The death of massive stars

The death of massive stars - I. Observational constraints on the progenitors of type II-P supernovae

Abstract

We present the results of a 10.5 yr, volume limited (28 Mpc) search for supernova (SN) progenitor stars. In doing so we compile all SNe discovered within this volume (132, of which 27% are type Ia) and determine the relative rates of each sub-type from literature studies. The core-collapse SNe break down into 59% II-P and 29% Ib/c, with the remainder being IIb (5%), IIn(4%) and II-L (3%). There have been 20 II-P SNe with high quality optical or near-IR pre-explosion images that allow a meaningful search for the progenitor stars. In five cases they are clearly red supergiants, one case is unconstrained, two fall on compact coeval star clusters and the other twelve have no progenitor detected. We review and update all the available data for the host galaxies and SN environments (distance, metallicity and extinction) and determine masses and upper mass estimates for these 20 progenitor stars using the STARS stellar evolutionary code and a single consistent homogeneous method. A maximum likelihood calculation suggests that the minimum stellar mass for a type II-P to form is M and the maximum mass for II-P progenitors is M, assuming a Salpeter initial mass function holds for the progenitor population (in the range ). The minimum mass is consistent with current estimates for the upper limit to white dwarf progenitor masses, but the maximum mass does not appear consistent with massive star populations in Local Group galaxies. Red supergiants in the Local Group have masses up to 25M and the minimum mass to produce a Wolf-Rayet star in single star evolution (between solar and LMC metallicity) is similarly 25-30M. The reason we have not detected any high mass red supergiant progenitors above 17M is unclear, but we estimate that it is statistically significant at 2.4 confidence. Two simple reasons for this could be that we have systematically underestimated the progenitor masses due to dust extinction or that stars between 17-25M produce other kinds of SNe which are not II-P. We discuss these possibilities and find that neither provides a satisfactory solution. We term this discrepancy the “red supergiant problem” and speculate that these stars could have core masses high enough to form black holes and SNe which are too faint to have been detected. We compare the Ni masses ejected in the SNe to the progenitor mass estimates and find that low luminosity SNe with low Ni production are most likely to arise from explosions of low mass progenitors near the mass threshold that can produce a core-collapse.

keywords:
stars: evolution - stars: supergiants - supernovae: general - supernovae: individual - galaxies : stellar content
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1 Introduction

Stars which are born with masses above a critical threshold mass of around 8M have long been thought to produce supernovae when their cores collapse at a point when nuclear burning no longer provides support against gravity. Supernovae were first suggested to be a new class of astrophysical phenomena by Baade & Zwicky (1934) and since then detailed study has allowed them to be split into physical types : the thermonuclear explosions and core-collapse supernovae (CCSNe). The CCSNe form when their cores evolve to iron white dwarfs and detailed stellar evolutionary models predict a minimum mass for this to occur of between 7-12M(Heger et al., 2003; Eldridge & Tout, 2004b; Siess, 2007; Poelarends et al., 2008) . The CCSNe form a diverse group in terms of their spectral and photometric properties and the classification scheme has arisen primarily based on the appearance of their optical spectra, but also supplemented with their photometric behaviour (Filippenko, 1997). There are the H-rich type II SNe, which are sub-classified into II-P (plateau lightcurves), II-L (linear decline lightcurves), IIn (narrow emission lines), and some peculiar events, generically labelled II-pec. The H-deficient SNe are split into Ib and Ic depending on whether He is visible and a hybrid class of IIb (type II events which metamorphose into Ib SNe) has also been uncovered. The evolutionary stage of the progenitor star (i.e. its position in the HR diagram and chemical composition of its atmosphere) very likely dictates what type of CCSN is produced.

Determining what types of stars produce which types of SNe and what mass range can support a CCSN is a major goal in modern studies of these explosions. The first attempts relied primarily on linking the results of stellar evolutionary models to the spectral (and photometric) evolution of the SNe. (e.g. Arnett, 1980; Chevalier, 1976) More recently Hamuy (2003) and Nadyozhin (2003) have studied the lightcurves and ejecta velocities of II-P SNe to estimate the mass of the material ejected. These studies tend to favour quite large masses for progenitor stars, with Hamuy suggesting ranges of 10-50M and Nadyozhin 10-30M. However when SN 1987A exploded a new opportunity arose. The SN was in a galaxy close enough that its progenitor star could be easily identified. A blue supergiant star of around 15-20M was identified and it is clear that this object no longer exists (Gilmozzi et al., 1987; Walborn et al., 1989; Podsiadlowski, 1992) The fact that it was a compact blue supergiant was a key factor in enabling the community to understand the event as a whole. A progenitor was also detected for the next closest explosion (SN 1993J in M81) and the binary nature of the progenitor helped understand the physical reason behind the II-b type given to the event (Aldering et al., 1994; Podsiaklowski et al., 1993).

Studies of the environments of CCSNe after discovery have been ongoing for many years with authors looking for correlations between the ages of starformation regions and the type of SNe that occur. For example van Dyk (1992) and van Dyk et al. (1996) suggested that there was no clear difference in the spatial distributions of type Ib/c and type II SNe compared to giant H ii regions in their host galaxies. They concluded that they hence arose from parent populations of similar mass. However recently both James & Anderson (2006) and Kelly et al. (2008) suggest that the stripped type Ic SNe are more likely to follow regions of either high surface brightness or high H emission than type II SNe. A larger sample of nearby core-collapse events and H correlations has been compiled by (Anderson & James, 2008) indicating that there is a progressive trend for Ib/c SNe to be associated with H emission regions, in the sense that Ic show the closest association with galactic H emission, then comes the Ib and then type II. While these efforts are very valuable to discern differences in progenitor channel, it is difficult to assign definitive mass ranges to the progenitor systems from spatial correlations alone.

A much more direct way to determine the type of star that exploded is to search directly for progenitors in images of the host galaxies taken before explosion. The ease of access to large telescope data archives makes this search feasible for nearby events. There are now a number of groups around the world that are competitively searching for progenitor stars in such archive images. Particularly with the Hubble Space Telescope (HST) it has become possible to resolve massive stellar populations out to at least 20Mpc. In this case the information on each progenitor is much more detailed and quantitative than can be achieved with the unresolved environment studies, but there are fewer events which allow such a study.

Early work with HST concentrated on looking at the environments of SNe (Barth et al., 1996; Van Dyk et al., 1999). But it has now become possible to search directly for progenitor stars and carry out concerted campaigns on the nearest events. Three of the first type II SNe to have excellent HST and ground-based pre-explosion images were the II-P SNe 1999gi, 1999em and 2001du (Smartt et al., 2001, 2002, 2003; Van Dyk et al., 2003b). In all there was no detection of a progenitor, but meaningful limits were derived. Leonard et al. (2003) and Leonard et al. (2002) subsequently showed the importance of having reliable distances to the host galaxies of the SN progenitors in order to constrain the upper mass limits. Efforts to find progenitors continued (Smartt et al., 2003; Van Dyk et al., 2003a) until the first confirmation of a red supergiant progenitor of a type II-P explosion in prediscovery HST and Gemini-North images (Smartt et al., 2004). Unambiguous detections in HST images require the SN to be located on the pre-explosion images with accuracies of around 10 milliarcseconds, which requires follow-up images of the SN to be taken at HST or corrected adaptive optics ground-based resolution (Maund & Smartt, 2005; Gal-Yam et al., 2005; Crockett et al., 2008) The next clear and unambiguous detection of a progenitor star was also a red supergiant in NGC5194 (SN2005cs ; Maund et al., 2005; Li et al., 2006). And the recent discovery of SN2008bk in NGC7793 (3.9 Mpc) has produced detections in of a red progenitor star (Mattila et al., 2008). The near-IR spectral energy (SED) distribution of the SN2008bk progenitor is the best sampled SED yet of any red supergiant progenitor and matches a late M4I spectral type with moderate extinction of and an initial mass around 8-9M. There have been claims of the detections of others such as 2004A (Hendry et al., 2006), 2004et (Li et al., 2005), 2006my and 2006ov (Li et al., 2007) and we review these in this paper. An additional method that has much to offer this field is locating SNe directly coincident with compact, coeval star clusters. If the age of the cluster can be determined then a main-sequence turn-off age, and turn-off mass can lead directly to an estimate of the progenitor star mass (e.g. 2004dj in NCG2403 as studied by Maíz-Apellániz et al., 2004). The detection and characterisation of progenitor stars has the potential to directly link the type of star to the SN explosion characteristics, (e.g. the amount of Ni synthesised in explosive O and Si burning and the total energy of the explosion) and also to set quantitative limits on progenitor mass ranges. The latter is of great interest to compare to the highest mass white dwarf progenitors and to the stars that form neutron stars and black holes after core-collapse.

Work in this field has progressed substantially in the last 8 years and compilations of progenitor properties have been made by Smartt et al. (2003); Gal-Yam et al. (2007); Li et al. (2007); Kochanek et al. (2008). However these compilations are somewhat ad-hoc, incomplete and potentially biased as they do not define the selection criterion for inclusion rigorously. In addition the results are based on different methods for estimating the progenitor masses and upper limits (in terms of measurement and the theoretical models employed). The goal of this series of two papers is to define the selection criteria for inclusion (a volume and time limited survey) and to determine the physical parameters of the progenitor stars (luminosities and masses, or limits thereon) in a homogeneous and consistent way. Only then is it possible to reliably estimate the population parameters. This paper specifically deals with the type II SNe and all but two of the final sample of twenty have been confirmed as type II-P. A companion paper will discuss the stripped SNe of types IIb, Ib and Ic which are drawn from the same volume and time limited survey (Crockett et al. 2008, in prep).

In addition to the supernovae with pre-explosion images we discuss in the paper there are three SNe with progenitor detections that fall outside either our time or volume definition. Those are SN 1987A, SN 1993J and SN 2005gl. Discussions of the first two are well documented in the literature (e.g. Walborn et al., 1989; Aldering et al., 1994; Van Dyk et al., 2002; Maund et al., 2004); 1987A will be discussed later in this paper and the implications of 1993J will be discussed in the 2nd paper in this series. SN 2005gl is a type IIn in NGC266 at approximately 66 Mpc, hence although a progenitor is detected by Gal-Yam et al. (2007) it does not fall within our distance limit. Gal-Yam et al. (2007) suggest that this was a very massive star with and very likely a luminous blue variable. Although with only a detection in a single filter the blue colour is not confirmed, and there is not enough data to determine if the source was indeed variable. This is evidence that very massive stars do explode as bright SNe and is a point we will return to in the discussion.

This paper starts with defining the sample from which the targets with high quality pre-explosion images are drawn. A consistent and homogeneous analysis method is then defined and justified. We then review previous detections (and add some new data) to build the data required for analysis and then statistically analyse the results. We follow this with an extensive discussion.

2 The sample of Local Universe supernovae

The observational data for this paper are compiled from many sources in the recent literature but the sample selection requires some justification and explanation if the later comparisons and discussions of physical parameters are to be meaningful. We have selected SNe for inclusion based on the following selection criteria, and we justify the choice of criteria where appropriate.

2.1 Definition and selection

We consider all core collapse SNe discovered in the ten year period between 1998 January 1 and 2008 June 30. The earlier date was chosen as the sensible start point for the concerted efforts to find SNe in archive pre-discovery images due to the fact that the local SN discovery rate had reached a significant level (van den Bergh et al., 2005), and we estimate the amount of imaging of nearby galaxies in the Hubble Space Telescope (HST) archive had become rich enough that coincidences were likely to occur. This was also the effective date of the start of concerted efforts to search for SN progenitors. Since the late 1990’s our group (Smartt et al., 2001, 2002), and others (e.g. Van Dyk et al., 2003a; Gal-Yam et al., 2005) have been systematically searching for pre-explosion images of core-collapse SNe in nearby galaxies. We have further restricted our sample to galaxies with recessional velocities less than 2000 , effectively restricting us to a volume limited sample. The recessional velocities, corrected for the infall of the Local Group towards Virgo cluster, of all nearby galaxies hosting SNe were taken from the HyperLEDA3 (Paturel et al., 2003) database. We emphasise that we have used the corrected velocities to apply the selection criterion of 2000 and assuming , this local volume has a limit of 28 Mpc.

During this period, and in this volume, there have been 138 SNe candidates discovered and all are listed in the Asiago4, CfA5 and Sternberg Astronomical Institute 6 catalogues. Of course these are simply compilations of discoveries reported in the International Astronomical Union (IAU) Circulars and these catalogues normally list the discovery magnitudes and types reported in the first IAU announcement. It often happens that the SN classification is revised or refined with subsequent higher quality spectra, or longer monitoring. Both can reveal peculiarities and transformations, or simply give a more secure classification. In particular the sub-classification of II-P can be added when significant light curve information is gathered. Hence we have carefully checked the classification of each event, and have gone further and classified those supernovae listed as “II” into the subtypes II-P and II-L or IIn where possible. This was done using the following criteria in order. Firstly the refereed literature was searched and a classification taken from published photometric and spectroscopic results. Secondly unpublished, professional spectra and lightcurves where taken from reliable sources such as those of the Carnegie Supernova Project (Hamuy et al., 2006) and the Asiago data archive (Turatto, 2000). Thirdly amateur lightcurves available on the web were checked and, if possible, a II-P classification was made if a clear and unambiguous plateau lasting longer than 30 days was recorded. The vast majority of II-P SNe have plateau phases lasting significantly longer than 30 days, in fact most are around 90-110 days (Pastorello, 2003; Hamuy, 2003; Pastorello et al., 2004) and there is no clear evidence that plateaus of shorter duration are particularly common. However to observe such a long plateau necessarily means the SN must have been discovered close to explosion. This is often not the case, and we have chosen to take 30 days simply as an indicator that an extended plateau phase is evident. In all cases of our subclassifications of type II SNe, we believe the designations not to be controversial or ambiguous and for only 9 events classed as type II were we unable to assign a subtype. In these cases the supernovae were generally discovered late in the nebular phase. It is often difficult to distinguish Ib and Ic SNe from single spectra taken at an unknown epoch, and indeed there are 6 events for which authors have listed Ib/c classifications and we cannot improve on these classifications. All of the individual SNe are listed in Table 3. There are only two SNe which have not had a classification spectrum reported in the literature, 1998cf and 1999gs and these are ignored in the following frequency comparison.

We realise that the classifications into the standard bins is somewhat simplistic. In particular there are some SNe that show evidence of interaction with the circumstellar medium, which result in narrow lines (usually of H or He) superimposed on the spectrum. When narrow lines of H dominate the spectrum then the IIn designation is often used by the community, but some II-P and Ibc SNe do show evidence of this behaviour at a weaker level. The most striking example recently is that of the SN2006jc-like objects and the two examples in our sample are 2006jc and 2002ao (see Pastorello et al., 2007; Foley et al., 2007; Pastorello et al., 2008). These show broad lined spectra resembling type Ic SNe (in that they do not exhibit H or He in the high velocity ejecta), but have strong and narrow He emission lines and weak H emission. This has led Pastorello et al. (2008) to term this class of objects Ibn. However rather than introducing this small and very specific class of events, we will class them as Ic SNe as this is a fair description of the underlying spectrum of the SN ejecta. Giving them a simple Ib label could be argued as being misleading in that they do not exhibit the broad, He absorption typical of this class of H-deficient events. The label Ibn is certainly a valid type for them but in this paper it is too specific to be a useful addition to the compiled subtypes. We will discuss these objects further in the second paper in this series which concerns the stripped events (Crockett et al. in prep.).

