Connecting the Light Curves of Type IIP Supernovae to the Properties of their Progenitors
Brandon L. Barker, Chelsea E. Harris, MacKenzie L. Warren, Evan P. O'Connor, Sean M. Couch
DD RAFT VERSION F EBRUARY
3, 2021Typeset using L A TEX twocolumn style in AASTeX63
Connecting the Light Curves of Type IIP Supernovae to the Properties of their Progenitors B RANDON
L. B
ARKER , ∗ C HELSEA
E. H
ARRIS , M AC K ENZIE
L. W
ARREN , E VAN
P. O’C
ONNOR , AND S EAN
M. C
OUCH
1, 4, 5, 61
Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA AI Research Group, 5x5 Technologies, St Petersburg, FL 33701 USA The Oskar Klein Centre, Department of Astronomy, Stockholm University, AlbaNova, SE-106 91 Stockholm, Sweden Joint Institute for Nuclear Astrophysics-Center for the Evolution of the Elements, Michigan State University, East Lansing, MI 48824, USA Department of Computational Mathematics, Science, and Engineering, Michigan State University, East Lansing, MI 48824, USA National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824, USA (Received February 3, 2021)
Submitted to ApJABSTRACTObservations of core-collapse supernovae (CCSNe) reveal a wealth of information about the dynamics ofthe supernova ejecta and its composition but reveal very little direct information about the progenitor star.Constraining properties of the progenitor and the explosion, such as explosion energy, requires coupling theobservations with a theoretical model of the explosion. Here, we use a new model for driving turbulence-aided neutrino-driven core-collapse supernovae in 1D (STIR) which contains a non-parametric treatment of theneutrino transport while also accounting for turbulence and convection. We couple this with the SuperNovaExplosion Code to produce bolometric light curves from a landscape of CCSNe driven from self-consistentCCSN simulations with robust neutrino transport. We compare our results to several well observed bolometriclight curves of Type IIP CCSNe and find that our best fitting models differ from those found in previous studiesusing thermal bomb explosions, indicating ZAMS masses as much as about 10 M (cid:12) greater than previous studies.Using our large sample of 136 self-consistent CCSN explosions, we explore correlations between observablefeatures of the light curves and properties of the progenitor star. Among other significant correlations, we finda robust linear relationship between light curve plateau luminosity and the iron core mass of the progenitor.This relationship allows for properties of the core of the progenitor to be constrained for the first time fromphotometry alone. Keywords:
Core-collapse supernovae (304), Type II supernovae (1731), Computational methods (1965), Hydro-dynamical simulations (767), Supernova neutrinos (1666), Supernova dynamics (1664), Radiativetransfer (1335) INTRODUCTIONCore-collapse supernovae (CCSNe) are the explosivedeaths that result from the ends of stellar evolution for mas-sive stars. These stars, with zero-age main sequence (ZAMS)masses M ZAMS (cid:38) M (cid:12) , undergo successive cycles of nu-clear burning until, at the ends of their lives, they build upa degenerate iron core and undergo gravitational collapse.These iron cores reach the effective Chandrasekhar mass Corresponding author: Brandon L. [email protected] ∗ NSF Graduate Research Fellow limit (Baron & Cooperstein 1990) at which point electrondegeneracy pressure is insufficient to balance gravity, hydro-static equilibrium fails, and the core collapses. The collapseis accelerated by runaway electron capture processes, whichproduces a vast number of electron neutrinos and robs thecore of electron degeneracy support. Eventually, the innercore becomes so dense that the residual strong force becomesrepulsive and the core abruptly rebounds, sending pressurewaves through the still-collapsing outer core and forming anoutward-propagating shock. Ultimately, this shock fails tounbind the progenitor star and stalls in the outer core. Theproblem of rejuvenating the stalled shock has been the sub-ject of decades of work and still remains a subject of ac-tive investigation (for in-depth reviews of the CCSN mecha- a r X i v : . [ a s t r o - ph . H E ] F e b B ARKER ET AL .nism, see, e.g., Bethe 1990; Janka et al. 2007, 2012, 2016;Burrows 2013; Hix et al. 2014; M¨uller et