Exploring the diversity of double detonation explosions for type Ia supernovae: Effects of the post-explosion helium shell composition
MMNRAS , 1–21 (2021) Preprint 26 January 2021 Compiled using MNRAS L A TEX style file v3.0
Exploring the diversity of double detonation explosions for type Iasupernovae: Effects of the post-explosion helium shell composition
M. R. Magee , ★ , K. Maguire , R. Kotak , S. A. Sim School of Physics, Trinity College Dublin, The University of Dublin, Dublin 2, Ireland Astrophysics Research Centre, School of Mathematics and Physics, Queen’s University Belfast, Belfast, BT7 1NN, UK Tuorla Observatory, Department of Physics and Astronomy, FI-20014 University of Turku, Finland
Accepted 2021 January 13. Received 2021 January 12; in original form 2020 August 24.
ABSTRACT
The detonation of a helium shell on top of a carbon-oxygen white dwarf has been argued as a potential explosion mechanismfor type Ia supernovae (SNe Ia). The ash produced during helium shell burning can lead to light curves and spectra that areinconsistent with normal SNe Ia, but may be viable for some objects showing a light curve bump within the days followingexplosion. We present a series of radiative transfer models designed to mimic predictions from double detonation explosionmodels. We consider a range of core and shell masses, and systematically explore multiple post-explosion compositions forthe helium shell. We find that a variety of luminosities and timescales for early light curve bumps result from those modelswith shells containing Ni, Fe, or Cr. Comparing our models to SNe Ia with light curve bumps, we find that these modelscan reproduce the shapes of almost all of the bumps observed, but only those objects with red colours around maximum light( 𝐵 − 𝑉 (cid:38)
1) are well matched throughout their evolution. Consistent with previous works, we also show that those models inwhich the shell does not contain iron-group elements provide good agreement with normal SNe Ia of different luminositiesfrom shortly after explosion up to maximum light. While our models do not amount to positive evidence in favour of the doubledetonation scenario, we show that provided the helium shell ash does not contain iron-group elements, it may be viable for awide range of normal SNe Ia.
Key words: supernovae: general — radiative transfer
One of the most debated aspects of research on type Ia supernovae(SNe Ia) is whether multiple progenitor systems are needed to ex-plain the entire population (see Livio & Mazzali 2018; Wang 2018;Jha et al. 2019; Soker 2019 for recent reviews of SNe Ia). Despitesignificant work throughout the years, the question remains whetherSNe Ia primarily result from Chandrasekhar or sub-Chandrasekharmass white dwarfs.To trigger the detonation of a sub-Chandrasekhar mass whitedwarf, early models invoked scenarios in which a massive heliumshell ( (cid:46) 𝑀 (cid:12) ) accumulates on the surface of the white dwarf (e.g.Livne 1990; Livne & Glasner 1991; Woosley & Weaver 1994). Asthe mass of the helium shell increases through accretion, the densityand temperature at the base of the shell also increase. Eventuallyconvective nuclear burning may develop and potentially transition toa detonation. Following ignition of the shell, a secondary detonationmay be triggered in the core. This secondary detonation can be trig-gered in multiple ways (converging shock, edge-lit, or scissors mech-anism; Livne 1990; Livne & Glasner 1991; Moll & Woosley 2013;Gronow et al. 2020), however the end result is the same – completedisruption of the white dwarf. This is the so-called double detonationscenario. Within these models, most studies find that burning in the ★ E-mail: [email protected] helium shell proceeds mostly to nuclear statistical equilibrium (NSE)– producing a large amount of Ni and other iron-group elements(IGEs). Such a large mass of IGEs in the outer ejecta leads to signif-icant line blanketing that generally does not agree with observationsof SNe Ia (Hoeflich & Khokhlov 1996; Nugent et al. 1997).Given the adverse impact of the helium shell ash on the light curvesand spectra, there has been significant interest in minimising itseffects. Neglecting any helium shell altogether, models invoking puredetonations of isolated, bare sub-Chandrasekhar mass white dwarfshave been shown to broadly reproduce the light curves and spectra ofnormal SNe Ia (Sim et al. 2010b; Shen et al. 2018; Goldstein & Kasen2018). Such white dwarfs however, will not spontaneously detonateand therefore these explosions do not occur naturally. Alternatively,models with thin helium shells may also be a viable pathway toexplain normal SNe Ia. Bildsten et al. (2007) showed that ignitionwithin the helium shell can be achieved for much lower masses of ∼ 𝑀 (cid:12) , but they did not not consider the possibility of coreignition following the initial helium shell detonation. Subsequentcore ignition was shown to be robustly achieved by Fink et al. (2007),Fink et al. (2010), and Shen & Bildsten (2014) for high-mass whitedwarfs ( (cid:38) 𝑀 (cid:12) ). In spite of these lower shell masses, modelspresented by Kromer et al. (2010) and Gronow et al. (2020) remaininconsistent with the observed light curves and spectra of normal SNeIa. Recently, Polin et al. (2019) presented a suite of double detonationmodels covering a range of core and shell masses (from 0.6 – 1.2 𝑀 (cid:12) © a r X i v : . [ a s t r o - ph . H E ] J a n M. R. Magee et al. and 0.01 – 0.1 𝑀 (cid:12) , respectively) and find that some models with thinhelium shells do produce spectra that resemble normal SNe Ia.In addition to producing strong line blanketing, the presence ofIGEs in the helium shell ash has an important consequence for thelight curves predicted by double detonation explosions. Noebaueret al. (2017) and Jiang et al. (2017) have shown that the productionof short-lived radioactive isotopes ( Ni, Fe, and Cr) in the shellresults in a distinct bump in the early light curve (within approxi-mately three days of explosion). Studies of samples of SNe Ia (e.g.Bianco et al. 2011; Olling et al. 2015; Papadogiannakis et al. 2019;Miller et al. 2020b) have shown that the evidence for clear bumps isrelatively rare, but a few candidate objects have been proposed (e.g.Jiang et al. 2017; Hosseinzadeh et al. 2017; Li et al. 2019; De et al.2019; Miller et al. 2020a).Qualitatively similar bumps in the early light curves of SNe Iaare also suggested to be produced via different mechanisms, such asthe presence of a Ni excess in the outer ejecta (Magee & Maguire2020), interaction with a companion star (Kasen 2010), or interac-tion with circumstellar material (CSM; Piro & Morozova 2016). Anexcess of Ni in the outer ejecta may result from plumes of burnedash rising to the surface of the white dwarf during explosion. Asthe Ni decays to Co, the radiation produced is able to quicklyescape from the ejecta surface and results in a light curve bump. Theluminosity and duration of the bump depends on both the mass anddistribution of Ni. In the interaction scenarios, a light curve bumpmay be produced due to cooling of the shocked ejecta following theinteraction. For companion interaction, the bump is affected by thenature of the companion, with more evolved stars producing strongerinteraction signatures. In both cases, the mass and extent of the in-teracting material will also determine the luminosity and duration ofthe bump.Maeda et al. (2018) specifically investigate the different early lightcurve signatures predicted by the double-detonation scenario andinteraction. The models presented by Maeda et al. (2018) show sig-nificant overlap between these two scenarios, in terms of the durationand luminosity of the bump, but the double detonation in general pro-duces somewhat redder colours. Maeda et al. (2018) show that thisis at least partially due to the specific IGEs present in the shell.Aside from the mass of the helium shell, it has also been suggestedthat its composition can play an important role during nuclear burn-ing, and can dramatically affect the post-explosion observable prop-erties. Kromer et al. (2010) presented a model in which the heliumshell was polluted by carbon (34% by mass) and found that burningwithin the shell did not proceed to NSE, but instead stalled earlier inthe 𝛼 -chain. In this case, the lack of IGE in the shell produced lightcurves and spectra that are generally consistent with normal SNe Ia.In addition, Townsley et al. (2019) recently showed that the inclu-sion of other isotopes, besides carbon, can also dramatically affectthe post-explosion composition of the shell and produce observablescomparable to normal SNe Ia. Therefore, there is considerable scopefor variation in the burning products produced in the shell.In this work, we present radiative transfer simulations exploring arange of ejecta models that are designed to parameterise and broadlymimic predictions from double-detonation explosion models. Weperform the first large-scale exploration of various compositions forthe helium shell following explosion, and determine the range ofmodels that do and do not reproduce observations of SNe Ia. Al-though different helium shell compositions in parameterised modelswere previously studied by Maeda et al. (2018), here we explore awider range of compositions in the helium shell, as well as multipleshell masses for a given core mass. In Sect. 2, we discuss the radiativetransfer code used in this work, TURTLS (Magee et al. 2018). Sect. 3 A b s o l u t e B m a g A b s o l u t e V m a g This workNo FeNo CrNo Fe or CrNoebauer+17 A b s o l u t e R m a g B V Figure 1.
Comparison between the sub-Chandrasekhar mass double detona-tion model calculated by Noebauer et al. (2017) using STELLA (black) andour calculation using TURTLS (blue). presents our approach to constructing parameterised double detona-tion models. In Sect. 4, we discuss the impact of the helium shellcomposition on the model observables, while in Sect. 5 we show theimpact of the mass of burned material above the core. The rise timesand early light curve bumps of our models are discussed in Sect. 6. InSect. 7, we compare to existing models with varying Ni distribu-tions. Comparisons to observations of normal SNe Ia are presentedin Sect. 8, while in Sect. 9 we compare to SNe Ia showing a bump inthe early light curve. For all spectral comparisons, spectra have beencorrected for Milky Way and host extinction, where appropriate, andwere obtained from WISeREP (Yaron & Gal-Yam 2012). Finally, wepresent our conclusions in Sect. 10.
We use the one dimensional radiative transfer code TURTLS (Mageeet al. 2018) to perform our simulations. All model light curvesand spectra presented in this work are freely available on GitHub .TURTLS is described in detail by Magee et al. (2018). Here we pro-vide a brief overview of the code and outline changes implementedfor this study.TURTLS is a Monte Carlo radiative transfer code following themethods of Lucy (2005) (see Noebauer & Sim 2019, and referencestherein, for a review of Monte Carlo radiative transfer methods).TURTLS is designed for modelling the early time evolution of ther-monuclear supernovae. For each simulation, the density and com-position of the model ejecta is defined in a series of discrete cells.Monte Carlo packets representing bundles of photons are injectedinto the model region, tracing the decay of radioactive isotopes. Wehave updated TURTLS to account for energy generated by the Fe → Mn → Cr and Cr → V → Ti decay chains, which cancontribute significantly to the luminosity and overall evolution ofthe model in the double detonation scenario (Noebauer et al. 2017).Isotope lifetimes and decay energies are taken from Dessart et al.(2014).For all simulations presented in this work, we use a start time of https://github.com/MarkMageeAstro/TURTLS-Light-curvesMNRAS , 1–21 (2021) he diversity of double detonation explosions 𝛾 -packets (representing 𝛾 -ray photons) andtreated with a grey opacity of 0.03 cm g − . Following an interactionwith the model ejecta, 𝛾 -packets are converted to optical radiationpackets ( 𝑟 -packets). For these packets, we use TARDIS (Kerzendorf& Sim 2014; Kerzendorf et al. 2018) to calculate the non-grey ex-pansion opacities and electron-scattering opacities within each cellduring the current time step. During each time step, we extract a ‘vir-tual’ spectrum using the so-called event-based technique (e.g Long& Knigge 2002; Sim et al. 2010a; Kerzendorf & Sim 2014; Bullaet al. 2015; Magee & Maguire 2020). Light curves are calculated viathe convolution of synthetic virtual spectra with the desired set offilter functions at each time step.In Fig. 1, we show a comparison of our model light curves in-cluding the new decay chains to those calculated by Noebauer et al.(2017), using the radiative transfer code, STELLA (Blinnikov et al.1998, 2006), for the same model structure. This model involves thedetonation of a 0.055 𝑀 (cid:12) helium shell on a 1.025 𝑀 (cid:12) carbon-oxygen white dwarf. The resulting explosion leads to the productionof 0.55 𝑀 (cid:12) of Ni in the white dwarf core. The helium shell ash fol-lowing explosion is dominated by IGEs, which includes ∼ 𝑀 (cid:12) of Ni, 0.006 𝑀 (cid:12) of Fe, and 0.004 𝑀 (cid:12) of Cr. Figure 1 ver-ifies that with our implementation of the additional decay chains,TURTLS can broadly match the light curves of Noebauer et al.(2017). The early light curve bump observed in our models is some-what less pronounced than in the Noebauer et al. (2017) model,which is likely a result of differences in the treatment of opacities,for example.We also show light curves in Fig. 1 calculated including eitherthe Fe → Mn → Cr chain, the Cr → V → Ti chain,or neither, as a further demonstration of their contribution to theearly luminosity. We note that in all cases, the Ni → Co → Fedecay chain is included. Including these additional chains producesa ∼ 𝑡 / = 0.345 d and 0.015d,respectively), the Fe → Mn → Cr chain contributes signifi-cantly to the early luminosity within the first few days of explosion.For this model, the early bump reaches a peak 𝐵 -band magnitudeof − ∼ . × erg s − and dominates the luminosity output ofthe model, which is consistent with expectations from Arnett’s law(Arnett 1982). Table 1.