2.2 The relative frequencies of core-collapse SNe

In Table 1 we list the relative frequency of each subtype occurring in our sample. This is a volume limited relative frequency rate of SN types. There may well have been undiscovered local SNe in this period e.g. dust extinguished events, or events which exploded in solar conjunction which were missed at late times. The distance limit imposed (=32.3) and the range in the absolute magnitudes of each subtype (Richardson et al., 2002) would initially suggest that it is unlikely that there is a serious bias in the relative number of the different subtypes. However there are two arguments which can be put forward against this. The first is if there is a substantial number of intrinsically faint SNe that may have gone undetected if they have typical magnitudes below about . The nature of the faint optical transient in M85 (Kulkarni et al., 2007; Ofek et al., 2008) is currently debated, and could conceivably be a core-collapse SN (Pastorello et al., 2007, see Sect. 2.4). If a large number of intrinsically very faint SNe are evading discovery by current pointed surveys it could lead to a dramatic change in our understanding of the link between progenitor star and SN explosion. Secondly there is an issue with the lack of type Ia SNe discovered recently within 10 Mpc. In the 10.5 yr considered there are about 13 core-collapse that have been discovered within 10 Mpc (the exact number depends on some individual galaxy distance estimates and how strictly one enforces the distance limit; for a more in depth discussion see Kistler et al., 2008). But there have been no type Ia SNe discovered and with a relative frequency of 27%, one might have expected to have seen 3-4 SNe. The Poisson probability of this being a statistical fluctuation is not zero, but is small (2-5%) and one could invoke the argument that there are more core-collapse SNe (perhaps of the fainter type II) beyond 10 Mpc which are being missed and hence the relative rate of CCSNe/Ia is intrinsically much higher than we currently believe (also see Thompson et al., 2008).

van den Bergh et al. (2005) have presented a homogeneous sample of 604 recent SNe discovered (or recovered) by the Lick Observatory Supernova Search (LOSS) with the KAIT telescope (Filippenko et al., 2001). The galaxy search sample spans a much larger volume ( ) than we are considering and a significant majority of our sample in the overlapping time frames (85 per cent of the core collapse events between 1999-2004) are listed in the van den Bergh et al. summary of the LOSS survey. The ones which are not are predominantly more southern than . Hence our sample is very similar to that which would be obtained if one selected a distance and time limited sample from the discovered and recovered events of van den Bergh et al. (2005). The relative number of type Ia SNe in the full LOSS catalogue is significantly higher than within our smaller volume (44 per cent compared to 27 per cent that we find here). This is very likely due to type II-P SNe going undetected at the largest distances. At , with a moderate amount of foreground reddening at least half of the II-P distribution of Richardson et al. (2002) would be missed at the limiting magnitude of 19 of the KAIT survey. The type Ib/c SNe appear slightly more abundant in our local sample (29 per cent of all core-collapse) compared to the van den Bergh et al. (2005) frequency (25 per cent), although the difference is not significantly greater than the expected Poisson scatter.

Relative Core-Collapse only
Type No. / per cent / per cent
II-P 54 39.1 58.7
II-L 2.5 1.8 2.7
IIn 3.5 2.5 3.8
IIb 5 3.6 5.4
Ib 9 6.5 9.8
Ic 18 13.0 19.6
Ia 37 26.8
LBVs 7 5.1
Unclassified 2 1.4
Total 138 100 100
Total CCSNe 92 66 100
Table 1: The relative frequency of SNe types discovered between 1998-2008 (10.5 yrs) in galaxies with recessional velocities less than 2000 kms, and type taken from Table 3. The relative frequency of all types and the relative frequency of only core-collapse SNe are listed separately.

The 9 SNe which were classed as type II (and could not be further sub-classified) can be split proportionally over the type II subtypes, which assumes that that there was no particular bias underlying their poor observational coverage. As they were all discovered late in the nebular phase, this is likely to hold. We put 8 in the II-P bin, and split the other 1 equally between the IIn and II-L, as they have equal numbers of confirmed types; hence the fraction which appears in table 1. In a similar manner the 6 Ib/c SNe are split proportionately into the Ib and Ic bins based on the measured ratio of Ib:Ic = 7:14 (which comes from those events where a Ib or Ic classification seems secure). We did not include the 2 unclassified SNe in any of the rate estimates. Seven of the events originally announced as SNe in Table 3 have been shown to actually be outbursts of luminous blue variables (LBVs) similar to those seen historically in Local Group LBVs such as -Carinae and P-Cygni. These are 1999bw (Filippenko et al., 1999), 2000ch (Wagner et al., 2004), 2001ac (Matheson & Calkins, 2001), 2002kg or NGC2403-V37 (Weis & Bomans, 2005; Maund et al., 2006; Van Dyk et al., 2006), 2003gm (Maund et al., 2006), 2006fp (Blondin et al., 2006), 2007sv (Harutyunyan et al., 2007). Hence we remove these from the rates of CCSNe since they are not true SN explosions. Table 1 lists the relative frequencies of core-collapse SNe. It is clear that the types II-L and IIn are intrinsically quite rare and the majority of core-collapse events are SNe II-P. Such a breakdown of subtypes has been suggested before (Li et al., 2007; Cappellaro et al., 1999) although this is the first time quantitative volume limited statistics have been compiled and presented. The preliminary analysis by Li et al. (2007) of 68 LOSS only discovered events (within 30Mpc) in 9 years suggests 68:26:2:4 per cent breakdown between II:Ib/c:IIb:IIn. Perhaps the ratio of most interest is the Ibc/II ratio which has been used by previous studies to try to place constraints on progenitor populations (Prieto et al., 2008; Prantzos & Boissier, 2003; Eldridge, 2007). These three studies have estimated the ratio as a function of metallicity finding that, at approximately solar metallicity (Z), the ratio is (Poissonian uncertainty) and this goes down to around 0.1 at 0.3Z (although with fairly small numbers in each metallicity bin). The ratios at approximately Z are fairly similar to what we find () and as discussed below in Sect.4 and Sect.5 our SN population is likely drawn from metallicities in the range 0.5-1.0Z due to the fact that nearby, high starformation rate galaxies are those that are most frequently monitored for SNe. A full analysis of the chemical composition of the sites of the SNe in this volume limited sample would be desirable. We will discuss the SN rates more in Sect. 8.2.

The absolute rates of the different types in the standard supernova units (1SNu = 1 SN(100yr)(10)) is much more difficult to assess given that detailed knowledge of the sampling frequency for each galaxy and search strategy is required (see Cappellaro et al., 1999). The LOSS team will address this (Leaman et al., 2004) and will provide the best estimate of the local rates so far. While we cannot derive the SN rate in standard units, the numbers in Table 1 serve as a good guide to the relative numbers of SNe expected in future surveys, when used in conjunction with absolute magnitude distributions (assuming the local galaxy population is cosmically representative). If bias factors affecting the relative rate of discovery of the different types are minor, then these rates are a direct consequence of the initial mass function combined with stellar evolution which is dependent on mass, metallicity, duplicity and initial rotation rate. The numbers of SNe we have tabulated give a lower limit on the number of types per Gpcyr, which is at least a useful comparison to higher redshift estimates and also when considering the rates of Gamma-Ray Bursts (GRBs) and X-ray Flashes (XRFs). The volume enclosed by the 28 Mpc limit is  Gpc; hence the local rate of CCSN explosions is likely to be  Gpcyr and the local Ibc SN rate is  Gpcyr. The latter is in reasonable agreement with the  Gpcyr put forward by Guetta & Della Valle (2007), based on the Cappellaro et al. (1999) rates and local galaxy luminosity functions.

One further point to bear in mind when considering the relative rates is the likely number of local SNe which are not discovered because they are in faint hosts which are not monitored. The Sloan Digital Sky Survey Data Release 5 (5713 sq degrees) contains about 2200 faint galaxies with and with recessional velocities less than 2000. Hence over the full 40,000 square degrees of sky, there are about 15,000 of these faint hosts within about 28 Mpc. These are generally not monitored by the LOSS and the amateur efforts, who typically target the most luminous 10,000 galaxies within about 100-140 Mpc. Young et al. (2008) estimate that such galaxies (with metallicities corresponding roughly to oxygen abundance dex) would contribute about 5-20% of the total star formation locally. Hence at least this fraction of core-collapse SNe are missing from the local samples and all of them are within faint hosts and low metallicity progenitors. This could mean that very bright events like SNe 2005ap, 2006tf and 2008es (Quimby et al., 2007; Smith et al., 2008a; Gezari et al., 2009; Miller et al., 2009) found in blank-field searches (and faint hosts) could be missed. Although the true rate of such events appears to be quite small and likely less than 1% (Miller et al., 2009). Discovery of these events locally should be possible with future all-sky surveys such as Pan-STARRS and LSST (for an estimate of rates see Young et al., 2008).

Of the 100 core-collapse SNe and LBV classified outbursts, the host galaxies of 46 of them were imaged by HST with either the Wide-Field-Planetary-Camera 2 (WFPC2) or Advanced Camera for Surveys (ACS) before explosion. However given the small field of view of both of these cameras (2.6 and 3 respectively) the site of the SNe did not always fall on the field-of-view (FOV) of the cameras. Of these 46, only 26 had images of the SN site in the camera FOV, an overall hit rate of 26 per cent. A column is included in Table 3 which specifies whether or not the galaxy was observed by HST before explosion and if the SN falls on one of the camera FOVs. A further 6 have had high quality ground-based images of the SN site taken before explosion and they are also included in this compilation. The observational sample for this paper, and its companion studying the stripped events (Crockett et al. 2008, in prep.) is thus all of the core-collapse SNe which fulfill the above criteria and have good quality pre-explosion imagery. We have confirmed that there are no other SNe in Table 3 with HST pre-discovery images. We cannot make the same definitive statement about ground-based images given the amount of inhomogeneous imaging data around. But our manual searching of all well maintained large telescope archives suggests it is highly unlikely that further high quality images of any of these events will surface i.e. images with sub-arcsec resolution with the depth to detect a large fraction of the galaxy’s massive stellar population. As such we have a well defined sample in terms of distance and time. The rest of this paper focuses on the progenitor properties of the 20 type II SNe listed in Table 2, of which 18 are confirmed II-P and two are of uncertain subtype (1999an and 2003ie). The other twelve supernovae which are likely to have had stripped progenitors: 2000ds (Ib), 2000ew (Ic), 2001B (Ib), 2001ci (Ic), 2002ap (Ic), 2003jg (Ib/c), 2004gt (Ib/c), 2005ae (IIb), 2005V (Ibc), 2005cz (Ib), 2007gr (Ic), 2008ax (IIb), will be discussed in a companion analysis paper (Crockett et al. in prep.).

2.3 The relative frequencies of SN1987A-like events

In this volume limited sample, there is only one SN which has been conclusively shown to be similar to SN1987A, that is SN1998A (Pastorello et al., 2005). SN1987A had a peculiar lightcurve and distinctly strong Ba ii lines (probably a temperature effect) and an asymmetric H profile during its first 40 days of evolution and the community would have been very unlikely to miss such events as they would have created great interest. There is one other relatively nearby event that has a SN1987A-like appearance, which is 2000cb (Hamuy, 2001) in IC1158. This one however has a , which puts it just beyond our selection criteria. We shall see in Sect.5.9 that Harutyunyan et al. (2008) suggest that a single spectrum of SN2003ie shows similarities to 1987A but it is not well studied enough to be definitive. Hence even if we would include 2000cb and 2003ie in our sample we can certainly say that 1987A events are intrinsically rare and probably less than around 3% of all core-collapse events.

2.4 SN2008S and the M85 and NGC300 optical transients

Recently three optical transients have been reported whose nature is still ambiguous and intensely debated. The optical transient in M85 reported by Kulkarni et al. (2007) was suggested by the authors to be a “luminous red nova” which most likely arose from a stellar merger. However this view was challenged by Pastorello et al. (2007) who suggested a CCSN origin could not be ruled out. Since then two other optical transients of similar absolute magnitude have been discovered. One has been termed a supernova (SN2008S; Stanishev et al., 2008) although Smith et al. (2008) suggest it could be a supernova imposter and the outburst of a moderately massive star rather than a core-collapse. The other, in NGC300 (Bond et al., 2009; Berger et al., 2009), has not yet received an official supernova designation, hence we refer to it as NGC300 OT2008-1 (as in Berger et al., 2009) SN2008S has already been subject to a study of its pre-explosion environment and a detection of a source in Spitzer mid-IR images has been suggested to be a dust enshrouded red supergiant which is visually obscured (Prieto et al., 2008). A similar dust dominated object has been found to be coincident with the optical transient NGC300 OT2008-1 (Thompson et al., 2008; Bond et al., 2009). Thompson et al. (2008) suggested that all three could be the similar explosion of massive stars embedded in optically thick dust shells. The early studies of the evolution of SN2008S, NGC300 OT2008-1 and their comparisons with M85OT2006-1 and other erupting systems have so far not favoured a core-collapse supernova explanation for the physical source of the outburst (Smith et al., 2008; Bond et al., 2009; Berger et al., 2009) The transients lack broad lines from high velocity ejecta; their spectra are very slowly evolving and dominated by narrow H-emission. Strangely they also don’t appear to be similar to the V838 Mon variable system or M31 luminous red variable as initially suggested by both Kulkarni et al. (2007) and Bond et al. (2008). Based on the mid-IR progenitor detections, Thompson et al. (2008) argue that the precursors may have been going through a short evolutionary phase which ends in a weak, electron-capture supernova. A full multi-wavelength study of the evolution of SN2008S from early to late times, and comparisons with the other two suggest there is some evidence for the supernova explanation (Botticella et al., in prep.; Kotak et al. in prep). All these studies reveal that the three objects are incredibly similar in their properties. As their nature is ambiguous and currently debatable, we will not consider them further in this paper. It is certain, however, that they are not normally type II-P SNe.

3 The stellar evolutionary models

As discussed above, observational and theoretical studies both now strongly suggest that the progenitors of type II-P are typically red supergiants. To estimate an initial mass for observed red supergiant progenitors we require stellar models to obtain a theoretical initial mass to final luminosity relation, as shown in Figure 1. The stellar models we use were produced with the Cambridge stellar evolution code, STARS, originally developed by Eggleton (1971) and updated most recently by Pols et al. (1995) and Eldridge & Tout (2004a). Further details can be found at the code’s web pages7. The models are available from the same location for download without restriction. The models are the same as those described in Eldridge & Tout (2004a) but here we use every integer initial mass from to and integer steps of 5-10M above.