al. 2016; Couch2017). The current understanding is that for some fractionof these events, the stalled shock will not be revived, result-ing in failed explosions in which the star inevitably collapsesto a black hole (BH) (O’Connor & Ott 2011; Lovegrove &Woosley 2013; Ertl et al. 2016; Sukhbold et al. 2016; Adamset al. 2017b; Sukhbold et al. 2018; Couch et al. 2020), anevent that may or not not have an associated electromag-netic (EM) transient detectable by LSST and other telescopes(Lovegrove & Woosley 2013; Adams et al. 2017a; Quataertet al. 2019). For stars that do produce explosions, the currentunderstanding favors the so-called delayed neutrino-drivenmechanism (Bethe & Wilson 1985), although the magneto-rotational mechanism is likely responsible for rare CCSNe(Akiyama et al. 2003). In the former case, neutrinos emittednear the surface of the proto-neutron star (PNS) heat materialbeneath the stalled shock through charged-current absorptioninteractions. This heating drives convection and other hydro-dynamic instabilities and, for some fraction of CCSN pro-genitors, revives the stalled shock and drives the explosion.Whatever the case may be, it is certain now that a rich inter-play of physics is necessary to truly understand these eventsand their outcomes.CCSNe are detectable by three primary messengers – EMwaves, neutrinos, and gravitational waves (GWs). Neutrinoand GW signals have the very desirable property that they areemitted directly from the core of the star at the time of col-lapse and may reveal information about the structure there(e.g., Pajkos et al. 2019, 2020; Warren et al. 2020; Sotani &Takiwaki 2020), unlike photons which are emitted from thephotosphere in the very outer layers of the supernova ejectauntil the remnant phase. However, to date there has been onlyone detection of neutrinos from a supernova (Arnett et al.1989, SN1987A). With modern neutrino detectors, only CC-SNe occurring within our galaxy may be detectable (Schol-berg 2012). Similarly, there have been no confirmed detec-tions of GW emission from a CCSNe. The current suite ofdetectors (aLIGO, Virgo, and KAGRA) can only detect GWsfrom a CCSNe if it occurs within a distance of ≤ kpc(Abbott et al. 2016). It is the case, however unfortunate, thatthe overwhelming majority CCSNe will only be observed inEM signals.The focus of this paper is connecting EM signals to pro-genitor properties for Type IIP SNe, the most common kindof CCSN, characterized by a distinctive plateau in their lightcurve powered by H recombination in the expanding H-richejecta (see, e.g., Branch & Wheeler 2017). These events havebeen shown to originate from red supergiant progenitors (VanDyk et al. 2003; Smartt 2009; Van Dyk et al. 2019). Theseprogenitors maintain a significant fraction of their H enve-lope throughout their lives. Despite being the most common type of CCSNe, their diversity of observable features – suchas light curve morphologies – is still not fully understood(e.g., Anderson et al. 2014; Valenti et al. 2016). Connect-ing properties of progenitors with observable features of lightcurves – such as the duration and shape of the fall off of theplateau – is an area of active work. The connection betweenType IIP and IIL supernovae still remains an open question– whether IIL’s are the limit of IIP’s as the H envelope is de-pleted or a separate class (Barbon et al. 1979; Blinnikov &Bartunov 1993; Morozova et al. 2015).Understanding the connection between Type IIP SN lightcurves and stellar progenitors has a new urgency. Comingnext-generation telescopes such as the Vera C. Rubin Obser-vatory and its primary optical photometry survey, The Ru-bin Observatory Legacy Survey of Space and Time (LSST)(Ivezi´c et al. 2019), will allow for extremely deep imagingof the entire sky every couple of nights. One of the most in-teresting science prospects for LSST is the study of transientevents such as CCSNe. LSST will allow for statistical stud-ies of populations of CCSNe of an unprecedented scale. Cur-rent statistical studies of Type II supernova populations (see,e.g., Anderson et al. 2014; Guti´errez et al. 2017a,b) have in-cluded around 100 events. The LSST is expected observe 10million transient events per night (Ivezi´c et al. 2019) greatlyexpanding the sample of observed CCSNe and allowing formuch larger