notable exception of PTF11rks, which shows weak broad absorption profiles of heavy elements such as Fe ii, Mg ii and Si ii between 3000Å and 6500Å. A weak Ca ii H&K absorption line is barely detected in PTF11rks, as is the case for SN 2011ke and SN 2012il. Redwards, Mg ii λ4481 and the Fe ii multiplet λλ4924, 5018, 5169 are visible in PTF11rks. Other Fe ii lines are barely visible in the region around 4500Å, while  a shallow absorption due to Si ii λ6347 is also present. None of these lines are clearly detectable in SN 2011ke and SN 2012il at a similar phase.
Two weeks after maximum, SN 2011ke shows Mg ii, Fe ii and Si ii lines together with a clearer Ca ii feature, albeit still shallower than for PTF11rks. The spectra obtained around 30d for SN 2011kf and PTF10hgi have a low signal to noise (S/N) ratio of ∼ 10 which makes line analysis problematic. However, the comparison with the other spectra indicates broad absorption profiles from Mg ii and Fe ii. The only line visible in the red part of the spectrum (> 7000Å) is O i λ7775 in SN 2011ke.
From ∼ 30d after maximum onwards there is no strong evidence of new broad features emerging blueward of 8000Å, with the exception of the rise of Mg i] λ4571. The absorption lines of Mg and Fe become shallower, resulting in the emission components becoming more prominent from ∼50d onwards. The Fe ii emission line at ∼ 5200Å is broader than Mg i] suggesting it may be a blend. The only exception to this general trend is PTF10hgi. In the last two available spectra PTF10hgi shows Ca ii H&K (possibly blended with Mg ii), three distinct absorptions related to the individual components of the Fe ii multiplet (λλ4924, 5018, 5169) and Na iD λλ5890,5896. Although the spectral evolution is relatively homogeneous, two of the sample have noticeable differences. In the first two weeks of evolution of PTF11rks the absorption line strengths look stronger, with EW PTF11rks ∼ 4 × EW SL−SNeIc . The later phase line formation in PTF10hgi also looks different, with narrower absorption lines more similar to velocities seen in Type Ic SNe (see the comparison with SN 2007gr in Fig.10) Weak, narrow emission lines (Hα, Hβ and [O iii] λ4959, λ5007) from the host galaxies are also visible in all spectra, except those of PTF10hgi. These will allow metallicity and star formation rate measurements in the host, which is underway in a companion paper (Chen et al., in prep). Fig. 9 shows the complete spectrum of SN 2012il taken at ∼ 53d with VLT+XShooter, which has the widest wavelength coverage for a SL-SNe obtained to date. As previously mentioned, bluewards of 8000Å, Ca ii H&K, Mg i], shallow Fe ii and O i are present. A strong Ca ii NIR triplet λλ8498, 8542, 8662 is visible, with the bulk of the absorption component at v = 12000±2500 km s −1 . This is higher than the other absorption components (e.g. O i v ∼ 9500 km s −1 ) and comparable with the velocities of the broad emission components of Ca ii H&K, Mg i]. At about 7300Å a weak emission line is evolving and we tentatively identify it as [Ca ii] λλ7291,7324 emission feature. The presence of [Ca ii] and the emission lines around 4500Å imply that the SNe is evolving, slowly, toward the nebular phase. This seems to coincide with the change in slope of the light curve. In the NIR the S/N∼5 in the continuum is less than in the optical (S/N∼30), although it is still adequate to identify the strongest lines. We identify Mg ii around 9200Å and Mg i λ15024, although the last identification is less certain due to the low S/N and the proximity of a strong telluric feature. Most significantly, we identify He i λ10830, the first sign of the presence of He in this group of SL-SNe Ic. We note that the only other ions which have transitions at this wavelength are Ar ii, Fe i, Si I and C I.   (Taubenberger et al. 2006) and 1994I (Baron et al. 1996). At ∼10d post maximum PTF11rks is already more developed than SN 2011ke and SN 2010gx. Middle: comparison at about ∼ 30d post peak of the same objects as for the previous panel, but showing PTF11rks instead of PTF10hgi. Bottom: comparison of the spectrum of PTF10hgi at ∼ 67d with those of SN 2010gx at the pseudo nebular phase, SN 2004aw at maximum light during the photospheric period, and Type Ic SN 2007gr (Valenti et al. 2008;Hunter et al. 2009). The spectrum of PTF10hgi is more similar to those of SNe 2004aw and 2007gr at 29d rather than those of SN 2010gx at 57d and SN 2004aw at 8d (as noted in Pastorello et al. 2010). expected to be intrinsically weaker than He i. There are no strong sky lines at the observed postion of this line ∼ 12725Å. Although we do not see other He i lines in the spectrum, this is not unexpected. In the Case B recombination in the temperature regime T < 10000 K and electron density 10 2 ≤ n e ≤ 10 6 -the λ10830 line is expected to be stronger than λ5876 line (the strongest in the optical region) by a factor 2 to 10.
