Synthetic observables for electron-capture supernovae and low-mass core collapse supernovae
Alexandra Kozyreva, Petr Baklanov, Samuel Jones, Georg Stockinger, Hans-Thomas Janka
aa r X i v : . [ a s t r o - ph . S R ] F e b MNRAS , 1–19 (2020) Preprint 5 February 2021 Compiled using MNRAS L A TEX style file v3.0
Synthetic observables for electron-capture supernovae and low-mass corecollapse supernovae
Alexandra Kozyreva , ⋆ , Petr Baklanov , , Samuel Jones Georg Stockinger , , Hans-Thomas Janka Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85748 Garching, Germany, Alexander von Humboldt Fellowship NRC “Kurchatov Institute” – ITEP, Moscow, 117218, Russia National Research Nuclear University Moscow Engineering Physics Institute, Moscow, 115409, Russia X Computational Physics (XCP) Division and Center for Theoretical Astrophysics (CTA), Los Alamos National Laboratory, Los Alamos, NM 87545, USA Physik-Department, Technische Universität München, James-Franck-Str. 1, 85748 Garching, Germany
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
Stars in the mass range from 8 M ⊙ to 10 M ⊙ are expected to produce one of two types of supernovae (SNe), either electron-capturesupernovae (ECSNe) or core-collapse supernovae (CCSNe), depending on their previous evolution. Either of the associatedprogenitors retain extended and massive hydrogen-rich envelopes, the observables of these SNe are, therefore, expected to besimilar. In this study we explore the differences in these two types of SNe. Specifically, we investigate three different progenitormodels: a solar-metallicity ECSN progenitor with an initial mass of 8.8 M ⊙ , a zero-metallicity progenitor with 9.6 M ⊙ , and asolar-metallicity progenitor with 9 M ⊙ , carrying out radiative transfer simulations for these progenitors. We present the resultinglight curves for these models. The models exhibit very low photospheric velocity variations of about 2000 km s − , therefore,this may serve as a convenient indicator of low-mass SNe. The ECSN has very unique light curves in broad bands, especially the U band, and does not resemble any currently observed SN. This ECSN progenitor being part of a binary will lose its envelopefor which reason the light curve becomes short and undetectable. The SN from the 9.6 M ⊙ progenitor exhibits also quite anunusual light curve, explained by the absence of metals in the initial composition. The artificially iron polluted 9.6 M ⊙ modeldemonstrates light curves closer to normal SNe IIP. The SN from the 9 M ⊙ progenitor remains the best candidate for so-calledlow-luminosity SNe IIP like SN 1999br and SN 2005cs. Key words: supernovae: general – supernovae – stars: massive – radiative transfer
According to the Salpeter initial mass function, stellar populationsare dominated by low-mass stars, with initial masses below 8 M ⊙ (Salpeter 1955; Kroupa 2001). The majority of them live quiet,billion-year long lives if single and isolated, like our Sun. Some ofthem with initial masses 4 – 8 M ⊙ form degenerate carbon-oxygencores, end up as white dwarfs and, if part of a binary, may becomeprogenitors of thermonuclear supernovae (SNe, see e.g. Miyaji et al.1980; Hillebrandt & Niemeyer 2000; Neunteufel et al. 2016). Mas-sive stars with initial masses of 10 – 40 M ⊙ (referred to as “typ-ical” massive) end their lives in more spectacular explosions trig-gered by neutronisation of the iron-core and subsequent gravitationalcollapse (Woosley et al. 2002; Heger et al. 2003; Ertl et al. 2016;Sukhbold et al. 2016).The narrow range of initial masses between 8 M ⊙ and 10 M ⊙ isthoroughly explored (see e.g., Jones et al. 2013, 2014; Doherty et al. ⋆ E-mail: [email protected] ± M ⊙ around 8 M ⊙ , 7.8 – 8.2 M ⊙ , assuming single stellar evolution (Siess2007; Doherty et al. 2015). Progenitors in a wider initial stellar massrange between 13.5 M ⊙ and 17.6 M ⊙ result in ECSNe while con-sidering stellar evolution within a binary (Poelarends et al. 2017;Siess & Lebreuilly 2018). Consequently, this leads to a higher rateof ECSNe among core-collapse explosions, although they might lookas SNe IIb or SNe Ib/c (Tauris et al. 2015).Predicted observables depend strongly on the outcomes of stellarevolution simulations, e.g. whether the envelope is hydrogen rich(Pumo et al. 2009), and the post-explosion calculations, i.e. the de- © A. Kozyreva et al. gree of macroscopic mixing. Therefore, the real explosion can beadequately modelled as a thermal bomb. However, details of the ex-plosion simulations may strongly affect the distribution of chemicalelements, erasing the chemically-stratified structure. For example,strong mixing between chemically confined layers happens when thereverse shock passes through the expanding stellar ejecta acceleratedby the forward shock. This may be caused by asymmetries whichoccur at the earlier phase of the explosion, i.e. during shock revival.It is worth mentioning that super-asymptotic-giant-branch (super-AGB) stars and those at the low-mass end of the core-collapse SN(CCSN) progenitors are important contributors to the chemical evo-lution of the Galaxy (Karakas 2010; Doherty et al. 2014; Karakas2016; Jones et al. 2019b; Kobayashi et al. 2019). Namely, the maincontribution of massive and super-AGB stars to Galactic chemicalevolution prior to explosion is probably only isotopes produced inhot-bottom-burning and some small subset of s-process isotopes. Ifthese stars are stripped being part of a binary then they probablywould not make either of these contributions. If they explode as acore-collapse or a thermonuclear explosion, they are major contrib-utors of neutron-rich isotopes as Ca, Ti, and Cr, Fe, Ni, Se, and Kr and several isotopes beyond the iron-peak, e.g., Zn –Zr (Jones et al. 2019b).In this study, fully self-consistent calculations of three progenitorswith initial masses 8.8 M ⊙ , 9 M ⊙ , and 9.6 M ⊙ are presented, in-cluding stellar evolution simulations, core-collapse explosion simula-tions, and radiative transfer simulations. We consider our treatment as“self-consistent” in the sense that the pre-collapse models from stel-lar evolution calculations were mapped into PROMETHEUS-HOTBor PROMETHEUS-VERTEX to perform 3D explosion calculationswith a detailed treatment of the neutrino energy deposition that trig-gers and powers the explosions, and then mapped 1D-averages ofthe 3D explosion models into the radiation transport code STELLAwithout adding any additional explosion energy and Ni. We presentphysically consistent calculations of:(i) stellar evolution from the zero-age main sequence (ZAMS)through the nuclear burning stages until formation of the iron-core;(ii) core-contraction, bounce, shock revival, finally SN explosionuntil the shock breakout (Stockinger et al. 2020);(iii) hydrodynamics of the SN ejecta and evolution of the radiationfield;(iv) multi-band light curves and spectral energy distribution.The goal of the study is to explore differences in observables forthe progenitors in the narrow initial mass range of 8 to 10 M ⊙ whichmay either be ECSNe or iron CCSNe. We describe our models inSection 2, as well as our methodology of computing post-explosionhydrodynamical evolution and radiative transfer. Section 3 presentsbolometric and broad band light curves and their dependences on theprogenitor metallicity, explosion energy, hydrogen-to-helium ratioin the envelope, and the radius of the progenitor. We compare oursimulations with observed SNe in Section 5 trying to find any ob-served candidates matching our models. We present our conclusionsin Section 6. We use three self-consistently modeled SN simulations as presentedby Stockinger et al. (2020) for this study, namely, the ECSN modele8.8, and two low-mass CCSN models z9.6 and s9.0. e8.8 is a 1Dsolar-metallicity stellar evolution model which was constructed thefollowing way before being mapped into the
PROMETHEUS code: a log R [cm] -10-50510 l og [ g / c m ] e8.8 z9.6s9.0 L15 b Mr/Mtot -10-50510 e8.8z9.6s9.0 L15 a Figure 1.
Density structure of the models e8.8, z9.6, s9.0, and L15 prior tothe explosion. The top plot shows the density profiles versus mass coordinaterelative to total mass. The bottom plot presents the same density profilesversus radius. M ⊙ core was initially calculated by Nomoto (1987). The en-velope was computed with MESA (Jones et al. 2013), then trun-cated and attached to the core that was slightly reduced in mass(Nomoto & Leung 2018; Leung et al. 2020). The reduced envelopemass is explained by the pre-collapse stellar evolution which con-tains numerous shell-burning flashes, i.e., pulsation-driven mass-lossepisodes, and steady-state mass-loss (Poelarends et al. 2008). Fur-thermore, the available prescriptions for the mixing processes andmass-loss remain the overarching uncertainty in the final outcomeof the models in the range between 8 M ⊙ and 10 M ⊙ (Jones et al.2013). The final total mass of 5.83 M ⊙ was chosen to match theestimated mass of the Crab Nebula (Hillebrandt 1982; Nomoto et al.1982; Tominaga et al. 2013). The model e8.8 is relatively physicallylarge, having a radius of 1200 R ⊙ which is similar to the average redsupergiant. However, we show that the extended tenuous envelopemakes the observational properties of this particular model quiteunique.Model z9.6 is a zero-metallicity stellar evolution model with initialmass of 9.6 M ⊙ calculated with the KEPLER code (Weaver et al.1978). With no metals in the original chemical mixture this modelis relatively compact, its radius at the moment of iron-core collapsebeing 214 R ⊙ , i.e. the star is somewhere at the boundary between blueand red supergiants (Heger & Woosley 2010). The solar-metallicitymodel s9.0 is a star with initial 9 M ⊙ also produced with KEPLER (Sukhbold et al. 2016).The choice of the models in the present study is explained by thefollowing aspects:(i) One of the purposes of our study is to explore differences andsimilarities in the resulting supernova observables between models Modules for Experiments in Stellar Astrophysics http://mesa.sourceforge.net/ (Paxton et al. 2011, 2013, 2015,2018, 2019). M ⊙ model has the final mass of 8.544 M ⊙ (see Table 1 in Jones et al.2013).MNRAS , 1–19 (2020) CSNe and Low-mass CCSNe Table 1.
