A meta analysis of core-collapse supernova $^{56}$Ni masses

TL;DR

This meta-analysis compiles 258 measurements of $^{56}$Ni masses in core-collapse supernovae, revealing significant differences among types and highlighting potential issues with current estimation methods and progenitor models.

Contribution

It provides a comprehensive comparison of observed $^{56}$Ni masses across supernova types and evaluates their consistency with theoretical models.

Findings

Stripped-envelope SNe have higher $^{56}$Ni masses than SNeII.

Observed $^{56}$Ni distributions in SE-SNe exceed model predictions.

Potential inaccuracies in current $^{56}$Ni estimation methods for SE-SNe.

Abstract

A fundamental property determining the transient behaviour of core-collapse supernovae (CCSNe) is the amount of radioactive $^{56}$Ni synthesised in the explosion. Using established methods, this is a relatively easy parameter to extract from observations. Here I provide a meta analysis of all published $^{56}$Ni masses for CCSNe. Collating a total of 258 literature $^{56}$Ni masses I compare distributions of the main CCSN types: SNeII; SNeIIb; SNeIb; SNeIc; and SNeIcBL. Using these published values, I calculate a median $^{56}$Ni mass of 0.032${\rm\ M}_\odot$ for SNeII (N=115), 0.102${\rm\ M}_\odot$ (N=27) for SNeIIb, SNeIb = 0.163${\rm\ M}_\odot$ (N=33), SNeIc = 0.155${\rm\ M}_\odot$ (N=48), and SNeIcBL = 0.369${\rm\ M}_\odot$ (N=32). On average, stripped-enevelope SNe (SE-SNe: IIb; Ib; Ic; and Ic-BL) have much higher values than SNeII. These observed distributions are compared to those predicted from neutrino-driven explosion models. While the SNII distribution follows model predictions, the SE-SNe have a significant fraction of events with $^{56}$Ni masses much higher than predicted. If the majority of published $^{56}$Ni masses are to be believed, these results imply significant differences in the progenitor structures and/or explosion properties between SNeII and SE-SNe. However, such distinct progenitor and explosion properties are not currently favoured in the literature. Alternatively, the popular methods used to estimate $^{56}$Ni masses for SE-SNe may not be accurate. Possible issues with these methods are discussed, as are the implications of true $^{56}$Ni mass differences on progenitor properties of different CCSNe.

Tables

Table 1. Table 1: CC SN 56 Ni statistics. In the first column I list the SN distribution and the number of events within that distribution in brackets. Means, standard deviations, and medians of the distributions are then presented in the second, third and fourth columns respectively. In the last two columns I list the minimum and maximum value in each distribution (these latter values are those from the individual literature measurements, while in Fig.  1 the mean values for each SN are plotted).

SN distribution (N)	Mean (​$M_{\odot }$)	Standard deviation (​$M_{\odot }$)	Median (​$M_{\odot }$)	Max (​$M_{\odot }$)	Min (​$M_{\odot }$)
SN II (115)	0.044	0.044	0.032	0.360	0.001
SE-SN (143)	0.293	0.295	0.184	2.400	0.030
SN IIb (27)	0.124	0.061	0.102	0.280	0.030
SN Ib (33)	0.199	0.146	0.163	0.920	0.030
SN Ic (48)	0.198	0.139	0.155	0.840	0.030
SN IcBL (32)	0.507	0.410	0.369	2.400	0.070

Table 2. Table 2: KS statistical differences between the various different CC SN 56 Ni distributions. In the first column the two distributions being compared are listed together with the number of events within each distribution in brackets. In the third column the D parameter is given while in the last column the p value is presented.

SN distributions (N)	D	p
SN II (115)–SE-SNe (143)	0.773	1.2$\times$10-34
SN II (115)–SN IIb (27)	0.687	6.1$\times$10-10
SN II (115)–SN Ib (33)	0.774	1.5$\times$10-14
SN II (115)–SN Ic (48)	0.801	3.0$\times$10-20
SN IIb (27)–SN Ib (33)	0.323	0.07
SN IIb (27)–SN Ic (48)	0.375	0.01
SN Ib (33)–SN Ic (48)	0.227	0.23
SN Ic (48)–SN IcBL (32)	0.635	1.3$\times$10-7

Full text

*Aims. *I provide a meta analysis of all published 56Ni masses for CC SNe.

*Methods. *Collating a total of 258 literature 56Ni masses I compare distributions of the main CC SN types: SNe II; SNe IIb; SNe Ib; SNe Ic; and SNe IcBL.

*Results. *Using these published values, I calculate a median 56Ni mass of 0.032${\rm\ M}_{\odot}$ for SNe II (N=115), 0.102${\rm\ M}_{\odot}$ (N=27) for SNe IIb, SNe Ib = 0.163${\rm\ M}_{\odot}$ (N=33), SNe Ic = 0.155${\rm\ M}_{\odot}$ (N=48), and SNe IcBL = 0.369${\rm\ M}_{\odot}$ (N=32). On average, stripped-enevelope SNe (SE-SNe: IIb; Ib; Ic; and Ic-BL) have much higher values than SNe II. These observed distributions are compared to those predicted from neutrino-driven explosion models. While the SN II distribution follows model predictions, the SE-SNe have a significant fraction of events with 56Ni masses much higher than predicted.