As will be discussed in Sect. 4, we can estimate the metallicity of the exploding star from the nebular abundances in the disks of the host galaxies, hence we have calculated stellar evolutionary models for three metallicities; solar, LMC and SMC where we assume mass fractions of Z=0.02, 0.008 and 0.004 respectively. All the models employ our standard mass-loss prescription for hydrogen-rich stars (Eldridge & Tout, 2004b): we use the rates of de Jager et al. (1988) except for OB stars, for which we use the theoretical rates of Vink et al. (2001).

In Figure 1 we plot the range of luminosity for a star from the end of core helium burning to the model end point at the beginning of core neon burning (for a solar metallicity model). The beginning of core neon burning is only a few years before core-collapse and this point is likely to be an accurate estimate of the pre-SN luminosity. The estimate of final mass from the observational limits will depend on uncertainties in these stellar models, which is a systematic that is difficult to constrain. To allow for this we assume that the range of reasonable luminosities for progenitor stars is somewhere between the end of core helium burning (dashed line in Fig. 1a) to the model end point at the beginning of core neon burning (solid line in Fig. 1a). For the lower mass stars that undergo the process known as second dredge-up to become AGB stars, we also consider the luminosity before second dredge-up occurs. After second dredge-up the models have much higher bolometric luminosities but their observable characteristics are quite different to red supergiants (Eldridge et al., 2007). We have previously shown that in the case of SN2005cs the progenitor could not have been a super-AGB star in the 5-8M range. Hence we assume throughout this paper that such stars are not the progenitors of the SNe discussed, and their positions in Fig. 1 are shown for completeness. A full discussion of this is given in (Eldridge et al., 2007). In Fig. 1b we show the final luminosity ranges for the three metallicities, and the most appropriate metallicity for each SNe is used when the initial masses are calculated in Sect. 5.

In Sect. 5, when we estimate a progenitor initial mass from Figure 1, we will assume that the models are reliable enough to predict correctly that SNe will undergo core-collapse after helium burning, so we use the full range of luminosities between the start of helium burning and the model endpoints in a conservative way. The mass estimate should be reasonable for all cases where the progenitor is a red supergiant.

Figure 1: (a): The initial mass compared with the final luminosity of the stellar models for . Each mass has the luminosity range corresponding to the end of He-burning and the end of the model, just before core-collapse (these are the thin grey vertical lines). From a limit of luminosity an upper limit to the initial mass can be determined. The solid line is the luminosity of the model end-point, the dashed line the luminosity at the end of core helium burning and the dash-dotted line is the luminosity after second dredge-up when the lower mass stars become AGB stars. (b): The same as (a) but with three metallicities shown for comparison, and with the vertical joining bars omitted for clarity. This illustrates that the choice of metallicity for the tracks is not critical, but we do use the most appropriate track to remove any systematic error.

4 Metallicities of the progenitor stars

As the stellar evolutionary tracks do differ slightly, to make sure that there are no underlying systematics in our analysis we require an estimate of the initial metallicity of the exploding star. There is good observational evidence now to show that mass-loss from massive stars is metallicity dependent, and that the the lifetimes of stars in various phases as they evolve depend on metallicity (e.g. Massey, 2003; Mokiem et al., 2007). Models predict that mass-loss and metallicity are driving forces behind stellar evolution (Heger et al., 2003; Meynet & Maeder, 2003; Eldridge & Tout, 2004b).

The most reliable determination of the metallicity of the progenitor star would be a measurement of the interstellar medium abundance in the galactic disk at the position of the event. In some cases the SNe have exploded in, or very close to, a previous catalogued H ii region which has published spectroscopy and emission line fluxes. For these events we use these fluxes and calculate the nebular abundance of oxygen, using the strong-line method of the ratio of the [O II]  3727 plus [O III]  4959,5007 to H  (see Bresolin, 2006, for a discussion). Recently there has been much debate in the literature over which calibration to use to determine the nebular oxygen abundances from this method. Bresolin (2006) has shown that the calibration of Pilyugin & Thuan (2005) best matches the abundances determined in nearby galaxies where it is possible to measure the strength of the electron temperature sensitive lines and hence determine a simple empirical calibrations for the strong-line method. The result is that the empirical determinations of Bresolin et al. (2004) and the calibrations of Pilyugin & Thuan (2005) and Pettini & Pagel (2004) give significantly lower abundances (by a factor 0.3-0.4 dex) than photoionisation models (of Kewley & Dopita, 2002, for example). Trundle et al. (2002) have shown that photospheric abundances of massive stars in M31 (B-type supergiants) are in much better agreement with the “lower” metallicity scales of the method employed by Pilyugin & Thuan (2005), and the empirical determinations form auroral lines. The recent downwards revision of the solar oxygen abundance to (Asplund et al., 2004; Asplund et al., 2005) and the agreement with all the other estimators of the Milky Way’s ISM abundance at the solar radius (B-stars, young F& G stars, H ii regions, diffuse ISM) would also suggest that our adopted, lower, scale is appropriate (Simón-Díaz et al., 2006; Daflon et al., 2004; Sofia & Meyer, 2001). Hence in this paper we will favour the calibrations of Bresolin et al. (2004) and Pilyugin & Thuan (2005) to determine nebular abundances.

Modjaz et al. (2008) have investigated the metallicities at the sites of type Ic SNe and GRB related SNe and show the importance of comparing abundances derived by self-consistent methods. By employing consistent abundance indicators they find that GRB related SNe tend to have significantly lower metallicities within their host galaxy environments than broad lined type Ic SNe without GRBs. Their study illustrates the need to adopt consistent methods and compare abundances differentially.

We chose which stellar tracks to estimate the initial masses as follows. We use the observed present day oxygen abundances as compiled by Hunter et al. (2007) for the Sun, LMC and SMC (8.65, 8.35, 8.05) to guide our choice of model. For those SNe which have estimated ISM oxygen abundances of we choose to use the metallicity tracks (solar). For those in the range we use the tracks (LMC). We would have used the tracks for anything below (SMC), but none of our targets have such low metallicity.

Supernova SN Galaxy Galaxy Distance [O/H] ZAMS
Type Class Mpc Method (kpc) (dex) (dex) (M)
1999an II IC 755 SBb 18.5 1.5 TF 0.40 0.19 4.7 0.82 8.3
1999br II-P NGC 4900 SBc 14.1 2.6 Kin. 0.06 0.06 3.1 0.69 8.4
1999em II-P NGC 1637 SBc 11.7 1.0 Cep. 0.31 0.16 1.6 0.28 8.6
1999ev II-P NGC 4274 SBab 15.1 2.6 Kin. 0.47 0.16 5.3 0.46 8.5 16
1999gi II-P NGC 3184 SABc 10.00.8 Mean 0.65 0.16 3.1 0.30 8.6
2001du II-P NGC 1365 SBb 18.3 1.2 Cep. 0.53 0.28 14.7 0.53 8.5
2002hh II-P NGC 6946 SABc Mean 5.2 0.2 4.1 0.45 8.5
2003gd II-P NGC 628 Sc 9.3 1.8 Mean 0.43 0.19 7.5 0.58 8.4
2003ie II? NGC 4051 SABb 15.5 1.2 TF 0.04 7.3 0.66 8.4
2004A II-P NGC 6207 Sc 20.3 3.4 Mean 0.19 0.09 6.7 0.79 8.3
2004am II-P NGC 3034 Sd Cep. 3.7 2.0 0.64 0.14 8.7 Cluster
2004dg II-P NGC 5806 SBb Kin. 0.74 0.09 4.3 0.50 8.5
2004dj II-P NGC 2403 SABc Cep. 0.53 0.06 3.5 0.37 8.4 Cluster
2004et II-P NGC 6946 SABc Mean 1.3 0.2 8.4 0.92 8.3
2005cs II-P NGC 5194 Sbc PNLF 0.43 0.06 2.7 0.22 8.7
2006bc II-P NGC 2397 SBb Kin. 0.64 1.4 0.30 8.5
2006my II-P NGC 4651 Sc TF 0.08 4.4 0.37 8.7
2006ov II-P NGC 4303 SBbc TF 0.07 2.3 0.26 8.9
2007aa II-P NGC 4030 Sbc Kin. 0.09 10.3 0.91 8.4
2008bk II-P NGC 7793 Scd TRGB 1.0 0.5 3.9 0.66 8.4

Table 2: The results of the homogeneous reanalysis of the all the SN progenitors. The galaxies, their class, distance and extinction along the line of sight to the SNe are listed. The methods employed in the literature to determine distances are listed (TF = Tully Fisher; Kin. = Kinematic; Cep. = Cepheid; PNLF = Planetary Nebulae Luminosity Function; TRGB = Tip of the Red Giant Branch; Mean = mean of several methods which are detailed in Section 5). Kinematic distances are based on . The de-projected galactocentric radii are calculated as well as the radius with respect to the value (the radius at which the surface brightness drops to 25 mag arcsec). Oxygen abundances of the galactic ISM at the positions of the SNe are quoted (). The final estimated luminosities, or luminosity limits are in solar luminosity units. The zero-age main-sequence (ZAMS) masses and upper mass limits as discussed in Sect.5 are listed in the final column.

5 The masses of the progenitors of Type II-P supernovae

We expect that the progenitors of various subtypes of type II SNe are hydrogen rich stars which have evolved from main-sequence stars of an approximate initial mass of 8M and above. If objects are detected in pre-explosion images then their colours and luminosities can be determined. If there is no star detected at the SN positions then the sensitivity of the images can be used to determine an upper luminosity limit and hence upper mass limit (see for example Smartt et al., 2003; Van Dyk et al., 2003c; Maund & Smartt, 2005). In the papers presenting the original results, slightly different methods of determining the luminosity and mass limits from the prediscovery images have been adopted. A mixture of 3 and 5 limits have been quoted, uncertainties treated in varying manners, different stellar evolutionary models adopted and distances used which were not always the most recent and most accurate. In order to compare the sample as a whole, this calls for some homogenisation, and we adopt the following method.

In the cases where there is no detection of a progenitor (13 in total) we determine the upper luminosity limit corresponding to the 84 per cent confidence limit. First we take the 3 detection limit for each pre-explosion image, where this is the detection magnitude in the filter system employed. To convert this to a bolometric luminosity one requires a measurement of extinction, distance and bolometric correction (with respect to the filter employed) for the progenitor. The 1 uncertainties of these quantities are combined in quadrature to give a total 1 uncertainty on the upper limit. If one assumes that the progenitor star was a red supergiant just prior to explosion then the bolometric and colour corrections for an M0 supergiant (Drilling & Landolt, 2000) are appropriate. This assumption seems well justified as nearly all the SNe in our sample have been shown to type II-P, which require extended atmospheres physically similar to red supergiants (Arnett, 1980; Chevalier, 1976). Recent detections of the UV shock breakout from two type II-P SNe determined the radii of the progenitor stars which adds further weight to the idea of the progenitors being red supergiants (Schawinski et al., 2008; Gezari et al., 2008). The uncertainty in the bolometric correction is taken to be corresponding to the 1 range of values for red supergiants between late-K and late M-type supergiants (Levesque et al., 2005). Assuming that the uncertainties are representative of a normal distribution of measurements, the 84 per cent confidence limit for the upper luminosity limit is 1 above the best estimate i.e. there is an 84 per cent chance that the progenitor stars have luminosities below this value given the individual uncertainties in the calculation. The 1 distance and extinction errors are taken from the quoted sources as listed in the notes on the individual events below. These 84 per cent upper luminosity limits are then plotted on the final mass-luminosity plot discussed in Section 3. We determine the upper mass limit to be the maximum mass of a star which does not have part of its post-He burning track within the 84 per cent luminosity limit.

This method is equivalent to that previously employed by Smartt et al. (2003, 2002) and Maund & Smartt (2005) (for example) which an exclusion region of the HR diagram was determined as a function of effective temperature and an upper mass limit from the red supergiant region was determined. If an -band (or -band like) filter is employed both methods have the advantage of being fairly insensitive to the effective temperature of the assumed red supergiant progenitor as the peak of the stellar SED at this temperature range is 8300Å(e.g see Figs. 5 and 6 of Smartt et al., 2003). In all cases we have revised the distances to the galaxies to the most reliable, in our opinion, and most recent in the literature. Where no other distance is available we have calculated a kinematic distance estimate using the host galaxy radial velocity corrected for the local group infall into Virgo ( from the LEDA8 galaxy catalogue) and a value of the Hubble constant of . In such cases we employ an uncertainty of the local cosmic thermal velocity 187(Tonry et al., 2000), equivalent to Mpc. If the value of adopted were either 65 or 85 Mpc, the systematic effect on the distance scale would provide systematic luminosity differences of  dex and  dex for the five SNe which have kinematic host galaxy distances (1999br, 1999ev, 2004dg, 2006bc, 2007aa). We will discuss the effects of this systematic difference in Sect. 7. When determining the extinction in each wavelength band, we use the law of Cardelli et al. (1989).

In the cases where we have a direct detection of the progenitor (4 in total) the uncertainties in the luminosity are trivially determined and discussions of the individual events are listed below.

Two others (2004dj and 2004am) fall on bright, compact star clusters which are not resolved into individual stars (Maíz-Apellániz et al., 2004; Wang et al., 2005; Vinko et al., 2008, Mattila et al. 2008, in prep). These papers have determined the total cluster mass and age and hence the turn off mass at the top of the main-sequence. From this the mass of the progenitor has been determined. Hence the stellar mass determination is somewhat indirect and relies on the assumption that the timescale of star formation in the cluster is significantly less than the current estimated age. The results are based on population synthesis codes which use different individual stellar evolutionary codes as input to those we have employed. The Maíz-Apellániz et al. (2004); Vinko et al. (2008) results are based on the stellar synthesis codes which uses the Geneva models (e.g. Schaller et al., 1992) as input, and the discussion in Section 6.1 indicates that the choice of stellar model does not introduce significant uncertainties. Hence although the analysis method, and hence mass determination, is different for these two events, we believe the mass estimates are worth including in this compilation. If they are left out, the main conclusions of this paper are not altered in any significant way.

5.1 1999an

IC755 is an SBb spiral with (from LEDA). As no direct abundance study of this galaxy has been done, we attempt to infer a probable abundance at the position of the progenitor from the relation of Pilyugin et al. (2004). For galaxies between , the characteristic oxygen abundance (the oxygen abundance at a galactocentric distance of ) is typically in the range  dex. The mean abundance gradient of this sample is  dex/. Hence at a de-projected distance of 0.8, the metallicity of the progenitor star of SN1999an can be approximated at 8.3 dex. This is somewhat uncertain given the large uncertainties on the gradient and the range of characteristic abundances and the error is likely to be 0.3 dex. However it is the best estimate that can be derived with the current data in the literature.