Ejecta model parameters
Core mass Helium shell Fraction of Dominant burningmass shell burned product in shell 𝑀 (cid:12) 𝑀 (cid:12) S – Ni1.00 0.01, 0.04, 0.07, 0.10 0.20, 0.50, 0.80 S – Ni1.10 0.01, 0.04, 0.07, 0.10 0.20, 0.50, 0.80 S – Ni1.20 0.01, 0.04, 0.07, 0.10 0.20, 0.50, 0.80 S – Ni In the following section, we discuss our approach to creating a pa-rameterised description of the ejecta in double detonation explo-sions. Our strategy is based on capturing and exploring the vari-ation present across a range of published models in a systematicway. Each of our models is controlled by the following parameters:the mass of the carbon-oxygen core, the mass of the helium shell,the fraction of the helium shell burned during the explosion, andthe dominant 𝛼 -chain product produced in the shell burning. Therange of input parameters used is shown in Table 1. The name ofeach model is also derived based on these parameters, for exam-ple WD1.00_He0.04_BF0.50_DP56Ni refers to a model with a coremass of 1.0 𝑀 (cid:12) , a helium shell mass of 0.04 𝑀 (cid:12) , of which 50%is burned, and the dominant product produced in the shell is Ni.The range of parameters explored was chosen to broadly cover andbracket the values predicted by various explosion models, but westress they are not exact reproductions of existing models.For each model, we require a density profile for the ejecta. Thedensity profiles presented in Magee et al. (2018) and Magee et al.(2020) were designed to broadly mimic those from a variety of ex-plosion scenarios. In particular, the exponential density profile witha kinetic energy of 1.4 × erg from Magee et al. (2020) bears astriking similarity to the models of Kromer et al. (2010) and Polinet al. (2019), although the density in the outer ejecta is slightly higher.We therefore take this model as our nominal profile shape and sim-ply scale the density to the appropriate ejecta mass, which is givenby the sum of the core and helium shell masses. A demonstrativecomparison between model 3 of Kromer et al. (2010) and two of ourmodels is shown Fig. 2(a). We note that the core mass of model 3(1.025 𝑀 (cid:12) ) is slightly higher than these models (1.0 𝑀 (cid:12) ), and weshow two shell masses (0.04 and 0.07 𝑀 (cid:12) ) to bracket the 0.055 𝑀 (cid:12) shell of model 3. Previous studies of double detonation explosions have shown thatthe amount of Ni produced in the carbon-oxygen core during theexplosion is directly related to the total mass of the white dwarf. InFig. 3(a) we show the core Ni mass produced as a function of totalmass for a sample of models from the literature (Kromer et al. 2010;Shen et al. 2018; Polin et al. 2019; Gronow et al. 2020; Kushnir et al.2020). As shown in Fig. 3(a), there is disagreement between studiesover the total amount of Ni produced. For example, the Polin et al.(2019) models predict a Ni mass of ∼ 𝑀 (cid:12) for a total white dwarfmass of ∼ 𝑀 (cid:12) whereas Kushnir et al. (2020) predict ∼ 𝑀 (cid:12) .Models presented by Kromer et al. (2010), Polin et al. (2019), andGronow et al. (2020) focus on helium-shell detonations, while thoseof Shen et al. (2018) and Kushnir et al. (2020) are instead detonationsof bare, sub-Chandrasekhar mass white dwarfs. For this reason, we MNRAS000
Core mass Helium shell Fraction of Dominant burningmass shell burned product in shell 𝑀 (cid:12) 𝑀 (cid:12) S – Ni1.00 0.01, 0.04, 0.07, 0.10 0.20, 0.50, 0.80 S – Ni1.10 0.01, 0.04, 0.07, 0.10 0.20, 0.50, 0.80 S – Ni1.20 0.01, 0.04, 0.07, 0.10 0.20, 0.50, 0.80 S – Ni In the following section, we discuss our approach to creating a pa-rameterised description of the ejecta in double detonation explo-sions. Our strategy is based on capturing and exploring the vari-ation present across a range of published models in a systematicway. Each of our models is controlled by the following parameters:the mass of the carbon-oxygen core, the mass of the helium shell,the fraction of the helium shell burned during the explosion, andthe dominant 𝛼 -chain product produced in the shell burning. Therange of input parameters used is shown in Table 1. The name ofeach model is also derived based on these parameters, for exam-ple WD1.00_He0.04_BF0.50_DP56Ni refers to a model with a coremass of 1.0 𝑀 (cid:12) , a helium shell mass of 0.04 𝑀 (cid:12) , of which 50%is burned, and the dominant product produced in the shell is Ni.The range of parameters explored was chosen to broadly cover andbracket the values predicted by various explosion models, but westress they are not exact reproductions of existing models.For each model, we require a density profile for the ejecta. Thedensity profiles presented in Magee et al. (2018) and Magee et al.(2020) were designed to broadly mimic those from a variety of ex-plosion scenarios. In particular, the exponential density profile witha kinetic energy of 1.4 × erg from Magee et al. (2020) bears astriking similarity to the models of Kromer et al. (2010) and Polinet al. (2019), although the density in the outer ejecta is slightly higher.We therefore take this model as our nominal profile shape and sim-ply scale the density to the appropriate ejecta mass, which is givenby the sum of the core and helium shell masses. A demonstrativecomparison between model 3 of Kromer et al. (2010) and two of ourmodels is shown Fig. 2(a). We note that the core mass of model 3(1.025 𝑀 (cid:12) ) is slightly higher than these models (1.0 𝑀 (cid:12) ), and weshow two shell masses (0.04 and 0.07 𝑀 (cid:12) ) to bracket the 0.055 𝑀 (cid:12) shell of model 3. Previous studies of double detonation explosions have shown thatthe amount of Ni produced in the carbon-oxygen core during theexplosion is directly related to the total mass of the white dwarf. InFig. 3(a) we show the core Ni mass produced as a function of totalmass for a sample of models from the literature (Kromer et al. 2010;Shen et al. 2018; Polin et al. 2019; Gronow et al. 2020; Kushnir et al.2020). As shown in Fig. 3(a), there is disagreement between studiesover the total amount of Ni produced. For example, the Polin et al.(2019) models predict a Ni mass of ∼ 𝑀 (cid:12) for a total white dwarfmass of ∼ 𝑀 (cid:12) whereas Kushnir et al. (2020) predict ∼ 𝑀 (cid:12) .Models presented by Kromer et al. (2010), Polin et al. (2019), andGronow et al. (2020) focus on helium-shell detonations, while thoseof Shen et al. (2018) and Kushnir et al. (2020) are instead detonationsof bare, sub-Chandrasekhar mass white dwarfs. For this reason, we MNRAS000 , 1–21 (2021)
M. R. Magee et al. )10 D e n s it y a t s a f t e r e xp l o s i on ( g c m ) (a) Kromer+10 model 3Low mass shellHigh mass shell M a ss fr ac ti on a t s a f t e r e xp l o s i on (b) NiSiHe A b s o l u t e f l ux + c on s t a n t ( e r g s c m Å ) (c) Figure 2.
Comparison of properties for Kromer et al. (2010) model 3(1.025 𝑀 (cid:12) core, 0.055 𝑀 (cid:12) helium shell) and our models with a 1.0 𝑀 (cid:12) core and 0.04 𝑀 (cid:12) (red) and 0.07 𝑀 (cid:12) (blue) helium shell. Panel a:
Compar-ison between model density profiles.
Panel b:
Comparison between modelcompositions.
Panel c:
Maximum light spectra for all models (see Sect. 3 forfurther details). Spectra are offset vertically for clarity. we use the former set of models as reference points throughout thisstudy, allowing us to consistently select parameters for our modelhelium shells and cores masses. Between ∼ 𝑀 (cid:12) there isan approximately linear relation and broad agreement between thesedifferent model sets. As the Polin et al. (2019) sample covers a largerange of total masses and different ignition conditions, we use a linearfit to this model set to determine the core Ni mass of our models.The core Ni mass is therefore given by: 𝑀 ( Ni ) = . × ( 𝑀 core + 𝑀 shell ) − . , (1)where 𝑀 core is the mass of the carbon-oxygen core and 𝑀 shell is themass of the helium shell. All variables are in units of 𝑀 (cid:12) . This fit isshown as a dashed line in Fig. 3(a).In Appendix. B, we present additional models exploring Nimasses based on the Shen et al. (2018) and Kushnir et al. (2020)models. Given the uncertainty in the amount of Ni produced, thetotal white dwarf mass should not be taken as a prediction fromour models. Throughout this work, we give the values of core andshell masses simply as reference to identify each model. Instead,we consider the total luminosity (i.e. the Ni mass) to be a robustprediction and expect that there may be a range of white dwarfproperties that produce such a Ni mass.For the distribution of Ni within the core, we follow the func-tional form used by Magee et al. (2018). The Ni mass fraction atmass coordinate 𝑚 is given by: Ni ( 𝑚 ) = ( 𝑠 [ 𝑚 − 𝑀 Ni ] / 𝑀 (cid:12) ) + , (2)where 𝑀 Ni is the total Ni mass in units of 𝑀 (cid:12) . The scaling param-eter, 𝑠 , is used to control how quickly the ejecta transitions from a Ni-rich to -poor composition. The models with 𝑠 =
21 presented byMagee et al. (2020) produce a Ni distribution qualitatively similar C o r e N i m a ss ( M ) (a) Kromer+10Shen+18Polin+19Gronow+20Kushnir+20This work F r ac ti on o f s h e ll bu r n e d (b) Figure 3.
Panel a: Ni mass produced in the carbon-oxygen core as afunction of total mass of the white dwarf (sum of core and shell mass).Literature values are taken from their respective papers (Kromer et al. 2010;Shen et al. 2018; Polin et al. 2019; Gronow et al. 2020; Kushnir et al. 2020).For total masses between 0.90 – 1.30 𝑀 (cid:12) , we show a linear fit to the Polinet al. (2019) models, which is used to determine the core Ni mass of ourmodels.
Panel b:
Fraction of the helium shell that is burned (i.e. convertedto elements heavier than helium following the explosion) as a function oftotal mass. Dashed horizontal lines show fractions of 0.2, 0.5, and 0.8. Blackpoints show the specific models calculated in this work, which broadly extendthe range predicted from a variety of explosion models. to those of Kromer et al. (2010) (Fig. 2(b)), therefore we fix 𝑠 = ∼ − – 10 − 𝑀 (cid:12) ) of unburned carbon and oxygen assuming a Gaussiandistribution (width ∼ 𝑀 (cid:12) ). The mass and distributionof this unburned material is comparable to that predicted by explo-sion models (e.g. Kromer et al. 2010; Polin et al. 2019), althoughin general a symmetric distribution is not predicted for all explosionparameters. We note that we have also tested narrower and broaderdistributions (width ∼ 𝑀 (cid:12) ) and find the exact distribu-tion does not have a significant impact on the model observables anddoes not affect our conclusions. The remaining material in the coreis filled in with intermediate mass elements (IMEs). The composition of the helium shell following the explosion remainsone of the uncertain properties of double detonation explosions. The
MNRAS , 1–21 (2021) he diversity of double detonation explosions O Mg S Ca Cr NiIsotope0.00.20.40.60.81.0 M a ss fr ac ti on i n s h e ll bu r n e d m a t e r i a l Kromer+10 model 3Kromer+10 model 3mStandard distributionBroad distributionNarrow distribution Ne Mg Si S Ar Ca Ti Cr Fe Ni D o m i n a n t bu r n i ng p r odu c t i n s h e ll Figure 4.
