Analyzing the Largest Spectroscopic Dataset of Hydrogen-Poor Super-Luminous Supernovae

I. Introduction

Over the last 10 years, the systematic discovery of Super-luminous Supernovae (SLSNe) has captured the attention of the supernova community, causing heated debates about their powering source and their progenitors. SLSNe are defined as SNe that have peak magnitudes more luminous than around $-21$ magnitude, making them at least $\sim 100$ times more luminous than normal stripped-envelope core-collapse SNe (stripped SNe) and at least $\sim 10$ times more luminous than SNe Ia (Gal-Yam 2012; Gal-Yam 2016). Based on their spectra, SLSNe are classified into Type I SLSNe (SLSNe I) that do not show hydrogen lines in their spectra near peak, and Type II SLSNe (SLSNe II) that do show hydrogen lines (Quimby et al. 2011; Gal-Yam 2012).

Currently, three distinct mechanisms have been suggested for powering the brilliance of SLSNe I: (1) pair-instability SNe (Rakavy & Shaviv 1967; Gal-Yam et al. 2009, e.g.,), (2) engine-driven, either via a magnetar (Kasen & Bildsten 2010; Woosley 2010; Inserra et al. 2013; Nicholl et al. 2013; Metzger et al. 2015; Chen et al. 2016a; Suzuki & Maeda 2016; Gilkis et al. 2016; Soker 2016) or via accretion onto a black hole (Dexter & Kasen 2013), and (3) interaction of the supernova ejecta with a circumstellar material that is free of hydrogen and helium and that had been ejected before the explosion (Chevalier & Irwin 2011; Ginzburg & Balberg 2012; Chatzopoulos et al. 2013; Ofek et al. 2014, e.g.,), possibly due to pulsations in the stages immediately before the explosion, as in the pulsational pair instability SN (PPISN; Woosley et al. 2007; Waldman 2008; Woosley 2016). Recently, hybrid models have invoked several of these mechanisms for the same object to explain the peculiar light curves (e.g., PTF12dam by Tolstov et al. 2016, iPTF13ehe by Wang et al. 2016, ASASSN-15lh by Chatzopoulos et al. 2016). Based on current observations of SLSNe, the PISN origin has been disfavored for most of the SLSNe I (Gal-Yam et al. 2009, except for SN 2007bi;) for a number of reasons. Many PISN models provide overly broad light curves and spectra that are too red compared to observations (Dessart et al. 2012b; Dessart et al. 2013, e.g.,).

SLSNe I show spectra devoid of hydrogen (H) and helium (He) lines, Except for SN 2012il that appears to show He I $\lambda$10830 in emission, but none of the optical He I lines (Inserra et al. 2013) and iPTF13ehe that showed broad H$\alpha$ emission only in nebular spectra (Yan et al. 2015). which is also the case for SNe Ic and SNe Ic-bl. Thus, we denote SLSNe I as SLSNe Ic in this work, following the same name convention as in other works (e.g., Inserra et al. 2013). The similarity in the absence of absorption lines of H and He motivates us to compare spectra of SLSNe Ic, SNe Ic, and SNe Ic-bl. A basic question is whether they are truly distinct populations, or whether there is a smooth transition between them. Given the large number of SLSN Ic spectra, as well as recent systematic explorations of other members of the SN Ic family (i.e, SNe Ic and Ic-bl) by us (Liu et al. 2016; Modjaz et al. 2016), the time is ripe to conduct a similar systematic spectroscopic population study for SLSNe Ic. In Section II, we summarize SN samples used in this study and discuss the potential caveats of our samples. In Section III, we discuss our spectral analysis methods and report our measurements of absorption velocities as well as the construction of average spectra. In Section IV, we conduct spectral comparisons between SLSNe Ic, SNe Ic-bl and SNe Ic. In Section V, we compare measured velocities in this work with predicted velocities in the interaction model and the one-dimensional magnetar model. In Section VI, we compare several special SLSNe Ic to average spectra to see if these SLSNe Ic are typical SLSNe Ic. Finally, we summarize our conclusions in Section VII.

