ABSTRACT

We investigate the fundamental properties of core-collapse Supernova (SN) progenitors from single stars at solar metallicity. For this purpose, we combine Geneva stellar evolutionary models with initial masses of Mini = 20 ? 120 M⊙ with atmospheric/wind models using the radiative transfer code CMFGEN. We provide synthetic photometry and high-resolution spectra of hot stars at the pre-SN stage. For models with Mini = 9 ? 20 M⊙, we supplement our analysis using publicly available MARCS model atmospheres of RSGs to estimate their synthetic photometry. We employ well-established observational criteria of spectroscopic classiication and ind that massive stars, depending on their initial mass and rotation, end their lives as red supergiants (RSG), yellow hypergiants (YHG), luminous blue variables (LBV), and Wolf-Rayet (WR) stars of the WN and WO spectral types. For rotating models, we obtained the following types of SN progenitors: WO1–3 (Mini ≥ 32 M⊙), WN10–11 (25 < Mini < 32 M⊙), LBV (20 ≤ Mini ≤ 25 M⊙), G1 Ia+ (18 < Mini < 20 M⊙), and RSGs (9 ≤ Mini ≤ 18 M⊙). For non-rotating models, we found spectral types WO1–3 (Mini > 40 M⊙), WN7–8 (25 < Mini ≤ 40 M⊙), WN11h/LBV (20 < Mini ≤ 25 M⊙), and RSGs (9 ≤ Mini ≤ 20 M⊙). Our rotating models indicate that SN IIP progenitors are all RSG, SN IIL/b progenitors are 56% LBVs and 44% YHGs, SN Ib progenitors are 96% WN10-11 and 4% WOs, and SN Ic progenitors are all WO stars. We ind that not necessarily the most massive and luminous SN progenitors are the brighter ones in a given ilter, since this depends on their luminosity, temperature, wind density, and how the spectral energy distribution compares to a ilter bandpass. We ind that SN IIP progenitors (RSGs) are bright in the RIJHKS ilters and faint in the UB ilters. SN IIL/b progenitors (LBVs and YHGs), and SN Ib progenitors (WNs) are relatively bright in optical/infrared ilters, while SN Ic progenitors (WOs) are faint in all optical ilters. We argue that SN Ib and Ic progenitors from single stars should be undetectable in the available pre-explosion images with the current magnitude limits, in agreement with observational results. Key words. stars: evolution – stars: supernovae: general – stars: massive – stars: winds, outlows – stars: rotation