Input models for our radiative transfer simulations. Note, that both the e8.8 and s9.0 stellar models are initially at solar metallicity, but the model e8.8was computed with abundances from Asplund et al. (2009), having metallicity Z ⊙ , and the model s9.0, taken from Sukhbold et al. (2016), was made with theassumption of solar abundances from Lodders (2003) having metallicity Z (1) ⊙ . “Fe” stands for the mass fraction of stable iron in the stellar envelope. “E kin ”represents terminal kinetic energy of the entire ejecta. “Time” means time since bounce, i.e. the point where the models were mapped into STELLA, andapproximately corresponds to time of the shock breakout. The comparison model L15 from Utrobin et al. (2017) is listed at the bottom as well.M fin /M ej [ M ⊙ ] Z X(Fe) R [ R ⊙ ] M cut [ M ⊙ ] Time [days] E finkin [ erg] Ni [ M ⊙ ]e8.8 3D 5.83/4.5 Z ⊙ × − SMC × − Energy-study3e49-2D 0.3 0.00096e49-2D 0.55 0.00111e50-2D 0.92 0.00131.5e50-2D 1.37 0.0012Radius-studye8.8 evol 5.82/4.5 Z ⊙ SMC × − Z ⊙ × − Z (1) ⊙ × − s9.0 8.75/7.4 Z (1) ⊙ × −
409 1.356 4.2 0.68 0.0051L15-nu 15/13 Z (1) ⊙ × −
627 2 0 5.5 0.036L15-tb 15/13.47 Z (1) ⊙ × −
627 1.53 0 5.4 0.036 in the narrow range of initial ZAMS masses between 8 M ⊙ and10 M ⊙ .(ii) Pre-collapse model e8.8 is the latest version of a super-AGBECSN progenitor available to us.(iii) The z9.6 progenitor has a density structure prior to the col-lapse similar to e8.8, namely, a steep density gradient at the core-envelope interface (see Figure 1).(iv) Pre-collapse model s9.0 is the representative of low-mass pro-genitors and explodes fairly easily in self-consistent 3D simulations,having similar energy as the other two cases (see Radice et al. 2017;Glas et al. 2019; Stockinger et al. 2020).We note that adding 3D simulations of more progenitors or moremodel variations is computationally expensive and currently not fea-sible. One of the reasons is the long time, up to 5 days, required forthe shock to break out from these very extended progenitors. Theapproximate time for the shock breakout is definited as: t SBO ∼ .
91 days R E M , (1)where R = R/
500 R ⊙ , E = E exp / erg, and M = M ej /
10 M ⊙ (see, e.g., Shigeyama et al. 1987; Goldberg et al. 2019).The macroscopic mixing processes proceed over this time. Conse-quently, the computational time is very long in order to catch allrelevant dynamical effects.These models were mapped into the PROMETHEUS code in orderto simulate the contraction, bounce, shock formation, shock revivaland shock propagation until the moment of shock breakout. Thedetails of the simulations are fully described in the recent paper by Stockinger et al. (2020), therefore, we direct the reader to thiscomprehensive study for the details to avoid repetition.In Table 1, we list relevant properties of the default models. Fur-thermore, we add the subsets of models we used for our study asexplained in sections below. E.g. we did a “Tracer”-study for themodel e8.8 in which we modified the mass of radioactive nickel Niaccording to the amount of so-called “Tracer” material (Section 3.6).We deem an exploration of metallicity dependence very importantfor the observational properties of our models. In order to do this,we constructed a subset of models for e8.8 by tuning the iron con-tent in the hydrogen-rich envelope, either setting iron mass fractionto zero or to 0.00014, thus mimicking the zero-metalicity progenitorand the progenitor at Small Magellanic Cloud (SMC) metallicity. Wedid the same experiment for model z9.6, studying three additionalmetallicities: solar metallicity (set to 0.014 and 0.02 in accordancewith Asplund et al. 2009 and Lodders 2003) and SMC metallicity(Section 3.4). For the model e8.8, we carried out an analysis of theinfluence of a different ratio between hydrogen and helium fractionin the outer envelope, as this ratio may differ taking the uncertaintyof stellar evolution calculations into account (Section 3.5). We alsocarried out the radius-dependence study for e8.8, in which we pro-duced 3 additional models with the radius of 400 R ⊙ , 600 R ⊙ , and900 R ⊙ , while truncating the original 1D stellar evolution profileprior to the collapse.In the current study, the models were mapped into the radiationhydrodynamics code STELLA (Blinnikov et al. 2006). This code iscapable of processing hydrodynamics as well as radiation field evo-
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A. Kozyreva et al. -3-2-10 1 2 3 4 5 6(A) e8.8-3-2-10 1 2 3 4 5 6 7 8 9 10(B) z9.6-3-2-10 1 2 3 4 5 6 7 8 9(C) s9.0-3-2-10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16(D) L15-3-2-10 1 2 3 4 5 6 l og M a ss f r a c t i o n H He C O-3-2-10 1 2 3 4 5 6 7 8 9 10-3-2-10 1 2 3 4 5 6 7 8 9Mass [M ⊙ ]-3-2-10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Figure 2.
Chemical structure (hydrogen, helium, carbon, and oxygen profiles) of the ejecta. Model designation as labeled. Dashed lines indicate the pre-collapsechemical structures of the models while solid lines present post-explosion structures. lution and computing light curves, spectral energy distribution andresulting broad-band magnitudes and colours. We used the standardparameter settings, well-explained in many papers involving
STELLA simulations (see e.g., Kozyreva et al. 2019; Moriya et al. 2020) .We compare our radiative transfer results to the CCSN progeni-tor model L15 (Limongi et al. 2000; Utrobin et al. 2017), which ispresented in Table 1 as L15-nu and L15-tb. We use this model asa “reference” CCSN model, even though the progenitors of CCSNeand their explosions are diverse. This model approximates the ex-plosion of a massive progenitor with an initial mass of 15 M ⊙ at We note that the thermalisation parameter was set to unity in contrast to thevalue of 0.9 recommended by the most recent study Kozyreva et al. (2020b). solar metallicity, neglecting wind mass-loss (Limongi et al. 2000).We note though that the published light curves (Utrobin et al. 2017)mistakenly did not account for metallicity, i.e. there is no stable ironcontent in the hydrogen-rich envelope. We correct for this oversightin our calculations and figures. Even though there is a minor effecton the bolometric light curve, the bigger impact is observed for the U -band magnitude and colour temperature (see Section 3.4). Themodel’s final mass is thus the same as the initial mass, the resultingejecta mass is 13.5 M ⊙ , and the radius at the moment of core-collapseexplosion is 627 R ⊙ . For comparison, we used two types explosionsfor this model. The first explosion, named “L15-nu”, was done as a 3Dneutrino-driven model with PROMETHEUS (Utrobin et al. 2017), i.e.the
PROMETHEUS output was mapped directly into
STELLA . The re-
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CSNe and Low-mass CCSNe sulting light curve and observables are labelled “L15-nu” in the plotsbelow. The second explosion, named “L15-tb”, was performed as adetonation of the progenitor L15 using the thermal bomb method,assuming an explosion energy of 0.9 foe (1 foe = erg) andreaching a terminal kinetic energy of 0.54 foe. The result of thesesimulations is labelled “L15-tb” in the plots below. The principal dif-ference between a 3D neutrino-driven explosion and thermal bombexplosion lies in the absence of macroscopic mixing of the chemicalcomposition in the latter case mapped into STELLA .In Figure 2, we provide the input chemical profiles for the modelsin our study as well as the chemical structure of L15 for compar-ison. Dashed lines present pre-explosion chemical structures whilesolid lines present post-explosion distributions of hydrogen, helium,carbon and oxygen. The different chemical structures of the modelsis easily seen in the plot. The reference massive star model priorto the explosion exhibits a stratified chemical structure: the outer,hydrogen-rich, envelope rests on top of a thick 2 M ⊙ pure heliumshell, which in turn lies on an almost pure oxygen shell. In contrast,the low-mass model z9.6 has a thin 0.5 M ⊙ helium layer and nooxygen layer, and the low-mass model s9.0 has no distinct heliumshell at all. This is a result of macroscopic mixing occuring duringthe passage of the shock. At the same time the model L15 expe-riences macroscopic mixing and has the sharp chemical interfaceswashed out to some degree. The ECSN model e8.8 exhibits a uniquechemical structure, having only a hydrogen-rich envelope, pollutedby a high fraction of helium and some amount of carbon and oxygenbecause of dredge-out episode, depending on metallicity. The verydifferent chemical structure of the SN ejecta of these models leads toa variety of observational properties of the resulting SN light curveswhich we discuss in detail in the following sections.Further, Figure 1 shows the pre-SN density structure prior to thecollapse in order to illustrate the difference in the pre-explosion den-sity profiles. The layers around the final neutron star in the modele8.8 look very unique compared to the other low-mass models (s9.0and z9.6) and the reference CCSN model L15. The most importantdifference in model e8.8 is a very steep density gradient at the edgeof the core culminating in a very tenuous hydrogen-rich envelope.The latter condition was shown by Grasberg & Nadezhin (1976) toprevent fast recombination in typical SN ejecta. The low-mass pro-genitors s9.0 and z9.6 differ from the reference massive progenitor.These models have no appreciable helium layer, while the referencemassive star explosion L15 has a relatively massive helium shell( . < M r /M tot < . ) prior to the explosion. Apparently, thedensity structure is washed out after the passage of the shock. How-ever, the shock propagation is different in these three different modelsand unavoidably influences a variety of properties of the ejecta andresulting observables. In Figure 3, bolometric light curves for the models explored in thecurrent study are displayed. The bolometric light curves for the mod-els e8.8 and z9.6 clearly differ from the canonical CCSN light curve,e.g. the curve labeled “L15-tb” and “L15-nu” from Utrobin et al.(2017). The difference consists in the sharp and pronounced drop be-tween the plateau and the radioactive tail. The obvious explanation isthat the models in our study produce too small amount of radioactivenickel Ni, about 0.001 M ⊙ (see Table 1). In contrast, the models9.0 produces slightly higher amount of Ni, about five times more
Time [days] l og Lbo l [ e r g / s ] e8.8z9.6 s9.0 L15-nu -- L15-tb
Figure 3.