The spectral evolution of the SL-SNe sample in this paper, provides additional information to that reported in Pastorello et al. (2010). In the top panel of Fig. 10 the comparison of the early time spectra with those of SN 2010gx , and the Type Ic SNe 1994I (Baron et al. 1996) and 2004aw (Taubenberger et al. 2006) highlights a difference in the line evolution between PTF11rks and other SL-SNe. The spectrum at 9.8d is similar to that of a Type Ic close to maximum light showing a faster transition to a Type Ic SNe than the others. In contrast, other SL-SNe such as SN 2011ke match normal Type Ic SNe only after ∼30d (middle panel Fig. 10 SNe Ic. Again the low S/N of the spectrum of PTF10hgi (32.7d) precludes a precise analysis, although there are hints of a peculiar line evolution at wavelengths redder than 5500Å. In the bottom panel, SN 2010gx resembles SN 2004aw at ∼ 10d after peak whereas PTF10hgi matches normal Type Ic SNe at ∼30d, with a good match to SN 2007gr. From this comparison it appears that PTF11rks and PTF10hgi evolve to into Type Ic SN on timescales of about 20 days quicker than other SL-SNe. The "fainter" luminosity (M> −21) of these two objects and their faster evolution to Type Ic SNe may provide another clue to understand the evolutionary path of these transients. It appears from these objects that the lower the peak luminosity, the faster the evolution of the photospheric spectra, with a time delay of 10 days to the Type Ic phase instead of the usual 30 days shown by most SL-SNe Ic.

Expansion velocity
The expansion velocities measured for PTF11rks, SN 2011ke, SN 2012il, PTF10hgi and SN 2011kf are reported in Tab. 3, and are compared with those of SN 2010gx and the standard Type Ic SN 2007gr (Hunter et al. 2009) in Fig. 11. In the photospheric phase these were derived from the minima of the P-Cygni profiles and their errors were established from the scatter between several independent measurements. During the phase in which the objects appear to be transitioning to the nebular phase (i.e. beyond about 50 days) the velocities were computed as the FWHM of the emission lines (we will call this the pseudo-nebular phase). These are not tracers of the photospheric velocity and are reported for completeness; they will be discussed further in Sect. 6.2. We used Fe ii λ5169, Mg ii λ4481 and O i λ7775 to measure velocities during the photospheric phase, and Ca ii H&K and Mg i] λ4571 during the pseudo-nebular phase. The Fe ii velocity evolution monotonically declines for all transients, ranging from ∼ 18000 km s −1 around peak to ∼ 8000 km s −1 at 50d. After this epoch we have only PTF10hgi spectra, and they still show clear absorption components of Fe ii. The decline in velocity is faster and it reaches ∼ 4600 km s −1 at the last epoch of 80 days, which is quite similar to the Fe ii velocity of SN 2007gr. Mg ii in the photospheric phase is always seen at higher velocity than Fe ii, and decreases linearly by ∼ 1000 km s −1 every 10 days. The O i velocity is comparable with that of Fe ii, with the exception of SN 2011ke where it is slower than all other ions (albeit with large uncertainties due to the low S/N). Ca ii and Mg i] appear after ∼40d from maximum light and show the same intensity and velocity of ∼ 11000 km s −1 in the entire sample.
The PTF10hgi spectra after 60d show Ca ii absorption at late epochs, similar to normal Type Ic SNe. Fig. 11 shows evidence for decreasing line velocity with time, especially from 10d post peak as seen for SN 2010gx (previously reported as a comparison in Chomiuk et al. 2011). Our analysis shows a clear sign of change in the rate of photospheric expansion (30 − 40d), with a decline which resembles that typically observed during the photospheric phase of a CCSN explosion.