*Conclusions. *If the majority of published 56Ni masses are to be believed, these results imply significant differences in the progenitor structures and/or explosion properties between SNe II and SE-SNe. However, such distinct progenitor and explosion properties are not currently favoured in the literature. Alternatively, the popular methods used to estimate 56Ni masses for SE-SNe may not be accurate. Possible issues with these methods are discussed, as are the implications of true 56Ni mass differences on progenitor properties of different CC SNe.

1 Introduction

CC SNe are the explosive end of massive stars. A range of physical processes power their electromagnetic output, however the vast majority of explosions show a common property: they produce a significant amount of radioactive material that powers their luminosity at some epoch. The dominant radioactive decay chain for the first several hundred days of SN evolution is 56Ni to 56Co to 56Fe (Arnett, 1996). Therefore the mass of 56Ni synthesised in the explosion is a critical parameter to understand. The amount of 56Ni produced in an explosion is dependent on the explosion properties and the progenitor core structure (see e.g. Ugliano et al. 2012; Pejcha & Thompson 2015; Sukhbold et al. 2016; Suwa et al. 2019 and references therein). How the decay of this material affects the subsequent transient properties then depends on the ejecta structure, the degree to which the 56Ni is mixed outwards, and how asymmetric the 56Ni production is. Constraining the 56Ni yield in different SN types and its effect on their transient behaviour is key to further our understanding of massive star explosions.

CC SNe can be broadly separated into those showing strong, long-lasting hydrogen in their spectra: hydrogen-rich SNe II, and those that do not: hydrogen-poor SE-SNe. SNe II show a large diversity in their photometric and spectroscopic behaviour (e.g. Anderson et al. 2014; Gutiérrez et al. 2017). However for the purpose of this work SNe II are not split into slower or faster decliners (IIP and IIL respectively in historical classification terminology, Barbon et al. 1979), nor peculiar events. Importantly, the vast majority of SNe II are understood to be the result of massive stars exploding with large hydrogen-rich envelopes still present, where their luminosity is powered by shock energy for the first few months post explosion. Once their initially ionised hydrogen-dominated ejected are fully recombined, their light curves show a drop in luminosity until they fall onto their radioactively powered s3 decline (e.g. Anderson et al. 2014).

SE-SNe can be split into different types depending on the presence or absence of specific lines in their optical spectra (see Filippenko 1997 and Gal-Yam 2017 for reviews on SN classification). These differences are thought to imply a sequence of increasing envelope stripping prior to explosion. SNe IIb do display hydrogen features in their early-time spectra, however these features disappear post maximum light and the SNe transition to be more similar to SNe Ib. This latter class lacks hydrogen but show strong helium features. Finally, in the spectra of SNe Ic hydrogen and helium are usually both absent (Modjaz et al., 2016)111Although see the case of SN 2016coi (Yamanaka et al., 2017; Prentice et al., 2018).. A small subset of SNe Ic show much broader spectral features and are thus named SNe IcBL (broad line). While SE-SNe display diversity in their light-curve properties (absolute magnitudes, decline rates), their overall morphologies are more homogeneous than SNe II, generally displaying a characteristic bell-shaped luminosity evolution (see samples of light curves in e.g. Drout et al. 2011; Taddia et al. 2015; Lyman et al. 2016; Prentice et al. 2016; Stritzinger et al. 2018). SE-SNe are therefore understood to be powered by radioactive decay (Arnett, 1982) for the vast majority of their evolution (the exception being the very early phases) with the decay of 56Ni powering the peak luminosity and 56Co becoming dominant several weeks later.

The clear observational differences between SNe II and SE-SNe imply significant differences in progenitor evolution to produce different pre-SN stars that then lead to distinct observational classifications. Initially it was thought that SE-SNe were the result of single Wolf-Rayet (WR) stars (more massive than 25-30${\rm\ M}_{\odot}$) where their envelopes have been lost through strong stellar winds (e.g. Begelman & Sarazin 1986; Schaeffer et al. 1987). However, there is now mounting evidence (see e.g. Smith 2014 and discussion below) that at least a significant fraction SE-SNe arise from lower mass progenitors where the envelope stripping is achieved through interaction with a close binary companion (e.g. Podsiadlowski et al. 1992). In this latter scenario SE-SN progenitors have similar initial masses to those of SNe II. Therefore, while the outer structures of progenitors at explosion epoch are different, their inner core structures should be similar. In the single massive star scenario SE-SN and SN II progenitor cores evolve differently due to their distinct initial masses. Given that it is this core structure that determines the resulting details of explosion, constraining how these are similar or different between SN types is key for our understanding of CC SNe.

In the case of SNe II, direct detections of progenitor stars on pre-explosion images has provided strong evidence that the majority arise from red supergiants with initial masses between 8 and 18${\rm\ M}_{\odot}$ (see Smartt 2015 and references therein). There is some suggestion of a lack of higher mass progenitors, an observation dubbed the ‘red supergiant problem’ (Smartt et al. 2009, although see e.g. Davies & Beasor 2018). Searches for progenitors of SE-SNe have been less conclusive. Eldridge et al. (2013) used 12 non-detections at the explosion sites of SE-SNe to argue against $\geq$25${\rm\ M}_{\odot}$  Wolf-Rayet stars being their progenitors. However others have claimed that such progenitors would be hard to detect in the usual band-passes available, given their hot temperatures and correspondingly blue spectral energy distributions (e.g. Yoon et al. 2012).