Mass fractions of isotopes along the 𝛼 -chain produced in theshell. The relative abundances are shown for the Kromer et al. (2010) modelsassuming a pure helium shell (model 3; black) and a shell that has beenpolluted with 34% carbon pre-explosion (model 3m; grey). Coloured linesshow the mass fractions of all isotopes, assuming burning progresses to aspecific point along the 𝛼 -chain – given by the colour. Solid lines show ourstandard isotope distributions, based on model 3m. The dashed line showsa broad distribution designed to mimic that of model 3 from Kromer et al.(2010), while the dotted line shows a narrow distribution in which more massis burned to the dominant shell product. goal of this work is to present models covering a large parameterspace and systematically investigate differences in observables thatresult from various assumptions about the helium shell. In Fig. 3(b)we show the fraction of the helium shell that is burned following theexplosion (i.e. converted from helium into heavier elements) for aselection of model sets from the literature. It is clear that there canbe a large spread in how much of the shell is consumed, dependingon different assumptions made within the models (such as whenand how ignition is triggered). To investigate the impact of this onthe observables, we choose fractions that bracket those predicted bythe different explosion models. Specifically, for each total mass wecalculate models for which 20%, 50%, and 80% of the helium shell isburned to other elements. These fractions are shown as black dashedlines in Fig. 3(b), while the individual models calculated in this workare shown as black points.Aside from simply investigating how much of the shell is burned,we also aim to demonstrate the effects of elements that are producedduring shell burning. This is strongly dependent on the initial com-position of the shell. Kromer et al. (2010) present a model in whichthe helium shell is polluted and contains 34% C (model 3m). Thisis shown in Fig. 4, along with the composition of the unpollutedmodel (model 3). The choice of 34% was specifically made to createa helium shell that is mostly burned to Ar, which does not pro-duce strong spectroscopic features. As discussed in other studies (e.g.Shen & Bildsten 2009; Waldman et al. 2011; Gronow et al. 2020)the presence of carbon has an important role to play in regulatinghelium burning and shaping the nucleosynthetic yields of the heliumshell. Therefore, the final composition of the helium shell could betuned by varying the level of pollution before explosion (Waldmanet al. 2011). Piro (2015) has demonstrated that a wide range of car-bon pollution fractions could indeed be achieved in the helium shell,depending on specifics of the binary system.This picture is complicated further however, by the presence of other isotopes besides C. In particular, Townsley et al. (2019) haveshown that 𝛼 -chain burning can stall at much lower pollution frac-tions ( ∼ C, N, and O. It is clear that thenucleosynthetic yields of the helium shell could show significant vari-ations following explosion. Linking these to specific compositionspre-explosion is a challenging prospect. Therefore, in this study weexplore a wide variety of options and assume that burning in thehelium shell could stall at any point along the 𝛼 -chain. We make noclaims about specific pre-explosion compositions that could producesuch yields. In the following, we refer to the point at which burningstalls as the dominant product in the shell.We calculate models for dominant shell products ranging from Sto Ni. In our standard model distribution, the relative abundancesof other isotopes along the 𝛼 -chain are taken following from the3m model of Kromer et al. (2010). We chose model 3m for ourstandard isotope distribution as it represents an intermediate case tothe other distributions explored in this work. In addition, Kromeret al. (2010) present abundances for each isotope produced in thehelium shell. Although Ar is the dominant shell product in thismodel, some amount amount of other isotopes are produced aboveand below Ar in the chain. This is demonstrated in Fig. 4, whichshows that Ar is produced with a mass fraction of ∼
60% whilethe previous 𝛼 -chain isotope ( S) has a mass fraction of ∼
30% andthe next isotope ( Ca) has a mass fraction of ∼ 𝛼 -chainisotopes, for a given dominant shell product. Explosion models anddetailed predicted yields covering a range pollution fractions withinthe helium shell are currently unavailable. Therefore, assuming thatsome amount of isotopes above and below the dominant shell productare also produced seems reasonable. Taking a functional form similarto an existing explosion model is a pragmatic choice, but we notethat the exact quantities are unclear.In Fig. 2(c), we verify that our parameterised approach producesspectra comparable to Kromer et al. (2010). We show a comparisonbetween the maximum light spectrum of model 3 (core mass of1.025 𝑀 (cid:12) , shell mass of 0.055 𝑀 (cid:12) ) and two of our models withsimilar parameters (core mass of 1.0 𝑀 (cid:12) , shell masses of 0.04 and0.07 𝑀 (cid:12) ). In general, our models show similar results, howeverthe velocities are typically too high. The purpose of Fig. 2(c) is todemonstrate that our parameterised description of the ejecta is nota limiting factor for the method used here. As discussed in Mageeet al. (2018), differences in the radiative transfer code used here(TURTLS) and that of Kromer et al. (2010) (ARTIS; Kromer &Sim 2009) can lead to different observables. This is reflected inthe spectra for our models, which are generally bluer than thoseof Kromer et al. (2010). In addition, the differences in the densityprofile will have some impact and a combination of these factorsappears to result in a shift of features to higher velocities. We againstress that our models are not intended to be reproductions of existingmodel sets, but are designed to explore a large parameter space. Aspreviously mentioned, by adopting a similar structure to the modelsof Magee et al. (2020) and Magee & Maguire (2020), we allow fora direct comparison with models from these works, which were allcalculated with the same radiative transfer code. In an effort to quantify the significance of our choice for the relativeabundances of isotopes, we calculate two additional sets of models.Firstly, we consider a broad distribution similar to that found formodel 3 of Kromer et al. (2010). This corresponds to a higher mass
MNRAS , 1–21 (2021)
M. R. Magee et al. A b s o l u t e B m a gn it ud e A b s o l u t e g m a gn it ud e Ni dominated shell Fe dominated shell Cr dominated shell Ti dominated shell Ca dominated shell Ar dominated shell S dominated shell A b s o l u t e r m a gn it ud e g r ( m a g ) Figure 5.
Light curves and colours for models with different shell composi-tions. All models shown have a 1.0 𝑀 (cid:12) core and a 0.07 𝑀 (cid:12) shell, of which50% is burned to elements heavier than helium. The dominant 𝛼 -chain prod-uct produced in the shell is given by the colours. The relative fractions of allother isotopes in the shell are given following from Fig. 4. fraction of other isotopes relative to the dominant product in the shell.We also consider a narrow distribution in which the mass fractionsof all other isotopes decreases relative to the dominant product. Bothcases are shown in Fig. 4 as a dashed and dotted line for an Fe and Ar dominated shell, which are the dominant products producedin the standard model 3 and model 3m of Kromer et al. (2010),respectively.Together these two sets of models serve to bracket the distribu-tions assumed throughout this work. The effects of these differentcompositions are discussed further in the appendix in Sect. C, butwe note that in general the differences are relatively minor.
In the following section we discuss the results of our radiative transfermodelling. We demonstrate the significant impact of the helium-shellcomposition on the model light curves and spectra. We comparemodels with the same core (1.0 𝑀 (cid:12) ) and shell (0.07 𝑀 (cid:12) ) masses,but different shell compositions for our standard isotope distribution(Sect. 3.2, Fig. 4). For this comparison of the effect of differentdominant products in the helium shell, we focus on the models inwhich 50% of the helium shell is burned to heavier elements. Othermodels within our set show similar variations for different shellcompositions. Figure 5 shows the effect of the shell composition on the light curveand colour evolution. Similar to previous studies, we find that thosemodels with 𝛼 -chain burning progressing to IGEs ( Ti – Ni),which therefore have relatively large amounts of short-lived radioac-tive isotopes in their shells ( Ni, Fe, and Cr), display prominentbumps in their light curves within the days following explosion. Al-though these bumps are most pronounced at shorter wavelengths,they are also clearly seen in redder filters (e.g. 𝑟 -band). Aside fromthe shape of the light curve, models with IGE-dominated shells also show a distinct colour inversion. The colours are initially blue andquickly reach a peak red colour within a few days of explosion. Atthis point the colour evolution turns over and the models becomesomewhat bluer again, before again turning over and becoming pro-gressively redder towards maximum light.For those models in which the shell is dominated by IMEs ( S or Ar), no early bump is observed due to the lack of the additional ra-dioactive material. Instead, these models show a smooth rise to max-imum light, as well as broader and brighter 𝐵 -band light curves thanour IGE-dominated shell models. Our IME-dominated shell modelsalso show a relatively flat colour evolution beginning approximatelyfive days after explosion. We have also calculated models for whichthe assumed 𝛼 -chain burning stalls earlier than S ( Ne, Mg, and Si), however these models are very similar to each other and the S-dominated model. Therefore, our models show that provided theinitial composition of the helium shell is such that burning stops atIMEs, the relative abundances of this burned material are generallyunimportant for shaping the evolution of the observables further.Interestingly, our Ca-dominated model represents an interme-diate case between the IME- and IGE-dominated shells. No earlylight curve bump is observed and the 𝐵 -band in particular shows alonger dark phase (i.e. the time between explosion and the first lightemerging from the supernova) than all other models. At the sametime, the colour evolution does not show an inversion similar to theIGE-dominated shells, but is significantly redder at maximum lightcompared to the IME-dominated shells. Although Ca is the dom-inant product in the shell ( ∼
55% of the burned material), a smallamount of Ti is also present ( ∼
5% of the burned material). Theadditional opacity contribution from Ti will act to more effectivelyblanket the blue flux than in the other IME-dominated shell models,which do not contain Ti. On the other hand, the Ca-dominatedmodel also lacks a contribution from any radioactive material in theshell, as in the case of the IGE-dominated shell models. Together,both of these properties will cause the lack of additional flux at earlytimes and the redder colours at later times.
In Fig. 6, we show the spectral evolution of our models with differentshell compositions. Spectra are shown at 2.25 d, 7.25 d, and 18.25 dafter explosion. At 2.25 d after explosion, our models dominatedby Ni and Fe are substantially bluer than all other models andshow relatively featureless spectra. Despite still containing short-lived isotopes near the surface of the ejecta, Fig. 6 shows that our Cr-dominated model spectrum is much redder than either the Ni-or Fe-dominated model spectra. As shown in Fig. 1, Fe is thedominant source of luminosity for the early light curve bump – dueto its short half-life. Although some Fe is present in the shell of our Cr-dominated model, it has a much lower fraction than in the Ni-or Fe-dominated models – hence there is a lower luminosity andless heating, producing a fainter and redder spectrum during the earlybump. Our Cr-dominated spectrum also shows a strong absorptionfeature due to S ii at ∼ 𝜆 Ar- and S-dominated models, as well as the S iifeature around ∼ Cr-dominatedmodel.One week after explosion, the Ni- and Cr-dominated shellmodels have become significantly redder. Much of the flux below (cid:46)
MNRAS , 1–21 (2021) he diversity of double detonation explosions Ni dominated shell Fe dominated shell Cr dominated shell Ti dominated shell Ca dominated shell Ar dominated shell S dominated shell N o r m a li s e d f l ux + ( e r g s c m Å ) (b) 7.25d4000 4500 5000 5500 6000 6500 7000 7500Rest wavelength (Å)01020 (c) 18.25d Figure 6.
Spectra for models with different shell compositions. All modelsshown have a 1.0 𝑀 (cid:12) core and a 0.07 𝑀 (cid:12) shell, of which 50% is burnedto elements heavier than helium. The dominant 𝛼 -chain product produced inthe shell is given by the colours. The relative fractions of all other isotopes inthe shell are given following from Fig. 4. Spectra are shown at three epochs:2.25 d, 7.25 d, and 18.25 d after explosion. All spectra are normalised to theflux between 7 000 – 7 500 Å. Features discussed in the main text are shownas shaded regions. Ti ii around ∼ Ni-dominatedmodel, which does not contain Ti in the shell). Our Cr modelshows remarkably little spectral evolution between the two epochspresented here relative to other models within our set. In the IGE-dominated models, a few additional features are produced at longerwavelengths (most notably the Si ii 𝜆 Ar- and S-dominated models, the spectra arenow considerably bluer than the IGE-dominated models. Absorptionprofiles due to IME, such as Si ii 𝜆 ∼ ∼ ∼ ∼ 𝜆 𝜆 A b s o l u t e f l ux ( e r g s c m Å ) TotalCoreShell
Figure 7.
Contribution of material in the helium shell and core to the ob-served spectra at different phases. Spectra are calculated by binning packetsseparately, depending on the location of their last interaction. last interaction. In Fig. 7, we show separate spectra produced bybinning Monte Carlo packets that last interacted with material ineither the shell or the core. We note that we are only able to trackthe location of real packets (rather than virtual packets; see Magee& Maguire 2020), therefore the signal-to-noise ratio of these spectrais lower than others presented throughout this work. Nevertheless,Fig. 7 shows that within the first approximately one week sinceexplosion, the shell material does contribute to the production ofhigh velocity features. Specifically, the Si ii 𝜆 Our models clearly show the impact of the post-explosion heliumshell composition on the observables. Those models in which theshell is burned mainly to IGE show an early bump in the light curve,a colour inversion, and significantly reddened spectra from approx-imately one week after explosion. Conversely, our models in whichthe shell mostly contains IMEs do not show an early bump and in-stead have a relatively flat colour evolution. In addition, we findthat as long as burning within the shell does not progress to IGEs,the model observables show much smaller variations than those forwhich the shell is dominated by IGEs. This would indicate that metic-ulous fine-tuning is not necessary to avoid the impact of the heliumshell ash on the observables – provided burning ceases at a certainpoint, the exact composition of the shell is mostly irrelevant.