ON THE NATURE OF SL-SNE IC
The SN sample presented in this paper provides new data for understanding the nature of super-luminous events. The similarity within this family is well established: high luminosity, similar spectral evolution and an origin in faint host galaxies. The overall spectral evolution is indeed similar to that of SNe Ib/c, although SL-SNe spectroscopically evolve on a much longer timescale. However, the observed parameters of SL-SNe present several problems in interpreting the explosion. The enormous luminosity at peak cannot be powered by radioactive 56 Ni Quimby et al. 2011a;Chomiuk et al. 2011;Leloudas et al. 2012) which is the canonical energy source for SNe Ic emission. However, we showed in Section 4 that the tail phase luminosity in some objects declines in a similar fashion as to what would be expected from 56 Co decay.
In the following subsections we use this most extensive dataset to constrain plausible models for the origin of these SNe, particularly using the bolometric luminosity from -30 to 200d and the temperature and velocity information. In this paper we focus on quantitative modeling of the magnetar spin down scenario (Sect. 6.2). Several other models have been proposed, which we briefly review in Sect. 6.1. The bolometric light curves used in this Section are corrected for flux missed in both UV and NIR as described in Section 4. shock breakout from dense mass loss (Chevalier & Irwin 2011); or pulsational pair instability in which collisions between high velocity shells are the source of multiple, bright optical transients (Woosley et al. 2007).
The first scenario considered is the pulsational pairinstability model, where the luminosity is powered by the collision of shells of material ejected at different times by the pulsations (see , for the implementation of this on SL-SNe Ic). The outbursts are expected to be energetic, reaching very high peak luminosities and creating hot (T eff ≈ 25000 K), optically thick photospheres (Woosley et al. 2007). PS1 has occasionally observed the explosion sites of the five SL-SNe presented here, and SN 2010gx on 3-5 occasions (per event) in one of g P1 r P1 i P1 z P1 y P1 filters, reaching typical AB magnitudes of 22, 21.6, 21.7, 21.4, 19.3 (see Sect.2). This would correspond to absolute magnitudes of roughly −16 to −19. We found no detection of any previous outburst to these magnitude limits in the 1-2 year periods before explosion. Typically there were 5-10 epochs of images from PS1. This is not a constant monitoring period, and it does not rule out that pre-explosion outbursts occur, but we have found no evidence for them. The second scenario is that of circumstellar interaction proposed by Chevalier & Irwin (2011) in which the interaction between the ejecta and the CSM converts the ejecta's kinetic energy into radiation. This requires the diffusion radius of the SN to be about the radius of the stellar wind expelled by the SN progenitor. Based on this model of Chevalier & Irwin (2011), Chomiuk et al. (2011 determined the dense wind and ejecta parameters for the observed z ≃ 1 SL-SNe. This requires a mass-loss rate of 6 M ⊙ in the last year before the SN explosion, with an outer radius of around 40000 R ⊙ , and ejecta mass of 10 M ⊙ (consistent with the estimates reported in Moriya & Tominaga 2012). The rise times of our low-z SNe are similar to that of PS1-10awh (from Chomiuk et al. 2011) -around 10-30 days which would lead to similar estimates of masses. The detection of He i in SN 2012il at ∼ 53d is perhaps some hint that the dense CSM wind could be plausible, since it is difficult to find any known massive star example in the Local Universe which has a dense and extended wind comprising 6 M ⊙ of C+O material only. Although the S/N in the NIR is low, the He i line is relatively broad, indicating that it arises from ejecta. Although most SL-SNe have similar rise times which are feasible in the diffusion model of Chevalier & Irwin (2011), the light curves of SN 2010gx , PTF11rks and SN 2012il are not symmetric, which one would expect in this dense wind scenario. However, Ginzburg & Balberg (2012) showed as the rise and fall times can be different. They also showed that the tail phase can be explained as diffusion from the inner layers which can slow the decline. We have not investigated in this scenario in depth, but a combination of this model plus a 56 Ni tail would be unlikely because of the necessity of full γ-ray trapping (see Sec. 4).
A variant of the previous scenario was proposed by Blinnikov & Sorokina (2010) claiming high luminosities from a radiative shock in a massive C-O shell. The shells have radii and density profiles that are similar to the dense wind of Chevalier & Irwin (2011), with a density gradient of ρ(r) ∝ r −1.8 and radii of the order 10 5 R ⊙ . Considering a total ejecta mass M ej 1 M ⊙ , which collides with a shell of mass 5 M ⊙ , these models have initial energies (2 − 4 × 10 51 erg) higher than those retrieved by the expansion velocities during the pseudo nebular phase in our set of spectra (∼ 1 × 10 51 erg). Moreover, the light curves are too shallow and they are not able to reproduce the SN 2010gx decline after 30d post maximum light. We find no unequivocal signs of interaction in the spectra of the objects.