In recent years, a larger number of possible SE-SN progenitor detections have been published. Van Dyk et al. (2018) and Kilpatrick et al. (2018) studied the first possible identification of a SN Ic progenitor (SN 2017ein). Both concluded that the visible point source was consistent with a $\geq$45${\rm\ M}_{\odot}$ initial mass progenitor, however later observations are required to determine whether the point source is the actual progenitor or a compact cluster222Although if the source is cluster its spectral energy distribution is also consistent with the SN arising from a very massive progenitor (Van Dyk et al., 2018).. In the case of SNe Ib, there is also only one possible progenitor identification; that of iPTF13bvn. While Cao et al. (2013) initially argued for a massive, compact WR star progenitor, Eldridge et al. (2015) and Kim et al. (2015) later revised the pre-explosion photometry and concluded that the progenitor was more likely to be of lower mass (i.e. $\leq$20${\rm\ M}_{\odot}$, also see Folatelli et al. 2016). The SN IIb class has larger sample of progenitor detections. All such observations favour low-mass ($\leq$20${\rm\ M}_{\odot}$) progenitors formed through binary interaction (SN 1993J; e.g. Maund & Smartt 2009, SN 2011dh; e.g. Van Dyk et al. 2013, SN 2016gkg; e.g. Tartaglia et al. 2018). In conclusion, while the statistics are still low, the direct detection of progenitor stars on pre-SN images does not currently favour a significant difference in initial progenitor mass between SNe II anad SE-SNe (although the only possible detection of a SN Ic progenitor is intriguing).

Constraints on pre-SN stars - that are then used to infer zero age main sequence (ZAMS) masses - can also be obtained through modelling SN light curves and spectral velocities. For SNe II, while in some cases hydrodynamic modelling studies have claimed $\geq$20${\rm\ M}_{\odot}$ progenitors (e.g. Utrobin & Chugai 2017), most published results fall within a similar mass range to those of progenitor detections333A systematic offset to higher masses from hydrodynamic modelling if often discussed in the literature (see e.g. Bersten et al. 2011). While this may exist, in the main the offset is not huge and does not significantly affect the progenitor mass range for the purpose of the discussion here. (see e.g. Barbarino et al. 2015). (Also note the difficulty in inferring initial progenitor mass estimates from hydrogen envelope mass/ejecta constraints, see Dessart & Hillier 2019.) SE-SN ejecta masses have been estimated using the application of both analytical and hydrodynamic modelling, with results consistently arguing for low mass ejecta and therefore low initial progenitor masses consistent with binary evolution and inconsistent with most single-star evolution models (see Drout et al. 2011; Taddia et al. 2015; Lyman et al. 2016; Taddia et al. 2018a; Bersten et al. 2018; Prentice et al. 2019). However, there are suggestions that the light curves of some SNe Ic constrain their progenitors to be of higher initial mass (see e.g. Valenti et al. 2012; Taddia et al. 2016).

Less direct constraints on SN progenitors come from analyses of the environments in which they are discovered. Studies of resolved stellar populations surrounding SN explosion sites (Maund, 2017, 2018) have argued for a decreasing progenitor age sequence from SNe II through SNe IIb, Ib, and Ic, i.e. an increasing progenitor mass sequence: SNe II-IIb-Ib-Ic. Further afield, studies of unresolved stellar populations have also suggested parent stellar population age differences, with SNe Ic consistently being found within younger stellar populations, and therefore arising from higher mass progenitors then other CC SN types (Anderson et al., 2012; Kangas et al., 2017; Kuncarayakti et al., 2018; Galbany et al., 2018). Finally, SNe IcBL and specifically those accompanying long-duration gamma ray bursts (GRBs), have environments consistent with coming form the highest mass progenitors of all SNe discussed here (Kelly et al., 2008; Kelly & Kirshner, 2012).

In addition to constraints on progenitor ages, environment studies have investigated parent stellar population oxygen abundances, which are then used as progenitor metallicity proxies (Modjaz et al. 2008; Anderson et al. 2010; Leloudas et al. 2011; Sanders et al. 2012b; Kuncarayakti et al. 2018; Galbany et al. 2018; Modjaz et al. 2019). Most CC SN types do not show significant differences, however SNe Ic are consistently found in higher metallicity regions than SNe II and SNe Ib, while SNe IcBL (see Modjaz et al. 2019) are systemtically found in galaxies of lower metal abundance than SNe Ic and all other CC SNe. Such metallicity differences may be key in explaining the origin of some of the diversity within the CC SN family. These environment studies (both resolved and unresolved) are somewhat in contradiction to the statistical studies of the ejecta masses of SE-SNe discussed above: environment studies suggest significant mass differences between some CC SN types, while estimated ejecta masses suggest very similar initial progenitor masses between SNe II and SE-SNe.

Progenitor mass constraints can also be derived from spectroscopy of SNe at nebular times (several hundred days post explosion) when the ejecta has become optically thin and the inner core material is revealed. Observations at these epochs constrain the core mass that is predicted to strongly correlate with the ZAMS mass (Woosley et al., 2002). Nebular spectroscopic studies have generally concluded for SN II progenitor masses similar to those from direct detections (see e.g. Jerkstrand et al. 2015; Valenti et al. 2016, although see Anderson et al. 2018). Nebular-phase observations of SE-SNe are less common, but the statistical analysis of Fang et al. (2018) concluded that SNe Ic appear to show spectra consistent with more massive progenitors than SNe Ib.