MNRAS000
MNRAS000 , 1–21 (2021)
M. R. Magee et al. A b s o l u t e B o l o m e t r i c m a gn it ud e Fe dominated shell S dominated shell A b s o l u t e U m a gn it ud e A b s o l u t e B m a gn it ud e A b s o l u t e g m a gn it ud e A b s o l u t e r m a gn it ud e g r ( m a g ) Figure 8.
Light curves and colours for models with different shell masses.All models shown have a 1.0 𝑀 (cid:12) core and we assume 80% of the shell isburned to elements heavier than helium. We show two representative cases inwhich the composition of the shell is dominated by either S or Fe.
In this section, we demonstrate how the amount of burned materialabove the core affects the model observables. To focus our discussion,we limit our comparisons to models with a core mass of 1.0 𝑀 (cid:12) .Our models are controlled by both the mass of helium shell and theamount of the shell that is assumed to be burned during the explosion.As the mass of the helium shell also determines the amount of Niproduced during the explosion, which will have a significant impacton the model observables, it is not possible to explore solely theeffect of the total amount of material burned. Therefore, in Sect. 5.1we discuss the effects of the helium shell mass and in Sect. 5.2 wediscuss the role of the burned fraction.
In Fig. 8 we show the light curve and colour evolution for modelswith varying shell masses, while the spectral evolution is shown inFig. 9. We limit our comparison to the Fe- and S-dominatedshells, which are representative of trends observed for IGE- andIME-dominated shells, respectively (see Sect. 4).As discussed in Sect. 4, our S-dominated shell models do notproduce an early bump in the light curve, but there is still some vari-ation among the different shell masses. This is not primarily drivenby material in the shell, but rather the different Ni masses in thecore of the white dwarf (Sect. 3.1, Fig. 3). Therefore, models withmore massive shells are brighter and somewhat bluer simply dueto the increased ejecta mass and hence Ni mass. Figure 9 showsthat these models also produce similar spectra, with the primary dif-ferences being the luminosity and colour. Differences between thespectra of models with different shell masses are most pronounced at early times, where lower mass shells show stronger Si ii and S ii fea-tures, likely due to their lower temperatures. For our IME-dominatedmodels we also note there is also a degeneracy between the coreand shell masses. For the models presented here, provided the totalejecta mass is the same, the distinction between the core and shell isunimportant. For example our S-dominated model with a 1.0 𝑀 (cid:12) core and 0.1 𝑀 (cid:12) shell and model with a 1.1 𝑀 (cid:12) core and 0.01 𝑀 (cid:12) shell produce similar light curves and spectra.For our Fe-dominated shells, Fig. 8 shows that all models pro-duce a light curve bump. The timescale of the bump varies signifi-cantly ( ∼ S-dominated shellmodels, the shell mass has a considerable impact on the colour evo-lution for the Fe-dominated models. Smaller shell masses producea more rapid and extreme change in colour within the first five daysafter explosion. In addition, beginning approximately 10 days afterexplosion, the lowest mass shell model (0.01 𝑀 (cid:12) ) shows a relativelyflat colour evolution towards maximum light. In contrast, modelswith more massive shells become significantly redder over this sameperiod. The 0.10 𝑀 (cid:12) shell model remains redder than both the 0.07and 0.04 𝑀 (cid:12) shell models for all times presented here, however theoverall difference between their respective colours decreases withtime. This likely points to two competing effects – the influence ofline blanketing from the shell and the different Ni masses causingdifferent temperatures. More massive shells will produce more lineblanketing and hence one may expect redder colours, but this is notobserved for the models presented here. In this case, as the core massis the same, the increase in the shell mass results in an increased Nimass that keeps the ejecta hotter and bluer. Figure 9(d) shows that,at 2.25 d after explosion, the temperature is the primary differencebetween the models and few features are present. At later epochs, ourmodels show that larger shell masses produce broader Si ii 𝜆 The amount of material in the shell converted from helium to heavierelements is also a free parameter of our models. We have investigatedburned fractions of 20%, 50%, and 80%, which approximately spanthe range predicted by different explosion models (see Fig. 3(b)).The differences between these models are fairly straightforward andfollow the trends one may expect. For IME-dominated shell models,the burned fraction has no effect on the resultant observables. ForIGE-dominated shell models, a higher burned fraction will result ina brighter bump at early times and redder colours at later times.
Here we discuss the rise times and peak magnitudes of the modelspresented in this work and demonstrate the range of magnitudesand timescales for early light curve bumps. In Fig. 10(a) we showthe 𝐵 -band rise times and peak absolute 𝐵 -band magnitudes for ourmodels with the standard isotope distribution. The difference betweenour IGE- and IME-dominated shell models is readily apparent. Wefind that, in general, those models with IGE-dominated shells showshorter rises, with a median rise time of 13.8 ± MNRAS , 1–21 (2021) he diversity of double detonation explosions S-dominated shell0.02.55.07.5 N o r m a li s e d f l ux ( e r g s c m Å ) Fe-dominated shell0123 N o r m a li s e d f l ux ( e r g s c m Å ) Figure 9.
Spectra for models with different shell masses. All models shown have a 1.0 𝑀 (cid:12) core and we assume 80% of the shell is burned to elements heavierthan helium. We show two representative cases in which the composition of the shell is dominated by either S or Fe. Spectra are shown at three epochs:2.25 d, 7.25 d, 18.25 d after explosion. All spectra are normalised to the flux between 7 000 – 7 500 Å.
Figure 10.
Panel a:
Peak absolute 𝐵 -band magnitudes against rise time to peak 𝐵 -band magnitude. Panel b:
Peak absolute 𝐵 -band magnitudes of the early lightcurve bump against time to reach the peak of the bump. We note that all models with IME dominated shells and some models with high core masses do notshow early bumps and therefore are neglected. For models in which the light curve is already declining at the start of our simulation (0.5 d), we consider theseas upper limits and show them as black arrows. In both panels, each model is coloured based on the dominant element produced in the shell. The size of eachpoint is proportional to the burned mass of the helium shell (i.e. the product of the shell mass and burned fraction), while the shape of each point denotes themass of the core. MNRAS000
Peak absolute 𝐵 -band magnitudes of the early lightcurve bump against time to reach the peak of the bump. We note that all models with IME dominated shells and some models with high core masses do notshow early bumps and therefore are neglected. For models in which the light curve is already declining at the start of our simulation (0.5 d), we consider theseas upper limits and show them as black arrows. In both panels, each model is coloured based on the dominant element produced in the shell. The size of eachpoint is proportional to the burned mass of the helium shell (i.e. the product of the shell mass and burned fraction), while the shape of each point denotes themass of the core. MNRAS000 , 1–21 (2021) M. R. Magee et al. of 17.6 ± 𝑀 (cid:12) core, some models withlow-mass shells (0.01 and 0.04 𝑀 (cid:12) ) can show longer rise times thansimilar models with higher mass cores. In these cases, the longer risetimes result from a combination of the compact Ni distributionand less extreme line blanketing of the low-mass shell. For our IME-dominated models, the scatter in the peak absolute 𝐵 -band magnitudeis driven simply by differences in Ni mass due to the variouscore and shell masses explored here. Models with IGE-dominatedshells however, show a significantly larger scatter ( (cid:38) ∼ 𝑟 -band), both the IGE- and IME-dominated shell models show a similar scatter in peak magnitudes(again, due to the differences in the Ni mass), although the IGE-dominated models are systematically brighter as much of the blueflux has been reprocessed to longer wavelengths by the shell.Figure 10(b) shows the properties of the early light curve bumps.We calculate the time since explosion to reach the peak of the bumpand the magnitude at this point. For some models, the light curve isalready declining at the beginning of our simulations (0.5 d after ex-plosion). We therefore consider these points as limits and show themas black arrows in Fig. 10(b). We do not include models with IME-dominated shells as they do not show a bump at early times. In addi-tion some models, such as those with large total masses ( (cid:38) 𝑀 (cid:12) ),do not show pronounced bumps in their light curves due to their high Ni masses and extended distributions. In other words, there is noclear decline in the light curve within the first few days of explosion.These models are also not included in Fig. 10(b). Among the modelsshown in Fig. 10(b), there is a general trend that brighter bumpsare also typically longer lasting. Models with Ti-dominated shellshowever, deviate from this trend. Following from Fig. 4, in our Tidominated model only a small amount of Cr is contained withinthe shell. Therefore this set of models contain a significantly smallermass of radioactive isotopes in the shell compared to our other IGEdominated models. We also note that the models shown as limits inFig. 10(b) hint at the possibility of bright and very short lived bumps– less than 0.5 d. It is highly likely that such bumps could be missedin most current surveys. Ni EXCESS
Magee & Maguire (2020) present light curves and spectra of Chan-drasekhar mass models that contain an excess of Ni (a Ni shell) inthe outer ejecta. Qualitatively, these models show similar behaviour(light curve bumps at early times and line blanketing closer to max-imum light) to double detonations in which a significant fraction ofIGEs is produced in the shell. Here we perform a comparison be-tween these two cases and investigate ways in which they may bedistinguished from each other, based on the early light curve bumpand spectra at maximum light.In Fig. 11(a), we show the Ni distributions of Chandrasekhar-mass model with and without a Ni excess compared to the sub-Chandrasekhar double detonation models explored in this work. Weshow one of the Chandrasekhar mass models from Magee & Maguire(2020) that does not contain a Ni excess (black in Fig. 11; describedas the fiducial SN 2018oh model in Magee & Maguire 2020), along )0.00.51.0 N i m a ss fr ac ti on a t s a f t e r e xp l o s i on (a) 0 5 10 15 20Days since explosion201510 A b s o l u t e B m a gn it ud e (b)4000 5000 6000 7000 8000 9000Rest wavelength (Å)0.00.10.20.30.40.50.60.7 A b s o l u t e f l ux ( e r g s c m Å ) (c)18.25 d Chandrasekhar mass modelsNo excessW/ Ni excessNo excess, w/ extended Ni distributionDouble detonation models Ni-dominated shell S-dominated shell
Figure 11.
Panel a:
Comparison between the Ni distributions for mod-els presented here. We show a Chandrasekhar mass model from Magee &Maguire (2020) that contains a Ni excess in the outer ejecta and the corre-sponding model without an excess, in addition to a model with an extended Ni distribution. Double detonation models with a Ni- and S-dominatedshell (red and purple, respectively) are also shown.