1. Introduction

Massive stars are ubiquitously present in the local and far Universe. Due to their short lives and the physics of star formation, they are easily outnumbered by their low-mass siblings like the Sun. Nevertheless, the impact of massive stars through cosmic time is far from negligible, as they are the main responsible for the input of ionizing photons, energy, and recycling mass into the interstellar medium through stellar winds and Supernova (SN) explosions. Mass loss and angular momentum evolution play a key role in determining the properties of massive stars across their evolution and the properties of the SN progenitor and the ensuing explosion (for recent reviews see Maeder & Meynet 2012; Langer 2012). The current generation of Geneva evolutionary models (Ekstr?m et al. 2012; Georgy et al. 2012) predict that single rotating stars with initial masses (Mini) in the range 8 M⊙ . Mini . 17 M⊙ end their lives as red supergiant (RSG) stars before a SN event of the type IIP (i.e., with H lines dominating the spectrum and a plateau in the lightcurve). This scenario is well supported by the observations of SN IIP progenitors in pre-explosion images, which have been shown to be RSGs with 8.5 M⊙ . Mini . 16.5 M⊙ (Smartt et al. 2009). The agreement between theory and observations of SN progenitors is much less satisfactory for stars with Mini & 17 M⊙. One problem is related to the fact that Galactic RSGs are observed to evolve from stars with Mini up to 25-30 M⊙ (Levesque et al. 2005). If these stars die as RSGs, this raises the issue of why no RSG more massive than about 16.5 M⊙ has been detected in pre-explosion images of SN progenitors (“the red supergiant problem", Smartt 2009). A possible solution to this problem would be the presence of circumstellar extinction around RSGs, which would underestimate the luminosity and mass determinations from the pre-explosion images (Smith et al. 2011a; Walmswell & Eldridge 2012). It may also be that the most massive stars evolve away from the RSG phase and end their lifetime in a bluer portion of the HR diagram (Vanbeveren et al. 1998; Salasnich et al. 1999; Yoon & Cantiello 2010; Georgy et al. 2012; Georgy 2012; Meynet et al. 2013). For instance, rotating models predict that stars with 20 M⊙ . Mini . 25 M⊙ are born as O dwarfs and exhibit a spectrum reminiscent of the rare luminous blue variable (LBV) stars before the SN explosion (Groh et al. 2013). The models indicate that a small amount of H is present in the envelope (a few 10?2 M⊙), making it diicult to infer the kind of SN that will follow core collapse (SN IIL, SN IIb, or even SN IIn if signiicant circumstellar material surrounds the progenitor). The situation becomes even hazier for stars with Mini & 25 M⊙. According to evolutionary models, they reach the ZeroAge Main Sequence as O-type stars burning hydrogen in their cores and evolve to Wolf-Rayet (WR) type, helium-core burning stars (see e.g., Maeder & Meynet 2000; Meynet & Maeder 2003; Langer et al. 2007). Between the O-type and WR stages, the star may or may not go through an unstable, short-lived stage, usually associated to the LBV phase, and/or through a RSG phase. The models predict that core-collapse SN occur after the WR phase, and are of the type Ibc (Georgy et al. 2012, 2009). However, this scenario has yet to be observationally conirmed, specially because WR stars have not been directly detected as SN Ibc progenitors yet (Smartt 2009; Eldridge et al. 2013). The non-detection could be due to the intrinsic faintness of WRs in the optical bands, which are the ones usually available for the SN explosion site (Yoon et al. 2012), or because SN Ibc progenitors have lower masses and result from binary evolution (Podsiadlowski et al. 1992; Smartt 2009; Eldridge et al. 2013), or both. In addition, observations suggest that some massive stars can explode as SNe already during the LBV phase (e.g. Kotak & Vink 2006; Smith et al. 2007; Pastorello et al. 2007; Gal-Yam & Leonard 2009). Some of these progenitors likely had Mini & 50 M⊙, which is much higher than the range of LBVs that can be SN progenitors based on single stellar evolution models (20 M⊙ . Mini . 25 M⊙; Groh et al. 2013). Such glaring discrepancies between observations and the stellar evolution theory exposes a main gap in the understanding of massive stars and highlights our incomplete view of their postMain Sequence evolution and fate. Several reasons exist for explaining our limit knowledge of massive stars. For instance, binarity plays an important role in the evolution of massive stars, as a signiicant fraction of massive stars seems to be in systems that will interact (Sana et al. 2012). Neglecting the efects of binaries on the properties of an average population of massive stars would likely yield inconsistent results. An equally important reason for our limited knowledge concerns the challenging comparison between observed data and stellar evolution models. Stellar evolution models are able to predict the stellar parameters only up to the stellar hydrostatic surface, which is not directly comparable to the observations when a dense stellar wind is present. This is the case for massive stars, in particular at their post-Main Sequence evolution, when they lose mass at enormous rates (10?6 to 10?3 M⊙yr?1). When the stellar wind becomes dense, eventually the photosphere becomes extended and is formed in a moving layer. Numerous emission lines arise in the wind, veiling (sometimes completely) the underlying spectrum from the hydrostatic surface that would be observable otherwise. As a consequence, the outputs of massive star evolution models, such as temperature, luminosity, and surface abundances at the hydrostatic surface, are diicult to be directly compared to observed quantities, such as a spectrum or a photometric measurement. To solve this issue, it is necessary to couple stellar evolutionary calculations to radiative transfer models of the stellar atmosphere and wind. In Groh et al. (2013) we presented, for the irst time, combined stellar evolution and atmospheric modeling at the pre-SN stage, for stars with Mini = 20 and 25 M⊙. Surprisingly, we found that these stars end their lives remarkably similar to LBVs, showing that in a single stellar evolution framework, massive stars can explode as LBVs. Here we present a theoretical investigation of core-collapse SN progenitors from single stars with initial masses in the range 9–120 M⊙ at solar metallicity. We analyze how they appear to a distant observer, predicting observables such as the highresolution spectrum, absolute magnitudes, colors, and bolometric corrections. The comparison between observations of SN progenitors and models can shed light on several properties of the progenitor, such as its mass, chemical composition, and initial rotation rate. The motivations for our investigation are numerous. First, it allows a better constrain of the stellar evolution models. The classiication of SNe generally traces the presence of chemical elements in the spectrum and the shape of the lightcurve (see e.g., Filippenko 1997 for a review). Studying the relative rate of the diferent core-collapse SN types is an important constraint for stellar evolution. This is because the chemical abundances in the ejecta supposedly relects those from the progenitor before the SN explosion. Second, it allows to link a given observed SN rate to a given star formation history. This is only possible if we know suiciently well the nature of the progenitors for the diferent types of core-collapse SNe. Finally, producing realistic observables from single-star evolution models also allows one to properly gauge whether a binary evolution scenario must necessarily be invoked to explain the observed properties of a given SN progenitor. This paper is organized as follows. In Sect. 2 we describe our modeling approach. In Sect. 3 we revisit the expected fraction of the diferent kinds of core-collapse SNe from single stars and how they compare to recent observations. In Sect. 4 the location of the SN progenitors on the HR diagram, luminosity, and efective temperature are presented. Their spectroscopic appearance and spectral classiication are performed in Sect. 5, while Sect. 6 compares our results with previous classiications of spectral types of SN progenitors based on chemical abundance criteria. The absolute magnitudes and bolometric corrections as a function of initial mass of the progenitor are presented in Sect. 7. We investigate the detectability of progenitors of the diferent types of core-collapse SN in Sect. 8. We discuss the surprising inding that WO stars are progenitor of type Ibc SNe in Sect. 9, while in Sect. 10 we discuss the possibility that LBVs are SN progenitors. We present our concluding remarks in Sect. 11. In a series of forthcoming papers, we will present the results for the complete evolution of massive stars and for a larger metallicity range, and investigate the efects of several physical ingredients, such as magnetic ields, on the inal appearance of massive stars.