In Sects. 3.1 and 4 we have presented detections of the SNe at later times than published to date, due to our focus on low redshift candidates. We detect a flattening of the lightcurve and a tail phase in four out of five transients and this slope appears to be consistent with 56 Co decay. In summary these interaction scenarios can reproduce the peak energy and diffusion time. However the ejecta/shell velocity should be lower (by about a factor of 2) than those observed. And one still needs another power source for the late time luminosity that we now detect in these SL-SNe Ic.
As  Leloudas et al. (2012), the lightcurve peaks cannot be fit with a physically plausible 56 Ni diffusion model like normal SNe Ic, and our similarly shaped lighcurves result in the same conclusion. If the tail phase was actually due to 56 Co powering, then approximately 1-4 M ⊙ of 56 Ni would be required. But this would not be enough to power the peak luminosity solely through radioactive heating. In Fig. 12 we also show the best fitting 56 Ni-powered models, under the assumptions that the 56 Ni mass must be <50% ejecta mass, and that the ejecta velocities are less than 15000 km s −1 . The first assumption is based on the implausibility of a pure 56 Ni ejecta; Umeda & Nomoto (2008) found typical 56 Ni masses which are at most 20% of the ejecta, while if the ejecta was comprised of more 56 Ni than this, we would expect to see spectra dominated by Fe-group rather than intermediate mass elements. The velocity constraint is motivated by the observed velocities in our sample. Thus we derived kinetic energies of 6.2 E(10 51 erg) 15.0, ejecta masses of 5.9 M ej (M ⊙ ) 13.0 and 56 Ni masses of 2.9 M56 Ni (M ⊙ ) 6.0 (see Appendix D.5 for further details). From the fits appear that no physical and consistent solutions for 56 Ni heating can be determined, as found by previous authors Quimby et al. 2011a;Chomiuk et al. 2011;Leloudas et al. 2012). One could invoke a combination of CSM interaction to explain the peak luminosity and then 56 Ni masses of 1-4 M ⊙ to account for the tail phases. But as discussed above, this requires full γ-ray trapping and somewhat fine tuning of the two scenarios to work in unison. Kasen & Bildsten (2010); Woosley (2010); Dessart et al. (2012) have already proposed that a rapidly spinning magnetar can deposit its rotational energy into a supernova explosion and significantly enhance the luminosity. This appears to be an appealing scenario as the model is fairly simple, and this additional power source can potentially transform a canonical Type Ic SN into a SL-SN Ic. To investigate this further and quantitatively compare our extensive lightcurves with this model we have derived a semi-analytical diffusion models. We use standard diffusion equations derived by Arnett (1982) and add magnetar powering (as in Kasen & Bildsten 2010) to fit the light curves of our five objects. A full description can be found in Appendix D.

Magnetar model
Assuming full trapping of the magnetar radiation 18 , the ejecta mass M ej , explosion energy E k , and the opacity κ only influence the bolometric light curve through their combined effect on the diffusion time-scale parameter (see Appendix D) (2) The magnetar luminosity depends on two parameters, the magnetic field strength B 14 (expressed in terms of 10 14 G) and the initial spin period P ms (in milliseconds). Combined with the explosion date t 0 , we therefore have four free parameters to fit. Tab. 4 lists the best-fit parameters for each object, and Fig. 12 shows the fits. As the χ 2 fitting gives good matches to models without 56 Ni, we have no need to introduce 56 Ni as an additional free parameter. All the models have M( 56 Ni) = 0 M ⊙ and we investigated the sensitivity to the assumed 56 Ni mass by recomputing the fits including 0.1 M ⊙ of 56 Ni in the ejecta (the typical 56 Ni yield in core collapse SNe). We find virtually the same fit parameters as we do without the nickel. As can be seen from Fig. 14 (top), the two magnetar models (B 14 = 5, P ms = 5, M ej = 5 M ⊙ ) with (red dashed) and without 56 Ni (black solid) are similar. The late decline rate in the magnetar model (>100d) is actually quite similar to the 56 Co decay rate as shown in Fig. 14 (bottom), but fully trapped γ-rays are required. As Fig. 14 shows, this full trapping is different from the typical light curve of a radioactivity-powered Type Ib/c SN in which full trapping is not observed. Recently, Dexter & Kasen (2012) showed that fall-back accretion can give a similar asymptotic behaviour of the light curve (L t ∝ t −5/3 ) which is a scenario that would need further investigation.