SNe IcBL and those associated with GRBs (in particular) show specific properties that may differentiate them from other CC SNe. Specifically, (as above) the broad-line designation means large ejecta velocities and this implies significantly higher energy explosions than other CC SN types. Significant asphericities have also been discussed to explain the properties of SNe IcBL (Maeda et al., 2003; Dessart et al., 2017a). Such high explosion energies are probably inconsistent with these events arising from standard explosion mechanisms (see further discussion below), which brings caveats to discussing their analysis in a similar vain to other types.

In summary, there is a large body of work attempting to constrain CC SN progenitor mass differences. Most studies suggest significant overlap in the ZAMS mass of SNe II and SE-SNe. This suggests that at least a significant fraction of SE-SNe arise through binary evolution (stripping the outer envelope) but from stars with initially very similar masses to SNe II. At the same time, observations do suggest that some SNe Ic arise from more massive progenitors that may evolve as single stars (i.e. they may be massive enough to lose their envelope through stellar winds). Further constraints are required to shed light on progenitor differences between CC SN types and to constrain the explosion mechanism.

As outlined earlier, a critical parameter for understanding how a SN explosion proceeds is the mass of synthesised 56Ni. Müller et al. (2017) compared a sample of observed SN II 56Ni masses with those from explosion models (Sukhbold et al., 2016) finding consistent results. Additional observational samples of SN II 56Ni masses can be found in e.g.: Hamuy (2003); Anderson et al. (2014); Spiro et al. (2014); Valenti et al. (2016). SE-SNe are generally analysed separately from SNe II, and various work has provided distributions of 56Ni masses, see e.g. Drout et al. (2011); Lyman et al. (2016); Prentice et al. (2016); Taddia et al. (2015, 2018b). These latter studies present distributions with higher mean 56Ni values than those of SNe II. However, there does not appear to be any formal study analysing SN II and SE-SN 56Ni mass distributions in comparison. This is the aim of the current paper: to provide a meta analysis of CC SN 56Ni masses to investigate whether there exist statistical differences between different CC SN types and discuss the implications that follow.

This paper is organised as follows. In the next section I outline how the meta sample is produced and summairse its characteristics. Section 3 discusses the main methods used in the literature for estimating 56Ni masses. In Section 4 I present 56Ni masses for: SN II; SN IIb, SN Ib; SN Ic; SN IcBL (including GRB-SNe), and compare these statistically. This is followed by a discussion of possible explanations of these results including caveats on the commonly used methods for 56Ni mass estimation in Section 5. Final conclusions are presented in Section 6.

2 A meta sample of CC SN 56Ni masses

The aim of this work is to collate and then compare literature CC SN 56Ni masses. In the later discussion section I outline possible systematics in how these values are estimated and how these may affect my results and conclusions. However, here I do not attempt to remeasure 56Ni masses. Following this there is no preference for any specific method for estimating these values. To produce this sample I simply searched the literature for all published masses. Specifically, the SAO/NASA ADS astronomy query form444http://adsabs.harvard.edu/abstract_service.html was used, searching for articles with ‘supernova’ and ‘type II’, then ‘supernova’ and ‘type IIb’ and so forth in manuscript abstracts. The resulting lists of articles were then scanned to find published 56Ni masses. While the vast majority of values have probably been collated (through to August 2018)555Two additional samples were published after this date. Prentice et al. (2019) published a sample of SE SNe, while Taddia et al. (2018a) published a sample of SNe IcBL. These additional values are in line with those presented for the meta sample here, and their inclusion would not affect the results nor conclusions of the present study., it is probable that some have been missed. In the many cases of multiple literature values for individual SNe a mean mass is calculated. A full reference list for all 56Ni masses can be found in the appendix. The two main methods for estimating 56Ni in SNe II and SE-SNe are outlined next.

3 Standard procedures to estimate 56Ni masses

While there are many variations on the exact details of how authors estimate 56Ni masses in SNe, there are two standard methods. First, in SNe II the tail luminosity is used as a robust estimate of the synthesised mass of radioactive material. Once the hydrogen ejecta has fully recombined the light curves of SNe II fall down to their s3 radioactive tails. At this stage their luminosity is powered by the decay of 56Co. This is well established (e.g. Woosley 1988) and the s3 slope follows the predicted decline (from the rate of decay of 56Co) extremely well in most SNe II (as the radioactive emission is fully trapped by the ejecta, see Anderson et al. 2014 for a discussion of SNe II where this is not the case). It is therefore reasonably straightforward to extract the 56Ni mass using the bolometric luminosity of a SN II if one also has reasonable constraints on the explosion epoch (see e.g. Hamuy 2003 for an outline of one possible procedure).