Bolometric light curves for the models e8.8, z9.6, s9.0, and L15-tb/L15-nu (Utrobin et al. 2017). (0.005 M ⊙ ). Additionally the models e8.8 and z9.6 maintain theirstratified structure even at the moment when all mixing processescease. In contrast, there is significant large-scale mixing in the models9.0. Concequently, the transition from the plateau to the radioactivetail is shallower in s9.0. The steepess of the transition in the mod-els e8.8 and z9.6 is also caused by a lack of a distinct oxygen shell(Figure 2, Jones et al. 2013; Stockinger et al. 2020). As seen, theplateau luminosities for the low-mass CCSN models z9.6 and s9.0are lower than that of a canonical CCSN originating from a standardmass progenitor , this is due to the relatively lower explosion energy.Nevertheless, the plateau luminostity for the ECSN model e8.8 iscomparable to the normal CCSN as a result of the large radius of theprogenitor ( L bol ∼ R . , Goldberg et al. 2019).In order to illustrate the overall energetics of the explosions, weshow the photospheric velocity evolution for the models consideredhere together with the SN IIP reference models L15-nu and L15-tbin Figure 4. The photospheric velocity is the velocity of the massshell in which the accumulated optical depth in B broad band isequal 2/3. It is easily seen that the photospheric velocity in all ofour models, i.e. both the ECSN model and low-mass CCSN mod-els, is systematically lower than the photospheric velocity for thereference SN IIP models L15-nu/L15-tb because of the lower ex-plosion energy. Indeed photospheric velocity at the earliest phase isalready very low, 2500 km s − , while the reference CCSN modelexhibits velocity of about 7000 km s − , typical for observed SNe IIP(Jones et al. 2009). The photospheric velocity remains steady at a The light curves L15-nu and L15-tb perform explosion with almost thesame terminal kinetic energy of 0.54/0.55 foe, i.e. the plateau luminosity isexpected to be the same. However, the light curve “L15-nu” has higher lumi-nosity due to the additional heating from the extended mixing of radioactive Ni which is responsible for an extra energy budget (Kozyreva et al. 2019).MNRAS000
Bolometric light curves for the models e8.8, z9.6, s9.0, and L15-tb/L15-nu (Utrobin et al. 2017). (0.005 M ⊙ ). Additionally the models e8.8 and z9.6 maintain theirstratified structure even at the moment when all mixing processescease. In contrast, there is significant large-scale mixing in the models9.0. Concequently, the transition from the plateau to the radioactivetail is shallower in s9.0. The steepess of the transition in the mod-els e8.8 and z9.6 is also caused by a lack of a distinct oxygen shell(Figure 2, Jones et al. 2013; Stockinger et al. 2020). As seen, theplateau luminosities for the low-mass CCSN models z9.6 and s9.0are lower than that of a canonical CCSN originating from a standardmass progenitor , this is due to the relatively lower explosion energy.Nevertheless, the plateau luminostity for the ECSN model e8.8 iscomparable to the normal CCSN as a result of the large radius of theprogenitor ( L bol ∼ R . , Goldberg et al. 2019).In order to illustrate the overall energetics of the explosions, weshow the photospheric velocity evolution for the models consideredhere together with the SN IIP reference models L15-nu and L15-tbin Figure 4. The photospheric velocity is the velocity of the massshell in which the accumulated optical depth in B broad band isequal 2/3. It is easily seen that the photospheric velocity in all ofour models, i.e. both the ECSN model and low-mass CCSN mod-els, is systematically lower than the photospheric velocity for thereference SN IIP models L15-nu/L15-tb because of the lower ex-plosion energy. Indeed photospheric velocity at the earliest phase isalready very low, 2500 km s − , while the reference CCSN modelexhibits velocity of about 7000 km s − , typical for observed SNe IIP(Jones et al. 2009). The photospheric velocity remains steady at a The light curves L15-nu and L15-tb perform explosion with almost thesame terminal kinetic energy of 0.54/0.55 foe, i.e. the plateau luminosity isexpected to be the same. However, the light curve “L15-nu” has higher lumi-nosity due to the additional heating from the extended mixing of radioactive Ni which is responsible for an extra energy budget (Kozyreva et al. 2019).MNRAS000 , 1–19 (2020)
A. Kozyreva et al. U ph [ k m s − ] Time [days]e8.8z9.6s9.0L15-thL15-nu01234567 0 50 100 150
Figure 4.
Time evolution of the photospheric velocity, U ph , for the modelse8.8, z9.6, s9.0, and L15-tb/L15-nu. level of 1000–2000 km s − thoughout the entire plateau in all ourmodels. However, the ECSN model exhibits roughly 500 km s − higher velocity during the plateau, i.e. slightly faster ejecta com-pared to the low-mass CCSN models in our study. This is explainedby the fact of relatively lower ejecta mass. Velocity scales with en-ergy v ∼ p E/M , i.e. an increase a magnitude in energy (expectedexplosion energy for a ECSN is erg, while typical explosionenergy of an CCSN is erg) leads to an increase in velocity aboutthree times over, as seen in the plot. We suggest to use this diagnos-tic as a distinct feature in the identification of low-mass explosions,both ECSNe and low-mass CCSNe, which is in agreement with thesuggestions by Pumo et al. (2017) and Tomasella et al. (2018). We show the light curves in the standard Bessel broad-bands for themodels e8.8, z9.6, and s9.0 in Figures 5, 6, and 7, respectively.The broad-band light curves for the model e8.8 look similar tobroad-band magnitudes for a reference SN IIP, excepting the first50 days. The distinguishing feature of the model e8.8 is a 50-dayblue plateau, i.e. the U band magnitude remains constant and evenslightly increases over the first half of the plateau (see Figure 5),while normal SNe IIP usually exhibit a decreasing U -band magni-tude across the entire plateau. We directly compare the U band mag-nitudes of the ECSN model and the CCSN model in the next section.We note that the original progenitor’s metallicity has a strong im-pact on the behaviour of the light curve in the U band, specifically,the higher metallicity leads to overall redder light curves (see e.g.,Lentz et al. 2000). We explore the metallicity dependence in the Sec-tion 3.4 below. However, the model e8.8 shows blue colours even atsolar metallicity. Reasons for this are the colour temperature evolu-tion and the conditions during, and the time of, start of recombina-tion (Grasberg et al. 1971; Goldfriend et al. 2014; Sapir & Waxman2017). In contrary to normal CCSNe, recombination settles in at rela-tively late times depending on the explosion energy (Shussman et al.2016; Kozyreva et al. 2020a): t rec ∼ M . R . E − . , (2) where M is ejecta mass in 15 M ⊙ , R is progenitor radius in 500 R ⊙ ,and E is explosion energy in 1 foe. The ejecta mass for ECSNprogenitors is generally expected to be lower than that of CCSNe(e.g. for both our low-mass and the reference models). The explosionenergy is also expected to be lower (see e.g., Melson et al. 2015;Radice et al. 2017; Stockinger et al. 2020). The progenitor radius ofthe ECSN e8.8 1200 R ⊙ is significantly larger than the 214 R ⊙ ofmodel z9.6 (the latter being zero metallicity) and the 408 R ⊙ ofmodel s9.0. Note that the e8.8 radius is still in the range of referenceprogenitor radii of red supergiants (100 – 2850 R ⊙ , Levesque et al.2005, 2006). The larger radius of the ECSN progenitor (the super-AGB star), is a consequence the dredge-out episode (Nomoto 1987;Ritossa et al. 1999; Jones et al. 2013). Accordingly, the hydrogen-rich envelope of the model e8.8 is very tenuous and recombinationhard settles in, which in turn forces the overall electron-scatteringphotosphere to recede more slowly (Grasberg & Nadezhin 1976).The zero-metallicity model z9.6 demonstrates a quite unusual be-haviour in the broad-band light curves compared to a normal SN IIP.We show in the next sections that the same model at solar metallicityshould have colour behaviour quite standard for SNe IIP. Neverthe-less, the zero-metallicity low-mass CCSNe, as demonstrated by themodel z9.6, have monotonically rising U , B , V , R , and I light curves,and constant colours during the plateau phase. This means that theshape of the spectrum persists more or less unchanged for the first100 days, i.e. while