II. SN spectral samples

We list our SLSN Ic sample in Table 1. Our samples of SNe Ic and of SNe Ic-bl, roughly half of which were connected with GRBs, are the same as in Modjaz et al. 2016. Since we want to analyze SLSN Ic spectra as a function of phase in a statistical way, we have collected the spectra of all available SLSNe Ic that have a date of maximum light published before April of 2016. These SLSNe Ic were mainly discovered and observed by the All-Sky Automated Survey for Supernovae (ASAS-SN), the Catalina Real-Time Transient Survey (CRTS), the Dark Energy Survey (DES), the Hubble Space Telescope Cluster Supernova Survey, the Pan-STARRS1 Medium Deep Survey (PS1), the Public ESO Spectroscopic Survey of Transient Objects (PESSTO), the Intermediate Palomar Transient Factory (iPTF) as well as the Palomar Transient Factory (PTF), and the Supernova Legacy Survey (SNLS).

We have included two special SLSNe Ic, namely SN 2011kl, which constitutes the first detection of a supernova explosion associated with an ultra-long duration gamma ray burst (ULGRB), and ASASSN-15lh (also known as - AKA - SN 2015L), which is claimed to be the most luminous SN ever discovered, although whether it is a SN or not is still debated. We did not include transients in the SN-SLSNe gap (Arcavi et al. 2016), which include PTF10iam, SNLS04D4ec, SNLS05D2bk, and SNLS06D1hc, since the first object is a weird type II SN, the following two objects have no spectra classifications, and the last object only has a featureless spectrum obtained three weeks after the explosion. We did not include PS1-10afx, which was first classified as a SLSN Ic (Chornock et al. 2013), but turned out to be a lensed SN Ia (Quimby et al. 2013).

The question of whether all SLSNe Ic are aspherical explosions is an important one, and includes whether their geometry would introduce a selection effect for sample comparison purposes. Observationally, there are only few SLSNe Ic for which the geometry of the explosion has been directly constrained. Out of two objects that have polarimetric observations, only one, SN2015bn, appears to show strong polarization (Inserra et al. 2016; Leloudas et al. 2017). Late time spectra and observations of SN remnants (e.g., Omand et al. 2017) can also be used to probe the geometry of the explosions. For example, Inserra et al. 2017 suggested multiple emission regions for the same emission line in the late time spectra of LSQ14an. However, this could be due to asphericity of the ejecta or due to interactions, and thus, it is not clear whether LSQ14an was a large-scale aspherical explosion. Thus, we conclude that while certainly more data are needed to address the question of asphericity in SLSNe Ic, we have good reasons to believe based on current data that selection effects will probably not be significant for our sample.

We note that although every SLSN Ic in our sample has a date of maximum light, the reference band is not consistent. The potential effects of different peak epochs in different filters will be discussed in subsection II.1. Another caveat is that since some SLSNe Ic are at high redshifts, their spectra taken at optical wavelengths may not cover the full optical range when the observed spectra are converted to rest wavelength. We will discuss the potential effects of different redshifts for different SN samples in subsection II.2.

Table 1 lists the dates of maximum light, which were provided by the published papers in different filters for the different SLSNe Ic. Most of the rest-frame filters are in $u$, $B$, $g$, $r$, or $R$-bands. Since there are no established relationships for the peak epochs in different filters of SLSNe Ic, we could not convert these peak epochs to the same filter. Since there is no common filter in which light curves of all SLSNe Ic in our sample are available in the literature, we could not compute peak epochs in the same filter. Based on the relationship between peak epoch in $U$, $B$, $V$, and $R/r^{\prime}$-bands for stripped-envelope core-collapse SNe from Bianco et al. 2014, we roughly estimate that compared to peak epoch in $V$-band (JDvmax), the peak epochs used in our analyses will be off by $-3$ days (peak happened before the JDvmax) and $2$ days the most (peak happened after the JDvmax). This should not impact our comparisons of average spectra (see Section III.2 and sections that used average spectra of SLSNe Ic), since we use a bin size of 5 days for each average spectrum. Neither should this have much influence on our analysis of the bulk velocity evolution (see Section IV.1), since we calculate the moving weighted average velocities smoothed with a Gaussian kernel with a standard deviation of 5 days when studying the velocity evolution of the different SN populations.