In the case of SE SNe the tail in the light curves generally decline significantly quicker than that predicted by the 56Co decay rate (Wheeler et al., 2015) due to incomplete trapping666Although 20-30 days post maxmium most of the emission is trapped and it may be possible to use this epoch in the same way as for SNe II to estimate 56Ni masses (Dessart et al., 2015).. Therefore the tail luminosity has not been used for SE-SN 56Ni estimates. SE-SN 56Ni masses are generally estimated using ‘Arnett’s rule’ (Arnett, 1982)777For a fraction of the current meta sample SE-SN 56Ni masses are estimated through spectral modelling of nebular-phase observations (see e.g. Mazzali et al. 2009), or through modeling of observations around maximum light (see e.g. Bersten et al. 2018).. Arnett’s rule states that the SN luminosity at peak brightness equals the instantaneous rate of energy deposition (from radioactive decay). This assumes that radioactive decay is the only energy source at peak magnitude and involves a number of assumptions that are outlined and questioned in Khatami & Kasen (2018) and Dessart et al. (2016) (as will be discussed later). The method used for SE-SNe is therefore more indirect than that for SNe II.

It is important to note the various uncertainties involved in 56Ni mass estimations. The above methods require that observed photometry are converted into bolometric luminosities. Measurements have to be corrected for line of sight extinction, distance, and the missing flux outiside the observed wavebands. All three of these corrections can have significant uncertainties. In addition, photometry may be contaminated by underlying galaxy light. These observational errors then sum with those arising from the 56Ni estimation method. The latter assume an exclusive contribution from 56Ni together with spherical asymmetry. As noted above, Arnett’s rule also has a range of assumptions that are not necessarily valid for all SNe.

How these uncertainties may affect the results presented in this work is further discussed in Section 5. However, it appears unlikely that they can explain all the differences in 56Ni masses between CC SNe that will now be presented.

4 Results

Figure 1 presents cumulative 56Ni distributions of all CC SNe. Mean, median and standard deviations for each are presented in Table 1. Table 2 lists the Kolmogorov-Smirnov (KS) statistics between the 56Ni mass distributions of the different types. The SN II distribution is clearly skewed towards significantly lower 56Ni masses than SE-SNe. The median value for the SNe II is a factor of three lower than the SNe IIb and a factor of five lower than the SNe Ib and SNe Ic. The SN II distribution is statistically distinct from all other distributions (Table 2).

Inspecting the minimum and maximum values for each class is also particularly telling: the mininum 56Ni mass for any SE-SN is 0.03${\rm\ M}_{\odot}$, while 45% of SNe II have lower values, the lowest being 0.001${\rm\ M}_{\odot}$888This may suggest an observational bias against detecting SE-SNe with low 56Ni masses. Such SNe would be much dimmer than the observed SE-SN population and may have gone undetected. If this is the case, then we should expect the current and future generation of discovery surveys - that search deeper and with a higher cadence than ever before - to start detecting such events.. At the higher end of the SN II distribution there is some overlap with SE-SNe: 100% of the SNe IIb overlap with the SNe II; 76% of the SNe Ib; and 60% of the SNe Ic. In general, it is the lack of low SE-SN 56Ni values that produces such statistically different distributions. The mean value for the 56Ni mass of SN 1987A (the nearest SN to Earth in the last $\sim$400 years) is 0.072${\rm\ M}_{\odot}$ and this is often used as the canonical value for SNe II. However, this value is a factor of two higher than the median 56Ni mass of SNe II in the current sample. Indeed, 83% of the SNe II have estimated values lower than SN 1987A. All six events classified as ‘87A-like’ have relatively high 56Ni estimates, with a mean value of 0.086${\rm\ M}_{\odot}$.

With respect to differences between the SE-SN classes, the SNe IIb appear to produce less 56Ni than the other types, while there is no statistically significant difference between the SNe Ib and SNe Ic. Meanwhile, the SN IcBL distribution (where GRB-SNe are also included) contains by far the largest number of high masses, with many SNe IcBL estimated to have synthesised more than 0.5${\rm\ M}_{\odot}$. To put this in context, Type Ia SNe produce on average 0.6${\rm\ M}_{\odot}$ (e.g. Scalzo et al. 2019). As shown in Table 1 and Fig. 1 the SNe Ib and SNe Ic distributions also contain such high values. To see how much these drive the differences seen between SNe II and SE-SNe, the average 56Ni values are recalculated after removing $>$ 0.35${\rm\ M}_{\odot}$ values. The SNe Ib and SNe Ic mean 56Ni are still a factor of four larger than the SNe II.

4.1 Comparison to model predictions from neutrino driven explosions

The most commonly studied and favoured explosion mechanism for CC SNe is the so-called ‘neutrino-driven explosion’ (see e.g. Janka 2017 for a recent review). Core-collapse is initiated when the iron core becomes too massive to support itself (through degeneracy pressure) against gravity. When the material from this resulting collapse reaches nuclear densities the collapse is halted and a shock wave drives through the still inwardly falling outer layers of the core. It has long been accepted that the initial shock from the core bounce stagnates. In the neutrino driven mechanism, the huge neutrino flux from the accreting proto-neutron star - assisted by turbulent motions - revives the shock and produces the CC SNe we observe. However, while some simulations have succeeded in producing successful explosions (e.g. Müller et al. 2012), many have not (see discussion in e.g. Takiwaki et al. 2014), and even those that do produce low-energy events. For these reasons, others have proposed alternative explosion mechanisms (see e.g. Papish et al. 2015). A full exploration of alternative models in the context of 56Ni production is beyond the scope of this paper, but the reader should be aware that the below comparisons are made with only a specific theoretical framework that may not be the dominant one in Nature.