There is no detection of a progenitor star in the WFPC2 pre-explosion images presented by Maund & Smartt (2005) and Van Dyk et al. (2003a). Both studies calculated similar sensitivity limits for the images, and we adopt the 3 limit of Maund & Smartt (2005) of . Solanes et al. (2002) report a mean distance modulus for the host galaxy IC755 of or . Applying a line of sight extinction of (Maund & Smartt, 2005) and assuming an M-type supergiant as the progenitor (for the colour correction between and Johnson ; see Maund & Smartt 2005) results in absolute upper limit of . For an M0 supergiant this corresponds to an upper luminosity limit of , and an 84 per cent confidence limit of . From Fig. 1 this implies an upper mass limit of 18M.

5.2 1999br

NGC4900 is an SBc spiral, and similar to the case of IC755 discussed above it does not have a published abundance study. The same arguments as in Section 5.1 can be used (NGC4900 has ) to infer an oxygen abundance at the galactocentric radius of SN1999br () of approximately 8.4 dex.

With no detection of a progenitor object at the SN position, Maund & Smartt (2005) place an upper limit on the magnitude of any progenitor of . This is significantly brighter than that of Van Dyk et al. (2003a) , and we adopt the former as the more conservative result. For the host galaxy (NGC4900) only a kinematic distance modulus is available, with the Virgo infall corrected velocity giving Mpc. The extinction to this event appears very low (Maund & Smartt, 2005; Van Dyk et al., 2003a; Pastorello et al., 2004) and we adopt the foreground value quoted in these papers of . As for SN1999an, we assume that the progenitor was a red supergiant and apply a colour correction and bolometric correction to determine an upper luminosity limit of and an 84 per cent confidence limit of . From Fig.1 this implies an upper mass limit of 15M.

5.3 1999em

van Zee et al. (1998) have published line strength measurements and abundances for 15 H ii regions in NGC1637. Using the calibration of Bresolin et al. (2004) we have redetermined the abundance gradient and at the galactocentric distance of SN1999em, the metallicity is  dex. The nearest H ii regions to 1999em are 510 pc and 794 pc, when de-projected, from the site of SN1999em and have oxygen abundances of 8.5 and 8.7 dex respectively. Hence we adopt  dex.

The updated distance to NGC1637 of  Mpc is taken from the Cepheid variable star estimate of Leonard et al. (2003) and the reddening value of is adopted from Baron et al. (2000). Smartt et al. (2002) present deep ground based images of NGC1637 before explosion in filters and from these results we have determined a upper limit of . The -band is the most sensitive to red supergiant progenitors and between the supergiant spectral types of K2-M4 this corresponds to an upper luminosity limit of , and an 84 per cent confidence limit of . From Fig.1 this implies an upper mass limit of 15M.

5.4 1999ev

NGC4274 is an SBab spiral, and also has no abundance study of its H ii regions. The same arguments as in Section 5.1 can be used (NGC4274 has ) to infer an oxygen abundance at the galactocentric radius of SN1999ev () of approximately 8.5 dex.

SN1999ev was recovered in late, deep HST ACS images by Maund & Smartt (2005) and is coincident with a progenitor object found on a pre-explosion WFPC2 F555W image. Although Van Dyk et al. (2003a) originally suggested two other stars as possible progenitors, the HST follow-up clearly ruled this out and points to the object of magnitude , at 4.8 significance (Maund & Smartt, 2005). There is no distance measurement to the galaxy NGC4274 apart from a kinematic estimate, which is  Mpc, from LEDA (Virgo infall corrected). Maund & Smartt (2005) determined the extinction to the nearby stellar population of . We again assume that the progenitor was a red supergiant and apply a BC of to determine a final luminosity of . The tracks in Fig.1 imply the star would have been of mass 16M.

5.5 1999gi

Smartt et al. (2001) suggested that the H ii region number 3 of Zaritsky et al. (1994) at a position of N E is coincident with the star-forming region, or OB association that hosted SN1999gi. The calibration of Bresolin et al. (2004) using the value of Zaritsky et al. (1994) gives an oxygen abundance of 8.6 dex.

A study of the progenitor site of SN1999gi was carried out by Smartt et al. (2001), but the distance to this galaxy was then improved in a compilation study of Leonard et al. (2002) and Hendry (2006). Here we adopt the result in Hendry (2006) which is a mean of four estimates  Mpc, and the extinction of Leonard et al. . The four distance methods detailed in Hendry (2006) are Tully Fisher, expanding photosphere method (EPM), kinematic and the tertiary distance indicators of de Vaucouleurs (1979). The 3 detection limit determined by Smartt et al. (2001) is , which results in an upper luminosity limit for an M-type supergiant of , after the colour and bolometric corrections are applied. This gives an 84 per cent confidence limit of and, from Fig. 1, this implies an upper mass limit of 14M.

5.6 2001du

As discussed in Smartt et al. (2003) the H ii region RW21 (Roy & Walsh, 1997) is from SN2001du, and it is likely the metallicity of this region is representative of the progenitor star composition. The calibration of Bresolin et al. (2004) to the value of Roy & Walsh (1997) gives an oxygen abundance of 8.5 dex.

The host galaxy NGC1367 was observed as part of the HST Cepheid Key Project, hence the most accurate and recent distance estimate is taken from Paturel et al. (2002), . The extinction toward the SN was measured by three different methods by Smartt et al. (2003) to be , giving , which is similar to that adopted () by Van Dyk et al. (2003c). Smartt et al. (2003) and Van Dyk et al. (2003c) presented pre-explosion images in the WFPC2 filters F336W, F555W, F814W and the most sensitive of these to red supergiants is the F814W. We determine the upper limit from the Smartt et al. results to be , similar to the sensitivity of Van Dyk et al. (2003c). Between the supergiant spectral types of K2-M4 this corresponds to an upper luminosity limit of , and an 84 per cent confidence limit of . From Fig.1 this implies an upper mass limit of 15M.

5.7 2002hh

None of the 9 H ii regions in NGC6946 compiled by Pilyugin et al. (2004) are near the location of 2002hh. Hence we use the abundance gradient determined by Pilyugin et al. (2004) and the de-projected galactocentric radius of the SN position to determine the likely metallicity. As discussed above, the calibration of Pilyugin et al. (2004) is similar to the simple linear calibration of Bresolin et al. (2004), hence these should be on a similar scale. We determine an oxygen abundance of 8.5 dex.

A deep pre-explosion -band archive image of NGC6946 from the Isaac Newton Telescope Wide Field Camera (INT-WFC) will be presented in a forthcoming paper (See Sect.5.14). Although this SN suffered significant extinction, the proximity of the galaxy and the depth of the 3600s -band image still places useful restrictions on the progenitor star. The 3600s image is composed of 6600s exposures, with a final image quality of 1. There is no object visible at the position of SN2002hh, and the 5 detection limit for a point source was estimated to be =22.8. This instrumental magnitude can be converted to a standard using the well calibrated colour transformations for the INT-WFC (Irwin & Lewis, 2001) 9. We employ the reddening law determined in Pozzo et al. (2006) to estimate the extinction in the band of . A distance of  Mpc is used which is a mean of the distance values from the compilation of Botticella et al. (2009 in prep.) using the methods of Tully Fisher, brightest supergiants, sosies, PLNF, EMP (applied to 1980K) and standard candle method (SCM) applied to SN2004et. SN2002hh appears to be a normal II-P, but behind a large dust pocket (Pozzo et al., 2006), hence we assume the progenitor was a red supergiant of type between K0-M5. The falling bolometric correction combined with the rising intrinsic between K0-M5 means that the bolometric luminosity limit stays approximately constant in this spectral range at . Hence the 84 per cent confidence limit is and from Fig.1 this implies an upper mass limit of 18M. We note that this is consistent with the progenitor mass of 16-18M estimated by Pozzo et al. (2006) from the [O i] 6300,6364Å doublet.

5.8 2003gd

None of the previously catalogued H ii regions in NGC628 which have spectra and the ratio measured are particularly near the spatial position of SN2003gd. Hence we use the abundance gradient determined by Pilyugin et al. (2004) and the de-projected galactocentric radius of the SN position to determine the metallicity at this position. The parameters derived are Table 2, with an abundance of 8.4 dex derived.

The progenitor star was detected by Smartt et al. (2004) and Van Dyk et al. (2003c), and an extensive compilation of distance measurements to NGC628 and reddening towards the SN was carried out in Hendry et al. (2005). Those distance and extinction values determined were close to those employed in Smartt et al. (2004) to estimate the progenitor luminosity and mass. The Hendry et al. (2005) distance listed in Table 2 is a mean of the three methods : kinematic, brightest supergiants and standard candle method (applied to SN2003gd). The intrinsic colour is consistent with a supergiant in the spectral type range K5-M3, which Smartt et al. (2004) used to determine a luminosity of . In the diagram of Fig.1 the best value of 4.3 is closest to the termination point of the 7M track, if we assume the progenitor did not go through 2nd dredge-up. The uncertainties would bracket the 5M and 13M post-He burning tracks, hence we adopt the value M. Although the most likely value is below the lowest mass that is normally assumed possible to provide an iron core-collapse (8-10M; see Heger et al., 2003; Eldridge & Tout, 2004b), the range of masses comfortably brackets the theoretically predicted limits.

5.9 2003ie

NGC4051 is a Seyfert 1 galaxy of morphological type SABb and has no published abundance study of its H ii regions. Hence we can estimate a probable abundance at the position of the progenitor as in Sect. 5.1. The galaxy has a , using our adopted distance and the corrected band magnitude given in . At this magnitude the the characteristic oxygen abundance (at a galactocentric distance of ) is approximately  dex (Pilyugin et al., 2004) Again using the typical gradient of the galaxy sample (as in Sect. 5.1 of  dex/, the oxygen abundance at 0.66 is approximately 8.4 dex. As stated above this is quite uncertain (0.3 dex) given the lack of detailed study of the galaxy but does show that it is unlikely to be a particularly low metallicity environment. The SN was not studied in great detail by any group (as far as we know), but a single photospheric spectrum shows P-Cygni features of H i (Harutyunyan et al., 2008). The best match for the spectrum found by Harutyunyan et al. (2008) is that of 1998A, which itself appears like a 1987A-type event. Hence this event may not be a normal II-P SN and we have no lightcurve information to consider. As we shall see below, the mass limits for the progenitor are not particularly restrictive and if the object were to be left out the conclusions of the paper would be unchanged.

The pre-explosion site of SN 2003ie was recovered in archive -band observations of NGC4051 taken with the INT-WFC. This image was taken on 1999 November 11, with an exposure time of 900s and image quality of arcsec. We determined the position of SN 2003ie within an error circle of arcsec (using an image of the SN from 2003 provided to us by Martin Mobberley). There is no progenitor object detected within this error circle and we derive a 3 detection limit of . This instrumental magnitude was converted to a standard using the well calibrated colour transformations for the INT-WFC (Irwin & Lewis, 2001), giving . Pierce & Tully (1988) calculate the distance to the Ursa Major Cluster to be Mpc using the Tully-Fisher method and we adopt this distance for NGC4051. We have no measure of the internal extinction towards this SN and simply adopt the Galactic extinction value of (Schlegel et al., 1998). We assume once again that the progenitor is a red supergiant and apply appropriate bolometric and colour corrections to determine a luminosity limit of and an 84 per cent confidence limit of . From Fig. 1 this implies an upper mass limit of 24M.

5.10 2004a

There are no measurements of H ii regions in NGC6207 and we use the arguments presented in Hendry et al. (2006) to estimate the metallicity at the galactocentric distance of SN2004A. This paper based the results on typical abundance gradients measured by Pilyugin et al. (2004) hence again the estimate is on the same scale as the rest of the values. We point out that there is a typographical error in that paper, where is quoted as 4 kpc, whereas it should be 8.6 kpc. However, repeating the same method, this does not change the calculated metallicity at the position of SN2004A which we estimate as 8.3 dex. The Hendry et al. (2006) distance listed in Table 2 is a mean of the three methods : kinematic, brightest supergiants and standard candle method (applied to SN2004A).

A faint object is detected at the position of SN2004A in Hendry et al. (2006), claimed as a 4.7 detection in the F814W filter, and it is not detected in the F435W or F555W. If we assume this detection to be valid, it provides a blue limit for the colour of the progenitor and hence a star in the spectral range G5-M5. This gives a bolometric luminosity in the range . On Fig.1 this implies a best estimate of 7M, and the errors bracket the 5M and 13M post-He burning tracks. Hence we adopt M. If the detection is not valid then the I-band detection sensitivity implies an 84 per cent confidence limit of =4.75 and an upper limit of 13M.

5.11 2004am

There is no extensive published study of SN2004am to date, which is surprising given its proximity and the fact it is the only optically discovered SN in the starburst M82 (NGC3034). However it is clearly a II-P from the unfiltered magnitudes of Singer et al. (2004) which stay constant for 76 days, and the spectrum of Mattila et al. (2004). Alignment of post-explosion near-IR images and HST pre-explosion images shows SN2004am is spatially coincident with the well studied super star cluster M82-L (Mattila et al., in prep). The distance to M82 is assumed to be that of the M81 group, estimated from Cepheids in M81 (NGC3031; Freedman et al., 2001).

A new study of M82-L has recently been carried out by Lançon et al. (2008) who modelled the integrated near infra-red m spectra. They used a population synthesis code (PÉGASE.2) and a new library of red supergiant observational and theoretical spectra to determine the age of M82-L. The fit to the overall SED and the individual molecular absorption features is impressive and gives an age estimate of  Myrs. With a lower than normal value of , Lançon et al. (2008) can also reproduce the optical SED of the cluster down to 6000Å (the value in Table 2 is taken from Lancon et al.). This age is somewhat younger than  Myrs that was first inferred by Smith et al. (2006) using only a limited range optical spectrum and the spectral synthesis code (Leitherer et al., 1999). Lançon et al. (2008) point out that by using a low value of they can reconcile the optical SED and the NIR molecular bands with the younger age and their updated spectral modelling technique and firmly exclude an age of 60 Myr. The cluster age provides quite a strong constraint on the mass of the progenitor star, assuming that the cluster formed coevally and the progenitor’s age is similar to that of the cluster. The STARS models predict that the cluster ages correspond to lifetimes of stars of masses  M. The models used in the population synthesis code of Lançon et al. (2008) were those of Bressan et al. (1993), which give very similar age-mass relationships to the STARS code (the uncertainty on the derived mass due to choice of code is within the error range).

In all of the above we have assumed solar metallicity for the stellar evolutionary tracks is appropriate. The fitting of Lançon et al. (2008) implies that this is appropriate. Also two recent papers have speculated on the abundances in the nuclear regions of M82, in environments close to super star cluster M82-L (Smith et al., 2006; Origlia et al., 2004). There is some uncertainty and difference in the abundances derived but the stellar abundances of red supergiants in these inner regions from Origlia et al. (2004) suggest a solar like oxygen abundance. The photospheric abundance in such objects are likely to be applicable to M82-L and the progenitor of SN2004am. Hence in the age estimations we chose the tracks close to 8.7 dex as the most appropriate.