statistical studies of photometric properties ofthese events. This new data set – powered by modern theo-retical tools – provides a powerful window to understandingCCSNe.Ultimately, properly characterizing the diversity in Type IIsupernova light curve morphology will require the union ofobservation and theory. On the theory side, this comprisesrealistic stellar evolution models including the core collapse,following the resulting explosion with robust physics, andcalculating EM light curves (as well as neutrino and GWsignals). The gold standard is full three-dimensional (3D),self-consistent simulations. Core-collapse supernovae andtheir progenitors are truly 3D in nature and the key to under-standing the diversity of light curve morphology lies in faith-fully modeling these asphericities (Dessart & Audit 2019).3D simulations are, however, computationally expensive toperform and, as such, are limited in number and the rangeof parameter space that they cover. Spherically symmet-ric (1D) simulations remain necessary for understanding theCCSNe explosion mechanism and their observables by sur-veying landscapes of possible CCSNe. Great progress hasbeen made in the last few years regarding 1D CCSN sim-ulations (Ebinger et al. 2017; Sukhbold et al. 2016; Couchet al. 2020), allowing for successful explosions in 1D usingneutrino-driven explosions across wide ranges of progeni-tor masses. These 1D simulations allow for large parame-ter studies performing potentially thousands of simulations YPE
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FLASH (Fryxellet al. 2000; Dubey et al. 2009) code using the new Super-nova Turbulence In Reduced-dimensionality (STIR) model(Couch et al. 2020). This 1D convection scheme has the ben-efit of being consistent with full physics 3D CCSN simula-tions. The initial conditions of these models are set by the1D stellar evolution models of Sukhbold et al. (2016), whichmake up a suite of 200 solar metallicity, non-rotating mas-sive stars between 9 and 120 M (cid:12) . We couple the final stateof the STIR simulations with the SuperNova Explosion Code(SNEC) (Morozova et al. 2015), which follows the explosionthrough the rest of the star and through the plateau and nebu-lar phases of the light curves. We will demonstrate that usinga more sophisticated 1D explosion model, versus a thermalbomb with arbitrary input explosion energy, has a qualitativeimpact on the light curves, highlighting the importance of theexplosion model used. With this set of light curves, we makeavailable a new set of theoretical predictions to compare di-rectly with observations, as we will demonstrate. Further-more, we investigate direct correlations between progenitorproperties and light curve properties. We recover known cor-relations, and we quantify the dependence of Type IIP SN lu-minosity on the progenitor iron core mass at time of collapse– thus providing a way of obtaining core properties from EMsignals without the need for the much rarer neutrino and GWsignals.This paper is laid out as follows: in Section 2 we discussthe various progenitors, codes, and statistical methods that http://flash.uchicago.edu/site/ are used in this study. Section 3 presents our results: 3.1 com-pares our light curves with those obtained with pure thermalbomb methods, 3.2 presents preliminary comparisons to ob-servations of Type IIP CCSNe, 3.3 shows correlations foundbetween light curve and progenitor properties. In Section 4,we summarize our results and briefly discuss comparison toother theoretical light-curve calculations and prospects forfuture work. METHODSFor this work, we begin with massive stellar progeni-tors evolved up to the point of core collapse in Sukhboldet al. (2016). The core collapse and following explosionor collapse to BH are simulated using the
FLASH simu-lation framework (Fryxell et al. 2000; Dubey et al. 2009)with the Supernova Turbulence In Reduced-dimensionality(STIR) model (Couch et al. 2020), the details of which arediscussed in Section 2.2. The output of the STIR simulationsare mapped into the SuperNova Explosion Code (SNEC)(Morozova et al. 2015, 2016, 2018) to generate bolometriclight curves as discussed in Section 2.3. In Section 2.4 wepresent the methods used to analyze statistical relationshipsbetween properties of the progenitor and observables.2.1.