2. Physics of the models

2.1. Stellar evolution

The evolutionary models are computed with the Geneva stellar evolution code. The majority of the models are those from Ekstr?m et al. (2012). To better determine the mass ranges of the diferent SN progenitors, we compute new models with Mini of 16.5, 18, and 28 M⊙ (rotating models), and 23 and 50 M⊙ (non-rotating models). All models are publicly available through the webpage http://obswww.unige.ch/Recherche/evol/-Database-. Here we summarize the main characteristics of the code, and refer the reader to the aforementioned papers for further details. The models assume solar metallicity (Z=0.014), initial abundances from Asplund et al. (2009), and the rotating models have initial rotational speed (υrot) of 40% of the critical velocity (υcrit). The prescription for the rotational difusion coeicients is taken from Zahn (1992) and Maeder (1997). Mass loss is a key ingredient of the models, afecting not only the inal position in the HR diagram but also the emerging spectrum of hot stars. Since the stellar evolution code requires previous knowledge of the spectral types to adopt a certain mass-loss recipe, criteria based on chemical abundances and efective temperatures are employed to estimate the type of massive star (OB, WR, RSG) at each time step(Smith & Maeder 1991; Meynet & Maeder 2003). The radiative mass-loss rates for OB stars follow the Vink et al. (2001) prescription, while for WR stars the Nugis & Lamers (2000) and Gr?fener & Hamann (2008) prescriptions are employed. For the RSGs, when log(Tef/K) > 3.7, the de Jager et al. (1988) prescription is applied for initial masses of 15 M⊙ and above. For log(Tef/K) ≤ 3.7, a linear it to the data from Sylvester et al. (1998) and van Loon et al. (1999) is applied (see also Crowther 2001). For the RSGs in models below 15 M⊙, the Reimers (1975, 1977) relation (with η = 0.5) is used. Because of variations in the ionization level of hydrogen beneath the surface of the star during the RSG phase, signiicant changes in opacity may occur. Thus, some layers might exceed the Eddington limit, possibly driving instabilities. In this case, the radiative mass loss is increased by a factor of three in our models with initial mass above 18 M⊙, which matches the M˙ determinations from van Loon et al. (2005). The efects of diferent M˙ recipes during the RSG phase on the evolution of massive stars has been investigated by Georgy (2012), to where we refer the interested reader for further details. As in Ekstr?m et al. (2012), the stellar evolution models employed here terminate at the end of core-carbon burning. We do not expect signiicant variations in the surface properties after this phase. To verify this assumption, we computed the non-rotating 60 M⊙ model until core O burning, and negligible changes in L? and Tef were seen (～ 0.01 dex).