5.12 2004dg

NGC5806 is an SBb spiral, and also has no abundance study of its H ii regions. The same arguments as in Section 5.1 can be used (NGC5806 has ) to infer an oxygen abundance at the galactocentric radius of SN2004dg () of approximately 8.5 dex.

The pre-explosion site of SN 2004dg was imaged using both WFPC2 (2001 July 5) and ACS (2004 April 3) cameras on-board HST (the SN was discovered on 2004 July 31). The WFPC2 exposure times were 460s in F450W and F814W filters. For the ACS images had total exposure times of 700s in F658N and 120s in F814W. We re-observed SN2004dg on (2005 March 10) with the ACS camera (in F435W, F555W and F814W, as part of GO10187) and recovered the SN at transformed magnitudes of . Alignment of the two sets of images allowed us to locate the position of the SN on the pre-explosion images to within 0.015 arcsec (see Maund et al., 2005; Crockett et al., 2008, for details of alignment procedures) Within this error circle there was no detection of a progenitor star in any of the image and filter combinations. A progenitor star was not detected at the SN position, therefore a 3 detection limit of was determined. There is no distance measurement to the galaxy apart from a kinematic estimate, which is  Mpc, from (Virgo infall corrected). The total reddening towards SN 2004dg was estimated to be , giving . Again we assume a red supergiant progenitor and find a luminosity limit of and an 84 per cent confidence limit of . From Fig. 1 this implies an upper mass limit of 12M.

5.13 2004dj

As discussed in Sect. 5, SN2004dj fell on the compact star cluster identified by Maíz-Apellániz et al. (2004) and Wang et al. (2005) and the analysis used to determine a progenitor mass is different to the direct identification and direct upper luminosity limits for the other SNe presented here. Maíz-Apellániz et al. (2004) determine an age of the compact star cluster of 14 Myrs and hence a main-sequence mass of 15M for the progenitor. Wang et al. (2005) determine an age of around 20 Myrs and hence a main-sequence mass of 12M. A new and improved study by Vinko et al. (2008) using new UV observations of the cluster and extensive comparison of SEDs based on different model atmospheres and evolutionary tracks suggests a most likely turn off mass (and hence progenitor ZAMS mass of between 12-20M. This age (10-16 Myrs) is consistent with the lack of H emission seen in the cluster spectrum of Vinko et al. (2008) and Humphreys & Aaronson (1987), as the ionizing O-stars have died out. Hence we favour the older age and will adopt M as the progenitor mass (if we adopt M as suggested by Vinko et al., 2008, it does not affect any of the results below). The distance to NGC2403 of  Mpc is from the HST Cepheid Key Project (Freedman et al., 2001)

Maíz-Apellániz et al. (2004) adopted solar abundances in using the Geneva tracks of . On closer inspection this may be too high. We used the abundance gradient determined by Pilyugin et al. (2004) and the de-projected galactocentric radius of the SN position to determine the metallicity at this position of 8.4 dex. Although the H ii regions in this galaxy have been studied extensively the only region which is physically close to the position of 2004dj is that of VS44 studied by Garnett et al. (1997), and even that is around 600pc from the cluster that hosted SN2004dj. The ratio provided by Garnett et al. (1997) also gives an abundance of 8.4 dex with the calibration of Bresolin et al. (2004), in good agreement with the abundance gradient measurement. Although our oxygen abundance is below that employed by Maíz-Apellániz et al. (2004), this does not significantly affect the age (and hence turn-off mass) estimate when we compare STARS models of such different metallicities. We note that Vinko et al. (2008) favour a solar metallicity in their SED fits.

5.14 2004et

As discussed for SN2002hh (Sect. 5.7), there is no H ii region near the galactic position of 2004et, which is some way from the centre of NGC6946. We use the same method as for 2002hh to determine a metallicity typical for the galactocentric radius of 2004et of 8.3 dex. The adopted distance to NGC6946 of  Mpc is discussed in Sect.5.7

Li et al. (2005) presented the detection of a candidate progenitor star of SN2004et in ground-based images from the Canada France Hawaii Telescope (CFHT) in both and filters. They suggested it was a yellow supergiant as the colours were matched with a G-type supergiant SED. From these colours and the models of Lejeune & Schaerer (2001), Li et al. (2005) determine a mass in the range M.

However it is now clear that the putative source detected by Li et al. (2005) was not a single star. Adaptive optics images of the site by Crockett et al. (2009) using Gemini North show that the source breaks up into several stars. In addition images taken 3 years after explosion show identical colours to the pre-explosion object, indicating that the progenitor star was not detected in the pre-explosion frame. A deep -band image (the same image as discussed above for SN2002hh) does show a clear detection of a progenitor compared to the late time -band image. Crockett et al. (2009) use the -band detection (after converting to Johnson; ) and limits on the magnitudes to infer that the progenitor was a red supergiant with . This implies an M4 spectral type or later, giving a bolometric magnitude of of and a progenitor luminosity of = 4.590.09. Comparing this to stellar models of LMC metallicity, we estimate its initial mass to be M (as in Crockett et al., 2009).

5.15 2005cs

Maund et al. (2005) have estimated the abundance at the galactocentric radius of SN2005cs in an identical manner as we have employed consistently in this paper, using the NGC5194 abundance gradient of Bresolin et al. (2004), hence it is already on our common calibration scale. They determine  dex, which we adopt in this paper.

The detection of the progenitor of SN2005cs is well documented by Eldridge et al. (2007), Li et al. (2006) and Maund et al. (2005) which all give similar mass estimates in the range 7-10M. Eldridge et al. (2007) have recently re-analysed all of the available photometry from the initial two discovery papers and suggested that the progenitor could not have been a super-AGB star that has gone through 2nd dredge up. This analysis was done with the STARS code in an identical manner as this study and they found likely progenitor range of M(assuming a distance of  Mpc). The Maund et al. (2005) luminosity estimate for the progenitor is and using the STARS tracks employed here this would suggest a mass of M. If the closer distance of  Mpc is chosen (from the mean of the compilation of Takáts & Vinkó, 2006) then the best estimate of mass would reduce slightly to around 6M. This would be rather low, but the uncertainty on the upper bound (3M) would still place it comfortably within the normal theoretical ranges for core-collapse.

5.16 2006bc

NGC2397 is an SBb spiral, and is the final galaxy in this sample which has no published abundance study of its H ii regions. The same arguments as in Section 5.1 are employed (NGC2397 has ) to infer an oxygen abundance at the galactocentric radius of SN2006bc () of approximately 8.5 dex.

The pre-explosion site of SN 2006bc was imaged using WFPC2 (2001 November 17) on-board HST with exposure times of 460s in each of the F450W and F814W filters (the SN position fortunately fell on the PC1 chip). We re observed SN2006bc on (2006 October 14, as part of GO10498) with the ACS Wide Field Camera (WFC) in three filters F435W 1400s, F555W 1500s and F814W 1600s). 10 Aligning the before and after explosion images allowed us to locate the position of the SN on the pre-explosion images to within 0.024 arcsec (again see Maund et al., 2005; Crockett et al., 2008, for details of alignment procedures). Within this error circle there was no detection of a progenitor star in any of the image and filter combinations. At the progenitor position we determined a 3 detection limit of = 24.45. There is no distance measurement to NGC2397 apart from a kinematic estimate, which is  Mpc, from LEDA (Virgo infall corrected). The Galactic extinction is estimated to be (Schlegel et al., 1998). Assuming that the progenitor was a red supergiant we find a luminosity limit of and an 84 per cent confidence limit of . From Fig. 1 this implies an upper mass limit of 12M.

5.17 2006my

SN2006my occurred at almost exactly at the galactocentric radius of the characteristic oxygen abundance measured in NGC4651 by Pilyugin et al. (2004). They measure a value of 8.7 dex at this position.

Li et al. (2007) claim the detection of a red supergiant progenitor of SN 2006my in pre-explosion HST/WFPC2 observations of NGC4651. In order to determine the position of the SN on the pre-explosion HST images Li et al. (2007) aligned these images with ground based observations of the SN from the Canada-France-Hawaii Telescope (CFHT). They derived an initial mass of M for the object which they find coincident with the SN position.

However in an improved analysis, Leonard et al. (2008) have shown that this is unlikely to be correct and the progenitor star is most likely not detected in the pre-explosion images. They used HST images of much higher resolution than CFHT which allows for object positions to be more accurately measured and ultimately leads to a more reliable transformation between the coordinate systems of the pre- and post-explosion images. They find that the offset between the SN and possible progenitor position is too large to support the claim that the two objects are associated (at about the 96% confidence level). In a completely independent manner, we used similar data to carry out the same image alignment and the details of this analysis are presented in our companion paper (Crockett et al., 2009). Using the HST post-explosion to HST pre-explosion transformation, we also find that the progenitor object proposed by Li et al. (2007) is 74 mas from the transformed SN position. Given our total astrometric error this is approximately a 1.8 separation. Hence we also find that this object is unlikely to be the progenitor of SN 2006my. Most likely it is not and the progenitor is undetected in the images, so we derive a 3 detection limit of = 24.8.

Solanes et al. (2002) have collected Tully-Fisher distance estimates for NGC4651 from seven different sources and derive a mean distance modulus (or Mpc). As in Li et al. (2007) we apply only a correction for the Galactic extinction of . Assuming that the progenitor star was a red supergiant we derive a luminosity limit of and an 84 per cent confidence limit of . From Fig. 1 this implies an upper mass limit of 13M.

5.18 2006ov

Pilyugin et al. (2004) redetermined the oxygen abundance gradient, and our calibrations are on this equivalent scale, hence we use the galactocentric radius and abundance gradient of Pilyugin et al. to determine an oxygen abundance of 8.9 dex. which is the highest in this sample.

Li et al. (2007) report the detection of a red supergiant progenitor of M for SN 2006ov in archival HST/WFPC2 observations of NGC4303. In this case the pre-explosion frames were aligned with HST observations of the SN in order to pinpoint the position of the progenitor on the archival images. Having performed PSF-fitting photometry using HSTphot (Dolphin, 2000) without detecting a progenitor star, it was noticed by Li et al. that a significant point source was still visible in the residual image close to the SN site. Li et al. (2007) suggest that this object in the residual image is in fact coincident with the SN position, and claim that by forcing HSTphot to fit a PSF at this position they detect an object of 6.1 significance in the F814W and F450W observations.

We have repeated the alignment of the pre- and post-explosion HST observations and find exactly the same transformed SN position as in Li et al. (2007). We also find the same point source still visible in the residual image after performing PSF-fitting photometry using HSTphot. However, we measure the centre of this point source to be some 63 mas from the SN position, which given our total astrometric error is a 2.5 separation. This casts significant doubt on the identification of this object as the SN progenitor. Furthermore we are unable to reproduce the photometry results of Li et al. (2007) by forcing HSTphot to fit at the transformed SN position. Rather we find detections of the highest significance (6.0 in F814W and 4.4 in F450W) when we force a fit at our own measured position of this point source, which as we have already said is not coincident with the SN position. A more detailed discussion of this analysis are presented in Crockett et al. (2009).

Since we cannot confirm that this object is the progenitor of SN 2006ov we derive a 3 detection limit of = 24.2.

Li et al. (2007) derive a mean distance modulus for NGC4303 (M61) of (or Mpc) from two Tully-Fisher distance estimates, and that value is adopted here. We apply only a correction for the Galactic extinction of . Again assuming that the progenitor star was a red supergiant we derive a luminosity limit of and an 84 per cent confidence limit of . From Fig. 1 this implies an upper mass limit of 10M.

5.19 2007aa

NGC4030 is an Sbc spiral with no study of its H ii regions published. The same arguments as in Section 5.1 can be used (NGC4030 has ) to infer an oxygen abundance at the galactocentric radius of SN2007aa () of approximately 8.4 dex.

The pre-explosion site of SN 2007aa was imaged using WFPC2 (2001 July 30) with exposure times of 460s in each of the F450W and F814W filters. We determined the position of SN 2007aa on these images using a ground-based image of 0.8 arcsec resolution taken with the AUX Port camera on the William Herschel Telescope on 2007 March 11 in the -band filter. Alignment of this image with the pre-explosion frames produced an error circle of 0.07 arcsec for the SN position on the F450W and F814W images. No object was detected within this region and hence a 3 detection limit of = 24.44 was determined. A kinematic distance estimate of  Mpc for NGC 4030 was calculated from its recessional velocity (Virgo infall corrected) as recorded in LEDA. Extinction due to the Milky Way is estimated to be (Schlegel et al., 1998). Assuming the progenitor was a red supergiant we find a luminosity limit of and an 84 per cent confidence limit of . From Fig. 1 this implies an upper mass limit of 12M.

5.20 2008bk

SN2008bk was recently discovered in NGC7793 a nearby galaxy with two distance modulus estimates of (Karachentsev et al., 2003) determined from the tip of the red giant branch and from a Tully Fisher distance in . We will adopt the distance modulus of ( Mpc). The galaxy is part of the oxygen abundance gradient study of Pilyugin et al. (2004). The galactocentric radius and the abundance gradient imply an oxygen abundance of between 8.2-8.4 dex at the SN position (Mattila et al. 2008), hence we adopt the LMC-type metallicity.

The galaxy has a wealth of prediscovery images available from the Very Large Telescope (VLT), with optical images from FORS1 and NIR images from HAWK-I and ISAAC. We have shown in a recent letter that SN2008bk is exactly coincident with a bright, red, source detected in the bands, using high resolution -images from the NACO system (Mattila et al. 2008). Although the foreground extinction toward the galaxy is low and the early observations of the SN appear to show no signs of significant extinction, Mattila et al. (2008) show that the progenitor SED can be fit with a late-type M4I spectral type with a visual extinction of . Using methods which are entirely consistent with our approach in this paper, Mattila et al. (2008) have estimated the luminosity and mass of this red supergiant. The distance of 3.90.4 Mpc and results in = -9.73 0.26. Levesque et al. (2005) show that using to determine M is preferable to using the optical bands. The best fit SED of around M4I would correspond to K and a bolometric correction (both from the Levesque et al. scale). This results in . and from Fig. 1 (at LMC metallicity) this corresponds to a mass of M.

Figure 2: The initial mass compared with the final luminosity of the STARS and Geneva stellar models. For each mass we plot the luminosity at the end of the model, just before core-collapse. For the STARS models this is up to the beginning of neon burning. The old Geneva models end after core carbon burning. For the newer Geneva models both end at silicon burning. The grey shaded region represents the range of luminosity for the STARS models from the end of core-helium burning to the luminosity at the on-set of core neon burning (see Sect. 3 and Fig. 1)
Figure 3: Similar to Figure 2 but with initial mass versus effective temperature at the end of the stellar model.
Figure 4: Similar to Figure 2 but with initial mass versus lifetime to the end of the stellar model.