II.2. Potential Impact of Different Redshift Distributions for Different SN subtypes

The next question is whether evolutionary effects for their progenitors is expected to be significant within such a redshift range. While the metallicity content of the universe does not change significantly between the redshift ranges for the SN Ic and the SN Ic-bl samples (Tremonti et al. 2004, both samples are within the extent of the star-forming galaxies of SDSS;), there is a slight trend towards lower metallicity for galaxies of the same mass at the median redshift of $z=0.3$ for SLSNe Ic (Zahid et al. 2011; Maier et al. 2015, e.g.,), compared to local star-forming galaxies. Indeed, SLSNe Ic host galaxies seem to be of low metallicity (Chen et al. 2013; Lunnan et al. 2013; Lunnan et al. 2014; Chen et al. 2016b; Perley et al. 2016; Schulze et al. 2016), even lower than those of SNe-GRBs (Leloudas et al. 2015), which in turn seem to be lower than those of SNe Ic and SNe Ic-bl without GRBs (Modjaz et al. 2008; Modjaz et al. 2011; Sanders et al. 2012; Kelly & Kirshner 2012; Modjaz 2012). However, low metallicity should not affect the velocities of the Fe II $\lambda$5169 line per se. Even the Fe II $\lambda$5169 line strengths should be unchanged for our sample of SLSNe Ic, since line strength changes only become important when the metallicity is by factors of 10 to 100 lower (Sauer et al. 2006), which is a much larger factor than observed based on host galaxy data.

III. Spectral Analysis Methods

Absorption velocities can provide clues about the dynamics of the explosion. In particular, the absorption velocity of Fe II $\lambda$5169 has been suggested to trace photospheric velocity by Branch et al. 2002. See Dessart et al. 2015; Dessart et al. 2016 and Modjaz et al. 2016 for discussions on what the definition of “photospheric” velocity is and which line to use. While there is some discussion about which line best traces the ejecta velocity, in any case, a systematic comparison of the same way of measuring the velocity from the same line for all SNe and SN subtypes is needed and yields relative values that are still powerful to test models. For more caveats, see Section V.3. In turn, the measurement of the photospheric velocity is needed to estimate explosion parameters, such as ejecta masses, from light curves and spectra (Drout et al. 2011; Cano 2013; Lyman et al. 2016; Taddia et al. 2015; Nicholl et al. 2015b). Moreover, the ejecta velocity as traced by Fe II $\lambda$5169 can be used to check the prediction of the one-dimensional magnetar model since the model predicts a flat evolution of velocity over time (Kasen & Bildsten 2010; Mazzali et al. 2016).

Since the Fe II features in SLSNe Ic are highly blended, as in SNe Ic-bl, we measured Fe II $\lambda$5169 velocities via the template fitting method (Appendix A of Modjaz et al. 2016), originally developed for spectra of SNe Ic-bl. First, we identify the spectral region of Fe II $\lambda$5169 in SLSNe Ic in our sample based on identifications and SYNOW fits given for the same SLSNe Ic in the literature, as well as spectral modeling for some SLSNe Ic in Dessart et al. 2012b. Then we measure Fe II $\lambda$5169 velocities in SLSNe Ic via the template fitting method described in Appendix A of Modjaz et al. 2016. This method is a data-driven method and the template is the average spectrum of SNe Ic. In our case, we would like to compare the velocities of the non-blended Fe II $\lambda$5169 in SNe Ic with the velocities of the blended Fe II $\lambda$5169 in SNe Ic-bl and SLSN I. We obtain the Fe II $\lambda$5169 velocities in SLSNe Ic by matching a broadened and blue-shifted SN Ic template to a SLSN Ic spectrum at similar phases, which is performed in a Markov-Chain-Monte-Carlo (MCMC) framework. As discussed in the Appendix A of Modjaz et al. 2016, the broadness and blue-shift of the line are quantified by the convolution velocity of the Gaussian kernel with which the SN Ic template is convolved and the amount of additional blueshift, respectively. The corresponding error bars are based on marginalized distribution of parameter values from MCMC samplers. An example of our velocity measurements for SLSNe Ic is shown in Table 2 for guidance. A full version of this table is available in a machine-readable form in the online journal.