the electron-scattering photosphere graduallyrecedes through the hydrogen-rich envelope. Later, i.e. after the endof plateau, there is a sharp reddening of the colours. The photo-sphere at this phase enters the inner region of the ejecta dominatedby iron-group elements which are the major contributors to the lineopacity. However, compatible zero-metallicity stars (Population III)exist only in the early Universe, therefore, the application of model9.6 is of limited usefulness, when observations in the nearby Universeare concerned. Predictions about observational properties of CCSNefor Population III stars are very useful for upcoming transient sur-veys like LSST (Whalen et al. 2013; Ivezić et al. 2019). However,the majority of known SNe IIP are found in non-zero metallicitygalaxies (Anderson et al. 2016), and theoretical predictions for theobservables of CCSNe at the SMC and solar metalicity are deemedmore useful. The numerics and physics input in the core-collapse simulations leadto uncertainties in the final explosion energy (Radice et al. 2017;Melson et al. 2020). As a remedy, Stockinger et al. (2020) providedsimulations for e8.8 with four different neutrino luminosity valuesin 2D corresponding to explosion energies of: × erg, × erg, × erg, and . × erg (see Table 1). Wewould like to emphasize that the explosion energy is unequal tothe terminal kinetic energy listed in Table 1. There are number ofreasons for this difference. (1) The explosion energy published byStockinger et al. (2020) is a direct integral of the total energy in2D or 3D. The multidimensional profiles were converted into 1D-profiles using an angle-averaging procedure. (2) Since STELLA isa hydrodynamics code, it requires some numerical relaxation whenmapping
PROMETHEUS output into it, which in turn is liable to causesome (up to 15 %) difference in the resulting integrated energy. (3)The supernova ejecta at the moment of shock breakout have not The Large Synoptic Survey Telescope which is the core of the Vera C. RubinObservatory.MNRAS , 1–19 (2020)
CSNe and Low-mass CCSNe Time [days] -18-17-16-15-14-13-12-11-10 m a gn i t ud es e8.8 UBVR I Figure 5.
Broad-band U , B , V , R , and I light curves for the model e8.8. Time [days] -16-15-14-13-12-11-10 m a gn i t ud es Vz9.6 I R B U
Figure 6.
Broad-band U , B , V , R , and I light curves for the model z9.6. yet reached the coasting phase. This causes some hydrodynamicalevolution and inelastic conversion of kinetic energy into thermalenergy. We note that the total mass of radioactive nickel Ni is keptthe same for different explosion energies. Nevertheless, it is expectedthat more energetic explosions naturally produce a higher mass of Ni (Ertl et al. 2016). However, we find that the resulting chemicalprofiles in the post-shock ejecta structure do not differ significantly.For different energies the hydrodynamical profiles explicitly scalewith the explosion energy. Otherwise, the final light curves obey thewell-known Popov’s relation for absolute magnitude in V band andduration of the plateau t p (Litvinova & Nadezhin 1985; Popov 1993;Sukhbold et al. 2016; Goldberg et al. 2019): V ∼ − .
67 log R + 1 .
25 log M − .
08 log E log t p ∼ .
167 log R + 0 . M − .
167 log
E , (3)
Time [days] -16-15-14-13-12-11-10 m a gn i t ud es s9.0 U B VR I Figure 7.
Broad-band U , B , V , R , and I light curves for the model s9.0. where R is radius in R ⊙ , M is ejecta mass in M ⊙ , and E is ex-plosion energy in foe. In Figure 8, bolometric and broad-band lightcurves and B – V colour for the model e8.8 computed with a vari-ety of energies are presented. Figure 8a also shows the result ofthe simulations for the model e8.8 in 3D for an explosion energyof × erg (bolometric light curve for the default model e8.8is displayed in Figure 3). The light curves for this case are almostidentical in 2D and 3D. This means that an explosion calculated in2D provides the same hydrodynamical and chemical ejecta structureas in 3D. The higher explosion energy leads to a more luminous andshorter plateau. The broad-band magnitudes for this case follow thebehaviour of the bolometric curve without major flux redistributionthoughout the spectrum. Figure 8 shows B – V colour for differentchoices in explsoion energy. There is no significant difference forcases of different energy. However, the colour tends to be slightlybluer for higher energies, e.g. B – V is 0.2 mag bluer an explosion en-ergy of × erg and . × erg in e8.8 at the end of plateauand later compared to the results for the lower explosion energy of × erg and × erg. In order to understand the influence of initial metallicity, we exploredtwo of the models from the study in greater detail: e8.8 and z9.6.Specifically, we modified the stable iron abundance in the hydrogen-rich envelope. The subset of the runs for model e8.8 has the follow-ing adopted metallicity: zero ( Z = 0 ), SMC ( Z = 0 . ), solar( X (Fe) = 5 × − ), the latter being the default metallicity ofthe model e8.8). The subset of the runs for the model z9.6 has theadopted metallicity: zero ( Z = 0 , the default metallicity of the inputmodel), SMC ( Z = 0 . , X (Fe) = 1 . × − ), and two differentruns for solar metallicity “solar” ( Z = 0 . , Asplund et al. 2009, X (Fe) = 5 × − , the default metallicity of the model e8.8) and“solar1” ( Z = 0 . , Lodders 2003, X (Fe) = 1 . × − , the de-fault metallicity of the model s9.0). Changing metallicity of the initialmodel unavoidably leads to different stellar evolution path, differentmass-loss, consequently different final mass and progenitor radius(Georgy 2012; Georgy et al. 2013; Jones et al. 2015; Renzo et al. MNRAS000
Broad-band U , B , V , R , and I light curves for the model s9.0. where R is radius in R ⊙ , M is ejecta mass in M ⊙ , and E is ex-plosion energy in foe. In Figure 8, bolometric and broad-band lightcurves and B – V colour for the model e8.8 computed with a vari-ety of energies are presented. Figure 8a also shows the result ofthe simulations for the model e8.8 in 3D for an explosion energyof × erg (bolometric light curve for the default model e8.8is displayed in Figure 3). The light curves for this case are almostidentical in 2D and 3D. This means that an explosion calculated in2D provides the same hydrodynamical and chemical ejecta structureas in 3D. The higher explosion energy leads to a more luminous andshorter plateau. The broad-band magnitudes for this case follow thebehaviour of the bolometric curve without major flux redistributionthoughout the spectrum. Figure 8 shows B – V colour for differentchoices in explsoion energy. There is no significant difference forcases of different energy. However, the colour tends to be slightlybluer for higher energies, e.g. B – V is 0.2 mag bluer an explosion en-ergy of × erg and . × erg in e8.8 at the end of plateauand later compared to the results for the lower explosion energy of × erg and × erg. In order to understand the influence of initial metallicity, we exploredtwo of the models from the study in greater detail: e8.8 and z9.6.Specifically, we modified the stable iron abundance in the hydrogen-rich envelope. The subset of the runs for model e8.8 has the follow-ing adopted metallicity: zero ( Z = 0 ), SMC ( Z = 0 . ), solar( X (Fe) = 5 × − ), the latter being the default metallicity ofthe model e8.8). The subset of the runs for the model z9.6 has theadopted metallicity: zero ( Z = 0 , the default metallicity of the inputmodel), SMC ( Z = 0 . , X (Fe) = 1 . × − ), and two differentruns for solar metallicity “solar” ( Z = 0 . , Asplund et al. 2009, X (Fe) = 5 × − , the default metallicity of the model e8.8) and“solar1” ( Z = 0 . , Lodders 2003, X (Fe) = 1 . × − , the de-fault metallicity of the model s9.0). Changing metallicity of the initialmodel unavoidably leads to different stellar evolution path, differentmass-loss, consequently different final mass and progenitor radius(Georgy 2012; Georgy et al. 2013; Jones et al. 2015; Renzo et al. MNRAS000 , 1–19 (2020)
A. Kozyreva et al.
Time [days] l og Lbo l [ e r g / s ] e8.8 a
2D 3e49 erg2D 6e49 erg2D 1e50 erg3D 1e50 erg2D 1.5e50 erg
Time [days] -18-17-16-15-14-13-12 U [ m a g s ] e8.8 b Time [days] -18-17-16-15-14-13-12 B [ m a g s ] e8.8 c Time [days] -18-17-16-15-14-13-12 V [ m a g s ] e8.8 d Time [days] -18-17-16-15-14-13-12 R [ m a g s ] e8.8 e Time [days] B - V [ m a g s ] e8.8 f Figure 8.