Progenitors
We begin with the 200 non-rotating, solar metallicity mod-els of Sukhbold et al. (2016). These models cover a rangeof ZAMS masses from 9 – 120 M (cid:12) and were created withthe KEPLER code assuming no magnetic fields or rotationand single star evolution. Progenitors with ZAMS massesabove 31 M (cid:12) experienced significant mass loss during theirlifetimes and did not explode as Type IIP supernovae andthis is the upper limit on our mass range (see Sukhbold et al.2016, for details on their stellar evolution). The more mas-sive Type I SNe progenitors are too few in number to performa meaningful statistical analysis and we defer their analysisfor future work. This leaves 136 progenitors producing TypeIIP supernovae used in this work.These progenitors span a wide range of possible CC-SNe progenitor properties. Figure 1 shows the H enve-lope mass as a function of pre-supernova radius (top) andthe stellar pre-supernova mass as a function of ZAMS mass(bottom). These progenitors become mass-loss dominatedaround 23 M (cid:12) , as seen in the bottom panel of Figure 1. Thiscomplicates correlations between quantities of interest andtends to cause them to deviate from monotonicity. This iskey to investigating observable trends in light curves acrossa wide range of progenitors, as we demonstrate later.A key result of systematic 1D studies of CCSNe are the so-called “islands of explodabilty” (Sukhbold et al. 2016). Thefinal result of stellar core collapse - a successful or failedexplosion - is not a monotonic function of ZAMS mass. In-stead, the explodability of the progenitor is sensitive to the B ARKER ET AL . . . . . . R preSN [500 R (cid:12) ] M e n v [ M (cid:12) ]
10 15 20 25 30 M ZAMS [M (cid:12) ] M p r e S N [ M (cid:12) ] Figure 1. (top) H envelope mass ( M env ) as a function of pre-supernova radius ( R preSN ). (bottom) Final stellar mass ( M preSN ),after mass loss, as a function of ZAMS mass. core structure at the time of collapse. While the placement ofthese islands is sensitive to the explosion model and the pro-genitors used, it is a feature that has now been seen amongstmany groups (O’Connor & Ott 2011; Perego et al. 2015;Sukhbold et al. 2016; Ebinger et al. 2019; Couch et al. 2020).However, studies using thermal bomb driven explosions can-not reproduce the explosion/implosion fate of a progenitorand are insensitive to this feature. Any systematic study oflight curves from populations of SNe must capture this com-plex behavior. 2.2. FLASH
The CCSN simulations were previously conducted usingthe
FLASH code framework with the STIR turbulence-aidedexplosion model (Couch et al. 2020). This model is a newmethod for artificially driving explosions in 1D CCSN sim-ulations that has been incorporated into
FLASH . Turbulenceis key in simulating successful, realistic explosions, as tur-bulence may constitute 50 % or more of the total pressurebehind the shock (Murphy et al. 2013; Couch & Ott 2015) and turbulent dissipation is important for post-shock heat-ing (Mabanta & Murphy 2018). The combined impact ofthese effects is to aid the explosion. The inclusion of tur-bulent effects allows for successful explosions in 1D simu-lations while reproducing the results seen in 3D simulations(Couch et al. 2020) without the need for parametrized neu-trino physics.STIR models turbulence using the Reynolds-averaged Eu-ler equations with mixing length theory as a closure. Thismodel has one primary scalable parameter, the mixing lengthparameter α Λ , inherited from mixing length theory whichscales the strength of convection. This parameter has beentuned to fit STIR simulations to full 3D simulations run with FLASH and reproduces 3D results seen in
FLASH and othercodes (for details, see Couch et al. 2020). We use the fiducialvalue found in Couch et al. (2020) for the mixing parameter, α Λ = 1 . .STIR includes neutrino transport using a state-of-the-arttwo moment method with an analytic “M1” closure (Shibataet al. 2011; Cardall et al. 2013; O’Connor 2015; O’Connor& Couch 2018). We simulate three neutrino flavors: ν e , ¯ ν e and ν x , where ν x combines the µ – τ neutrino and an-tineutrino flavors. M1 transport, unlike simpler methods, re-quires no tuning and has no free parameters (up to the choiceof a closure for the high-order radiation moments), allow-ing for truly physics-driven explosions. The STIR simula-tions use the now commonly adopted, empirically-motivated“SFHo” equation of state for dense nuclear matter (Steineret al. 2013). FLASH with the STIR model has the desireablebenefit that