The lightcurves are quite well reproduced with appropriate choices of parameters, and the tail phase luminosities that we measure can also be explained with this model. The diffusion time scale parameters are between 15-35 days, which corresponds to ejecta masses of 2-9 M ⊙ for κ = 0.1 cm 2 g −1 (see Appendix D for further details about κ) and where E mag is the total energy of the magnetar and E rad is the total radiated energy of the SN. We use a factor of 1/2 for an approximation of the average kinetic energy over the magnetar energy input phase, which we show in the Appendix D.4 produces good agreement with more detailed time dependent calculations of E k 19 . These ejecta masses are consistent with 18 Which is the case if the SED of the magnetar is dominated by X-ray radiation, as in the Crab pulsar for instance (Weisskopf et al. 2000). 19 We also investigated the sensitivity to this assumption by computing masses (as well as photospheric velocities and temperatures) also from E k = 10 51 + 0.4E mag where the 40% conversion to kinetic energy is a typical value (Woosley 2010). We found very small differences in the derived quantities. . Also shown is the total energy emitted by M( 56 Ni) = 0.1 M ⊙ (green dotted) and the light curve produced by this amount of 56 Ni in a 5 M ⊙ ejecta with E k = 10 51 erg (blue dot-dashed). Bottom: Comparison between magnetar and 56 Co decay rate. The grey box is the region where the two slopes are similar to within 25%. the ones derived for radioactivity-powered Type Ib/c ejecta (Ensman & Woosley 1988;Valenti et al. 2011;Drout et al. 2011;Eldridge et al. 2013). Furthermore, Fig. 13 shows that the evolution of photospheric velocities and temperatures match the observed ones reasonably well. While the velocity and temperature evolution as estimated from our models are crude, this good agreement is an important test for the physical self-consistency of the model. From the lightcurve fits to ejecta mass and kinetic energy, we estimate the ejecta velocities (V core , see eq. D11) which we compare to the observed velocities of the emission lines (Ca H&K and Mg I] λ4571, see Tab. 3), finding them reasonably similar.
From the plot of bolometric light curves shown in Fig.6, it appears that there is a gap between the faintest SL-SNe Ic, and the brightest normal Type Ic. One possibility is that this is an observational bias. As SL-SNe Ic are intrinsically rare (Quimby et al. 2011a(Quimby et al. , 2013, we find them at moderate redshifts simply due to the large survey volume required to find them. If intermediate objects were also as rare, then we would require wider field searches to encompass more local volume as they may evade detection at the higher redshifts of known population of SL-SNe. An alternative explanation is that the mechanism powering the SL-SNe has a minimum energy. From the semi-analytic magnetar model of Kasen & Bildsten (2010) which we have used to match our light curves, we see that the peak magnetar luminosity is inversely proportional to the square of the magnetic field (eq. 4 Kasen & Bildsten 2010). Hence, the question arises, could the apparent lower luminosity limit to the SL-SNe Ic be caused by some physical upper limit to the magnetic field in a magnetar? For our faintest SL-SNe, and using a minimum plausible ejecta mass of 1 M ⊙ , we determine an upper limit to the magnetar B-field of B < 1.4 × 10 15 G from Eq. 4 of Kasen & Bildsten (2010). If we consider that Kasen & Bildsten (2010) assume an angle between the B field and the spin axis of the magnetar of 45 o , then a factor of two higher than this value could be a plausible maximum. We hence adopt B < 3 × 10 15 G. The most conservative limit we can set is that the magnetic energy in the magnetar must be less than the gravitational binding energy of the neutron star (Chandrasekhar & Fermi 1953). This implies that which does not set a particularly stringent upper limit on the B-field. This limit is consistent with the B values retrieved from all the galactic magnetars studied so far which have B ∼ 10 14 − 10 15 G (Woods & Thompson 2006). However, magnetic fields are known to be a possible source of braking in stars (Meynet et al. 2011), while the magnetar models require an extreme magnetic field and fast rotational period. An explanation for both a small rotational period and a large magnetic field could be a large-scale helical dynamo, that is possible when the rotation period is comparable to the timescale of the convective motions (Duncan & Thompson 1992).

CONCLUSION
We have presented extensive photometric and spectroscopic coverage of five of the lowest redshift SL-SNe Ic. For one of them, SN 2011ke, we present a lightcurve from -30d to 200d, showing a well constrained rise time and a clear detection at 200d indicating a flattening of the luminosity. In four out of six SL-SNe, we show that there is significant luminosity in this late tail phase, and we illustrate that these measurements can aid our understanding of the power source and the possible progenitors of these ultra luminous transients.