Dependence on the explosion energy: Bolometric, broad-band light curves, and B – V colour for the model e8.8 simulated in 2D and 3D with explosionenergies as labelled.MNRAS , 1–19 (2020) CSNe and Low-mass CCSNe Time [days] l og Lbo l [ e r g / s ] a e8.8 Z=0e8.8 SMCe8.8 Solarz9.6 Z=0z9.6 SMCz9.6 Solarz9.6 Solar1 Time [days] -17-16-15-14-13-12-11-10 U [ m a g s ] S o l a r S o l a r bZ=0 S M C S o l a r Z=0 SMCz9.6 e8.80 50 100 150
Time [days] -17-16-15-14-13-12-11-10 B [ m a g s ] SolarSolar1 cZ=0 S M C S o l a r Z=0 SMCz9.6 e8.8 0 50 100 150
Time [days] -17-16-15-14-13-12-11-10 V [ m a g s ] S M C S o l a r dZ=0 SMC S o l a r Z=0 - Solarz9.6 e8.80 50 100 150
Time [days] -17-16-15-14-13-12-11-10 R [ m a g s ] - S o l a r S o l a r eZ=0 SMCSolar Z=0 SMCz9.6 e8.8
Time [days] B - V [ m a g s ] e8.8 z9.6 Z=0 SMCSolar
Z=0 SMC Solar
Solar1 f Figure 9.
Dependence on the initial metallicity: Bolometric and broad-band light curves, and B – V colour for the subset of runs based on the model e8.8 and z9.6with different stable-Iron content in the hydrogen-rich envelope, which corresponds to zero metallicity (“Z=0”), SMC metallicity (“SMC”), and solar metallicity(“Solar” and “Solar1”). “Solar” metallicity stands for the initial metallicity of the model e8.8 and has iron fraction of × − , while “Solar1” metallicitystands for the solar metallicity with the iron fraction of . × − (initial metallicity of the model s9.0). MNRAS000
Dependence on the initial metallicity: Bolometric and broad-band light curves, and B – V colour for the subset of runs based on the model e8.8 and z9.6with different stable-Iron content in the hydrogen-rich envelope, which corresponds to zero metallicity (“Z=0”), SMC metallicity (“SMC”), and solar metallicity(“Solar” and “Solar1”). “Solar” metallicity stands for the initial metallicity of the model e8.8 and has iron fraction of × − , while “Solar1” metallicitystands for the solar metallicity with the iron fraction of . × − (initial metallicity of the model s9.0). MNRAS000 , 1–19 (2020) A. Kozyreva et al. U and B , while the V , R ,and I magnitudes are less dependent on the iron content. This is dueto the blue flux being effectively absorbed by iron and redistributed tolonger wavelengths (Lucy 1999; Kasen 2006; Kozyreva et al. 2020b).Hence, a supernova may have a prominent 110-day plateau in U and B broad band in case of zero metallicity (e8.8 at Z = 0 ), while hav-ing a 50 day plateau with a subsequent decline in case of solar andSMC metallicity (e8.8 “solar” and e8.8 “SMC”). Interestingly, the U broad band light curve rises for the model z9.6 with the default zerometallicity, while it declines for solar/solar1 and SMC metallicity,similar to many typical SNe IIP. Similarly, the light curve rises in B band in case of zero metallicity, while the model z9.6 shows a plateauin B if the iron content in the hydrogen-rich envelope correspondsto solar or SMC metallicity. Hence, the U band light curve servesas a direct indicator of the initial metallicity of the progenitor forCCSNe (Dessart et al. 2013, 2014). The same is true for the ECSNmodel e8.8. However, the earlier 50-day U band light curve remainsunaffected by metallicity, because of the relatively long delay untilrecombination settles in (see Figure 5). Additionally, metallicity, i.e.iron content in the hydrogen-rich envelope, effectively determinesthe length of the plateau. Specifically, a difference of 5 to 10 daysis observed in duration of the plateau between runs with zero andsolar/SMC metallicity: the higher metallicity the longer the plateau(see e.g., Kasen & Woosley 2009). Different works (e.g., Nomoto 1987; Ritossa et al. 1999; Siess 2007,and other studies) report that one of the distinct properties of theevolution of stars in the narrow mass range around 8 M ⊙ , is a se-quence of carbon-shell burning flashes which lead to the dredge-outepisode. This later results in complete destruction of the helium layerand macroscopic injection of helium into the hydrogen-rich envelope.The stellar models consequently tend to have a decreased hydrogen-to-helium ratio in the envelope (see, however, Woosley & Heger2015). Tominaga et al. (2013) explored the consequence of differ-ent hydrogen-to-helium ratios on SN light curves. In their study, therelative hydrogen abundance in the envelope was set to 0.7, 0.5, and0.2. We carried out a similar study, this time assuming two differenthydrogen abundances in addition to the default value: 0.385 and 0.2(the default value of the hydrogen abundance is 0.6). The result-ing light curves are shown in Figure 10. The impact of a differenthydrogen-to-helium ratio is the same as found by Tominaga et al.(2013) and similar to that found by Kasen & Woosley (2009) fornormal SNe IIP. The lower hydrogen abundance leads to a slightlyshorter and brighter plateau. This is explained by the lower elec-tron abundance, in this case. The lower electron abundance leadsto a lower electron-scattering opacity which governs the dynamicsof the receding photosphere. According to Nomoto et al. (1982), thehydrogen-to-helium ratio in the Crab nebula, which is believed tooriginate from an ECSN explosion, ranges between 0.125 and 0.625with the hydrogen fraction in the range 0.2–0.3. Therefore, the greenlight curves in Figure 10 are more favourable for this ECSN candi-date. The B – V colour differs not significantly between variants ofe8.8 with different hydrogen-to-helium ratio, showing a scatter of 0.2 mag during the plateau phase. Otherwise the behaviour of thelight curves with different hydrogen-to-helium ratios is similar. The core-collapse explosion simulations for our models were carriedout with the
PROMETHEUS code, which provides a small 23-isotope(
VERTEX-PROMETHEUS ) and a 16-isotope (
PROMETHEUS-HOTB ) nu-clear network (for details, see Stockinger et al. 2020). The productionof iron-group elements in those studies is governed by the reduced setof nuclear species used in the treatment of nuclear statistical equilib-rium and in a simplified nuclear alpha-reaction network. The latterprovides an approximate estimate of the Ni yield. However, theexact amount of Ni depends on the electron fraction (or neutron-to-proton ratio) in the ejecta, which is not accurately determined withthe approximate neutrino transport used in the
PROMETHEUS-HOTB simulations of the model e8.8. In neutron-rich conditions (electronfraction Y e < . ) the code produces a so-called “tracer” nucleonthat traces neutron-rich nuclei. With more accurate Y e , some fractionof this tracer could actually be radioactive nickel Ni. To accountfor this uncertainty, we run two additional simulations for the samehydrodynamical profile of the default model e8.8 for which we set the Ni yield to be the following: Ni + Tracer / and Ni + Tracer .We show the result of the simulations in Figure 11. Different totalamounts of radioactive nickel Ni with the same shape of distri-bution throughout the ejecta largely affect the luminosity of the ra-dioactive tail and the extension of the plateau (Kozyreva et al. 2019).Inclusion of the entire mass of the Tracer into the Ni mass leadsto higher mass of the radioactive material, i.e. reduces the drop be-tween the plateau and the tail, and makes the ECSN bolometric lightcurve more similar to that of normal SN IIP of a massive progenitor(10 – 20 M ⊙ ). However, the overall spectral evolution and coloursremain the same as for the default model e8.8. It is known that the large fraction of stars are born in binary, triple ormultiple systems (Podsiadlowski et al. 1992). Similar to the famousAlgol paradox, stars lose its mass via critical Roche surface (Pustylnik1998). The stellar evolution of individual stars is strongly affectedif they are part of a close binary. Therefore, it is adequate to admitsome degree of uncertainty to the mass-loss. Additional mass-losshappens via mass transfer in a binary system, which is the channelfor some initially hydrogen-rich low-metallicity massive stars to re-sult in hydrogen-free supernovae SN Ib/c (Yoon et al. 2012). Georgy(2012) show that increasing the wind mass-loss rate by a factor of3 to 10 shrinks the progenitor, i.e. makes the more compact star.Multipling the rate of wind mass-loss may mimic the binarity, i.e.the enhanced mass-loss happening in a binary via Langrangian pointL1. Specifically, ECSNe may occur in binaries (Eldridge et al. 2008;Poelarends et al. 2017; Siess & Lebreuilly 2018). Tauris et al. (2015)and Jones et al. (2019a) show that a star that would otherwise resultin an ECSN will instead result in an ultra-stripped SN if part of aclose binary. Losing mass via close binary interaction, i.e. via theRoche lobe overflow, a star becomes more compact. Hence, we didadditional subset of runs based on the stellar evolution model e8.8which has radius of 1200 R ⊙ at the moment of collapse. Three an-other truncated models have radii of 900 R ⊙ , 600 R ⊙ , and 400 Rsun.We note that the main model e8.8 discussed above was evolved with PROMETHEUS up to the moment of shock breakout and then wasmapped into
STELLA . Truncating the main profile (the
PROMETHEUS
MNRAS , 1–19 (2020)
CSNe and Low-mass CCSNe Time [days] l og Lbo l [ e r g / s ] e8.8 a H=0.6 He=0.385 basicH=0.385 He=0.6H=0.2 He=0.78
Time [days] -18-17-16-15-14-13-12 U [ m a g s ] e8.8 b H=0.6 He=0.385 basicH=0.385 He=0.6H=0.2 He=0.78
Time [days] -18-17-16-15-14-13-12 B [ m a g s ] e8.8 c H=0.6 He=0.385 basicH=0.385 He=0.6H=0.2 He=0.78
Time [days] -18-17-16-15-14-13-12 V [ m a g s ] e8.8 d H=0.6 He=0.385 basicH=0.385 He=0.6H=0.2 He=0.78
Time [days] -18-17-16-15-14-13-12 R [ m a g s ] e8.8 e H=0.6 He=0.385 basicH=0.385 He=0.6H=0.2 He=0.78
Time [days] B - V [ m a g s ] e8.8 f H=0.6 He=0.385 basicH=0.385 He=0.6H=0.2 He=0.78
Figure 10.