III.1.2 Velocity Comparisons with Literature Measurements

III.2. Constructing Mean Spectra from SN Spectra

Mean spectra and the standard deviation contours can characterize the spectral properties of each SN subtype as a population. They can also be used to check whether spectra of a newly discovered transient are within the statistical diversity of the mean spectra of some SN types at certain phases. In order to compare the average spectra of various SN subtypes, as we will show in Section IV.2, we have used continuum-removed average spectra of SN Ic and of SN Ic-bl from Liu et al. 2016 and Modjaz et al. 2016, and constructed average spectra of SLSNe Ic in the same way. In order to compare two relatively special SLSNe Ic in our sample to average spectra of various SN subtypes, as we will show in Section VI, we have also constructed average spectra where the continuum is included for SN Ic-bl, SN-GRB, and SLSN Ic at needed phases. We have done our best to correct for Milky Way extinction in SLSN Ic spectra using E(B-V) values from the literature (Schlegel et al. 1998; Schlafly & Finkbeiner 2011). We did not correct for host extinction, since SLSNe Ic are generally in metal-poor galaxies, and thus the host extinction is small in most cases (Lunnan et al. 2014; Leloudas et al. 2015). All of the average spectra of SLSNe Ic that we have constructed are available on our group GitHub repository. https://github.com/nyusngroup

IV. Connections between SLSNe Ic, SNe Ic-bl, and SNe Ic

From line identifications and spectral modeling in various works, we know that SLSNe Ic, SNe Ic-bl and SNe Ic all show Fe II lines, but the Fe II lines can be usually identified in SLSNe Ic only after the date of maximum light, while for SNe Ic and SNe Ic-bl, they can be identified in spectra obtained starting before maximum light. As we will show in Sections IV.1 and IV.2, SLSNe Ic and SNe Ic-bl have similar spectral features and absorption velocities, which are broader and higher than those in SNe Ic. This indicates that SLSNe Ic and SNe Ic-bl may have similar explosion engines.

Spectra of SLSNe Ic show very blue continua (Quimby et al. 2007, e.g., ). Thus, if the continuum is a black-body, the derived temperature is high enough to produce O II lines. In fact, early spectra of almost all SLSNe Ic show a narrow ‘w’ feature near 4300 Å, which is identified as O II possibly due to high temperatures (Quimby et al. 2007; Quimby et al. 2011; Gal-Yam 2012; Nicholl et al. 2015b; Mazzali et al. 2016) and non-thermal excitation (Mazzali et al. 2016). As we will show in Section IV.3, this O II feature is not seen in SNe Ic-bl and SNe Ic. Actually, the narrow O II feature in SLSNe Ic is surprising, since we find that the Fe II $\lambda$5169 feature and other features later on are broad lines. We speculate that velocities of the ‘w’ feature do not reflect the global dynamics, but may be constrained to a small region in the outer layers where the conditions (e.g. ionization and/or temperature) are conducive.

IV.2. SLSNe Ic and SNe Ic-bl Have Comparable Spectral Features

IV.3. O II Feature Around 4300 Å Can be Used to Identify SLSNe Ic at Early Time

V. Comparisons of Measured Velocities with Model Predictions

V.2. Testing the One-dimensional Magnetar Model using Flat Velocity-evolution of Fe II λ\lambda5169

One promising power source model for SLSNe Ic is the magnetar model (Kasen & Bildsten 2010; Woosley 2010; Inserra et al. 2013; Nicholl et al. 2013; Metzger et al. 2015; Chen et al. 2016a; Suzuki & Maeda 2016, e.g.,). In the one-dimensional magnetar model, there will be a mass shell formed due to the magnetar bubble. Based on radiation hydrodynamic calculations, the mass shell is supposed to cause an observational imprint via a prolonged period of flat velocity-evolution, i.e., a velocity plateau, in the observed spectra (Kasen & Bildsten 2010). Some observational papers claim that they have detected such a velocity plateau in their analyses of SLSN Ic spectra. For example, the velocity plateau is claimed in PS1-10ky and PS1-10awh using lines of C II $\lambda$2330, Si III $\lambda$2540, and Mg II $\lambda$2800 (Chomiuk et al. 2011). Nicholl et al. 2014 reported velocity plateaus in SN 2013dg using Mg II $\lambda$4481 and Mg I] $\lambda$4571. Nicholl et al. 2015b have suggested that the Fe II $\lambda$5169 velocity of the following SLSNe Ic has a flat evolution as a function of time: PTF11rks, PTF12dam, SN 2013dg, and LSQ14mo.