The five SNe, namely PTF10hgi, SN 2011ke, PTF11rks, SN 2011kf and SN 2012il have absolute magnitudes −21.73 M g (mag) −20.42 similar to previous SL-SNe as well as a spectral evolution resembling SN 2010gx . There is some variation in the sample as two of the objects are fainter than the rest and spectroscopically evolve faster. PTF10hgi and PTF11rks have peak absolute magnitudes fainter than M g > −21 mag. The spectra of PTF11rks evolves faster than the rest and at 10d post maximum it resembles a normal Type Ic at peak. In contrast, SN 2010gx and three other SNe presented here typically take 30 days to evolve to this phase. The latest spectrum we have of PTF10hgi shows well developed lines of Fe ii at velocities which are more comparable with standard Type Ic SNe, significantly slower than the bulk of the SL-SNe Ic sample. Our xshooter spectrum of SN 2012il +52d is the only NIR spectrum of an SL-SNe Ic and we detect a broad He i λ10830 in emission implying that at least some SL-SNe Ic are not completely He-free. During the epochs of ±10 d around peak the temperatures and velocities are nearly constant and do not show a clear decrease until after that period. We find that the decay timescale in the 100-200d period is similar to that expected from the radioactive decay of 56 Co, but it requires the γ-rays to be fully trapped. This is in contrast to the faster decline observed in most Type Ib/c SNe, where γ-ray leakage has a significant effect from 50 days onwards (Sollerman et al. 2000). Hence it is unlikely that this is due to large amounts (1-4 M ⊙ ) of 56 Ni produced in the explosion.
We applied a semi-analytical diffusion model with energy input from a spinning down magnetar to fit the lightcurves of our five objects and SN 2010gx, including the diffusion peak and the tail phase detections. All lightcurves, including the tail phases are reproduced with feasible physical values for a magnetar. powered SL-SN. We require 3.6 B 14 7.4, 1.7 P ms 7.5 consistent with B of known galactic magnetars (B 14 ∼ 1 − 10) and with physically plausible periods (P ms > 1). We derived energies of 0.4 E mag (10 51 erg) 6.9 and ejected masses of 2.3 M ej (M ⊙ ) 8.6.
The well sampled data of the five SL-SNe Ic presented here combined with those of SN 2010gx point toward a SN explosion driven by a magnetar as a viable explanation for all the SL-SNe Ic. The lightcurves are reproduced and the model temperatures and velocities are in reasonable agreement with the observational data. However even if this is a reliable model, it still leaves other open questions such as • Do H-rich SNe powered by magnetars exist 20 ?
Possibly SN 2008es (Gezari et al. 2009) could be an example of such a luminous type II SN. In other words, why do we observe so many more H-free than H-rich SL-SNe?
• What is the role of metallicity in the progenitor stars evolution that will produce a H-free SL-SNe? It appears that they are all associated with faint dwarf galaxies and almost certainly low metallicity progenitors.
• Do realistic spectral calculations of magnetar driven SN reproduce the main observed features at late time?
• Where is the peak of the magnetar SED and how does the magnetar radiation deposit and thermalize in the nebular phase?
To address these, further observations are required combined with modelling. Theoretical modelling of high quality data in the nebular phase to determine the ejecta masses, composition and the mass of 56 Co contributing to the luminosity seems the most likely way to make progress. Optical spectroscopy at ∼300d post explosion appears to us to be the next step in probing the nature of these events. At z ∼ 0.1, the typical AB magnitudes of these sources are ∼ 23 ± 0.5, requiring approximately 1 night of 8m telescope time to gather a spectrum with high enough signal-to-noise to measure the expected Iclike emission lines with confidence.    Note.