Dependence on the hydrogen-to-helium-ratio: Bolometric and broad-band light curves, and the B – V colour for the subset of runs based on the modele8.8 with different hydrogen-to-helium-ratio: 0.385:0.6, 0.385:0.6, and 0.2:0.78. MNRAS , 1–19 (2020) A. Kozyreva et al.
Time [days] l og Lbo l [ e r g / s ] Ni=0.00127Msun Ni+Tr/2=0.00783Msun Ni+Tr=0.01435Msun e8.8
Figure 11.
Bolometric light curves for the subset of runs based on the modele8.8 with different Ni mass: “pure” Ni, Ni+Tracer/2, and Ni+Tracer,which correspond to 0.00127 M ⊙ , 0.00783 M ⊙ , and 0.01435 M ⊙ . output) leads to cut in the total energy budget. Therefore, we usedthe stellar evolution 1D output which was mapped into PROMETHEUS prior to the collapse. We detonate it with the thermal bomb methodwith according explosion energy. We note that the amount of explo-sion energy was set in a way to allow the subset models to reach thesame terminal kinetic energy of 0.86 × erg which is the explo-sion energy of the main model e8.8 in the study. The reduction of theradius by cutting numerically leads to some degree of inconsistency,since the star is supposed to relax into a new thermodynamical equi-librium. Another unavoidable side-effect consists in reduction of theejecta mass. Hence the total mass for the truncated sub-models are:1.8 M ⊙ , 2.4 M ⊙ , 4 M ⊙ for 400 R ⊙ , 600 R ⊙ , and 900 R ⊙ cases,respectively.In Figure 12, the resulting bolometric, broad-band light curvesand the B - V colour are shown. The artificially detonated stellar evo-lution model (labelled “1200 Rsun”) displays the same curve as themain model e8.8 exploded in a self-consistent manner (blue solidand dashed curves). There is some difference between these curvesdue to a few reasons. First, the detonated evolutionary model doesnot have any applied macroscopic mixing of chemicals. Second, PROMETHEUS simulations were performed without taking radiationtransport into account while
STELLA does hydrodynamics coupledwith radiation transport. I.e. this leads to a difference in propaga-tion of the radiation-dominated shock. Third,
PROMETHEUS does notinclude heating from radioactive Ni, while
STELLA does. The pres-ence of Ni results in variation in velocity, temperature and densityfield which is called “Ni-bubble” effect and leads to variation in,e.g., velocity upto 10 – 15 % in the region where Ni mass fractionis close to unity (Kozyreva et al. 2017). Fourth, the
PROMETHEUS
STELLA which leads to the slight variation in hydrodynamical profiles andmay cause some diversity in the resulting radiation transfer simula-tions.As seen in Figure 12, the more compact the progenitor the shorterthe plateau, which is consistent with Equation 3 (Popov 1993) andnumerical experiments by Young (2004). However, the plateau du-ration has the major impact from the ejecta mass which is connected to the reduction of the radius. The model e8.8 being truncated to400 R ⊙ has a very short living light curve lasting only 30 days,although it still retains hydrogen-rich envelope with the total massof hydrogen of 0.3 M ⊙ . The colour of the more truncated modelstends to be bluer since the hotter region of the ejecta gets closer tothe outer edge. The higher temperature also explains the bump in thebolometric light curves for the cases of 400 R ⊙ and 600 R ⊙ . For thesame reason U -band light curves for the 400 R ⊙ and 600 R ⊙ casesare relatively luminous. We conclude that ECSNe in the binarieshave fastly declining low-luminosity light curves and will be easilymissed even being exploded in the close vicinity. This is the reasonthat there is no solid detection of an ECSN yet. U and V broad-band light curves for three default models from ourstudy and the reference CCSN model L15-nu/L15-tb are shown inFigure 13. The U magnitude of the model z9.6 evolves significantlydifferently to other models due to its lack of metals. We study theeffect of metallicity and discuss our results in Section 3.4 above. Thelight curves of L15-tb and L15-nu in U -band decline 2 mags during50 days, i.e. evolves typically for the canonical SNe IIP. s9.0 U -bandlight curve behaves the same way as the reference CCSN model L15-nu/L15-tb with a systematically lower luminosity overall. There is noappreciable difference between plateau-like light curves in V bandfor the ECSN model e8.8 and the low-mass CCSN models z9.6 ands9.0 in comparison to the reference CCSN model L15-nu/L15-tb.The colours B – V , V – R , and V – I are bluer for z9.6 and e8.8 com-pared to the models s9.0 and L15-nu/L15-tb. This is a conquence ofthe lack of metals in the model z9.6 and the unusual colour temper-ature evolution for the model e8.8. We discuss the latter below.The colour temperature evolution for all models is shown in Fig-ure 14. The colour temperature is the black body temperature asestimated from the least-square method. It serves as the indicator ofthe maximum in the spectral energy distribution, i.e. represent thefrequency where the major flux is radiated. As was discussed above,recombination sets in at relatively late times in the model e8.8 com-pared to the other models. This is explained by a strong dependenceof the “recombination time” on the radius of the progenitor and en-ergy of the explosion (see Equation 2). The distinguishing propertyof ECSN progenitors is the large radius, and generally ECSN explo-sions are low energetic, therefore, the recombination time tends tobe relatively long. Specifically the radius of model e8.8 is 1200 R ⊙ ,quite large even for an average red supergiant. The explosion energyof the reference explosion model e8.8 is 0.1 foe. According to Equa-tion 2 (Shussman et al. 2016; Kozyreva et al. 2020a), recombinationis established at day 66 for the model e8.8, day 22 for the modelsz9.6 and L15, and at day 38 for the model s9.0.Hence the main feature which distinguishes ECSN explosions fromCCSN explosions are the behaviour of the blue flux, i.e. U and B magnitude, colour temperature, and colours. The specific features ofe8.8’s observables are:(i) the light curve in the U and B bands rising during the first50 days and then slowly declining,(ii) the light curve in V and other redder bands rising during thesame phase of 50 days and then holding at a plateau before the sharpdrop to the low-luminosity tail powered by a small amount of theradioactive nickel Ni.We emphasise that this unique behaviour is the consequence of therelatively extended hydrogen-rich envelope and the absence of helium
MNRAS , 1–19 (2020)
CSNe and Low-mass CCSNe Time [days] l og Lbo l [ e r g / s ] a e8.8 basic1200 Rsun900 Rsun600 Rsun400 Rsun Time [days] -17-16-15-14-13-12 U [ m a g s ] b e8.8 3D1200 Rsun900 Rsun600 Rsun400 Rsun Time [days] -17-16-15-14-13-12 B [ m a g s ] c e8.8 3D1200 Rsun900 Rsun600 Rsun400 Rsun Time [days] -17-16-15-14-13-12 V [ m a g s ] d e8.8 3D1200 Rsun900 Rsun600 Rsun400 Rsun Time [days] -17-16-15-14-13-12 R [ m a g s ] e e8.8 3D1200 Rsun900 Rsun600 Rsun400 Rsun Time [days] B - V [ m a g s ] f e8.8 3D1200 Rsun900 Rsun600 Rsun400 Rsun Figure 12.
Bolometric light curves for the subset of runs based on the stellar evolution model e8.8 with different degree of truncated envelope.MNRAS000
Bolometric light curves for the subset of runs based on the stellar evolution model e8.8 with different degree of truncated envelope.MNRAS000 , 1–19 (2020) A. Kozyreva et al.
Time [days] -17-16-15-14-13-12-11-10 U [ m a g s ] s9.0 -- L15-tb a L15-nu z9.6 e8.8
Time [days] -17-16-15-14-13-12-11-10 V [ m a g s ] s9.0 -- L15-tb b L15-nu z9.6e8.8
Figure 13. U and V broad-band light curves for the models e8.8, z9.6, s9.0, and L15-nu/L15-tb. Time [days] T c o l [ K ] e8.8z9.6s9.0L15-tbL15-nu Figure 14.