In our work, we have explored the velocity evolution of Fe II $\lambda$5169 using our own measurements that utilizes our novel technique (see Section III). First, we define flat (or slow) velocity-evolution SNe as SNe whose spectra span more than 10 days and for which the Fe II $\lambda$5169 velocities decrease by less than 2,000 km s-1. With this definition, we only identify two slow velocity-evolution SLSNe Ic (PTF10hgi and PS1-11ap) out of 13 SLSNe Ic that satisfy the phase requirement and plot them in Figure 4. In contrast, we also show fast velocity-evolution SLSNe Ic (PTF11rks, LSQ12dlf, and SN 2013dg) whose spectra cover more than 10 days, but whose velocities decrease by more than 8,000 km s-1. Changing the requirement for the time range over which the SLSNe Ic should have spectra from 10 days to a more lenient 5 days does not change our conclusions, since the only SLSNe Ic fulfilling the new requirement are the same objects as before. The slow-evolution SLSNe Ic are consistent with a dense shell model, while the fast-evolution SLSNe Ic are consistent with a simple spherical model. A dense shell can be formed in a magnetar model but there are other channels, e.g., via eruptions before SNe explode. We note that even for PTF10hgi and PS1-11ap, it is not clear that their velocity evolution should be used to argue for the one-dimensional magnetar model: PTF10hgi has a flat evolution in velocity, but like SNe Ic that show velocity plateaus at similar phases, this could be just indicating that the flat evolution is due to radiative transfer effects and not reflect a physical ejecta structure; PS1-11ap has a large error bar for the first data point, making it consistent with a high velocity value, and thus no flat evolution.

We conclude that as a whole population, the velocity evolution as traced by Fe II $\lambda$5169 of SLSNe Ic is not consistent with that predicted by the one-dimensional magnetar model (Kasen & Bildsten 2010), while individual SLSNe Ic might be. The obvious next step of performing magnetar calculations in two dimensions has been recently tackled. Chen et al. 2016a and (Suzuki & Maeda 2016) found that the dense shell which is commonly seen in one-dimensional simulations and which accounts for the predicted velocity plateau, is destroyed by multi-dimensional effects, including turbulence. Thus, while we await spectral synthesis calculations based on two-dimensional models for their predicted velocity evolution, it is reasonable to expect that two-dimensional models will not show such a velocity plateau and thus, will be more in line with our observational results. Moreover, Inserra et al. 2013 showed that a semi-analytical diffusion model in the magnetar scenario can reproduce light curves of SLSNe Ic well, but the predicted photospheric velocity evolution is not flat.

V.3. Caveats when Comparing Observations to One-dimensional Magnetar Model

In our analysis we have used Fe II $\lambda$5169 to trace the velocity structure of the SN Ic family. While using this line to perform inter-comparisons between different SN subtypes (Section IV.1) is valid and indeed required, since different lines have systematically different velocity structures (Modjaz et al. 2016), we now note some of the caveats when using that line to constrain theoretical models. Theoretical models assume a ‘photospheric velocity’ and the question is which observed line traces it best. On the one hand, Branch et al. 2002 suggest that Fe II $\lambda$5169 traces well the photospheric velocity based on their SYNOW models for stripped-envelope core-collapse SNe (stripped SNe). On the other hand, Dessart et al. 2015 conduct a careful exploration using progenitor, explosion and non-LTE radiative transfer models for stripped SNe and find that while the photosphere, and therefore its associated velocity, is poorly defined, the O I $\lambda$7774 velocity is a good indicator of the representative ejecta velocity for SNe Ib and Ic at the date of maximum light. We showed in Liu et al. 2016 that while the absolute values of the Fe II $\lambda$5169 and O I $\lambda$7774 velocities are somewhat different for SNe Ib and Ic, the systematic offset between the 2 subtype velocities was shown by both lines, i.e., the relative velocity values are correct. In this work, we did not use O I $\lambda$7774 as an indicator for photospheric velocity since most of our SLSN Ic spectra do not cover its wavelength range.