A number of studies have provided 56Ni yields from neutrino-driven explosion models of various levels of complexity (Ugliano et al. 2012; Pejcha & Thompson 2015; Sukhbold et al. 2016; Suwa et al. 2019999Most of these works only model the initial explosion and the estimated nucleosynthesis; they do not go on to produce light curves nor spectra that can be compared to observed events. Sukhbold et al. (2016) do produce such observables, and their explosions struggle to reproduce observed SE-SNe., 56Ni yields from other models are discussed below). While the exact results vary between studies (e.g. the dependence of the synthesised 56Ni on explosion energy and initial progenitor mass), the predicted 56Ni mass range is somewhat similar, as is the maximum predicted value. In the case of SNe II, Müller et al. (2017) showed that the 56Ni distribution predicted by Sukhbold et al. (2016) was in reasonable agreement with observed SNe II, and qualitatively we find the same result here with a much larger sample. SE-SNe however, have estimated values in significant excess of model predictions. The maximum predicted value in each of the four explosion-model studies cited above is: 0.15${\rm\ M}_{\odot}$ (Ugliano et al., 2012); 0.2${\rm\ M}_{\odot}$ (Pejcha & Thompson, 2015); 0.171${\rm\ M}_{\odot}$ (Sukhbold et al., 2016); and 0.226${\rm\ M}_{\odot}$ (Suwa et al., 2019). Taking the most extreme of these (0.226${\rm\ M}_{\odot}$), 30% of SN Ib have higher inferred values, together with 29% of SNe Ic and 84% of SNe IcBL (only 3% of SN II and 7% of SNe IIb have values in excess of this limit). Therefore, even in the most optimistic case (that many of the SE-SNe come from the highest values from explosion model predictions), a significant fraction of 56Ni estimated values for SE-SNe are outside of neutrino-driven model estimations101010Although see Umeda & Nomoto (2008) for much higher 56Ni masses produced from SNe more massive than 30${\rm\ M}_{\odot}$.. As Fig. 1 shows, a number of SE-SNe have values twice or even three times are large as this limit. The implications of these results, together with a series of caveats and possible explanations, are now discussed.

5 Discussion

Two main results are presented in this paper: 1) that values of 56Ni in the literature are systematically larger for SE-SNe than for SNe II, and 2) that a significant fraction of SE-SNe have published 56Ni masses in excess of the largest masses predicted by a range of different neutrino-driven explosion models. 1) implies significant differences in the progenitor structures and explosion properties between hydrogen-rich and hydrogen-poor CC SNe. However, 2) may suggest that the estimates for many SE-SNe are significantly in error, or that the currently most popular explosion model (neutrino-driven explosion) is not applicable to a significant fraction of CC SNe.

The general current consensus (although it is still debated) is that a significant fraction - if not the vast majority - of SE-SNe arise from binary systems where mass transfer is responsible for removing the outer hydrogen (type IIb, Ib) and helium (Ic) rich layers of the progenitors. In this hypothesis, the initial progenitor masses of SNe II and SE-SNe are similar (although those of SE-SNe are still probably higher on average). While their pre-SN outer structures are distinct, their core-structures should be somewhat indistinguishable (in most cases the core will evolve independently of surface processes). Therefore it is not clear how one could arrive at such distinct 56Ni masses (as presented in this study) if the progenitors have similar initial masses. If one postulates that SE-SNe actually have significantly more massive progenitors (and evolve either as single stars or in binary systems) then one may speculate that their cores have more material at sufficiently high densities to produce higher amounts of 56Ni during the explosion. However, this is not actually predicted by neutrino-driven explosion models (Ugliano et al., 2012; Pejcha & Thompson, 2015; Sukhbold et al., 2016; Suwa et al., 2019): a 25${\rm\ M}_{\odot}$ star does not necessarily produce more 56Ni than an e.g. 15${\rm\ M}_{\odot}$ star, and models do not produce 56Ni masses in excess of 0.2${\rm\ M}_{\odot}$. In summary, if literature 56Ni values are to be believed, then a) the progenitor structures (and by inference the initial progenitor properties) must be significantly more different between SNe II and SE-SNe that currently believed, and b) progenitor structures and/or explosion properties of SE-SNe must be distinct from those predicted by stellar evolution and currently favoured explosion models.

There are various sources of observational error that may affect 56Ni mass estimates: 1) errors in photometry; 2) errors in SN distances; 3) errors in extinction corrections; and 4) errors in bolometric corrections. If any of these corrections are systematically wrong for one SN type compared to another, this may produce some of the differences we observe. The errors from 1) can be assumed to be negligible compared to the rest. There is no reason to believe that errors in distances (2) are any different between SN types (although very large or very small individual 56Ni masses may be due to distance errors).