Colour temperature evolution for the models e8.8, z9.6, s9.0, andL15-nu/L15-tb. and oxygen shells which in turn is the result of the unique stellarevolution path of the super-AGB stars (see e.g., Doherty et al. 2015).The main differences between low- and normal-mass CCSNe are(1) an overall lower luminosity at the plateau, 0.5 – 1 dex for bolomet-ric luminosity or 1.5–2 mags in V broad band, (2) a low-luminosityradioactive tail, and (3) a large drop in luminosity between the plateauand the tail. All of these features are explained by the relatively lowerexplosion energy of low-mass explosions (below 0.1 foe) and a loweryield of radioactive nickel. In this section we consider the results of our radiative transfer sim-ulations for the ECSN model e8.8 and the low-mass CCSN models z9.6 and s9.0 in the context of observations. Particularly, we aimto find possible candidates matching our calculations. Further, weaim to point out the criteria for distingushing properties, specificallyfor the ECSNe and low-mass CCSNe. Immediately we encounter anobvious problem: namely that the number of detected and followed-up SNe increases every year at an exponential rate (Gal-Yam et al.2013). Therefore, in our analysis we opt to compare our syntheticlight curves to a representative sample and draw some general con-clusions.
For example, low-mass CCSNe are expected to be low energy and toproduce a small amount of Ni leading to a low-luminosity plateau,and a large drop towards the low-luminosity radioactive tail. There-fore, we choose SN 2005cs as the first example for our comparison.This event is famous for its low plateau luminosity and steep and pro-nounced drop towards the tail. We show the bolometric light curveof SN 2005cs (Pastorello et al. 2009) superposed on our simulatedbolometric light curves in Figure 16. It is apparent that none of themodels match the bolometric light curve of SN 2005cs. However,there are some conclusion to be drawn on the general energeticsand bolometric parameters of this particular SN and its possibleprogenitor. (1) SN 2005cs is likely not a ECSN explosion with anenvelope and energy as model e8.8, because the luminosity of theSN throughout the plateau phase is about 0.2–0.5 dex lower than theluminosity of the ECSN model e8.8. This means that the progenitorof SN 2005cs was likely more compact than our model (with a ra-dius of 1200 R ⊙ ), which is in agreement with the conclusion drawnby Eldridge et al. (2007). (2) The model s9.0 is likely more similarto the real progenitor of SN 2005cs. The remaining differences areexplained either by the radius of the progenitor larger than the ra-dius of the model s9.0 (408 R ⊙ ) or/and the explosion energy beinghigher than . × erg. The total mass of the radioactive Niin SN 2005cs is likely lower than the 0.005 M ⊙ contained in themodel s9.0. Pastorello et al. (2009) proposed the following param-eters for the progenitor based on their simulations: radius 100 R ⊙ ,ejecta mass 11.1 M ⊙ , and explosion energy × erg. Later MNRAS , 1–19 (2020)
CSNe and Low-mass CCSNe Time [days] B - V [ m a g s ] s9.0 -- L15-tb a L15-nu z9.6e8.8
Time [days] V - R [ m a g s ] s9.0 -- L15-tb b L15-nu z9.6 e8.8
Time [days] V - I [ m a g s ] s9.0 -- L15-tb c L15-nu z9.6e8.8
Figure 15. B – V , V – R , and V – I colours for the models e8.8, z9.6, s9.0, and L15-nu/L15-tb. Time [days] l og Lbo l [ e r g / s ] e8.8z9.6 s9.0 SN 2005cs
Figure 16.
Bolometric light curves for the models e8.8, z9.6 and s9.0 andobserved SN 2005cs (Pastorello et al. 2009).
Spiro et al. (2014) revised these numbers providing new parametersfor SN 2005cs: 350 R ⊙ , 9.5 M ⊙ , and 1.6 × erg. The photo-spheric velocity of SN 2005cs is at the same level as in our models(Figure 4), i.e. about 1000–2000 km s − . Hence, judging from thebolometric properties of the SNe, the progenitor is likely a low-massstar of moderate radius which exploded at relatively low energy, butstill higher than the low energy explosions in our study.We show the broad-band magnitudes of the model s9.0 andSN 2005cs in Figure 17. As discussed in the previous sections, U magnitude is a very unique indicator of many model parameters,such as iron and nickel content in the ejecta and the radius of theprogenitor. From the plot, we conclude that the model s9.0, which isthe most similar to a normal SN IIP judging from its U band lightcurve, still evolves too shallowly. On the one hand, this is explainedby the fact that radioactive nickel is mixed extensively in the ejecta ofs9.0, retaining flux in the blue bands to later times. On the other hand,increased short wavelength flux might be explained by a low stableiron content in the hydrogen-rich envelope. However, as the models9.0 is computed with solar metallicity, and the contained iron is ableto absorb the blue flux sufficiently. There are a few assumptions, e.g.using a super-solar metallicity model or reducing the mass and/orradius of the existing s9.0 model, which might result in the recom- Time [days] -16-15-14-13-12-11-10 m a gn i t ud es s9.02005cs U BVR I Figure 17.
Light curves for the model s9.0 and observed SN 2005cs inbroad bands Small and large circles correspond to the observed data takenfrom Tsvetkov et al. (2006) and Pastorello et al. (2009), respectively. Trian-gles present the upper limits for observed magnitudes. bination wave receding faster (i.e. U magnitude to decline sharper).Magnitudes in V , R , and I bands tend to rise after day 20, whileobserved SNe, particularly normal SNe IIP or other low-luminositySNe (as seen in Spiro et al. 2014), have light curves declining inbroad-bands B and V , or exhibit a plateau in R and I .There is another distinct feature seen in Figure 17: observed mag-nitudes have an significant flux excess compared to the synthetic lightcurves of the model s9.0. This may indicate that the true progenitoris more extended than the model s9.0. However, introducing a largerprogenitor radius unavoidably leads to higher luminosity during theplateau phase (Popov 1993). A number of low-luminosity SNe IIP have been observed(Pastorello et al. 2004; Spiro et al. 2014). We show a comparisonof broad-band light curves of the model s9.0 to one of these SNe(SN 1999br) in Figure 18. The distance to the parent galaxy ofSN 1999br (NGC 4900) is subject to uncertainty. We apply the up-to-date distance modulus from Karachentsev & Karachentseva (2019).Accordingly, the magnitudes for all observed broad-band magni-
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Time [days] -16-15-14-13-12-11-10-9 m a gn i t ud es s9.0 U BVR I Figure 18.
Light curves for the model s9.0 and observed SN 1999br in broadbands (Pastorello et al. 2004). tudes are well matched by the model. However, there is a flux excessat earlier time which suggests similarity between SN 1999br andSN 2005cs. Another reason for the luminosity excess at earlier timemay lie in the possibility of interaction of the SN ejecta with thecircumstellar matter, expelled by the progenitor as wind during ear-lier evolutionary stages (Morozova et al. 2017; Moriya et al. 2018;Goldberg & Bildsten 2020). However, adding a wind environment tothe model leads to certain consequences for observations. In partic-ular, the SN can be expected to exhibit an X-ray excess which is notobserved for every SN IIP.The low-luminosity SN 2008bk is considered to be similar toSN 1999br in its photometric evolution (Van Dyk et al. 2012). Ac-cording to Lisakov et al. (2017), SN 2008bk is best fitted by aprogenitor of initial mass 12 M ⊙ (model X in their study), pre-explosion radius 502 R ⊙ (consistent with 496 R ⊙ derived byPastorello et al. (2004) and 500 R ⊙ by Pumo et al. (2017)), ejectamass of 8.29 M ⊙ , ejected Ni mass of 0.0086 M ⊙ , and explo-sion energy . × erg. However, Lisakov et al. (2017) statethat this energy is too high to match photospheric velocity evolution(see also Lisakov et al. 2018). In contrast, our model s9.0 fits the ob-served velocity better due to a significantly lower explosion energy of . × erg and a lower ejecta mass of 7.4 M ⊙ ( E/M = 0 . in our study versus 0.3 in Lisakov et al. (2017)). Similarly, SN 1997Dwas explained by Chugai & Utrobin (2000) as a low-mass (6 M ⊙ )low energetic explosion ( × erg). It is worth mentioning that recently Zhang et al. (2020) andHiramatsu et al. (2020) presented evidence of SN 2018zd as anECSN candidate. However, the evolution of the broad-band mag-nitudes, specifically, the decline of the U band magnitude, is verysimilar to an average SN IIP. An analysis of spectra (FLASH-spectroscopy) and the time evolution of the photospheric velocityalso indicate the explosion of an average massive star in a surround-ing wind (Zhang et al. 2020). Hence, the most probable explanationis that SN 2018zd was a low- to intermediate-mass iron-CCSN. Notethat the distance to the host galaxy (NGC 2146) is estimated twotimes larger by Zhang et al. (2020) than by Hiramatsu et al. (2020),which directly affects all consequently derived values of the ex- plosion energy, the mass of radioactive nickel Ni, radius of theprogenitor and other parameters. Specifically, Zhang et al. (2020)estimate 0.033 M ⊙ of Ni while Hiramatsu et al. (2020) calculate0.0086 M ⊙ of Ni. Particularly, the latter conclude that SN 2018zdwas an ECSN based on the low mass of Ni. Nevertheless, it isdifficult to discriminate different kinds of progenitors relying on theestimated Ni mass, because the amount of Ni produced