Thus, our conclusions about the one-dimensional magnetar model in the preceding section may not stand if another line were to be used, since different lines have different velocity behavior (e.g, Si II $\lambda$6355 vs. Fe II $\lambda$5169, see Figure 4 in Modjaz et al. 2016). However, as we note in Section V.2, the same line needs to be used for both SNe Ic and SLSNe Ic to ensure that any plateau behavior seen in the velocities of SLSNe Ic is not due to radiative transfer effects, which would be reflected in the same plateau behavior for ordinary SNe Ic.

From the theoretical point of view, a few assumptions have to be adopted for the comparison between theory and observations. For specifically the one-dimensional magnetar model, we used the following prediction based on Equation 7 and Figure 2 in Kasen & Bildsten 2010: if the equation predicts a shell velocity of 10,000 km s-1, then based on the figure, the velocity plateau will start 10 days after the explosion. Of course if the magnetar energy were to be lower by a factor of 12–13, the phase range of the velocity plateaus would be at 100 days after the explosion, a regime not probed by the optical spectra in our sample.

V.4. Caveats if SLSNe Ic are explosions with large-scale asphericities that affect their luminosity

Determining the geometry of SLSNe Ic explosions is crucial for differentiating between the different powering mechanisms. For example, an explosion with a central engine may be an intrinsically asymmetric explosion and would leave imprints on polarimetric observations. As discussed in Section II, due to the lack of observations, it is hard to conclude whether all SLSNe Ic are non-spherical explosions. Indeed, our observations disfavor the spherically symmetric magnetar model in one-dimension (see Section V.2), though this does not necessarily mean that SLSNe Ic have to harbor large-scale asphericities. If SLSNe Ic are powered by highly aspherical engines, then one may speculate that the discovered SLSNe Ic appear luminous because they are seen on-axis, and thus the SLSNe Ic in our sample would be biased towards high luminosity explosions. Even if this conjecture entails that the population properties of SLSNe Ic may be biased, the velocity measurements of the individual SNe would still be valid, as well as our discussions in Sections V.1 and V.2, except that we would have to compare the velocities of SLSNe Ic to those of SNe Ic-bl with observed GRBs only, not the whole population of SNe Ic-bl, a change that would not change our conclusions.

VI. Special SLSNe Ic

Dong et al. 2016 claimed ASASSN-15lh (AKA SN 2015L) as the most luminous SN ever discovered. They found that the spectra of ASASSN-15lh are blue and featureless except for a deep and broad trough near 4100 Å. They also found that the trough in ASASSN-15lh resembles O II feature in PTF10cwr (AKA SN 2010gx). However, whether ASASSN-15lh is a SN or not is still debated. On the one hand, Leloudas et al. 2016 found that their observations are more consistent with a tidal disruption event (TDE), based on temperature evolution, transient location in the host galaxy, and other evidence. They also found that if the trough in ASASSN-15lh were due to O II lines, there would need to be an additional strong feature around 4400 Å, which is not observed in the spectra of ASASSN-15lh. Moreover, Margutti et al. 2016 favored a TDE origin for ASASSN-15lh based on analysis of X-rays from the host galaxy, although more monitoring of the X-rays is needed to truly distinguish between the two origins. On the other hand, spectra of ASASSN-15lh lack both hydrogen and helium emission lines, something that has not been observed in TDE spectra so far (Arcavi et al. 2014, e.g.,). The host galaxy does not resemble the typical hosts of SLSNe (Godoy-Rivera et al. 2016) and is too massive for a TDE (Dong et al. 2016). Moreover, the rebrightening in UV is also unexpected for both SLSNe and TDEs (Godoy-Rivera et al. 2016; Brown et al. 2016).