2.2. Atmospheric and wind modeling of hot stars

The model spectra computed here are publicly available through the webpage http://obswww.unige.ch/Recherche/evol/-Database-. To compute the output spectra of stars with T? > 8000 K we used the atmospheric radiative transfer code CMFGEN (Hillier & Miller 1998). CMFGEN is a spherically-symmetric, fully line blanketed code that computes line and continuum formation in non-local thermodynamical equilibrium. Since all evolutionary models discussed here present negligible surface rotation at the pre-SN stage, the use of spherical symmetry is well justiied. CMFGEN computes a self-consistent radiative transfer including the stellar hydrostatic surface and the wind. Wind (micro) clumping is included with a volume illing factor ( f ) approach, which assumes dense clumps and a void interclump medium. The wind is also assumed to be unclumped close to the stellar surface and to acquire full clumpiness at large radii. All models computed here assume f = 0.1. CMFGEN does not solve the momentum equation of the wind, and thus a hydrodynamical structure must be adopted. For the wind part, we assume a standard β-type law with β = 1, while a hydrostatic solution is computed for the subsonic portion. This is applied up to 0.75 of the sonic speed, where the hydrostatic and wind solutions are merged. The wind terminal velocity (υ∞) is computed using the parametrization from Kudritzki & Puls (2000) for OB stars and LBVs, and from Nugis & Lamers (2000) for WR stars of the WN and WC type. For WO stars, an iterative scheme is adopted. We initially compute a spectrum with the value of υ∞ as given by the Nugis & Lamers (2000) recipe, which is typically at most ～ 2800 km s?1. If a WO-type spectrum arises, we recompute a spectrum with υ∞ = 5000 km s?1 which is more representative of the observed Galactic WO stars (Drew et al. 2004; Sander et al. 2012). We use the outputs from the stellar structure calculations with the Geneva code, such as the radius, luminosity, mass, and surface abundances, as inputs in CMFGEN. For consistency, we adopt the same mass-loss rate recipe as that used by the Geneva evolution code. We use the temperature structure of the stellar envelope to merge the CMFGEN solution and the stellar structure solution. The outputs from the CMFGEN calculations that we discuss here are the synthetic spectrum, photometry, and the efective temperature Tef, deined as the temperature of the layer where the Rosseland optical depth is 2/3. The values of T? quoted here correspond to those predicted by the Geneva stellar evolution code without the correction due to the optical depth of the wind, and not to the temperature at a ixed Rosseland optical depth (usually 20).

2.3.Atmospheric modeling of cool stars

A realistic atmospheric analysis of luminous cool stars requires the inclusion of convection and H? and molecular opacities, which at the moment are not included in CMFGEN. Here, we employ the publicly available MARCS models (Gustafsson et al. 2008) to perform synthetic photometry of the SN progenitors that have Tef = 3400 ? 5400 K and thus are RSGs or YHGs. We use the model grids that have abundances corresponding to CN-processed material, which is characteristic of RSGs at the pre-SN stage. A mass of 5 M⊙ and turbulent velocity of 2 km s?1 are assumed. Since these MARCS models are available only at coarse Tef sampling (3400, 3600, and 3800 K for RSGs; 5000, 5250, 5500, 5750 K for YSG/YHG) and not at the exact luminosities predicted by the evolutionary models, the magnitudes and bolometric corrections of the cool SN progenitors were estimated by: 1) linearly interpolating the magnitudes (bolometric corrections) of two bracketing MARCS models in log Tef space to the desired Tef value predicted by the Geneva code. The bracketing MARCS models were previously scaled to the same luminosity; 2) scaling the interpolated magnitudes to the luminosities predicted by the Geneva code. This is a zeroth-order approximation to estimate the magnitudes and should be checked in the future against MARCS models computed speciically for the physical parameters (L?, Tef, M?, abundances) found at the pre-SN stage. Since these are unavailable at the moment, synthetic spectra of RSGs and YHGs are not provided. Still, the magnitude estimates computed here provide important insights into the nature of core-collapse SN progenitors.