SEQUENCE STARS FOR PTF10hgi
Here we report the average magnitudes of the local sequence stars of PTF10hgi used to calibrate the photometric zero points for non-photometric nights. They are reported in Tab. 12 along with their r.m.s. (in brackets). Their positions are marked in Fig.15 Fig. 8 but with all the spectra convolved with a factor of five and subsequently binned to a 5Å scale. Spectra of PTF11rks are in green, SN 2011ke in blue, SN 2012il in gold, PTF10hgi in red, SN 2011kf in magenta and SN 2010gx ) in black. The phase of each spectrum relative to light curve peak in the rest frame is shown on the right. The spectra are corrected for extinction and reported in their rest frame. The most prominent features are labelled. Arnett (1982) derived the solution for the bolometric light-curve of a homologously expanding ejecta subject to a total (absorbed) power P (t) as

MAGNETAR-POWERED LIGHT-CURVES
where τ m is the diffusion time-scale parameter, which in the case of uniform density (E k = 3 10 M ej V 2 ej ) is The parameter β has a typical value of 13.7 (Arnett 1982), which we use throughout. Apart from spherical symmetry and homology, the Arnett solution assumes a radiation pressure dominated gas, energy transport by diffusion, constant and grey opacity, and that the spatial distribution of energy input by the power source is proportional to the radiation energy density. The last assumption is for most cases the coarsest one, but the solutions are not critically dependent on deviations from it (Arnett 1982). The power function P (t) can generally be expressed as a sum of a set of source luminosities L i (t) multiplied by deposition functions D i (t): For radioactivity from 56 Ni and its daughter nucleus 56 Co, the luminosity functions are where M 56Ni is the amount of 56 Ni formed in the explosion, and τ 56Ni and τ 56Co are the decay times of the isotopes (8.7 and 111 days, respectively).
For a magnetar with a 45-degree angle between the magnetic axis and spin axis, the dipole spin-down luminosity is (Ostriker & Gunn 1971;Kasen & Bildsten 2010) L magnetar (t) = 4.9 · 10 46 B 2 14 P −4 where B 14 is the magnetic field strength in 10 14 G, P ms is the initial spin period in ms, and the spin-down time-scale τ p is τ p = 4.7 B −2 14 P 2 ms days .
With only magnetar powering, the light-curve parameters are thus τ m , B 14 and P ms . For a given fit to τ m , the ejecta mass is (from Eq. D2) M ej = 1 M ⊙ · τ m 10 d 4/3 κ 0.1 cm 2 g −1 −2/3 E k 10 51 erg 1/3 (D8) The weak scaling with κ and E k means that ejecta masses can be meaningfully estimated despite significant uncertainties in κ and E k .
When the energy input P (t)dt approaches or exceeds the explosion energy, accelerations will not be negligible and the homologous approximation becomes poor. A solar mass of 56 Ni emits a total energy of P (t)dt = 1.9 · 10 50 erg (including the 56 Co decay), so for an explosion energy of ∼ 10 51 erg, accelerations will not be important unless M( 56 Ni) 5 M ⊙ . A magnetar, on the other hand, has a rotation energy of 2 · 10 52 P −2 ms erg, so for fast braking with efficient trapping, the ejecta can be accelerated to far beyond its explosive velocities. This is a major limitation of using the homologous expansion approximation, and the consequences for the light curve can only be investigated with numerical radiation hydrodynamics (see Bucciantini et al. 2009, and reference therein for some examples).

The opacity
The opacity due to electron scattering is κ es = 0.2 Z /Ā 0.5 whereZ is the mean atomic charge,Ā is the mean atomic mass, and x e = n e /n nuclei is the ionization fraction. For any chemical mixture excluding hydrogen,Z/Ā ≈ 0.5, which we can assume since there is no trace of hydrogen lines in the spectra of these objects. The radiation temperature in a radiation-pressure dominated uniform sphere of internal energy E(t) is In LTE, and at relevant densities here, the ionization fraction of a pure oxygen plasma at T = 10 5 K is x e ∼ 6, for carbon it is x e ∼ 4, and for Fe is x e ∼ 10. It should thus be a reasonable approximation to use x e /Z = 0.5. With this choice κ es = 0.1 cm 2 g −1 , comparable to the value κ = 0.08 that Arnett (1982) uses.
In rapidly expanding media, line opacity can become comparable to or exceed electron scattering opacity (Karp et al. 1977), which complicates analytical light curve modelling. A common simplistic approach to take line opacity into account is to put a minimum value on the opacity. In previous works, values ranging between 0.01 and 0.24 cm 2 g −1 have been used (e.g., Herzig et al. 1990;Swartz et al. 1991;Young 2004;Bersten et al. 2011Bersten et al. , 2012. The implication of line opacity is that κ is likely to stay in the 0.01 -0.2 cm 2 g −1 range throughout the evolution, and κ = 0.1 cm 2 g −1 is probably not off by more than a factor of a few at any given time.

Deposition of magnetar radiation
The spectral and directional distribution of the magnetar radiation is highly uncertain. At early times, most radiation will undoubtedly be absorbed, but at later times, this is not certain (Kotera et al. 2013). X-rays are efficiently absorbed for a long time by photoionization from inner shell electrons, but gamma rays see a smaller opacity and start escaping after a few weeks for typical ejecta parameters.