6 Systematic uncertainties in the determination of stellar mass

6.1 Stellar evolution models

The luminosity estimates and limits used to determine stellar masses are obviously dependent on the stellar model used. Hence it is necessary to compare our stellar models to other contemporary models of massive stars. The constituent physics of modern codes is mostly identical, using the same nuclear reaction rates and opacity tables. The differences come from the adopted mass-loss rates, the numerical schemes employed to solve the stellar structure equations and the treatment of mixing, convection and rotation in the codes (see Langer & Maeder, 1995; Stancliffe, 2006, for example) Here we illustrate the differences between our models and those of Schaller et al. (1992), Hirschi et al. (2004) and Heger & Langer (2000). We consider three details of the end points of the stellar models, these are the final luminosity, the final effective temperature and the stellar lifetimes in Figures 2, 3 and 4.

One detail to note first is that the Geneva rotating models (Hirschi et al., 2004) predict a smaller maximum initial mass for red supergiant progenitors of 22 M rather than the 27 M from the STARS models, while the non-rotating Geneva models (Schaller et al., 1992) predict a maximum initial mass for red supergiant progenitors of 34 M. Beyond these masses the codes predict the stars will end as H-deficient WR stars (depending on the mass-loss recipe employed). One other noticeable feature is that only the STARS models follow the process of second dredge-up and produce massive AGB stars at low masses. This is because the other models have been stopped before it could occur. Second dredge-up is found at similar masses in other codes specifically designed to follow this stage (e.g. Poelarends et al., 2008; Siess, 2006, 2007).

In Figure 2 the difference in final luminosities between models is illustrated. The model sets with the greatest difference with our relation are the non-rotating Geneva and Heger & Langer models, while their rotating models have reasonable agreement with the STARS models and with the older Schaller et al. (1992) models. The main reason for the relationships not being exactly similar is because of different assumptions of mixing in the stellar models and also the tracks end at different points in the stars’ evolution. For example the old Geneva models have lower luminosities than the STARS models because they end after core carbon burning while the STARS models progress slightly further to the beginning of neon burning and we find the luminosity grows after core carbon burning. Also the Geneva models end after core helium burning and therefore it underestimates the final core mass and luminosity.

The newer Geneva models differ in the treatment of mixing and convection in the models which affects the vigour of the nuclear burning in the stars and therefore the luminosity. For example they use a smaller overshooting parameter than the older Geneva models as mixing is now also provided by the rotation. Thus the rotating models agree with our final luminosities but the non-rotating star luminosities are 0.3 dex lower. We emphasise that the new non-rotating models are artificially pushed to lower luminosities as the mixing efficiencies (from overshooting) have been significantly reduced. Otherwise employing the same mixing parameters as previously employed and adding rotational mixing would push all the luminosities too high to be consistent with observed HRDs.

In general the uncertainty in final luminosity due to the assumption of a certain set of stellar models is typically 0.1 dex between our STARS models and the most up to date rotating models. However the issue of how much mixing is included and by which mechanism can lead to an uncertainty of up to 0.3 dex. This does not pose a major problem to our estimates as we are using the luminosity at the end of core helium burning to estimate the 84%-confidence upper mass limits. In Fig. 2 one can see that the grey area (which highlights the region in the STARS code between end of core He burning and the end of the model as discussed in Sect. 3) brackets nearly all the tracks.

While the initial mass to final luminosity is uncertain the final helium core mass to final luminosity relationship is much tighter. This is because the size of the helium core is the major factor in determining a red supergiants luminosity. To remain consistent with progenitor masses measured from cluster turn-off ages and with previous studies we have determined initial masses () for our progenitors. Helium core masses () can then be estimated from these by using the following relation determined from the STARS stellar models:

The surface temperatures in Figure 3 show that the final predicted effective temperatures are all within 0.05 dex with the Heger & Langer (2000) models being coolest. At higher masses the temperature sharply increases as the hydrogen envelopes in these cases are low mass () as the star is stripped due to mass loss. These temperatures are highly sensitive to the boundary conditions in the stellar models as well as the opacities used, so it is not easy to simply identify the reason for the differences between the models. But the uncertainty ( K) is well below the uncertainty in the surface temperature implied from spectral types of observed SN progenitors (typically ( K, from the colour-spectral type estimates).

The stellar lifetimes in Figure 4 also show close agreement. The most discrepant are the rotating Geneva models. Rotation increases the hydrogen burning lifetime considerably by mixing fresh hydrogen into the core and extending the hydrogen burning lifetime of the star. The increase, however, is less than 0.1 dex and therefore masses derived from lifetimes (i.e. turn-off masses for 2004am and 2004dj) are consistent between stellar models.

Hence we conclude that the use of different stellar models are unlikely to have a significant effect on the estimated masses and mass limits we have derived, especially if a single method is employed and all masses are derived on a homogeneous scale. Furthermore while the initial masses may be somewhat dependent on the choice of single star models, the final helium core masses that our initial mass correspond to should be reliable.

6.2 Extinction determinations

It is likely that our largest source of error comes from the extinction that we assume is applicable to the line of sight toward each SN. This is not likely to be a simple systematic effect that would change all the mass estimates and limits by a constant. However we need to consider if we are consistently underestimating the extinction toward the progenitor stars and by what magnitude.

Figure 5: Histogram of the values adopted for the progenitor stars (shaded bars) compared to values of red supergiants in the LMC and the SMC from Levesque et al. (2006) (open bars). There are 18 SN progenitors plotted here in the shaded bars (2004am and 2002hh were excluded as explained in the text), and 73 RSGs from the combined SMC and LMC samples.

The extinctions which have been estimated for each of the progenitor stars come from several methods. All of these suffer from their own uncertainties and problems and in general we favour taking the mean of different results. The rationale is that no single method is clearly superior to the others and a mean of several, possibly problematic, estimates is better than adopting one. The extinctions have been estimated by some of the following techniques: measurements of the Na i ISM absorption lines and calibrating this using Turatto et al. (2003) ; comparing the early continuum slopes to the well observed and reliably modelled 1999em and also to unphysically hot black body continua ; fitting stellar spectral energy distributions (SED) to the surrounding massive star population within about 10-100 pc; and if the SN exploded within an H ii region or compact cluster then using the value determined from the nebular emission lines or the cluster SED. An example of the applications of all of these methods applied to SN2001du can be found in Smartt et al. (2003). In the latest case of SN2008bk there is no accurate extinction measurement toward the SN yet and Mattila et al. (2008) have employed to fit a late type M4I to the observed progenitor colours. An extinction of less than this results in a star which is intrinsically too red to be compatible with known massive red supergiants. We do not revisit the reliability of every method applicable to each event as this is dealt with in the relevant references cited in the subsections for the events above. However we should consider if these methods as a whole are applicable and what are the likely sources of error.

The primary concern is our assumption that the extinction toward the SN (and surrounding stellar population) is directly applicable toward the line of sight to the progenitor. Two methods probe the intervening line of sight directly to the SN. However the early soft X-ray, UV-optical flash of the explosion could conceivably have photo-evaporated substantial circumstellar dust close to the progenitor (Dwek, 1983). Waxman & Draine (2000) have suggested that the X-ray and UV afterglow of a GRB could photo-evaporate a large cavity surrounding the progenitor star. Scaling the GRB energy to the observed flux from recent shock breakouts observed for type II-P and Ibc SNe, Botticella et al. (in prep) have estimated how much dust could conceivably be destroyed in a dense circumstellar envelope. It would appear that it is quite possible for such a UV, soft X-ray flash to destroy dust masses that could provide several tens of magnitudes of extinction in the optical -band.

This is of obvious concern when one considers that the observations of luminous red supergiants in the Magellanic Clouds, the Galaxy and the Local Group are known to produce large quantities of dust (van Loon et al., 2005; Massey et al., 2005). A histogram of extinctions toward optically selected red supergiants in the LMC and SMC clusters by Levesque et al. (2006) suggests that RSGs tend to be redder (by on average ) compared to the extinctions toward the other OB-stars in their stellar associations. The mean extinction toward LMC and SMC RSGs is 0.60 and 0.73 respectively. The mean extinction that has been determined toward our SN progenitors is (from Table 2) and the large standard deviation is due to 2002hh with . In this calculation we have left out 2004am which clearly suffers from high extinction in line of sight in M82; its host cluster is heavily reddened hence its high is unlikely to be due to CSM dust shells (see Sect.5.11). This simple comparison would suggest there is no clear difference in the extinctions of the two samples. If we leave further exclude 2002hh (as an anomalously high extinction object), we have a mean extinction toward the 18 progenitors of In Fig. 5 we show the histogram of our estimates towards the likely red supergiant progenitors and compare them to the LMC and SMC combined population (disregarding the two highest values for 2004am and 2002hh). There is some evidence to suggest that we have more progenitors in the lowest bin than would be typical for RSG progenitors. This is not unexpected as for several of our SNe we have been forced to adopt the extinction towards the host galaxy alone due to lack of additional information. Given the low numbers of objects and the differences in the sample size, the distribution between does not appear to be a major cause for concern. There are five events for which we adopt a low (foreground Milky Way component only) extinction of . If these have been underestimated by , that would bring the mean of the progenitor sample into line with the SMC/LMC RSG populations. In doing so the luminosity and mass limits for each event would increase by : 1999br (=4.88, M) ; 2003ie, (=5.49, M) ; 2006my, (=4.55, M) ; 2006ov (=4.35, M) 2007aa (=4.6, M). This does not affect the lower mass limit that we derive below for the sample from the maximum likelihood analysis and has a minimal affect on the maximum mass as we shall see (Sect. 7).

The extinction remains the major source of uncertainty and there exist populations of dusty red supergiants which are obscured in the visual and near-IR (often by in the band) and are mid-IR bright as their optically thick dust shell is heated by the stellar luminosity and this light is preprocessed into thermal mid-IR emission from dust grains (van Loon et al., 2006; van Loon et al., 2005; Loup et al., 1997). These would not appear in the Massey & Olsen (2003) and Massey (2002) sample as they are too faint optically. However the relative numbers of red supergiants (excluding AGB stars, which are below the mass threshold to produce SNe) which are visually obscured (e.g. objects similar to those in van Loon et al., 1998, 2005) and those which suffer moderate extinctions (the optically detectable stars in Massey & Olsen, 2003) is unknown. Such a study to quantify the latest stages in stellar evolution in a complete manner would be highly desirable and the Magellanic Clouds would appear to be an excellent laboratory. Clearly we do see a large population of RSGs with low-moderate extinctions as shown by Levesque et al. (2006) and Massey & Olsen (2003), and we suggest that our progenitors are part of this population. How many dust obscured RSGs which are missing from optical and near-IR surveys remains to be seen.

Additionally if a mass-loss mechanism (such as pulsations) occurs during the final stages of evolution of most massive stars as core-collapse approaches one might envisage that the progenitors become systematically more obscured. This would invalidate the comparison with the LMC RSG population. Such severe mass-loss is not well constrained observationally or theoretically but if it occurred frequently one would expect to see signatures of circumstellar gas as well as dust. The type II-P tend to be low-luminosity radio and x-ray emitters and tend not to show narrow hydrogen or helium lines suggestive of CSM shells (Chevalier et al., 2006).

While there is no clear evidence that dense dust shells form around II-P progenitors, we at present cannot rule out some visual obscuration due to an optically thick dust shell which was then evaporated by a soft X-ray, UV and optical flash at shock breakout. This has been suggested as a possible mechanism for SN2008S (Prieto et al., 2008), see Sect. 2.4.

7 Maximum likelihood analysis of the masses of progenitor stars

Using the measurements of progenitor masses in Table 2 it is possible to estimate parameters that describe the progenitor population. The three parameters of the progenitors that we are interested in are the minimum initial mass for a type II-P SN, the maximum initial mass and the initial mass function (IMF) of the population.

Estimating these from a small sample is not difficult but the relatively small number of data points can restrict the accuracy with which one can constrain the most probable values. We therefore use the unbinned maximum likelihood method,e.g. Jegerlehner et al. (1996). For a large number of objects this effectively becomes a method. The likelihood is defined to be,

(2)

where is the probability of the th event to have mass . We must define a function for the probability of each event, , and then maximize the likelihood to find the parameters that give the most probable set of events.

To make the maximization more straight-forward we first take the natural logarithm of the likelihood function and so we are required to calculate a sum rather than a product,

(3)

The probability function that describes the probability that a progenitor will have mass within a certain mass range is essentially the IMF. We do need to treat the detections and the non-detections differently. For non-detections we adopt the probability function,

(4)

where is the value of the IMF, Salpeter being , is the minimum mass for a type II-P SN, is the maximum mass for a type II-P SN, and is the upper mass limit for the th non-detection. If is less than we set . If is greater than we set because our mass limits are 84 percent confidence limits so there is a chance that the progenitor could be more massive. This is only important for the mass limit from SN 2004et.

Figure 6: Plot of the likelihood function for the mass ranges of type II-P progenitors. The star indicates the parameters with the highest likelihood and the contours the confidence regions. The dotted grey lines show the results using the six detections only, which results in a lower mass limit of 8.5M. The solid black lines show the contours using the fixed lower limit and allowing the maximum mass to vary.

For detections the case is more complicated. The errors for the progenitor luminosity are roughly Gaussian, but converting to an initial mass affects the distribution. We first take the best estimated mass, , as the most probable value for each detection. Then above this mass we integrate the IMF up to the upper uncertainty on the mass estimate, . Below we assume the probability distribution is a straight line going to zero at the lower uncertainty on the mass limit, . While these error distributions are somewhat arbitrary they avoid skewing the overall distribution to higher or lower masses as happens when using a Gaussian distribution to describe the uncertainties. We have experimented with different probability functions for detection, for example using triangular and rectangular error functions at the low and high uncertainty limits. The and would typically vary by which is within the uncertainty we derive for these parameters. We feel our chosen method for describing the probability function in the case of detections is the best representation of the asymmetric errors on the mass estimates. Hence for detections we use the following probability distribution

If is lower or higher than and then the integral is truncated within these limits.

We calculate the likelihood using the masses for the SNe progenitors listed in Table 2 and allow and to vary, while fixing the IMF slope to Salpeter (). Originally we attempted to let the IMF vary as well as the maximum and minimum mass values but find it constrains the IMF only very weakly and we chose to fix it at three different values, as justified below.

Furthermore we estimate the confidence regions from,

(6)

where for two parameters when and we have the 68, 90 and 95 percent confidence regions (Press et al., 1992).

Figure 7: As in Figure 6 but with a shallower (left) and steeper (right) IMF.

We first estimate and using the six detections only (without incorporating the upper limits). The results can be seen in dashed contours in Figure 6. The parameters we estimate are and . We then recalculate the likelihoods using both the detections and upper limits in the analysis but fix the minimum initial mass to as derived from the detections alone. This is because the non-detections only provide meaningful information on the maximum initial mass . In contrast they provide only a weak constraint on as when combined with the IMF they would simply favour a low mass due to the rising probability of having more low mass stars. We suggest it is more reasonable to calculate from the detections and effectively this converges toward the lowest masses detected in the progenitor sample. The upper mass limits have a strong impact on the uncertainty on and we determine that . With the error on reduced significantly, this suggests that at 95% confidence level the maximum initial mass to produce a type II-P is 21M.