Estimation of accurate host galaxy extinction for CC SNe is notoriously difficult (see recent discussion for the case of SNe II: de Jaeger et al. 2018). Such estimates are generally derived from assuming some uniform intrinsic colour for a given SN type and correcting assumed reddened SNe to assumed unreddened events (see e.g. Stritzinger et al. 2018), or by measuring the strength of absorption from interstellar sodium (see e.g. Phillips et al. 2013). However, both of these methods have strong caveats. To investigate how these errors may affect the results from the current study, I also compile host galaxy extinction estimates employed by each study contributing 56Ni masses to this work. The median host galaxy visual extinction does increase from hydrogen-rich through the stripped-envelope classes: 0.12 mag for SNe II; 0.25 mag SNe IIb; 0.30 mag SNe Ib; 0.56 mag SNe Ic, while for the SNe IcBL the median is 0.12 mag. However, this is somewhat expected, given the increasing sequence of association from SNe II through to SNe Ic to bright H ii regions (Anderson et al. 2012, where one may expect higher levels of extinction). Still, in the extreme case of assuming that the host extinction estimates are systematically wrong between e.g. SNe II and SNe Ic, one can estimate that the addition of 0.44 visual magnitudes (the difference in the median values of SNe II and SNe Ic) to the bolometric luminosity of a SN II would only increase the median 56Ni value to 0.048${\rm\ M}_{\odot}$. In order to increase this to the median of the SNe Ic (0.155${\rm\ M}_{\odot}$), a difference of 1.7 mag is required. It seems extremely unlikely that such a difference has gone unnoticed.

Finally, if there were a systematic error in the way bolometric corrections were applied between SNe II and SE-SNe this could produce some difference in 56Ni masses. Bolometric corrections are either produced by using very well observed (in wavelength) SNe as templates and assuming similar spectral energy distributions for less well observed events, or through comparison to models. In this study 56Ni masses are compiled from many different sources and in many SNe there are multiple (up to eight) values from different studies. Comparing these values can give some idea of the differences resulting from different bolometric corrections. In the case of SNe II the mean standard deviation of multiple 56Ni mass estimates is 0.013${\rm\ M}_{\odot}$, while for e.g. SNe Ic it is 0.06${\rm\ M}_{\odot}$. If one assumes that this larger scatter for the SNe Ic is due to systematically incorrect bolometric corrections for some of the estimates for these SNe, then one can speculate that such an error propogates to differences in 56Ni mass estimates. However, the above difference is not sufficient to explain the significantly distinct 56Ni distributions. In summary, there does not appear to be any significantly large observational error that would negate the conclusion of large differences between the estimated 56Ni masses of SNe II and SE-SNe.

5.1 Alternative explanations

The methodology for estimating 56Ni masses from SN II observations is understood to be robust in a theoretical sense. However, doubt has often been cast as to the accuracy of using Arnett’s rule in the case of SE-SNe (the methodology used for the vast majority of literature values compiled here). Katz et al. (2013) published an ‘exact integral relation between the 56Ni mass and the bolometric light curve’, arguing that this overcomes issues with Arnett’s rule such as assumed opacities, density distribution, and the 56Ni deposition distribution into the ejecta. Dessart et al. (2015, 2016) published radiative transfer models of SE-SNe (IIb/Ib/Ic) based on explosions of the mass donor in a close-binary system. These authors concluded that for this set of models Arnett’s rule overestimates the 56Ni mass by around 50% (while suggesting that the Katz et al. 2013 procedure yields more reliable values). However, these models (and explosion models of SE-SNe in general, see e.g. Sukhbold et al. 2016 for another example) often struggle to accurately reproduce observations, with e.g. the model rise times being longer than those observed. More recently, Khatami & Kasen (2018) discussed in detail the assumptions that are contained within the classical Arnett model and argued - using comparison to numerical simulations - that Arnett’s rule does not hold in general (while presenting new analytic relations), only being valid in certain explosion configurations. It is important to stress: the difference in published values between SNe II and SNe Ib/SNe Ic is a factor of five (Section 4). This is significantly larger than the offsets discussed in e.g. Dessart et al. (2015) and Khatami & Kasen (2018).

As discussed above, the neutrino-driven explosion mechanism may not be at play in all CC SNe. Soker (2018) argues that jets are required to explode many if not all CC SNe, and that a paradigm shift is needed to move away from the neutrino-driven mechanism to a ‘jet-driven explosion mechanism that is aided by neutrino heating’. However, there are few studies of nucleosynthetic yields from non-standard explosion models (to my knowledge). Barnes et al. (2018) presented a model of a GRB central engine producing the accompanying SN IcBL through a jet-driven aspherical explosion. (Aspherical explosions may be applicable to the majority of SE-SNe, given the number of such events showing double-peaked nebular-phase spectral features, Maeda et al. 2008.) This model calculated the synthesised 56Ni mass through a temperature condition, and estimated a yield of 0.24${\rm\ M}_{\odot}$ of 56Ni. This is higher than for any of the explosion models discussed above, but it should be noted that there are many SE-SNe (and not just the IcBL) in Fig.1 that have values in excess of this. Additional explosion and nucleosyhthesis modelling is required to understand whether alternative models can indeed consistently produce 56Ni masses much higher than 0.2${\rm\ M}_{\odot}$.

In the case of SNe IcBL estimated 56Ni masses are extremely large, being of the same order as those for SNe Ia, together with a tail out to values higher than 1${\rm\ M}_{\odot}$. This seems to be beyond any available progenitor exploded through the neutrino-driven explosion model. As noted previously, one possibility is that SN IcBL explosions are significantly asymmetric, and we observe these events as SNe IcBL when the explosion direction is towards the observer (see e.g. Maeda et al. 2003; Dessart et al. 2017b). In such cases 56Ni masses derived assuming spherical symmetry (e.g. Arnett’s rule) will be overestimated (Dessart et al. 2017b, and ejecta masses will be underestimated). This explanation cannot work for the SE-SN sample at large as statistically one would expect to observe both high and low values depending on the viewing angle of the observer.