there is no need to tune the model to match aspecific observation. Instead, its one free parameter is tunedto be consistent with multi-physics 3D CCSNe simulations,removing the possibility of inserting biases into the results.The STIR models were run until one of three conditionsare met: the shock reaches the outer boundary of the compu-tational domain (15,000 km), a BH forms, or the simulationtime reaches 5 s post-bounce. We consider simulations thathave not generated explosions by 5 s post-bounce as failedexplosions. These progenitors, along with those that collapseto a BH, are not included in this study – about 50 of the orig-inal 200 progenitors. This limits our study to light curves ob-tained from progenitors that actually explode, allowing us toexplore solely relationships that come from physically-drivenexplosions.At the end of the STIR simulations, the explosion energiesfor all but the highest-mass progenitors have asymptoted. Itis commonplace in CCSNe work to define the explosion en-ergy as the sum total energy, from all sources, of materialthat has both positive total energy and positive velocity (e.g.,Bruenn et al. 2016). This is zero during the stalled shockphase, when all of the material is still gravitationally bound,and becomes positive if/when the shock begins to move out-
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10 15 20 25 30 M ZAMS [M (cid:12) ] . . . . . . . . E n e r gy [ e r g ] STIR Explosion EnergyTotal Energy
Figure 2.
Explosion energies realized in the STIR CCSNe simu-lations (black) and the final energy after removing the overburdenenergy of the progenitor (blue). ward again due to neutrino heating and other effects. Thisenergy, once it has reached its asymptotic value, representsthe energy that is injected into the rest of the star to drive theexplosion and unbind the stellar material. When discussingthe combined STIR + SNEC simulations, this is the explo-sion energy that we will reference. It is important to notethat this energy is different than the energy that would beinferred from hydrodynamical modelling (i.e., with thermalbomb explosions), which is the explosion energy as definedabove offset by the binding energy of the material betweenthe shock and the PNS surface (this material is already un-bound when the explosion energy is calculated as above, butin thermal bomb or piston-driven explosions it is not).Figure 2 shows the explosion energies obtained with STIR(black) alongside the explosion energy with the progenitor’soverburden energy subtracted (blue). The progenitor’s over-burden energy is the (negative) total energy above the shockthat the explosion must overcome to unbind the star (Bruennet al. 2016). The total energy, which we compute as the totalenergy on the computational domain after the explosion hasset in is closer to what will characterize the ejecta. Gaps inmass, such as from about 12 M (cid:12) to 15 M (cid:12) , indicate regionswhere progenitors failed to successfully launch an explosionin STIR. 2.3. SNEC
At the end of the STIR simulations, the final statesare mapped into the SuperNova Explosion Code (SNEC)(Morozova et al. 2015). SNEC is a spherically symmet-ric, Lagrangian, equilibrium flux-limited diffusion radiation-hydrodynamics code and is publically available . UnlikeSTIR, SNEC does not include any form of general relativis- http://stellarcollapse.org/SNEC tic gravity, neutrino transport, or dense matter EoS, whichare all important for modeling the explosion but not nec-essarily for computing the light curve. Instead, it followsthe basic physics needed for predicting bolometric supernovalight curves. SNEC includes Lagrangian Newtonian hydro-dynamics with artificial viscosity following the formulationin Mezzacappa & Bruenn (1993) and a stellar equation ofstate following Paczynski (1983) that includes contributionsfrom radiation, ions, and electrons with approximate electrondegeneracy. This is used in tandem with a Saha ionizationsolver that can follow ionization of any number of presentelements. At high temperatures SNEC uses OPAL Type IIopacities (Iglesias & Rogers 1996) suitable for solar matallic-ity. These opacities are supplemented by those of Fergusonet al. (2005) at low temperatures.In the present work we follow the ionization of H, He,and He, similarly to Morozova et al. (2015). H and He makeup the majority of the energy contributions from recombina-tion relevant for producing bolometric Type IIP light curves.Our STIR simulations do not currently track detailed com-positional information in their output. When