VI.2. The first SN-ULGRB connection SN 2011kl / GRB 111209A

SN 2011kl is another unusual SLSN Ic since it constitutes the first detection of a SN explosion associated with an ultra-long duration gamma ray burst (GRB), namely ULGRB 111209A (Greiner et al. 2015; Kann et al. 2016). SN 2011kl is more luminous than SNe Ic-bl associated with long-duration GRBs (SN-GRBs; for recent review, see e.g., Modjaz et al. 2011; Hjorth & Bloom 2012; Cano et al. 2016), but not as luminous as most, if not all, SLSNe Ic (Greiner et al. 2015; Kann et al. 2016). In Figure 6, we compare the spectrum of SN 2011kl to the average and standard deviation spectra of SN-GRBs and SLSNe Ic at similar phases. Note that we could not measure the Fe II $\lambda$5169 velocity in SN 2011kl due to the noisy spectra. Thus, we did not compare the Fe II $\lambda$5169 velocities. We find that the continuum of SN 2011kl’s spectrum does not resemble those of the population of SN-GRBs, but is fully consistent with those in the population of SLNe I; however, we find the spectrum of SN 2011kl to be too noisy to robustly evaluate whether the widths of the line features are as broad as in other SLSNe Ic and SN-GRBs. While Greiner et al. 2015 came to a similar conclusion based on fewer objects in their comparison set (only 3 SLSNe Ic and 1 SN-GRB), we have conducted this spectroscopic comparison with the full populations of SLSNe Ic and SN-GRBs. Thus, SN 2011kl could be a true SLSN I.

VI.3. SN 2007bi

VII. Conclusions and Next steps

In this paper we have conducted a comprehensive spectroscopic comparison between the members of the full spectroscopic SN Ic family: SNe Ic, SNe Ic-bl, including those connected with GRBs, and SLSNe Ic. We have collected all of the published spectra of SLSNe Ic, quantified the diversity of their spectral features, and produced average spectra by using the novel methods we developed in Liu et al. 2016 and Modjaz et al. 2016. Using the data products of SNe Ic-bl and of SNe Ic from Modjaz et al. 2016, we have compared the population properties of these three members of SN Ic family in a systematic way.

Thus, as the next step, it would be necessary to compute the velocity structure from multi-dimensional magnetar models that have been developed for SLSNe Ic (Chen et al. 2016a; Suzuki & Maeda 2016). In addition, future synthesized spectra based on magnetar models need to reproduce the large observed line widths in SLSNe Ic as a population (see Table 3 and Figure 2), since current magnetar models predict as well as show only narrow or moderate line widths that are in line with those in SNe Ic and SNe Ib (Kasen & Bildsten 2010; Dessart et al. 2012a), but not with the majority of SLSNe Ic. In general, we look forward to modeling attempts that combine hydrodynamical modeling with non-LTE radiative transfer calculations, produce spectra as a function of time, and predict velocity evolution as well as other observables.

Finally, we have compared a few peculiar luminous objects to the SLSN Ic sample. We have compared the most luminous SN ASASSN-15lh to our average spectra, although we note that there is recent evidence against it being a SN (e.g., Leloudas et al. 2016; Margutti et al. 2016). We have found that the spectra of ASASSN-15lh do not resemble average SLSN Ic spectra in terms of spectral features and continuum. We have also compared the SN spectral component of the first SN-ULGRB connection SN 2011kl / GRB 111209A with the average SN spectrum of SN-GRBs (i.e., SNe accompanying long-duration GRBs) and the average SLSNe Ic spectrum. We have found that the spectrum of SN 2011kl is consistent with the average spectrum of SLSNe Ic, but is much bluer than the average SN spectrum of SN-GRBs. In Greiner et al. 2015, a magnetar model is proposed to explain SN 2011kl. However, since only one spectrum of SN 2011kl was obtained, the velocity evolution is unknown and could not be used to check for any potential flat velocity-evolution as predicted in the one-dimensional magnetar model. Thus, before concluding that a magnetar model is responsible for SN 2011kl or SLSNe Ic in SN-ULGRB connections, more spectra are needed at multiple phases to verify the predicted velocity evolution based on the magnetar model.

One of the main outstanding questions in this field is whether there is a continuum in luminosity between SNe Ic and SLSNe Ic and how the luminosity distribution of SNe Ic-bl fits in this context, given the spectral connection between them and speculations by Gal-Yam 2012 that SNe Ic-bl may be intermediate events between radioactive powered SNe and engine powered SLSNe Ic. We suggest that future work tackles this question in a statistically robust way and includes SNe Ic-bl and SNe Ic from the same un-targeted surveys as the one that discovered SLSNe Ic.

All of the average spectra of SLSNe Ic and the weighted average velocities of Fe II $\lambda$5169 at all phases presented in this manuscript can be downloaded from our group GitHub repository. https://github.com/nyusngroup

References