Here, we assume full trapping of the magnetar radiation. Most of the energy input occurs over a few weeks after explosion, and it is a reasonable assumption that most of the energy emerges as X-rays, as in the Crab pulsar for instance (Weisskopf et al. 2000).

Photospheric velocities and temperatures
To estimate the photospheric velocities and temperatures for a given solution for ejecta mass, we approximate the ejecta density structure with a core + envelope morphology. The velocity of the homogenous core (which contains almost all the mass to force consistency with the diffusion calculation) is determined from 3 10 M ej V 2 core = E k (D11) and its density is given by ρ core (t) = M ej 4π 3 V 3 core t 3 . (D12) Outside we attach an envelope with density profile The optical depth of the envelope is where τ core (t) = κρ core (t)V core t .
One should in general distinguish between the photosphere and the thermalization layer, where the temperature of the continuum is determined. The position of these depend on the total opacity κ, and the absorption opacity κ a , respectively. However, due to our simple treatment such detail is unwarranted, and we approximate them to be the same, R * . As long as the atmosphere is optically thick (τ env > 1), R * (t) is found from solving ∞ R * (t) κρ(r, t)dr = 1 , (D19) If the photosphere has receded into the core, the expression is instead R * (t) = R core (t) − 1 − τcore α−1 κρ core (D20) Typical density profiles in Ib/c models show α ∼ 10 (e.g. Fig. 1 in Kasen & Bildsten 2010), which is the value we use here.
From the photospheric radius R * (t) we retrieved the velocity at the photosphere (V phot ) The effective temperature is found from application of the black-body formula, using the model luminosities at corresponding times.

Additional tests
To test the applicability of our approach, we perform three tests. The first one is to compare light-curves, photospheric velocities and temperatures to the radiation hydrodynamical simulations of Kasen & Bildsten (2010). Fig. 17 shows three representative examples. For these comparisons, we use eq. 3 to relate magnetar energy to ejecta kinetic energy, which shows itself a good approximation. Tab. 13 shows the derived parameters of M ej , B 14 , P ms and ∆t for a series of simulations in Kasen & Bildsten (2010). The magnetar properties (B 14 and P ms ) are reliably recovered to within 10-20% of their input values, whereas the ejecta mass can vary, tending to be too low in the fits. It is, however, always within a factor 2 of the correct value.
The second test is to derive parameters for the Type IIb SN 2011dh, using the approach described above (fixing E k = 10 51 erg, κ = 0.1, α = 10). The best-fit is shown in Fig. 18. The recovered values M ej = 2.2 M ⊙ and M 56Ni = 0.08 M ⊙ agree well with the results from Bersten et al. (2011), who used radiation hydrodynamical simulations.
While for the third one we tried to test our code on Type Ic SNe 1998bw (Galama et al. 1998;McKenzie & Schaefer 1999;Sollerman et al. 2000;Patat et al. 2001) and 2007gr (Valenti et al. 2008;Hunter et al. 2009) to explore its limits.

TABLE 13
Best-fitting values of system parameters (after the slash) compared to the actual simulation values of Kasen & Bildsten (2010) (before the slash). Derived parameters on the righ.  We fitted the first 200d with the magnetar model (fixing E k = 10 51 erg, κ = 0.1, α = 10), recovering M ej = 1.8 M ⊙ and B 14 = 9.8 G and P ms = 18.9 ms for SN 1998bw and M ej = 1.3 M ⊙ and B 14 = 22.9 G and P ms = 47.6 ms for SN 2007gr. Instead, trying to fit the entire dataset, we recover M ej = 19.9 M ⊙ and B 14 = 16.6 G and P ms = 0.5 ms for SN 1998bw and M ej = 2.5 M ⊙ and B 14 = 26.0 G and P ms = 42.6 ms for SN 2007gr. The best fit to those data are shown in Fig. 19 along with the fit of the radioactive decay. The applicability of the Arnett model to derive parameters for radioactivity-driven SNe has also been demonstrated by Valenti et al. (2011). The results imply that at those energies the magnetar contribution is more important after 150-200 d, highlighting the importance of obtaining late time data.

Ni fits parameters
For the 56 Ni models we computed γ-ray trapping as in Arnett (1982). along with the fit of the entire set (green) and the fit of radioactive decay (blue). Both models can fit the first 50-100d but are clearly differentiated at late times