In all of the above we have assumed a Salpeter IMF and it is reasonable to question the validity of this assumption. Elmegreen (2008) has recently reviewed evidence for the variation in the IMF slope in local star forming environments such as Galactic and Local Group Galaxy clusters and field populations within the Galaxy and the Magellanic Clouds. In clusters and OB associations with total masses between M there is little evidence for strong and real deviations from the Salpeter slope of above and beyond the RMS measurement errors determined in each region of high mass stars (with typical uncertainties of order to ). That is not to say that such real variations do not exist, only that stochastic affects mean that determining the true IMF in localised regions can at best reach the accuracy of a few tenths. There is some evidence that flatter IMF slopes exist in very dense starforming regions such as NGC3603 (; Stolte et al., 2006) and the Galactic centre (; Kim et al., 2006). Also there is evidence that the field population may show much steeper slopes, with applicable for a large sample of field stars lying outside clusters and associations in the LMC (Parker et al., 1998). Extreme values of around 3-4 have even been found (Massey, 2002; Gouliermis et al., 2002) though it is unclear to what extent this is simply due to stellar drift out of low mass clusters. Elmegreen (2008) surmises that appears to be fairly typical in moderate mass clusters and starforming regions and variation around this is, on the whole, limited to approximately 0.5. As our SNe, and their progenitors, seem to reside in typical star forming regions and the field of their host spirals there is no compelling evidence to favour an IMF too dissimilar to Salpeter. In Fig. 7 we have recalculated the maximum likelihood values with the extreme IMFs suggested in Elmegreen (2008) of and . For the shallow IMF slope of the best estimates of the minimum and maximum initial mass are unchanged but the uncertainties increase slightly to M and M. This shallow IMF is unlikely to be representative of our progenitor environments as they are not (apart from perhaps 2004am and 2004dj) in dense clusters such as seen in NGC3603 and the Arches cluster at the Galactic centre. For the steeper IMF, the most likely minimum initial mass increases to M and the 95% confidence limit for is pushed to the higher value of 22M. In summary there is no strong evidence (from Local Group studies as reviewed by Elmegreen, 2008) that our progenitor population should come from a massive stellar population with an IMF slope significantly different (i.e. by more than ) than Salpeter, and adoption of the either of those extreme values does not significantly affect the values of and .

Two remaining uncertainties are extinction and the value of . As discussed in Sect. 6.2, if we have underestimated the extinctions toward five events with non-detections and replace them with the slightly higher masses, and change by less than . As discussed in Sect. 5, if we employ , then the luminosity differences of the five progenitors for which we employ only a kinematic host galaxy distance (see Table 2) would change by  dex. This corresponds to approximately 2-3M in the ZAMS estimate. The value of does not change, but the the maximum mass increases to . This is due to SN1999ev having the most massive progenitor estimate and the host of SN1999ev has a kinematic distance only. Similarly, using keeps within 8-9M(as all the SNe which determine this number have distances from other methods), but the maximum mass reduces to M. This illustrates that in the future it is important to try to find the type II-P SNe from the highest mass progenitors to tie down as reliably as possible.

8 Discussion

With our analysis of the progenitor observations and mass estimates we are able to consider some outstanding questions on the nature of supernovae progenitors from a firm observational footing. There has recently been much discussion on the initial masses of progenitor stars of SNe of all types (Gal-Yam et al., 2007; Li et al., 2007; Smartt et al., 2003) and the nature of faint type II-P SNe (Pastorello et al., 2006; Nomoto et al., 2003; Zampieri et al., 2003, 1998)

Our maximum likelihood analysis reveals that the progenitors of type II-P arise from stars with initial masses between and M. The derivation of the mass range assumes that the stars are red supergiants, in that to transform the optical or near infra-red limiting magnitudes to a luminosity and mass we must assume a stellar progenitor spectrum with a suitable photospheric temperature (or range of temperatures). This is well justified in that four of the detections have colours consistent with them being late K-type to mid M-type supergiants and the requirement that a II-P lightcurve results from the explosion of a star which has an extended H-rich envelope. (R Arnett, 1980; Chevalier, 1976; Popov, 1993). The maximum initial mass is important to constrain what the final evolutionary stage of the most massive stars and the lowest initial mass that could produce a type Ib/c, or perhaps II-L and IIn, explosion. The minimum initial mass that can support a SN explosion is of great interest for explosion models, stellar evolution, comparing with massive WD progenitor masses and galactic chemical evolution.

The mass range that we find for the progenitors is much lower than ejecta masses of a sample of II-P SNe suggested by Hamuy (2003). This study estimated ejecta mass of between 14-56M from the application of the Nadyozhin (2003) formulae to determine energy of explosion, radius of progenitor and ejected mass. Even though the error bars on the masses are large there is a clear discrepancy between our results. The determination of the ejecta masses is very sensitive to how the mid-point in the lightcurve is defined to determine (the visual magnitude at 50 days) and (the ejecta velocity at the same point). The measurement of the latter is also highly dependent on which ionic species is used to measure the photospheric velocity and Nadyozhin (2003) suggests that the bolometric lightcurve should be used to define the plateau mid-point. It appears to us that the choice of the point at which to define the measured parameters has a critical effect on the physical values determined and caution should be employed when applying this method. We note that Nadyozhin (2003), with similar data to Hamuy (2003) has determined ejecta masses in the range 10-30M, closer to our progenitor mass range but still systematically higher. It is likely that the the mid-points of the plateau lightcurves defined by Hamuy (2003) (and the parameters thus arising) were not exactly compatible with those required for the Nadyozhin (2003) equations to be applied. The lower ejecta masses of Nadyozhin (2003) are probably more reliable in that they are estimated with the appropriate input parameters and are a better match to the progenitor masses we determine.

One may ask if a ZAMS mass of 8.5M is large enough for a long plateau phase to be sustained. In our model the star would loose 0.5M due to stellar winds and with a neutron star remnant of 1.5M, this leaves about 6.5M for the ejected mass. Hendry et al. (2006, 2005) showed that the low progenitor masses of SN2004A and SN2003gd (8-9M) were consistent with the observed recombination powered plateau duration, but only just within the error bars of both model estimates (see also Smartt et al., 2003) In a future paper we will analyse the lightcurves of a large subset of the SNe presented here to determine if their progenitor mass estimates are consistent with the ejected masses required to produce their plateau phases.

8.1 The minimum mass of II-P progenitors

Theory predicts that a few of the low-mass progenitors should be massive AGB stars, sometimes referred to as Super-AGB stars (Eldridge & Tout, 2004b; Siess, 2007; Poelarends et al., 2008). The cores of these objects never reach high enough temperatures to produce iron, rather the oxygen-neon core grows to the Chandrasekhar mass and an electron capture SN is triggered. These explosions have been predicted to produce less luminous SN than in normal iron-core collapse (Kitaura et al., 2006), and perhaps this signature could be used to find real candidates and to identify progenitor stars at the lowest mass range (see the Sect. 8.4 and references therein for a discussion of the lowest luminosity SNe). From their models of super-AGB stars, Poelarends et al. (2008) suggest that the number of these stars at solar metallicity would result in them producing 3 percent of the local core-collapse SNe. This increases to greater than 10 percent at metallicities below a tenth solar. From the observational properties, one of the best studied examples of a low-luminosity, low ejecta velocity event is SN2005cs, and indeed we do suggest it had a low progenitor mass of M. However Eldridge, Mattila & Smartt (2007) show that there is a clear observational signal for AGB stars, in that these progenitors should be much cooler than higher mass red supergiants and hence be quite bright at near infra-red (NIR) bands. Deep NIR pre-discovery images were available for SN2005cs, and we showed that it was unlikely to be a massive AGB star. Thus we suggest that all of the 20 progenitors were genuine Fe core-collapse events, and we have no evidence for any of them being electron-capture events in ONe cores. We also have no evidence to support the idea that stars in the range 7-9M go through 2nd dredge-up and end as quite high luminosity progenitors, either as S-AGB stars with ONe cores or genuine Fe core-collapse events. Our models (and those of Poelarends et al., 2008) would suggest that the luminosity of these events can reach which is significantly more luminous than any of the progenitors detected so far. Eldridge & Tout (2004b) and Poelarends et al. (2008) point out that this evolutionary phase is very dependent on the treatment of semiconvective mixing and convective overshooting. The fact that we don’t see luminous progenitors with  dex (the highest of our sample : SN2005cs) would apparently disfavour the scenario in which 7-9M stars increase their luminosity due to 2nd dredge-up before collapse. The apparent luminosity of the progenitors (around ) favours a lower limit than is normally assumed for core-collapse with no luminosity spike.

The lower mass limit we derive from Sect. 7 of M is interesting to compare with the maximum stellar mass that produces white dwarfs. A compilation of mass estimates of white dwarfs by Dobbie et al. (2006) suggests that, in Milky Way intermediate age clusters, stars up to 6.8-8.6M produce white dwarfs and they suggest this as the initial mass range for core-collapse SNe. Rubin et al. (2008) suggest that a homogeneous analysis of WDs in their Lick-Arizona White Dwarf Survey (LAWDS) confidently determines the maximum mass to be no less than 6M. Further recent evidence suggests that the mass limit is no less than 7.1M (Williams et al, 2009). A slightly higher mass limit is not ruled out as there is ongoing work on younger clusters to find WDs and determine their progenitor age (C. Williams, private communication). Hence the two, very different approaches, of SN progenitor mass and WD progenitor masses appear to be converging toward M. Unless both methods are significantly in error it would seem unlikely that the lower mass for a core-collapse SN is outside this range. Theoretically several mass-limits have been determined, ranging from 6 to 11M (Ritossa et al., 1999; Heger et al., 2003; Eldridge & Tout, 2004b; Poelarends et al., 2008, and references therein) depending critically on the amount of convective overshooting employed. In our analysis we have used models with convective overshooting as there is growing evidence that extra mixing is required above that predicted by mixing-length theory (e.g. Schroder et al., 1997; Aerts et al., 2003). We suggest that a minimum initial mass of 10M or more can now be ruled out for two reasons. Firstly we detect four progenitors with best estimated masses below 10M  although admittedly the individual uncertainties would not rule out a higher mass progenitor. Secondly in our maximum likelihood analysis masses at 10M and above are ruled out at over 95 percent confidence, even with a steep IMF of . This value is supported by the fact that type II-P SNe are not always associated with underlying H ii emission line regions in their host galaxies Anderson & James (2008) which would suggest their progenitors are from a population of less than 10 M.

We suggest that M is the current best estimate, based on observational constraints, for the lower limit to produce an Fe core-collapse driven SN of type II-P. This is in agreement with the mass range for the most massive progenitors of WDs.

Figure 8: The initial masses of all our type II-P progenitor stars, compared with our theoretical limits for production of supernovae of different types and type of compact remnant. The box symbols are shaded on a metallicity scale, the lighter the shade the lower the metallicity, with the values taken from Table 2.

8.2 The maximum mass of II-P progenitors

The maximum mass of a star that can produce a II-P supernova is an important threshold to constrain. In Fig. 8 we summarise the initial masses of all the progenitors. Similar plots were first shown by Heger et al. (2003) and Eldridge & Tout (2004b) with a large range of metallicity plotted on the vertical axis, from super-solar to metal free. As our progenitor stars cover a relatively small range in metallicity, we have removed the axis scale and instead flagged the points with a metallicity coded grey scale. Clearly the highest mass of a detected progenitor is 16M (SN1999ev) with one upper limit above 20M, due to shallow pre-explosion images (SN2003ie). Our estimated maximum initial mass for a II-P (Sect. 7) is M, with a 95% confidence limit (assuming Salpeter IMF ) of 21M. Fig. 8 is effectively a cumulative frequency distribution (CDF) which is constrained at the lower and upper mass limits and has an IMF with consistent with the limits in between (the CDF of the Salpeter IMF is plotted as the thick grey line). This Salpeter IMF is a good fit to the distribution of masses and mass limits, if the hard minimum and maximum masses for II-P progenitors hold. Stars more massive than about 20M would be easily detectable in our archive images, and there is unlikely to be any bias against detecting the most massive progenitors. Hence there does appear to be a real upper limit to the mass of stars that produce normal type II-P SNe. The one caveat to this is if the progenitor stars suffer large circumstellar extinctions which are photo-evaporated in the explosion. We discussed this in Sect. 6 and while we cannot see a compelling case for such an effect in our population we cannot rule it out.

We can compare this maximum mass limit with the ratios of CCSN types in Table 1. With a maximum possible stellar mass of 150M (Figer, 2005), the fraction of stars born with masses between 8.5-16.5M (for a Salpeter IMF, ) is per cent, closely mirroring the type II-P rate. One might immediately conclude that the agreement suggests that all stars above 17M produce the other varieties of CCSNe. However this is too simplistic and ignores our wealth of knowledge of massive stellar populations from Local Group studies and interacting binaries.

The red supergiant problem

Massive red supergiants have been frequently surveyed in the Milky Way and the Magellanic Clouds, and up until recently their luminosities as determined from model atmospheres implied that they are found at evolutionary masses up to 40-60M (Massey & Olsen, 2003; Humphreys, 1978). However using new MARCS atmosphere models Levesque et al. (2006) have shown that the effective temperatures of these stars have been revised upwards and they have combined this with revised bolometric luminosities based on band magnitudes. The result is that the highest luminosity red supergiants of Massey & Olsen (2003) and Levesque et al. (2005) now have warmer effective temperatures and luminosities that imply masses of between 12-30M. Massey et al. (2001) and Crowther (2007) suggest stars with an initial mass of around 25M could evolve to the WN phase in Galactic clusters, at solar metallicity. The mass estimates generally come from the estimated age of the stellar clusters as measured from the turn-off. Only two out of 11 in the Massey et al. study are as low as 20-25M and one can really only take this as a lower limit. The minimum initial mass to form a WR star in the LMC (and SMC) has been estimated at 30M (and 45M respectively) using similar methods (Massey et al., 2000). Stars above these masses, if they explode as bright SNe, should produce H-deficient (and He deficient) SNe like the Ib/c we observe. Hence there is good agreement between the maximum observed masses of red supergiants in the Galaxy and the LMC and the minimum mass required to produce a WR star, from the ages and turn-off masses of coeval clusters. Crowther (2007) points out that there are few Milky Way clusters that harbour both RSGs and WR stars which would suggest that there is a definite mass segregation between the two populations. The metallicity ranges of our progenitor sample (Table 2) range between solar and LMC, hence these studies of Local Group stellar populations would suggest the minimum initial mass for a single star to become a WR (probably of type WN) is 25-30M.