mapping intoSNEC, we fill the composition in the STIR part of the do-main to be pure He. This has no noticeable effect on thelight curves in this study (see Appendix A).The final, critical ingredient for powering a SNe light curveis radioactive heating from the Ni → Co → Fe de-cay chain. Radioactive Ni is produced in explosive nu-clear burning during the first epochs of the explosion in theinner parts of the star. Hydrodynamic instabilities mix the Ni outward. Gamma-rays emitted from the decay processdiffuse outward and provide an additional source of energy.Capturing this is crucial as, after the end of the plateau phase,the light curve is powered entirely by this radioactive decay.SNEC follows the radiative transfer of gamma-rays from the Ni and Co decays using the gray transfer approximation(Swartz et al. 1995) and the resulting energy release is cou-pled to the hydrodynamics independently from the rest of theradiation.Currently, neither our STIR models nor the public versionof SNEC include a nuclear reaction network. To alleviatethis issue, SNEC allows for a user specified amount of Nito be input by hand throughout a specified mass coordinate.Sukhbold et al. (2016) simulate the explosions of these pro-genitors including a large nuclear reaction network, and weuse the Ni yields as a function of explosion energy fromtheir work (see their Table 4, Figure 17) to estimate a massof Ni from that relationship to be distributed by SNEC.For all but the lightest progenitors, they find around 0.07 M (cid:12) of Ni. We disperse the Ni up to about 75 % of the waythrough the He shell – avoiding mixing into the H envelope.This is consistent with the fiducial description taken in Moro-zova et al. (2015). In that work, they varied the distributions B ARKER ET AL .and found little affect on the light curve while the Ni re-mained below the envelope.1D modeling cannot properly capture the mixing at com-positional interfaces due to Rayleigh-Taylor and Richtmyer-Meshkov instabilities, for example. Without mixing, sharpand non-physical compositional gradients appear that pro-duce features in light curves that are not observed in na-ture (Utrobin 2007). In these mixing processes, shock prop-agation outwards can cause light elements to mix inwardsand heavy elements to mix outwards (Wongwathanarat et al.2015). Of particular importance is the mixing of radioactive Ni, whose mixing extent affects the light curve properties(Morozova et al. 2015). SNEC applies boxcar smoothing thatsmooths out compositional profiles, simulating mixing andavoiding unphysical light curve bumps. We use the fiducialparameters of Morozova et al. (2015) for our boxcar smooth-ing.Typically, high fidelity CCSN simulations do not simu-late the entire star – instead focusing on the inner 15,000km or so necessary for launching the explosion. We muststitch the STIR simulation data, with the explosions devel-oped on the grid, onto the progenitor pre-explosion profileoutside the STIR boundary (15,000 km) in order to simulatethe full star. These combined STIR – pre-explosion progen-itor profiles are used as the inputs to SNEC. One advantageof using the STIR models as the initial conditions to SNECis that the high fidelity equation of state and neutrino trans-port yield a physically realistic remnant mass to motivate themass cut – an amount of material not included in light curvesimulations that should be close to the remnant mass. Weplace a mass cut outside the PNS at the point where the to-tal energy becomes positive – removing both the PNS anda small amount of still gravitationally bound material aboveit. For all of the simulations we use 1000 cells in the SNECdomain using a geometric grid, as in Morozova et al. (2015),that places higher resolution in the core around the shock andat the outer domain to resolve the photosphere. Our grid isslightly modified from that of Morozova et al. (2015) to placeadded resolution in the core over the already existing explo-sion. Simulations were run until 300 days when possible toadequately sample both the plateau and the tail for all events.To simulate CCSNe directly from progenitors, SNEC hasthe ability to artificially drive an explosion with a piston orthermal bomb. One of the primary qualities of our novelmethod is to eliminate the need for this and thus eliminatetunable parameters such as bomb deposition energy, replac-ing them with more physically motivated energetics. How-ever, for some of the more massive progenitors in this study,the explosion energies were still increasing by the time theshock reached the outer boundary. Eventually, energy gen-eration from neutrino heating and other sources will slow asthe shock expands and the explosions energies will asymp- tote. Since our computational domain is limited to 15,000km, some progenitors do not reach their “true” explosion en-ergies. In order to fully capture the energy of the explosionin STIR, we integrate the neutrino heating in the gain regionat the end of the