Panel b: 𝐵 -band lightcurve for models presented here. Panel c:
Comparison of spectra for ourmodels at 18.25 d after explosion. with a model in which a 0.03 𝑀 (cid:12) Ni shell has been added to theouter ejecta (Fig. 11, green). We present an additional Chandrasekharmass model without a Ni excess, but in which the Ni distributionhas been extended, such that Ni is present throughout the ejectawith a mass fraction that decreases monotonically towards the outerejecta (Fig. 11, grey). For our sub-Chandrasekhar mass double det-onation model with a 1.0 𝑀 (cid:12) core and a 0.07 𝑀 (cid:12) shell dominatedby Ni (WD1.00_He0.07_BF0.50_DP56Ni; Fig. 11, red), the to-tal Ni mass and Ni distribution in the outer ejecta is similar tothe Ni excess model. Finally, we also show the same model witha S-dominated shell (WD1.00_He0.07_BF0.50_DP32S; Fig. 11,blue) as representative of a sub-Chandrasekhar mass model withoutan excess of Ni in the outer ejecta. We note that the density profileand ejecta mass differs slightly between the double detonation andChandrasekhar mass models shown here.Figure 11(b) demonstrates that the sub-Chandrasekhar mass dou-ble detonation Ni-dominated shell model shows a more pro-nounced bump that rises and declines within a few days comparedto the more plateau-like shape of the Chandrasekhar mass Ni ex-cess model. Even for double detonation models with a lower Nimass fraction in the outer ejecta (i.e. different burned fractions), the Ni-dominated shells do not reproduce the shape of the Ni ex-cess models. Such a difference in light curve shape, despite similar Ni distributions, serves to further highlight the importance of theadditional radioactive isotopes produced in the double detonationmodels. For the Chandrasekhar-mass Ni excess model, Ni is theonly radioactive isotope considered in the ejecta, while the doubledetonation model also contains Fe and a small amount of Cr.Hence, the bump produced in the light curve of the Ni-dominatedshell model is more pronounced due to the presence of Fe, Mn,and Cr, which have considerably shorter half-lives compared to Ni. At later epochs, the double detonation model with a Ni-
MNRAS , 1–21 (2021) he diversity of double detonation explosions dominated shell becomes significantly redder and fainter than the Ni excess model. Again this points to important differences in theejecta composition – the presence of additional IGEs in the doubledetonation model will more effectively blanket blue flux than just the Ni decay chain as in the Ni excess model. For our S-dominatedshell model, the light curve shows a sharper rise and slightly longerdark phase than the model without a clump. In this case, the Ni dis-tribution is somewhat less extended and shows a more rapid changefrom Ni-rich to -poor ejecta than the Chandrasekhar mass modelwithout a Ni excess.In Fig. 11(c) we show the spectra of all models at 18.25 d afterexplosion. At this epoch, our Chandrasekhar mass model without a Ni excess and S-dominated shell model show extremely similarspectra (black and purple lines), with the most noticeable differencebeing that the double detonation model is marginally bluer. Con-versely, the Ni-dominated shell model (red line) is significantlydifferent from all other models, including the Chandrasekhar mass Ni excess model (green line). The flux below ∼ (cid:38) ∼ Ni excessmodel.Comparing Chandrasekhar mass models with a Ni excess in theouter ejecta and sub-Chandrasekhar mass double detonation modelsin which a Ni-dominated shell is produced as a result of heliumshell burning, we find that the two are easily distinguished despitequalitatively similar behaviour. Although thought to be created viaa different mechanism, models with Ni excess can also producean early light curve bump. The shape of the bump however, moreclosely resembles a plateau compared to the clear peak in the doubledetonation models. The significant amount of IGEs produced duringhelium shell burning leads to extremely red colours – even more sothan the Ni excess models, which also show red colours at max-imum. Finally, our IGE-dominated shell models also show shorterrise times than the Ni excess models of Magee & Maguire (2020).
In the following section, we discuss whether our double detonationmodels are consistent with observations of SNe Ia. We compareto light curves and spectra of two well-observed and prototypicalSNe Ia, SNe 2011fe (Nugent et al. 2011; Richmond & Smith 2012;Vinkó et al. 2012) and 2005cf (Pastorello et al. 2007; Garavini et al.2007). Figure 12 shows the light curves of both objects comparedto our models, while spectra are shown in Fig. 13. For SN 2011fe,we show a model with a 1.0 𝑀 (cid:12) core and 0.04 𝑀 (cid:12) shell dominatedby sulphur (WD1.00_He0.04_BF0.20_DP32S). The Ni mass ofthis model (0.49 𝑀 (cid:12) ) is comparable to estimates for SN 2011fe( ∼ 𝑀 (cid:12) ; Nugent et al. 2011). For SN 2005cf, we find that alarger total mass is required to reproduce the higher core Ni mass(0.7 𝑀 (cid:12) ; Pastorello et al. 2007). Our models with either a 1.0 𝑀 (cid:12) core and 0.10 𝑀 (cid:12) shell or 1.1 𝑀 (cid:12) core and 0.01 𝑀 (cid:12) shell bothproduce similar light curves and spectra for a S-dominated shelland may be considered interchangeable. Here we present the modelwith a 1.0 𝑀 (cid:12) core and 0.10 𝑀 (cid:12) shell for SN 2005cf. As previouslymentioned (Sect. 3.1), there is disagreement between various studiesover the amount of Ni produced for a given white dwarf mass duringexplosion. For this reason, the core and shell masses presented hereshould not be taken as predictions for the objects discussed here,but are simply given as reference to identify the comparison models shown. SN 2011fe has been corrected for a total extinction of 𝐸 ( 𝐵 − 𝑉 ) = 0.01 mag. (Nugent et al. 2011), while SN 2005cf has been correctedfor 𝐸 ( 𝐵 − 𝑉 ) = 0.1 mag. (Pastorello et al. 2007).Figure 12 demonstrates that our double detonation models with S-dominated shells provide good agreement with the light curveshapes of both objects beginning a few days after explosion and ex-tending to approximately maximum light. The largest discrepanciesbetween models and observations are observed in the 𝑈 -band, butwe note this is likely related to the simplified composition and ejectastructure used (see Magee et al. 2020), and will be explored in futurework. Townsley et al. (2019) have also previously shown that a dou-ble detonation model with a 1.0 𝑀 (cid:12) core and 0.02 𝑀 (cid:12) helium shelldominated by IMEs can reproduce the light curve of SN 2011fe. Forepochs (cid:46) Ni distributions, Magee et al. (2020) found that the earlylight curve points of SN 2011fe can be reproduced by a relativelyextended Ni distribution with a mass fraction in the outer ejecta of ∼ S-dominated shells, do not contain any Ni in the outerejecta. As shown in Fig. 2, the functional form used for the modelspresented here produces a Ni distribution that is somewhat morecompact than that predicted by Kromer et al. (2010). A slightly moreextended core Ni distribution for the double detonation modelswith S-dominated shells could likely reproduce the earliest detec-tions of SNe 2011fe and 2005cf, without adversely affecting the lightcurve at later times.Figure 13 shows a comparison between the spectra of SNe 2011feand 2005cf and their corresponding double detonation models with S-dominated shells. Previous comparisons to double detonationand bare sub-Chandrasekhar mass models have focused only on spec-tra around maximum light. Here we show spectra for both objects atmultiple epochs, beginning ∼ 𝜆 𝜆 𝜆 ∼ − applied and find improved agreement. As discussedin Sect. 3.2, the systematic shift to high velocities in our spectracould be due to simplifications made in our model density profiles,particularly in the outer regions. Closer to maximum light, velocitiesof many features (such as the S ii-W feature) in our model spectrashow good agreement with both SNe, although Si ii velocities arestill somewhat higher than those observed. In Sect. 4, we show howthe material in the helium shell can impact the spectroscopic featureswithin the first week of explosion. Qualitatively, this is similar tothe broad Si ii 𝜆 MNRAS000
In the following section, we discuss whether our double detonationmodels are consistent with observations of SNe Ia. We compareto light curves and spectra of two well-observed and prototypicalSNe Ia, SNe 2011fe (Nugent et al. 2011; Richmond & Smith 2012;Vinkó et al. 2012) and 2005cf (Pastorello et al. 2007; Garavini et al.2007). Figure 12 shows the light curves of both objects comparedto our models, while spectra are shown in Fig. 13. For SN 2011fe,we show a model with a 1.0 𝑀 (cid:12) core and 0.04 𝑀 (cid:12) shell dominatedby sulphur (WD1.00_He0.04_BF0.20_DP32S). The Ni mass ofthis model (0.49 𝑀 (cid:12) ) is comparable to estimates for SN 2011fe( ∼ 𝑀 (cid:12) ; Nugent et al. 2011). For SN 2005cf, we find that alarger total mass is required to reproduce the higher core Ni mass(0.7 𝑀 (cid:12) ; Pastorello et al. 2007). Our models with either a 1.0 𝑀 (cid:12) core and 0.10 𝑀 (cid:12) shell or 1.1 𝑀 (cid:12) core and 0.01 𝑀 (cid:12) shell bothproduce similar light curves and spectra for a S-dominated shelland may be considered interchangeable. Here we present the modelwith a 1.0 𝑀 (cid:12) core and 0.10 𝑀 (cid:12) shell for SN 2005cf. As previouslymentioned (Sect. 3.1), there is disagreement between various studiesover the amount of Ni produced for a given white dwarf mass duringexplosion. For this reason, the core and shell masses presented hereshould not be taken as predictions for the objects discussed here,but are simply given as reference to identify the comparison models shown. SN 2011fe has been corrected for a total extinction of 𝐸 ( 𝐵 − 𝑉 ) = 0.01 mag. (Nugent et al. 2011), while SN 2005cf has been correctedfor 𝐸 ( 𝐵 − 𝑉 ) = 0.1 mag. (Pastorello et al. 2007).Figure 12 demonstrates that our double detonation models with S-dominated shells provide good agreement with the light curveshapes of both objects beginning a few days after explosion and ex-tending to approximately maximum light. The largest discrepanciesbetween models and observations are observed in the 𝑈 -band, butwe note this is likely related to the simplified composition and ejectastructure used (see Magee et al. 2020), and will be explored in futurework. Townsley et al. (2019) have also previously shown that a dou-ble detonation model with a 1.0 𝑀 (cid:12) core and 0.02 𝑀 (cid:12) helium shelldominated by IMEs can reproduce the light curve of SN 2011fe. Forepochs (cid:46) Ni distributions, Magee et al. (2020) found that the earlylight curve points of SN 2011fe can be reproduced by a relativelyextended Ni distribution with a mass fraction in the outer ejecta of ∼ S-dominated shells, do not contain any Ni in the outerejecta. As shown in Fig. 2, the functional form used for the modelspresented here produces a Ni distribution that is somewhat morecompact than that predicted by Kromer et al. (2010). A slightly moreextended core Ni distribution for the double detonation modelswith S-dominated shells could likely reproduce the earliest detec-tions of SNe 2011fe and 2005cf, without adversely affecting the lightcurve at later times.Figure 13 shows a comparison between the spectra of SNe 2011feand 2005cf and their corresponding double detonation models with S-dominated shells. Previous comparisons to double detonationand bare sub-Chandrasekhar mass models have focused only on spec-tra around maximum light. Here we show spectra for both objects atmultiple epochs, beginning ∼ 𝜆 𝜆 𝜆 ∼ − applied and find improved agreement. As discussedin Sect. 3.2, the systematic shift to high velocities in our spectracould be due to simplifications made in our model density profiles,particularly in the outer regions. Closer to maximum light, velocitiesof many features (such as the S ii-W feature) in our model spectrashow good agreement with both SNe, although Si ii velocities arestill somewhat higher than those observed. In Sect. 4, we show howthe material in the helium shell can impact the spectroscopic featureswithin the first week of explosion. Qualitatively, this is similar tothe broad Si ii 𝜆 MNRAS000 , 1–21 (2021) M. R. Magee et al. A pp a r e n t m a gn it ud e SN2011feStandard distributionCore = 1.00 MShell = 0.04 MBurned Fraction = 0.20Dominant Product = St exp = 55796.79 = 29.10 mag I 12R 10r 8V 6g 4B 2U5 0 5 10 15 20 25Days since explosion A pp a r e n t m a gn it ud e SN2005cfStandard distributionCore = 1.00 MShell = 0.10 MBurned Fraction = 0.50Dominant Product = St exp = 53517.50 = 32.51 mag I 8R 6V 4B 2U5 0 5 10 15 20 25Days since explosion
Figure 12.
Comparisons between the optical light curves of SNe 2011fe and 2005cf (coloured circles) and our sub-Chandrasekhar double detonation modellight curves (dashed black lines). The model parameters and assumed distance modulus are given for each object. The estimated time of explosion (based on thecomparison with the model light curve) is shown as a vertical dashed line for each SN. with different helium shell masses are also capable of reproducingmultiple normal SNe Ia and at various epochs up to maximum light.While our models generally show good agreement from a few daysafter explosion, the initial rise of the light curve is sharper thanobserved, supporting the claims of Magee et al. (2020) that a moreextended distribution for Ni in the core may be required.
A handful of objects with early light curve bumps have now beendiscovered. Among these objects, two distinct groups are clearlyapparent based on their optical colour close to maximum light –those that are extremely red, with 𝐵 − 𝑉 (cid:38) 𝐵 − 𝑉 (cid:46) Ni produced(Sect. 3.1), but are given for reference. The shell masses presentedhere are likely more robust predictions as our models cover a widerange of burned masses and products, and the observed shape of thebump will be highly sensitive to the mass of the shell.
Figure 14 shows a comparison between the light curves ofSNe 2017cbv, 2018oh, 2019yvq, iPTF14atg, and four of our doubledetonation models with Ni-dominated shells. These models arebroadly able to reproduce the shape of the early light curve bump. InFig. 15, we compare spectra of each SN and model around maximumlight.The light curve of SN 2017cbv was previously compared to doubledetonation models by Maeda et al. (2018), however their models weresomewhat too faint (SN 2017cbv was a bright SN Ia and showed apeak absolute magnitude of 𝑀 B = − .