duringneutrino-driven explosions is mostly a function of the explosion en-ergy (Sukhbold et al. 2016; Ertl et al. 2020), and both ECSNe andlow-mass iron-CCSNe can explode with similar energies.Moreover, Reguitti et al. (2021) observed the low-luminositySN 2018hwm and suggested two possibilities: either it is an ECSNor a low-mass iron-CCSN. The authors do not favour one possi-bility over the other. However, a low plateau luminosity does notnecessarily indicate an ECSN candidate, i.e. an explosion of a super-AGB star, because the luminosity depends on the radius, and theradius of an ECSN progenitor might be very large. E.g. our ex-tended ECSN progenitor e8.8 exhibits a luminosity on the plateauof about × erg s − , i.e. comparable to an average SN IIP(Hamuy & Pinto 2002; Pejcha & Prieto 2015; Müller et al. 2017), aswe show in Figure 3. On the other hand, the very low photosphericvelocity of about 1500 km s − and very long plateau of 150 daysexplicitly point to a low explosion energy, 0.055 foe, as derived byReguitti et al. (2021). The very low mass of radioactive nickel Ni of0.002 M ⊙ also does not necessarily point the explosion as an ECSN,because our low-mass iron-core explosions produce as little Ni as0.0007 M ⊙ (model z9.6, see Table 1). Therefore, SN 2018hwm isalso most likely a low-mass iron-CCSN.To conclude, the published observations cannot exclude low-massiron-CCSNe as an explanation of SN 2018zd and SN 2018hwm. B – V colour diagnostics In Figure 19, we show the B – V colour for our models e8.8,z9.6, and s9.0, in comparison to five normal SNe IIP, namelythe typical SN 1999em, and also SN 2013fs, ASASSN 2014gm,ASASSN 2014ha, SN 2005cs (Pastorello et al. 2009; Faran et al.2014b,a; Valenti et al. 2016). As mentioned by Kozyreva et al.(2019), the B – V colour could serve as an indicator of the Ni mix-ing in the SN ejecta. Indeed, the models e8.8 and z9.6 have a strictlystratified chemical structure, leading to a sharp reddening at the endof the plateau, while the model s9.0 has extensive mixing of radioac-tive nickel in the ejecta. Extensive mixing of radioactive nickel leadsto colour reddening more gradually at the end of the plateau. Still,none of the models in our study matches the behaviour of the B – V colour for the typical SNe IIP in our sample. It is possible that themodel s9.0 might explain the colour of SN 2005cs while having asmaller mass of Ni. With 0.005 M ⊙ of Ni the colour reddens tomuch after the transition to the tail, meaning the absorption, i.e. lineopacity, is very strong in the inner ejecta.Contrary to the conclusions of Botticella et al. (2009), the lightcurve of SN 2008S is dissimilar to the ECSN model e8.8. The distin-guishing property of an ECSN, i.e. a super-AGB progenitor explo-sion, is not a low-luminosity plateau, but a distinct moderate lumi-nosity plateau accompanied by a sharp transition to a low-luminosityradioactive tail. Tominaga et al. (2013) also speculate that SN 2008Sis most likely not an ECSN explosion. However, they suggest thata more compact ECSN progenitor might be a good candidate forSN 2008S, especially taking the uncertainty of the wind mass-lossand pulsationally-driven mass-loss into account.The sub-class of very faint, faint, or/and low-luminosity SNe IIP(Pastorello et al. 2004, 2007; Spiro et al. 2014) are most likely explo-
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CSNe and Low-mass CCSNe Time [days] B - V [ m a g s ] e8.8z9.6s9.0 Figure 19.
The B – V colour for the models e8.8, z9.6 and s9.0 and observedSN 1999em, SN 2013fs, ASASSN 2014gm, ASASSN 2014ha. We also su-perpose the lower and upper limits for the B – V colour for normal SNe IIPderived by Faran et al. (2014a) represented by black lines. sions of low-mass progenitors, similar to our model z9.6 but at solarmetallicity and a lower energy, e.g. a few erg, and relatively lowmasses of ejected Ni. The very low energies of these explosions arefavoured by the low photospheric velocity during the plateau phase.
In this study, we present the evolution of the SN ejecta of three progen-itors: the ECSN progenitor e8.8, the low-mass zero-metallicity z9.6,and the low-mass solar-metallicity s9.0, with initial ZAMS masses of8.8 M ⊙ , 9.6 M ⊙ , and 9 M ⊙ , respectively. The models were explodedself-consistently with PROMETHEUS by Stockinger et al. (2020). Wecalculated the hydrodynamical evolution and radiative transfer simu-lations for these three models with
STELLA . The resulting light curvesdiffer from explosions of massive stars. We used 15 M ⊙ model L15(Limongi et al. 2000) as a reference CCSN model for comparison.Among the reasons for the differences are: • low explosion energy; • low mass of ejected radioactive nickel Ni; • absence of the distinct massive ( > ⊙ ) helium shell andoxygen layer.The distinct properties of the SNe arising from our default modelscan be summarised as: The model e8.8: • during the first 50 days: plateau in U band and rising magnitudesin B , V , R , and I bands. • after day 50: plateau in R and I bands. • the transition to the tail is steep and pronounced, more than twoorders in bolometric luminosity, or 6 mags in V band. • colour temperature remains above 6000 K until the middle ofthe plateau. The model z9.6: • relatively low luminosity on the plateau, log L bol ∼ erg s − , or –14.5 mags in V band. • pronounced and steep transition to the tail, about 1.5 orders inbolometric luminosity, or 4.6 mags in V band. • magnitudes in all broad bands increase starting at early times.The colours remain largely constant during the plateau phase. The model s9.0: • relatively low luminosity during the plateau phase, log L bol ∼ erg s − , or –14 mag in V band. • shallow transition to the tail due to extended macroscopic mix-ing of radioactive material. • the transition is less pronounced, about 3.5 mags in V band.The model s9.0 is the best candidate among our models for theobserved low-luminosity SNe IIP according to its broad-band lightcurves and colour evolution.For all our models, photospheric velocity is relatively low, 1000 –2000 km s − during the plateau. This feature is a convenient indicatorof low-mass explosions.We do not find a good candidate among our sample of observedSNe resembeling the observables of the ECSN model e8.8. Ac-cording to our models, low-luminosity SNe IIP like SN 1999br andSN 2005cs, can be explained by the explosion of low-mass CCSNe.However, the observed SNe show a clear flux excess at the earlierphase (before day 20). This requires either more extended progeni-tors or the presense of circumstellar matter (e.g. pre-SN wind), andinteraction of the SN ejecta with the circumstellar environment.Further we carried out the following studies:(i) Variations of the Ni mass produced in model e8.8. The more Ni is ejected, the longer is the plateau and the higher the luminosityon the tail. Slightly bluer colours (0.2 mags in B – V ).(ii) Variations of the explosion energy for the model e8.8. We findthat the light curves obey the standard relations from Popov (1993),i.e. the higher the energy the shorter and brighter the plateau. Slightlybluer colours (0.2 mags in B – V ).(iii) Variations of the hydrogen-to-helium ratio in the model e8.8.Here we find that the higher helium fraction in the hydrogen-richenvelope, the shorter and brighter the plateau. Slightly bluer colours(0.2 mags in B – V ).(iv) A metallicity study for the models e8.8 and z9.6. We findthat the higher the metallicity, i.e. the higher the iron abundancein the hydrogen-rich envelope, the redder the colours; the U bandmagnitude is good indicator for measuring the metallicity of the SNprogenitor; the B – V colour changes significantly: 1 mag betweenzero metallicity case and SMC/solar metallicity.(v) A radius-dependence study for the ECSN model e8.8. As-suming the ECSN explodes in a binary system, the progenitor maylose hydrogen-rich envelope via close binary interaction. We foundout that the light curves for the truncated models become shorter,namely, the sub-model with the radius 400 R ⊙ has the sharply de-clining 30 day light curve with a low-luminosity maximum phase.Therefore, ECSNe in binaries are mostly undetectable.Spectral synthesis simulations for our models similar toJerkstrand et al. (2018) will be useful, as synthetic spectra are moresensitive to the SN ejecta structure than broad-band light curves. ACKNOWLEDGMENTS
AK is supported by the Alexander von Humboldt Foundation.PB is sponsored by grant RFBR 21-52-12032 in his work on
MNRAS , 1–19 (2020) A. Kozyreva et al. the
STELLA code development. HTJ acknowledges support by theDeutsche Forschungsgemeinschaft (DFG, German Research Foun-dation) through Sonderforschungsbereich (Collaborative ResearchCenter) SFB-1258 “Neutrinos and Dark Matter in Astro- and ParticlePhysics (NDM)” and under Germany’s Excellence Strategy throughCluster of Excellence ORIGINS (EXC-2094)-390783311, and by theEuropean Research Council through Grant ERC-AdG No. 341157-COCO2CASA. The authors thank Andrea Pastorello for providingthe observed data in a suitable format and corresponding discussions.AK would like to thank Patrick Neunteufel for useful suggestions.
DATA AVAILABILITY
The data computed and analysed forthe current study are available via link .Results of the core-collapse explosion simulations are avail-able for download upon request on the following website: . REFERENCES
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