Finally, a remaining explanation is simply that for many SE-SNe radioactive decay is not the dominant power source of their luminosity. If an additional power source is present (e.g. a magnetar) then assuming that all the power comes exclusively from 56Ni will lead to an overestimate of such masses.

6 Conclusions

Using published 56Ni masses from the literature that employ standard methods for estimating the contribution of radioactive decay power to SN luminosities, I have shown that hydrogen-poor SE-SNe are estimated to produce around five times more 56Ni than hydrogen-rich SNe II. This difference is highly statistically significant. While the distribution of 56Ni for SNe II agrees with predictions from neutrino-driven explosion models, that of SE-SNe does not. These results imply that either SE-SN progenitors and their subsequent explosion are significantly distinct from those of SNe II, or that there is a systematic error in how 56Ni masses are calculated. This work serves to highlight these issues to the community. The amount of radioactive material synthesised in CC SNe is a critical parameter in understanding these explosive events. Therefore a detailed understanding of how well we derive such a property is vital to move our understanding forward.

Acknowledgements.

The anonymous referee is thanked for their comments and suggestions. Luc Dessart is thanked for providing detailed comments on a draft version of this manuscript. In addition, I acknowledge fruitful conversations with the following people that aided in the discussion sections of this paper: Takashi Moriya; Ondřej Pejcha; Tomas Müller; José Luis Prieto, Keiichi Maeda; Melina Bersten, Peter Hoeflich.

Appendix A Reference list for 56Ni mass values

Here all references used to compile the meta sample of CC SN 56Ni values used in this work are listed.

SNe II: Arnett et al. (1989); Turatto et al. (1998); Nadyozhin (2003); Hamuy (2003); Elmhamdi et al. (2003); Zampieri et al. (2003); Pastorello et al. (2004); Hendry et al. (2005); Pastorello et al. (2005); Vinkó et al. (2006); Gurugubelli et al. (2008); Pastorello et al. (2009); Kleiser et al. (2011); Bersten et al. (2011); Andrews et al. (2011); Roy et al. (2011b, a); Taddia et al. (2012); Pastorello et al. (2012); Otsuka et al. (2012); Inserra et al. (2013); Bose et al. (2013); Spiro et al. (2014); Pejcha & Prieto (2015); Huang et al. (2015); Bose et al. (2015); Jerkstrand et al. (2015); Barbarino et al. (2015); Takáts et al. (2015); Valenti et al. (2015); Yuan et al. (2016); Dhungana et al. (2016); Valenti et al. (2016); Terreran et al. (2016); Gutiérrez et al. (2017); Müller et al. (2017); Lisakov et al. (2017); Tomasella et al. (2018); Dastidar et al. (2018); Anderson et al. (2018); Huang et al. (2018); Hosseinzadeh et al. (2018); Tartaglia et al. (2018); Tsvetkov et al. (2018).

SE-SNe: Shigeyama et al. (1994); Iwamoto et al. (1994, 1998); Clocchiatti et al. (2000); Nakamura et al. (2001); Stritzinger et al. (2002); Foley et al. (2003); Mazzali et al. (2003, 2004); Anupama et al. (2005); Deng et al. (2005); Mazzali et al. (2006); Richardson et al. (2006); Tomita et al. (2006); Taubenberger et al. (2006); Folatelli et al. (2006); Sauer et al. (2006); Tominaga et al. (2008); Valenti et al. (2008); Mazzali et al. (2008); Silverman et al. (2009); Mazzali et al. (2009); Sahu et al. (2009); Hamuy et al. (2009); Roming et al. (2009); Stritzinger et al. (2009); Drout et al. (2011); Elmhamdi et al. (2011); Taubenberger et al. (2011); Benetti et al. (2011); Pignata et al. (2011); Valenti et al. (2011); Berger et al. (2011); Corsi et al. (2011); Oates et al. (2012); Bersten et al. (2012); Sanders et al. (2012a); Valenti et al. (2012); Bufano et al. (2012); Ben-Ami et al. (2012); Melandri et al. (2012); Milisavljevic et al. (2013b); Takaki et al. (2013); Milisavljevic et al. (2013a); Kumar et al. (2013); Roy et al. (2013); Bufano et al. (2014); Srivastav et al. (2014); Folatelli et al. (2014); Walker et al. (2014); Melandri et al. (2014); Chen et al. (2014); Morales-Garoffolo et al. (2015); Taddia et al. (2015); D’Elia et al. (2015); Liu et al. (2015); Milisavljevic et al. (2015); Prentice et al. (2016); Roy et al. (2016); Szalai et al. (2016); Fremling et al. (2016); Lyman et al. (2016); Pian et al. (2017); Mazzali et al. (2017); Corsi et al. (2017); Cano et al. (2017); Taddia et al. (2018b); Gangopadhyay et al. (2018); Bersten et al. (2018); Zhang et al. (2018); Kumar et al. (2018); Sahu et al. (2018)111111From Prentice et al. (2016) the ‘fully bolometric’ values are used.