4; Hosseinzadeh et al. 2017).In Fig. 14(a), we show that our model with a 1.1 𝑀 (cid:12) core and massivehelium shell of 0.10 𝑀 (cid:12) dominated by Ni can generally reproducethe shape of the early light curve of SN 2017cbv. The Ni massof this model is 0.94 𝑀 (cid:12) . For the model shown in Fig. 14(a), the 𝑈 -band shows a more pronounced bump than observed; we speculatethat minor changes to the composition within the helium shell couldbe made to find improved agreement in this band. Regardless of thisdiscrepancy, beginning approximately three weeks after explosionthe model light curves show a much faster decline in the bluer bands( 𝑈 , 𝐵 , and 𝑔 ) than SN 2017cbv. This is further demonstrated byFig. 15, which shows that the maximum light spectrum of our doubledetonation model with a Ni-dominated shell exhibits significantline blanketing that is inconsistent with SN 2017cbv. In addition, thespectral features are also inconsistent with SN 2017cbv. Our modelshows a significantly broadened Si ii 𝜆 𝜆 𝜆 𝜆 𝑅 (cid:12) sub-giant is able to reproduce the bump in the optical bands, the modelover-predicts the flux in the UV bands ( 𝑈𝑉𝑊 𝑈𝑉 𝑀
2, and
𝑈𝑉𝑊
MNRAS , 1–21 (2021) he diversity of double detonation explosions A b s o l u t e f l ux ( e r g s c m Å ) A b s o l u t e f l ux ( e r g s c m Å ) Figure 13.
Comparisons between spectra of SNe 2011fe and 2005cf (black), and our double-detonation models with S-dominated shells (red) at epochs from4 – 18 d after explosion, along with the parameters of both models. Spectra are shown on an absolute flux scale. For the first epoch, we also show model spectrashifted in velocity to provide better agreement to the observed features (blue). The phases of the observed spectra of SNe 2011fe and 2005cf relative to 𝐵 -bandmaximum are given in black, while the time since explosion for our model comparison spectra is shown in red. Hosseinzadeh et al. (2017) argue that this could indicate the fluxresulting from the interaction is not a black-body, or an alternativeexplanation is required. Based on nebular spectra hundreds of daysafter explosion, Sand et al. (2018) rule out the presence of any sig-nificant H 𝛼 signatures, which are expected if material is strippedfrom a non-degenerate companion. Finally, the presence of CSMwas also ruled out by Ferretti et al. (2017). Our models indicate thatSN 2017cbv likely did not result from a double detonation explosion.Taken together, the nature of SN 2017cbv is still uncertain.Dimitriadis et al. (2019) compare SN 2018oh to a double deto-nation explosion model with a 0.98 𝑀 (cid:12) core and 0.05 𝑀 (cid:12) heliumshell, which produces 0.45 𝑀 (cid:12) of Ni. To match the early lightcurve bump of SN 2018oh, Dimitriadis et al. (2019) invoke mixingof the SN ejecta after explosion. Therefore, the model does not pro-duce a well defined early bump in the light curve, but rather showsan extended ‘shoulder’ that more closely resembles SN 2018oh. It isnot clear however, whether such mixing could be achieved in dou-ble detonation explosions. Figure 14(b) shows that our model with a1.0 𝑀 (cid:12) core and thin helium shell of 0.04 𝑀 (cid:12) (i.e. a Ni mass of0.49 𝑀 (cid:12) ) with a narrow isotope distribution dominated by Ni pro-vides reasonable agreement to the light curve shape of SN 2018oh.A narrow isotope distribution is required to reduce the mass of Fein the shell and avoid the peak produced by its short lifetime. Evenfor this distribution however, the bump in the model Kepler bandlight curve is more pronounced than observed in SN 2018oh. Reduc-ing the Fe mass further may again provide improved agreementas Magee & Maguire (2020) have shown that the light curve bumpin SN 2018oh can be reproduced by a model containing a clump ofpure Ni in the outer ejecta. Although this model is less affected by line blanketing than themodel for SN 2017cbv, due to the lower mass of the helium shell,Fig. 15 shows that the spectral features of SN 2018oh are also incon-sistent with a double-detonation scenario. Dimitriadis et al. (2019)did not consider the spectra of their double-detonation models com-pared to SN 2018oh. In summary, our models indicate that SN 2018ohdid not result from a double-detonation explosion as we are unableto simultaneously match the spectroscopic features and early lightcurve bump, regardless of the composition of the helium shell.The favoured interpretation for SN 2018oh by Dimitriadis et al.(2019) is that of interaction with a non-degenerate companion. Againsimilar to SN 2017cbv, no evidence for material stripped from anon-degenerate companion has been found in late-time spectra ofSN 2018oh (Tucker et al. 2019). The case of interaction with CSMwas investigated by Shappee et al. (2019), who found that none oftheir interaction models could satisfactorily reproduce the initial earlylight curve shape of SN 2018oh. An alternative case of interactionfor SN 2018oh was suggested by Levanon & Soker (2019). In thisscenario, the explosion follows from the merger of two white dwarfs.An accretion disk forms around the primary (Raskin et al. 2012;Zhu et al. 2013), which serves as the source of the CSM. Afterexplosion, the SN ejecta shocks material in the disk, producing aflash of UV radiation that may be similar to that of SN 2018oh(Levanon et al. 2015). This scenario warrants further investigationwith radiative transfer simulations, as alternatives appear to be ruledout for SN 2018oh.In Fig. 14(c), we compare a double-detonation model toSN 2019yvq (Miller et al. 2020a). SN 2019yvq was a somewhatpeculiar SN – it was slightly under-luminous, but showed high ve-
MNRAS000
MNRAS000 , 1–21 (2021) M. R. Magee et al. A pp a r e n t m a gn it ud e SN2017cbvStandard distributionCore = 1.10 MShell = 0.10 MBurned Fraction = 0.50Dominant Product = Nit exp = 57821.50 = 31.34 mag (a)i 10r 8V 6g 4B 2U5 0 5 10 15 20 25Days since explosion A pp a r e n t m a gn it ud e SN2018ohNarrow distributionCore = 1.00 MShell = 0.04 MBurned Fraction = 0.50Dominant Product = Nit exp = 58144.50 = 33.61 mag (b)Kepler 4V 2g5 0 5 10 15 20 25Days since explosion A pp a r e n t m a gn it ud e SN2019yvqStandard distributionCore = 0.90 MShell = 0.04 MBurned Fraction = 0.20Dominant Product = Nit exp = 58845.00 = 33.04 mag (c)i 4r 2g5 0 5 10 15 20 25Days since explosion 56775 56780 56785 56790 56795 56800Time (MJD)5.07.510.012.515.017.520.022.525.0 A pp a r e n t m a gn it ud e iPTF14atgStandard distributionCore = 0.90 MShell = 0.01 MBurned Fraction = 0.20Dominant Product = Nit exp = 56779.79 = 34.90 mag (d)i 10R 8r 6V 4g 2B5 0 5 10 15 20 25Days since explosion
Figure 14.
Comparisons between SNe 2017cbv, 2018oh, 2019yvq, and iPTF14atg (coloured circles) and our double detonation models (dashed lines) with Ni-dominated shells. The model parameters and assumed distance modulus are given for each object. The estimated time of explosion (based on the comparisonwith the model light curve) is also shown as a vertical dashed line for each SN. locity spectral features. Miller et al. (2020a) compared observationsof SN 2019yvq to a variety of models, including double detonationexplosions. They found reasonable agreement to a double-detonationmodel with a 0.92 𝑀 (cid:12) core and 0.04 𝑀 (cid:12) shell. In Fig. 14(c) we showour model with comparable values – a 0.9 𝑀 (cid:12) core and 0.04 𝑀 (cid:12) shell dominated by Ni. The similarity of these values is unsurpris-ing, given that Miller et al. (2020a) use the same modelling treatmentas Polin et al. (2019), upon which our models are at least partiallybased. As in Miller et al. (2020a), our model generally matches theearly light curve bump in the redder bands ( 𝑟 and 𝑖 ), but the 𝑔 -bandshows a larger decrease in magnitude than is observed immediately following the peak of the bump. Even for models with different dom-inant products (e.g. Fe and Cr) in the shell, we are not able tosimultaneously match the bump in both the 𝑔 - and 𝑟 -bands. As withSNe 2017cbv and 2018oh, Fig. 15 shows that the maximum lightspectrum of SN 2019yvq is significantly bluer than the model anddoes not exhibit strong line blanketing.In addition to double detonation explosions, Miller et al. (2020a)investigate other scenarios to explain SN 2019yvq, including an ex-cess of Ni in the outer ejecta, a violent merger, and companioninteraction. None of the proposed scenarios fully explain all of theobserved features. One possible exception is the violent merger sce-
MNRAS , 1–21 (2021) he diversity of double detonation explosions SN2017cbv1.10 M core, 0.10 M shell A b s o l u t e f l ux ( e r g s c m Å ) SN2018oh1.00 M core, 0.04 M shell
SN2019yvq0.90 M core, 0.04 M shell iPTF14atg0.90 M core, 0.01 M shell
Figure 15.
Comparisons between SNe 2017cbv, 2018oh, 2019yvq, andiPTF14atg (black) and our model spectra (red) around maximum light, alongwith the parameters of all models. Spectra are shown on an absolute fluxscale. Phases of SNe relative to 𝐵 -band maximum are given in black, whilethe time since explosion for our model spectra is shown in red. nario. While it is likely that this scenario does produce some CSM,models including this material are currently unavailable. Based onthe identification of calcium in nebular spectra and favourable com-parisons with model nebular spectra, Siebert et al. (2020) argue thatSN 2019yvq was indeed the result of a helium shell detonation. Thelight curve curve of the model favoured by Siebert et al. (2020)however, does not reproduce what is observed in SN 2019yvq. Themodel is simultaneously too bright and does not show a pronouncedbump at early times. Whether it is possible to simultaneously matchthe early- and late-time observations of SN 2019yvq requires furtherinvestigation.Finally, Fig. 14(d) shows iPTF14atg compared to a double-detonation model with a 0.9 𝑀 (cid:12) core and thin helium shell of0.01 𝑀 (cid:12) . This model contains only 0.13 𝑀 (cid:12) of Ni. Unlike theother objects discussed here, the early bump observed in iPTF14atgwas less pronounced in the optical bands, but clearly apparent atUV wavelengths. (Cao et al. 2015). The origin of this early excesswas discussed by Cao et al. (2015), who argued that it is consistentwith theoretical predictions of the collision between the SN ejectaand companion star. They also discuss the possibility of this excessarising from Ni at the surface of the ejecta, such as in double det-onation models, and estimate that this would require a Ni mass A pp a r e n t m a gn it ud e Standard distributionCore = 1.00 MShell = 0.04 MBurned Fraction = 0.20Dominant Product = Fet exp = 57482.00 = 38.99 mag (a) r 2g0 10 20Days since explosion 57480 57490 57500Time (MJD)161820222426 A pp a r e n t m a gn it ud e Standard distributionCore = 1.00 MShell = 0.04 MBurned Fraction = 0.20Dominant Product = Nit exp = 57482.00 = 38.99 mag (b) 0 10 20Days since explosion57480 57490 57500Time (MJD)161820222426 A pp a r e n t m a gn it ud e Narrow distributionCore = 1.00 MShell = 0.04 MBurned Fraction = 0.50Dominant Product = Nit exp = 57482.00 = 39.09 mag (c) 0 10 20Days since explosion 57480 57490 57500Time (MJD)161820222426 A pp a r e n t m a gn it ud e Standard distributionCore = 1.00 MShell = 0.04 MBurned Fraction = 0.50Dominant Product = St exp = 57482.00 = 38.99 mag (d) 0 10 20Days since explosion Figure 16.