The question is what is the fate of the massive red supergiants between 17M and 25-30M ? They appear to exist in this mass range and one would expect them to produce SN of type II-P but they are missing from our progenitor population. A single star of initial mass of 17M does not have a high enough mass-loss rate to strip its outer layers of enough mass to become a WR star and hence a Ib or Ic SN (either observationally or theoretically). If our sample of 20 progenitor stars were really sampled from an underlying population of red supergiants, with initial masses in the region M, then a Salpeter IMF would suggest we should have 4 between M. The probability that we detect none by chance is 0.018 (or 2.4 significance). For a steeper IMF of the numbers are 3 stars, probability of 0.05 and 2 significance. We term this discrepancy the “red supergiant problem”, in that we have a population of massive stars with no obvious channel of explosion.

One could attempt to fill this mass-gap with the other SN types IIn and II-L and IIb. The fraction of stars born with masses between M (within an underlying population of M) is 18 per cent, and Table 1 suggests the combined rate of II-L, IIn and IIb is 12 per cent. Hence it is perhaps appealing to account for the red supergiant problem by saying that at least some of these stars form II-L, IIn or IIb SNe. But there is evidence arguing against this. Thompson (1982) presented a deep photographic plate of NGC6946 49 days before the maximum of the II-L SN1980K and found no progenitor or discernible stellar cluster. He suggested an upper mass limit of M and using our stellar tracks and more recent distance we recalculated this as M in Smartt et al. (2003). SNe IIb have been suggested to be from interacting binary systems and for SN1993J a viable model is a close pair of 14 and 15M stars. The binary companion to SN1993J’s progenitor was theoretically predicted and observationally detected (Podsiaklowski et al., 1993; Woosley et al., 1994; Maund et al., 2004). Ryder et al. (2006) suggest a similar scenario explains their detection of a stellar source at the position of the IIb SN 2001ig. A single 28M WNL star was favoured as the progenitor of the recent SN IIb 2008ax by Crockett et al. (2008), but a binary system cannot yet be ruled out. There is also evidence that very luminous type IIn arise from very massive LBV type stars, generally thought to be M and hence too high mass to solve the problem (see Sect.8.2.4).

One could appeal to rotation as a way out and the rotating Geneva models of Hirschi et al. (2004) predict an upper mass limit of 22M for a hydrogen rich progenitor (for stars rotating initially at 300 ). Above this mass a single star ends its life as a WR and hence a Ib/c SN. This is well above our estimated maximum initial mass 17M, but consistent with the 95% confidence limit. However this would mean every II-P progenitor would have to be rotating initially with speeds around 300 km s. This is clearly not what we see in the rotational velocity distributions in the Galaxy, or Magellanic Clouds, (Hunter et al., 2008; Dufton et al., 2006; Huang & Gies, 2006), which suggest less than 5 per cent of massive stars should be rotating at such intrinsic rotational velocities.

Black hole formation

An intriguing possibility is that the red supergiant problem is due to the vast majority of high-mass stars above 17M collapsing to form black holes and either very faint supernovae or no explosion at all. Theoretically this has been suggested for some time, for example most recently by Fryer (1999); Fryer et al. (2007) and Heger et al. (2003). Our model stars in the mass range of 20-27M end as hydrogen rich red supergiants with helium core masses of M  and such masses have been suggested to result in the formation black holes (this line is plotted for reference in Fig. 8; Fryer, 1999). The models of Limongi & Chieffi (2007, 2003) suggest the maximum mass to produce a type II-P SN is 30-35M and a minimum initial mass for black-hole formation is 25-30M. Although Fryer (1999) notes that the mass range to produce black holes is theoretically quite uncertain. For example reducing the mean neutrino energy by 20% could reduce the explosion energy by a factor 2 and push the minimum mass for black hole formation to as low as 15M.

As pointed out by Kochanek et al. (2008), the collapsar model in which a GRB is produced along with a type Ic SN, is likely to be too rare to produce the bulk of the black holes seen in our Galaxy (MacFadyen & Woosley, 1999). Although the collapsar scenario would have problems within massive hydrogen rich progenitors (the jet would have difficulty in escaping from a red supergiant MacFadyen et al., 2001). Young et al. (2005) suggest that bright II-L SNe may be black hole forming events, in which the collapsar mechanism occurs within a massive H-rich star.

Whatever the explanation we have evidence for a lack of progenitors above 17M and perhaps the minimum mass to form a black hole could be as low as this. It could be that stars in the 17-30M range produce SNe so faint that they have never been detected by any survey. In this case they would typically be fainter than . If the limit for black hole formation is low then it bodes well for surveys for disappearing stars. Kochanek et al. (2008) have suggested that a survey of nearby galaxies over several years would have a chance of detecting massive stars that disappear without an accompanying SN. From a similar comparison of a Salpeter IMF with the general progenitor compilation of Li et al. (2007) they also suggest there may be a dearth of massive star progenitors. Their calculation is somewhat inexact in that it includes 1999gi and 2001du as possible detections and is neither volume or time limited to minimise biases on SN and progenitor selection effects, and the masses come from many inhomogeneous methods. But it does support our quantitative mass range estimate for II-P progenitors.

Binaries and Ibc SNe

A further flaw in the argument that the type II-P rates match the mass range of 8.5-16.5M is that it ignores the consequence of binary evolution. Podsiadlowski et al. (1992) suggested that around 15% of SNe could be from interacting binaries in which mass transfer causes the primary to loose its H (and He) envelope. This assumes that about 30% of all massive stars are in close binaries that will interact in case A, B or C mass transfer. Recent results suggest that % of massive stars could be in close binaries Kobulnicky & Fryer (2007) leading Fryer et al. (2007) to claim that perhaps all local Ibc SNe could be formed in binary systems and the progenitors could thus have initial masses down to our limit of 8.5M. It appears very likely that at least some Ibc SNe are formed in moderate mass interacting binaries (Crockett et al., 2007; Eldridge et al., 2008)

At around solar metallicity Fryer et al. (2007) and Heger et al. (2003) argue that single, massive WR stars all have core masses large enough to form black holes and that they can’t be the progenitors of the local, normal Ibc SN population. They suggest that these should give weak SNe or no explosion at all. Current observations have not yet confirmed that massive WR stars are definitely the progenitors of Ibc SNe. The bulk of the population may form black holes with no explosion and a fraction (with low metallicity and high rotational velocities) may form black holes in the collapsar model with an accompanying GRB (Woosley & Bloom, 2006). The ejecta masses and pre-explosion limits of SNe Ibc (with no associated GRB) are consistent with them being stars of 10-20M stripped of their envelopes through close binary interaction (Mazzali et al., 2002; Crockett et al., 2007; Valenti et al., 2008). We don’t yet have a firm confirmation of a Ibc explosion (with no associated GRB) directly associated with a massive WR star, or with ejecta masses high enough to suggest a WR progenitor. Those broad lined SNe with a GRB associated do have high enough ejecta masses to be consistent with LMC type WC stars (Crowther, 2007). However there is a suggestion of a 28M WNL progenitor for the type IIb SN2008ax (Crockett et al., 2008) and this SN appears to be on the H abundance continuum between Ib and IIb events (Pastorello et al., 2008). We will discuss the Ibc progenitor scenarios further in the second paper in this series.

The type IIn population and their progenitors

There is clear evidence now that some very massive stars, above 25-30M do explode as very bright SN, SN2005gl is a type IIn at 65 Mpc and has a very luminous progenitor detected at (Gal-Yam et al., 2007). The latter is evidence that luminous blue variables are direct progenitors of some SNe and this is supported by studies of the energies and spectral evolution of other events (Kotak & Vink, 2006; Smith et al., 2007; Trundle et al., 2008; Smith et al., 2008b). The case of SN2006jc showed that an LBV-like outburst occurred directly coincident with a peculiar type of hydrogen deficient SN (Pastorello et al., 2007). SN2006jc resembles a type Ic with narrow lines of He arising from a circumstellar He-rich shell (Foley et al., 2007; Pastorello et al., 2008). Woosley et al. (2007) have suggested that both the super-bright IIn events (2006gy like; Smith et al., 2007) and the double outburst events (2006jc-like; Pastorello et al., 2008) may not be the canonical core-collapse mechanism, but be due to pulsational pair-instability in the cores.

Thus one might venture that above 17M the vast majority of stars form black holes at core-collapse and can’t produce bright explosions through the canonical neutrino driven convection mechanism. A fraction of them form collapsars due to a combination of rotation or binarity and low metallicity (see Woosley & Bloom, 2006). And a fraction may form H-rich luminous type IIn SNe through the pulsational pair-instability mechanism.

A caveat to this is the discovery of neutron stars in two young clusters (Muno et al., 2006; Messineo et al., 2008), which suggests the progenitors had initial masses greater than 40M and 20-30M respectively. These stars should perhaps have formed black holes but Belczynski & Taam (2008) suggests that under certain conditions, binary evolution could result in stars as massive as 50-80M ending up as neutron stars. A further argument against is that the locations of Ibc SNe tend to be more closely associated with H ii regions than II-P SNe, suggesting a higher initial mass range for the progenitors of Ibc (Anderson & James, 2008)

The nature of the deaths of the most massive stars, whether in black-hole forming events, or other explosion mechanisms, still remains to be determined. The combination of studies of direct progenitor detections, environment evaluation, SN ejecta and remnant properties will be a fertile field for discovery for many years to come.

The progenitor of SN 1987a : Sanduleak

Although the progenitor of SN 1987A is often quoted to be a 20M star, one needs to be careful with a simple interpretation of placing the progenitor on an HRD and taking the closest mass track. The spectral type and magnitudes from Walborn et al. (1989) suggest a B3-type supergiant (, from the calibration of LMC B-supergiants in Trundle et al., 2007) and hence . When placed on single-star evolutionary tracks this lies close to a 20M model just after the end of core-H burning. However it is not valid to assume 20M as the progenitor initial mass, as the model track is not at its endpoint and is no where near to having an Fe-core (or at least at the point of neon burning within a helium core). The luminosity of the He-core of an evolved massive star determines the stars luminosity and we estimate the corresponding He-core mass to be . The initial mass of a single star required to produce this core mass is . The interacting binary model in Maund et al. (2004) and Podsiaklowski et al. (1993) can produce a SN1987A like progenitor with a pair of 14 and 15M stars. And a merger involving a lower mass star of 3-6M with an evolved 15-16M primary can also account for the luminosity (Podsiadlowski, 1992; Morris & Podsiadlowski, 2007). In both scenarios an initially less massive star gains mass to explode with a final mass of 20M. However the helium core mass was that expected for a 15M star leading to its position in the blue part of the HRD. The ejecta mass has also been estimated at around 15M (Arnett, 1996b). Hence our suggestion of black holes coming from 17M stars and above is not directly disproven by the example of Sanduleak

8.3 Explosion mechanisms and production of Ni

The tail phase of type II-P SNe are thought to be powered by the radioactive decay of Ni and recent studies have shown that there can be a large range in tail phase luminosities. This would imply that a different mass of Ni has been ejected in the explosions. As Ni is created by explosive burning of Si and O as the shock wave destroys the star, it can be used as a probe of the explosion mechanism. For example Turatto et al. (1998), Pastorello et al. (2004), and Nomoto et al. (2003) predict that high mass stars may undergo fall back in which some of the Ni falls back onto a proto-neutron star or black hole and, hence, one might get a fainter supernova. This has lead to suggestions that plotting initial mass versus ejected mass of Ni could lead to a bimodal population. There are estimates of the mass of Ni for nine of the SNe in our sample (by ourselves and also from other groups, already published in the literature) and we can investigate this relation in a direct way.

The Ni mass can be estimated from the tail phase magnitudes using several different methods. For example, the bolometric luminosity of the tail phase (Hamuy, 2003), a direct comparison with SN 1987A (Turatto et al., 1998) and the “steepness of decline” correlation (Elmhamdi et al., 2003). For the two recent SNe 2004A and 2003gd, Hendry et al. (2005, 2006) have compared the three methods and find the first two in good agreement, while the mass from the “steepness of decline” relation gives somewhat lower results (at least for these two events). It is important that a consistent method is used to determine all the Ni masses if any comparison is to meaningful, particularly as the uncertainties on the estimates are often fairly large. Hence we determine Ni masses from one consistent approach. The values for SNe 2004A, 2003gd, 1999gi and 1999em were taken from Hendry (2006) who used the bolometric tail-phase luminosity method of (Hamuy, 2003), and the distances and reddening already adopted in Table 2. The mass for SN2004dj was taken from Zhang et al. (2006) who found that the bolometric luminosity of the tail-phase gave a value very similar to that from the “steepness of decline” relation. We take their value from the bolometric tail-phase luminosity to ensure consistency (M). This is very similar to the value determined by Vinkó et al. (2006) with a simple radioactive decay model applied to the bolometric tail luminosity (M). By a similar analysis, the value of SN2004et was determined with the Hamuy (2003) formula, to give M, the highest of our estimates.

The value for SN2004dg has been determined from the late-time, tail phase magnitudes from our HST imaging (see Sect.5.12). We determine and estimate an explosion epoch from spectra and photometry during the plateau phase. Applying the same bolometric tail phase method as above results in a value of M. A very low Ni mass for SN1999br has been reported in (Hamuy, 2003), although he used a distance of  Mpc, and to keep the analysis consistent we scaled his value to our larger adopted distance listed in Table 2, resulting in a value of M. This is is in good agreement with the value determined by Pastorello et al. (2004) of 0.002 who used a similar distance to ours to calculate the mass from a direct comparison with the tail phase luminosity of SN1987A. The estimates for SN2006ov and SN2006my have been calculated using a similar bolometric tail phase method as described above to give M and M respectively (Maguire et al., Spiro et al. in prep).

Finally we consider the case of SN2005cs. The early time spectra have been studied extensively by Pastorello et al. (2006), Takáts & Vinkó (2006) and Brown et al. (2007), who all find it to be a moderately faint II-P with low ejecta velocities. It appears a similar type of event to the faint SNe 1999br and 2002gd (Pastorello et al., 2006), and a measure of its luminosity in the tail phase is especially interesting particularly as it is one of the events with a detected progenitor and well determined mass (Table 2). Tsvetkov et al. (2006) present several photometric measurements of SN2005cs in the tail phase and suggest a Ni mass of 0.018M, which would be similar to 2003gd. As the progenitors are likely to have been red supergiants of quite similar masses one might be encouraged by this agreement. However (Pastorello et al., 2009) presents new measurements of the the tail phase magnitudes of SN2005cs finds it to be significantly fainter than reported in Tsvetkov et al. (2006). The difference is likely due to the differing methods employed to determine the luminosity in this faint phase. Pastorello et al. have used image subtraction to remove contamination of the host galaxy, which can be significant as the SNe fades. These fainter measured magnitudes suggest an ejected Ni mass of M, and we believe this to be a more realistic estimate. For reference, the determined value of 0.075M for SN1987A from Arnett (1996a) is also plotted in Fig. 9

Figure 9: Plots of initial mass vs. mass of Ni. The grey line is the