Comparisons between SN 2016jhr and a subset of our models.The model parameters and assumed distance modulus are given for eachobject. The estimated time of explosion (based on agreement with the modellight curve) is also shown as a vertical dashed line for each SN. In all cases,our model light curves have been transformed into the observer frame ofSN 2016jhr (redshift of 0.117). of ∼ 𝑀 (cid:12) at the surface. Figure 14(d) shows that even for ourmodel with a 0.01 𝑀 (cid:12) shell, the early light curve bump producedis inconsistent with iPTF14atg. Figure 15 also shows the maximumlight spectrum of iPTF14atg. Our model predicts a spectrum at max-imum light that is substantially redder than iPTF14atg, and showsstrong flux suppression for wavelengths (cid:46) Observations of SN 2016jhr were presented by Jiang et al. (2017),who found reasonable agreement with models of double detonationsand either sub- or near-Chandrasekhar mass white dwarfs. In Fig. 16,we show a comparison between some of our double-detonation mod-els and SN 2016jhr. We note that unlike Jiang et al. (2017), we donot apply K-corrections to the observed light curve as these may beuncertain due to the peculiar nature of SN 2016jhr. Instead, we trans-form our model spectra into the observer frame (redshift of 0.117)and calculate observer frame light curves. For all comparisons, weassume an explosion date of MJD = 57482.0, which is a few hoursbefore the first detection. We also assume a distance modulus of 𝜇 = 38.99 mag, which is 0.3 mag higher than that used by Jiang et al.(2017).Figure 16(a) shows our model with a 1.0 𝑀 (cid:12) core and 0.04 𝑀 (cid:12) helium shell dominated by Fe. The core and shell mass of modelsshown here is comparable to the models presented by Jiang et al.(2017) (1.03 𝑀 (cid:12) core and 0.054 𝑀 (cid:12) helium shell) and Polin et al. MNRAS000
Comparisons between SN 2016jhr and a subset of our models.The model parameters and assumed distance modulus are given for eachobject. The estimated time of explosion (based on agreement with the modellight curve) is also shown as a vertical dashed line for each SN. In all cases,our model light curves have been transformed into the observer frame ofSN 2016jhr (redshift of 0.117). of ∼ 𝑀 (cid:12) at the surface. Figure 14(d) shows that even for ourmodel with a 0.01 𝑀 (cid:12) shell, the early light curve bump producedis inconsistent with iPTF14atg. Figure 15 also shows the maximumlight spectrum of iPTF14atg. Our model predicts a spectrum at max-imum light that is substantially redder than iPTF14atg, and showsstrong flux suppression for wavelengths (cid:46) Observations of SN 2016jhr were presented by Jiang et al. (2017),who found reasonable agreement with models of double detonationsand either sub- or near-Chandrasekhar mass white dwarfs. In Fig. 16,we show a comparison between some of our double-detonation mod-els and SN 2016jhr. We note that unlike Jiang et al. (2017), we donot apply K-corrections to the observed light curve as these may beuncertain due to the peculiar nature of SN 2016jhr. Instead, we trans-form our model spectra into the observer frame (redshift of 0.117)and calculate observer frame light curves. For all comparisons, weassume an explosion date of MJD = 57482.0, which is a few hoursbefore the first detection. We also assume a distance modulus of 𝜇 = 38.99 mag, which is 0.3 mag higher than that used by Jiang et al.(2017).Figure 16(a) shows our model with a 1.0 𝑀 (cid:12) core and 0.04 𝑀 (cid:12) helium shell dominated by Fe. The core and shell mass of modelsshown here is comparable to the models presented by Jiang et al.(2017) (1.03 𝑀 (cid:12) core and 0.054 𝑀 (cid:12) helium shell) and Polin et al. MNRAS000 , 1–21 (2021) M. R. Magee et al.
Standard distributionCore = 1.00 MShell = 0.04 MBurned Fraction = 0.20Dominant Product = Fe A b s o l u t e f l ux ( e r g s c m Å ) Standard distributionCore = 1.00 MShell = 0.04 MBurned Fraction = 0.20Dominant Product = Ni Narrow distributionCore = 1.00 MShell = 0.04 MBurned Fraction = 0.50Dominant Product = S Standard distributionCore = 1.00 MShell = 0.04 MBurned Fraction = 0.50Dominant Product = S Figure 17.
Comparisons between SN 2016jhr (black) and our model spectra(red) around maximum light, along with the parameters of both models. (2019) (1.0 𝑀 (cid:12) core and 0.05 𝑀 (cid:12) helium shell). Our model contains0.49 𝑀 (cid:12) of Ni and is able to broadly reproduce the light curveshape of SN 2016jhr during the first few days after explosion, butshows a much faster decline in the 𝑔 -band than observed. Assuminga shell dominated by Ni (Fig. 16(b)), we again find that our modelcan reproduce the early light curve bump. We also find improvedagreement in the 𝑔 -band close to maximum light, however the modelstill declines somewhat faster than observed. In Fig. 16(c), we showa model assuming our narrow isotope distribution. In this model, amuch larger fraction of Ni is present in the shell relative to Fethan in our standard distribution. In this case, the 𝑟 -band light curvedoes not display a pronounced bump and instead shows a shoulderto the light curve that is still generally consistent with SN 2016jhr.For the 𝑔 -band, this model is clearly brighter during the bump thanthe observations, however a lower burned fraction may produce morefavourable agreement (the models shown in Fig. 16(a) & (b) both haveburned fractions of 0.2, while the model in Fig. 16(c) has a burnedfraction of 0.5). Around maximum light, this model also produces abroader 𝑔 -band light curve that more closely resembles SN 2016jhr.As a further point of comparison, we also show a model with a S-dominated shell (Fig. 16(d)). In this case, the model clearly does notreproduce the early light curve bump, but provides good agreementaround maximum light.In Fig. 17, we show spectra for the models presented in Fig. 16at 18.25 d after explosion and compare them to SN 2016jhr approx-imately two days before maximum light. As expected from the lightcurve comparison, Fig. 17 shows that our standard isotope distribu-tion models with Fe- and Ni-dominated shells do a reasonable jobof reproducing the maximum light spectrum. The Ni-dominatedshell produces better agreement at shorter wavelengths, while the Fe-dominated shell model shows more extreme flux suppression.In both cases, the continuum flux around ∼ 𝜆 S-dominated shell model, we find that the S ca l e d f l ux ( e r g s c m Å ) S ca l e d f l ux ( e r g s c m Å ) Figure 18.
Comparison between spectra of SN 2018byg (black) and ourmodel with a 0.9 𝑀 (cid:12) core and 0.1 𝑀 (cid:12) shell (red). Phases of SN 2018ybq aregiven relative to 𝑟 -band maximum, while days since explosion are given forour model. Spectra are shown in scaled flux. model spectrum provides excellent agreement with the velocities ofIMEs, such as Si ii and S ii. In contrast to the other models shown inFig. 17, the S-dominated model does not show enough flux sup-pression at shorter wavelengths and instead is bluer than SN 2016jhr.Taken together, our models corroborate the claims of Jiang et al.(2017) that SN 2016jhr is consistent with a double detonation explo-sion. The exact composition of the shell required is unclear, althoughit must include at least some amount of short-lived radioactive iso-topes. Minor changes to the models presented here could provideimproved agreement. Assuming a helium shell dominated by IMEs,we also find good agreement with the light curves and spectrum closeto maximum light, although the model spectrum is too blue, whichcould indicate an alternative explanation for the early light cure bumpis also possible. Indeed, a small Ni excess in the outer ejecta mayalso provide good agreement with the early light curve shape andproduce a redder spectrum consistent with SN 2016jhr.In addition to SN 2016jhr, SN 2018byg also shows a peculiar earlylight curve and extremely red colours close to maximum light. Theobservations of SN 2018byg were presented by De et al. (2019),who show that SN 2018byg displays a shoulder to the early riseof the 𝑟 -band light curve. De et al. (2019) argue that SN 2018byg isconsistent with the double detonation of a low mass white dwarf core( ∼ 𝑀 (cid:12) ) and massive helium shell ( ∼ 𝑀 (cid:12) ). De et al. (2019)were unable to reproduce the early light curve shape of SN 2018bygwithin the standard double detonation scenario and find all modelsproduce a significant light curve bump that is not observed. Instead,De et al. (2019) artificially performed mixing of the ejecta to matchthe light curve shape, as in Dimitriadis et al. (2019) for the case ofSN 2018oh. Again, it is not clear how such mixing could be achieved.As the parameter space of our model set does not cover the appro-priate Ni mass range predicted for SN 2018byg, our models are allmuch brighter than the observations. Therefore, in Fig. 18, we showspectra for one of our models with a low mass white dwarf (0.9 𝑀 (cid:12) )and thick helium shell (0.1 𝑀 (cid:12) ) dominated by Ni that is scaled tomatch the flux of SN 2018byg. Figure 18 shows that approximately10 d after explosion, our model generally reproduces the spectrumof SN 2018byg at −
10 d relative to maximum light. SN 2018bygshows a relatively flat continuum between ∼ MNRAS , 1–21 (2021) he diversity of double detonation explosions A pp a r e n t m a gn it ud e PTF10opsStandard distributionCore = 0.90 MShell = 0.01 MBurned Fraction = 0.20Dominant Product = Ni , St exp = 55381.50 = 37.12 mag i 6R 4r 2g Figure 19.
Comparison between the light curve of PTF10ops and our modelswith a 0.9 𝑀 (cid:12) core, 0.01 𝑀 (cid:12) shell and either a Ni-dominated (red) or S-dominated (purple) composition for the shell. The explosion epoch isshown as a vertical dashed line. reproduce the extreme flux suppression at wavelengths (cid:46) ∼ PTF10ops was a peculiar SN Ia that showed a light curve significantlybroader than expected for its low luminosity ( 𝑀 B = − . ± . 𝐵 -band maximum, while the next detection was six days later. Makinga definitive statement on the origin of PTF10ops is therefore a chal-lenging prospect. Here we discuss whether PTF10ops is consistentwith models of double detonation explosions.In Fig. 19, we show a comparison between the light curve ofPTF10ops and models with either a Ni- or S-dominated shell.These models contain a core mass of 0.9 𝑀 (cid:12) and shell mass of0.01 𝑀 (cid:12) . The mass of Ni produced in the core is 0.13 𝑀 (cid:12) . For the Ni-dominated shell, our model shows a short-lived bump approx-imately one day after explosion that is consistent with the earliestdetection of PTF10ops. The lack of detections in the following daysand in other bands means that the decline from this initial bumpcould have simply been missed. This model also provides a goodmatch to the later light curve evolution, but is slightly too faint in the 𝑔 -band. Conversely, the S-dominated model does not match theearliest detection. Again, this model is able to match the light curvetowards maximum light, but remains too faint in the 𝑔 -band.Figure 20 shows spectra for both models compared to PTF10opsapproximately one week before maximum light. While both models A b s o l u t e f l ux ( e r g s c m Å ) Ni-dominated shell S-dominated shell
Figure 20.
Comparison between the spectrum of PTF10ops approximatelyone week before 𝐵 -band maximum (black) and our models with a 0.9 𝑀 (cid:12) core, 0.01 𝑀 (cid:12) shell and either a Ni-dominated (red) or S-dominated(purple) composition for the shell. Phases for the model spectra are given asdays since explosion. All spectra are shown in an absolute flux scale. provide good agreement for wavelengths (cid:38) Ni-dominated shell model shows significant line blanketingthat is inconsistent with PTF10ops. The S-dominated shell modelprovides improved agreement, although it shows much stronger Ca iifeatures than those observed.Our models show that if PTF10ops did indeed have an excess offlux at early times, this was not due to a helium shell detonation as itsspectra do not show significant line blanketing. Double detonationmodels in which the helium shell is dominated by IMEs providebetter agreement overall, but they are not able to match the firstdetection in the light curve. As with normal SNe Ia (Sect. 8), thiscould indicate that a somewhat extended Ni distribution may berequired for these sub-Chandrasekhar mass models. Alternatively,any early excess emission could be due to interaction, but the lack ofnebular spectra and indeed the poorly sampled early light curve makesa definitive conclusion about the nature of PTF10ops a challengingprospect.
By comparing our models to observations of SNe Ia with earlybumps, we show that a variety of shell masses and compositions isnecessary to reproduce the diversity observed. While double detona-tion models can match the shapes of the early bumps for all objects(with the exception of iPTF14atg), only those with red colours atmaximum light are well matched both photometrically and spectro-scopically throughout their evolution following the bump. An inves-tigation of the extent to which double detonations can explain theseblue objects requires further observations for a larger sample of ob-jects. We note however, that all of the currently proposed mechanismsfor producing early light curve bumps appear inconsistent with theseblue objects in at least some way. These discrepancies may be dueto incorrect colours or lacking features predicted from models ofcompanion and CSM interaction in nebular spectra.
10 CONCLUSIONS
We have presented a large-scale parameter study of the double deto-nation explosion scenario. Using the Monte Carlo radiative transfer
MNRAS , 1–21 (2021) M. R. Magee et al. code presented by Magee et al. (2018), we calculated light curvesand spectra for parameterised ejecta structures that were designed tobroadly mimic predictions from theoretical explosion models (e.g.Kromer et al. 2010; Polin et al. 2019; Gronow et al. 2020). Weconsidered a range of white dwarf core masses (0.9 – 1.2 𝑀 (cid:12) ) andhelium shell masses (0.01 – 0.10 𝑀 (cid:12) ), which effectively amounts toa range of Ni masses. We also considered, for the first time, a largerange of possible compositions for the burned material produced inthe helium shell, which may result from different levels of pollutionin the shell pre-explosion (Shen & Bildsten 2009; Waldman et al.2011; Kromer et al. 2010; Gronow et al. 2020).Broadly, our model set may be separated into two categories: thosethat contain iron-group elements (IGE) in the shell and those that donot. Consistent with previous studies (e.g. Noebauer et al. 2017; Jianget al. 2017; Polin et al. 2019), we find that those models containingIGE in the shell produce a bump in their respective light curveswithin the days following explosion. The luminosity and timescaleof the bump can show considerable variation, reaching up to 𝑀 B ∼−
18 and lasting a few days for massive shells. Although the bumpis most pronounced for bluer bands (e.g. 𝐵 ), it is also visible atlonger wavelengths. At later times, light curves and spectra showextremely red colours and much of the flux below ∼ 𝐵 -band maximum typically around two weeks. Conversely,models that do not contain IGE in the shell show a relatively flat andblue colour evolution, and longer rise times that are more typical ofnormal SNe Ia.As shown previously (Kromer et al. 2010; Townsley et al. 2019),models that do not contain IGE in the shell provide good agreementwith observations of normal SNe Ia around maximum light. Here,we have extended this and shown that the double detonation scenariois consistent with normal SNe Ia beginning a few days after explo-sion. Our models do not provide evidence that the helium shell mustcontain specific elements (e.g. S), but rather show that it cannotcontain IGE and beyond this requirement the composition has littleeffect. Therefore, provided the helium shell does not produce IGEduring the explosion (which could be due to some amount of pollu-tion), the double detonation scenario may be considered viable fora range of normal SNe Ia and cannot be excluded. Future explosionmodels should investigate this further by exploring a range of coreand helium shell masses, as well as initial helium shell compositions.We also compared our models to SNe Ia that show early bumpsin their light curves. While we find that the bumps of all objects(with the exception of iPTF14atg) can be reproduced, only thoseobjects with red colours at maximum light ( 𝐵 − 𝑉 (cid:38)
1) are matchedthroughout their evolution. For blue objects, the model spectra atmaximum light typically show broader features than observed, inaddition to strong flux suppression. Regardless of the composition ofthe shell, we are unable to simultaneously match the early light curveand maximum light spectra of these blue events. The discovery ofadditional objects with early light curve bumps will help to determinethe limit of the double-detonation scenario in reproducing observedlight curve bumps.Given that our double detonation models are unable to reproducethe complete evolution of blue SNe Ia showing bumps at early times,this would indicate that an alternative source for the light curvebumps of these blue objects is necessary. Previous studies have alsoconsidered alternative scenarios and generally there is at least somedisagreement between these scenarios and the observations. Thismay be due to either an over- or under-prediction of UV flux orthe lack of features predicted by companion and CSM interactionscenarios in nebular spectra. It is therefore clear that there is much that remains unknown about the origin of the light curve bumps inSNe Ia. As current and future facilities, such as the Zwicky TransientFacility and the Vera C. Rubin observatory (LSST), discover moreSNe Ia within hours of explosion, an investigation of general trendsamong the class will become possible. This should provide furtherinsights into the nature of these enigmatic bumps.
ACKNOWLEDGEMENTS
We thank the anonymous referee for their detailed and constructivecomments, which helped to improve the clarity of our manuscript.We thank U. Nöbauer and A. Polin for providing densities and com-positions for models used in their respective works. This work wassupported by TCHPC (Research IT, Trinity College Dublin). Cal-culations were performed on the Kelvin cluster maintained by theTrinity Centre for High Performance Computing. This cluster wasfunded through grants from the Higher Education Authority, throughits PRTLI program. This work made use of the Queen’s UniversityBelfast HPC Kelvin cluster. MM and KM are funded by the EUH2020 ERC grant no. 758638. This research made use of Tardis, acommunity-developed software package for spectral synthesis in su-pernovae (Kerzendorf & Sim 2014). The development of Tardis re-ceived support from the Google Summer of Code initiative and fromESA’s Summer of Code in Space program. Tardis makes extensiveuse of Astropy and PyNE. This work made use of the HeidelbergSupernova Model Archive (HESMA), https://hesma.h-its.org.
DATA AVAILABILITY
All models presented in this work are available on GitHub . REFERENCES
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APPENDIX A: START TIME CONVERGENCE TEST
All models presented in this work were calculated assuming a starttime of 0.5 d after explosion, which is comparable to the decaytimescale of some of the radioactive isotopes included in the model.For packets injected before the start of the simulation, diffusion rel-ative to the matter in the ejecta is assumed to be negligible. Theenergy of these packets is also reduced to account for work done onthe ejecta (see e.g. Lucy 2005).In Fig. A1 we show Fe-dominated shell models calculated withearlier start times of 0.2 d and 0.4 d after explosion, as well as latertimes of 0.6 d, 0.8 d, and 1.0 d after explosion. As demonstrated byFig. A1, the choice of 0.5 d after explosion does not significantly im-pact the light curve. From ∼ (cid:46) Fe, for example, is shorter than our0.5 d start time, the light curves in this case do not show significantvariation when assuming earlier start times.
APPENDIX B: EFFECTS OF CORE Ni MASS
As discussed in Sect. 3.1, the Ni masses of our models are based onthose of similar models presented by Kromer et al. (2010) and Polin
MNRAS000
MNRAS000 , 1–21 (2021) M. R. Magee et al. A b s o l u t e B m a gn it ud e Ni dominated shell Fe dominated shell S dominated shell A b s o l u t e g m a gn it ud e Polin+19 basedKushnir+20 based A b s o l u t e r m a gn it ud e g r ( m a g ) Figure B1.
Light curves and colours for models with different core Nimasses. All models shown have a 1.0 𝑀 (cid:12) core and a 0.10 𝑀 (cid:12) shell, ofwhich 50% is burned to elements heavier than helium. We show models withdominant shell products of Fe and S, as representative of models withIGE- and IME-dominated shells. et al. (2019). Kushnir et al. (2020) present a detailed study of bare,sub-Chandrasekhar mass detonation models and show that the Nimasses presented in these works may be systematically lower thanthose determined by other studies. Predicted Ni masses calculatedby Kushnir et al. (2020) are shown in Fig. 3(a) for their default setup.Also shown are Ni masses presented by Shen et al. (2018) forwhite dwarfs in the range ∼ 𝑀 (cid:12) , which show only minorvariations for different metallicities and agree with those of Kushniret al. (2020).Figure 3(a) shows that differences in predicted Ni masses maybe relatively large – particularly for lower mass white dwarfs. Toaccount for this uncertainty in the Ni mass produced, we presentan additional set of models in which the core Ni mass is based onthe Kushnir et al. (2020) models. Using a linear fit to these models,the core Ni mass is given by: 𝑀 ( Ni ) = . × ( 𝑀 core + 𝑀 shell ) − . , (B1)where 𝑀 core and 𝑀 shell are again the mass of the carbon-oxygencore and helium shell, respectively, in units of 𝑀 (cid:12) . In Fig. B1,we show a comparison between models with Ni masses basedon Polin et al. (2019) (Eqn. 1) and those based on Kushnir et al.(2020) (Eqn. B1). As expected, those models with increased Nimasses show systematically brighter peak luminosities, earlier rises,and overall bluer colours compared to their lower mass counterparts.Figure B1 shows that the increased Ni mass results in brighter 𝐵 - and 𝑔 -band peaks by ∼ S-dominated shellmodel. This model also begins to rise slightly earlier (by ∼ (cid:46) Ni- and Fe-dominated shell models, thechanges from an increased Ni mass are more dramatic, particularlyin the 𝐵 -band. In these cases, the 𝐵 -band peaks are brighter by ∼ 𝑔 -band light curves experience slightly moremodest increases of ∼ Ni masses, the shapes of the early light curve bumpsare unaffected as these are primarily driven by the material in the Ni dominated shell Fe dominated shell S dominated shell A b s o l u t e f l ux + c on s t a n t ( e r g s c m Å ) (b) 7.25d Polin+19 basedKushnir+20 based
Rest wavelength (Å)
Figure B2.
Light curves and colours for models with different core Nimasses. All models shown have a 1.0 𝑀 (cid:12) core and a 0.10 𝑀 (cid:12) shell, ofwhich 50% is burned to elements heavier than helium. We show models withdominant shell products of Fe and S, as representative of models withIGE- and IME-dominated shells. shell. The rise time and magnitude of the bump peak is unaffected,however the decline after the peak of the bump is less pronounced. Asthe increased Ni mass models begin to rise earlier, the differencebetween the peak of the bump and the minimum after the bump isreduced. This may make bumps less distinguishable in some casesas the earlier rise of the light curve produces more of a ‘shoulder’in the light curve than a well-defined rise and decline (such as thoseshown in the 𝑟 -band in Fig. B1.In Fig. B1, we also show the colour evolution for these models.This is further reflected in Fig. B2, which shows spectra for eachmodel at 3.25 d, 7.25 d, and 18.25 d after explosion. For our S-dominated shell model, the 𝑔 − 𝑟 colour is bluer by (cid:46) Ni- and Fe-dominated shell models show larger changes.At their reddest points ( ∼ Ni massmodels show a shift to bluer 𝑔 − 𝑟 colours between ∼ ∼ Δ 𝑔 − 𝑟 for this transition decreases from ∼ ∼ Ni- and Fe-dominated shell modelswith increased Ni masses show a bluer 𝑔 − 𝑟 colour than the S-dominated shell model between approximately one and two weeksafter explosion. This is somewhat misleading, as Fig. B2 shows thatthe spectra at these epochs for our S-dominated shell model arebluer and this is indeed reflected in the 𝑈 − 𝐵 and 𝐵 − 𝑉 colours.The appearance of the bluer 𝑔 − 𝑟 colours for the Ni- and Fe-dominated shells is likely due to increased fluorescence emission atthese wavelengths. Similar to the S-dominated shell model, theincreased Ni mass also causes a slight shift to higher velocities forspectral features in the case of our Ni- and Fe-dominated shellmodels.
MNRAS , 1–21 (2021) he diversity of double detonation explosions A b s o l u t e B m a gn it ud e Fe dominated shell S dominated shell A b s o l u t e g m a gn it ud e Standard distributionBroad distributionNarrow distribution A b s o l u t e r m a gn it ud e g r ( m a g ) Figure C1.
Light curves and colours for models with different shell isotopedistributions. All models shown have a 1.0 𝑀 (cid:12) core and a 0.04 𝑀 (cid:12) shell, ofwhich 50% is burned to elements heavier than helium. We show models withdominant shell products of Fe and S, as representative of models withIGE- and IME-dominated shells.
APPENDIX C: EFFECTS OF RELATIVE ISOTOPEABUNDANCES
In Fig. 4, we show the assumed relative abundances of isotopes in thehelium shell for our models. In addition, we also show distributionsin which the relative mass fraction of the dominant shell product de-creases (broad distribution) or increases (narrow distribution). Herewe discuss how these different distributions affect the light curvesand spectra for our models.As demonstrated in Fig. C1, changes in the relative abundancesof isotopes in the helium shell have only minor effects on the lightcurves. For our S-dominated shell models, only a slight changein colour is observed at early times. For the Fe-dominated shellmodels, the effect is most pronounced in the 𝐵 -band at early times.Relative to our standard case, the broad distribution shows a some-what fainter early bump, which is not surprising given the decreasein mass fraction of radioactive isotopes. At later times, the narrowdistribution is brighter than both our standard and broad distribu-tions in the 𝐵 -band. In the narrow distribution, as the mass fractionof Fe increases, the relative fractions of all other isotopes decrease.Therefore, that the narrow distribution is brighter at later times likelypoints to the decreased contribution to line blanketing from havingfewer different elements present in the ejecta.In Fig. C2, we show how the spectra are affected by changes in therelative abundances of the shell isotopes. Again, it is clear that our S dominated shell model shows only minor changes throughoutits spectral evolution. At early times, the effect of a decreased Fefraction is clearly apparent from the fainter and redder spectrum.
This paper has been typeset from a TEX/L A TEX file prepared by the author. Fe dominated shell S dominated shell A b s o l u t e f l ux + c on s t a n t ( e r g s c m Å ) (b) 7.25d Standard distributionBroad distributionNarrow distribution
Rest wavelength (Å)
Figure C2.
Spectra for models with different shell isotope distributions. Allmodels shown have a 1.0 𝑀 (cid:12) core and a 0.04 𝑀 (cid:12) shell, of which 50% isburned to elements heavier than helium. We show models with dominant shellproducts of Fe and S, as representative of models with IGE- and IME-dominated shells. Spectra are shown at three epochs relative to explosion:3.25 d, 7.25 d, and 18.25 d. MNRAS000