FLASH simulations to estimate the asymp-totic explosion energy and add the difference – at most about0.3 × erg – as a thermal bomb over the shocked region.These additions are most necessary in the region of high en-ergy between about 21 M (cid:12) and 25 M (cid:12) where the final en-ergies were still readily increasing. This energy is what isdisplayed in Figure 2.The light curves presented in this work represent those 136progenitors (of the suite of 200) that both successfully launchan explosion (Section 2.2) and have light curves that wouldbe identified as a Type IIP SN, which we find is simply amass cut of M ZAMS ≤ (cid:12) .2.4. Correlations
We are interested in uncovering correlations between ob-servable properties of the explosion and properties of the pro-genitors. The size and fidelity of the sample allows us to ad-dress these connections necessary to understand light curvediversity. Our robust treatment of the explosion physics com-bined with large sample of progenitors makes us uniquelysituated to address correlations in a novel way. We proceedsimilarly to Warren et al. (2020), wherein the correlationsbetween observed neutrino and GW signals with progenitorproperties were addressed.We measure correlations with the Spearman’s rank corre-lation coefficient. The Spearman correlation coefficient mea-sures any monotonic relationships between variables, in con-trast to the Pearson coefficient which measures only linearcorrelations. It is important that we are able to access non-linear relationships that are seen in the data. The combinedeffect of a wide range of stellar progenitors with mass losseffects and non-linear, non-monotonic explosion energeticsover the range of progenitors produces robust and realistic –but not necessarily linear – relationships.The Spearman coefficient is obtained by first ranking thedata – replacing the values by their indices after sorting – and then computing the Pearson correlation of the trans-formed data, calculated by ρ = (cid:80) i ( x i − ¯ x ) ( y i − ¯ y ) (cid:113)(cid:80) i ( x i − ¯ x ) (cid:113)(cid:80) i ( y i − ¯ y ) (1)for transformed variables x and y with ¯ x and ¯ y being themean values. A value of +1(-1) represents an exact mono-tonic correlation (anticorrelation) and a value of 0 indicatesno monotonic relationship. We consider values | ρ | (cid:38) . to The data (4, 7, 1) would transform to (2, 3, 1).
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A common method for estimating CCSN progenitor prop-erties is to construct a grid of hydrodynamical models (with,say, SNEC, using a thermal bomb) with varying masses, ex-plosion energies, and Ni masses and distributions and se-lect the progenitor from that grid that best fits an observedlight curve (see Morozova et al. 2018; Martinez & Bersten2019; Martinez et al. 2020, for recent examples). We ac-complish this by finding the progenitor which minimizes theaverage relative error εε = 1 N t N (cid:88) t ∗ = t | L ( t ∗ ) − L ∗ ( t ∗ ) | L ∗ ( t ∗ ) (2)where L ∗ ( t ∗ ) is the observed bolometric luminosity at time t ∗ , L ( t ∗ ) is the synthetic bolometric luminosity at the sametime, and N is the number of observational data points. Thisis a straightfoward metric, i.e., an average error of 10% isrepresented by ε = 0 . ; note that because it is an aver-age, it can have a large value even if only a few data pointshave high error. Other approaches have been used, such as(historically) simply fittng by eye, χ minimization (Moro-zova et al. 2018), and Markov chain Monte Carlo methods(MCMC) (Martinez et al. 2020). We implemented severalminimization approaches and found that the above methodworked best for the current work. This is discussed more inSection 3.2.2. RESULTSWe consider the properties of the bolometric light curvesfollowed through the end of the plateaus and into the radioac-tive tails and the photospheric velocities for models withZAMS masses 9M (cid:12) ≤ M ZAMS ≤ (cid:12) for a total of 136progenitors. In an effort to find relationships with observ-ables that are easily detectable, we consider only the photo-metric and spectroscopic properties in the plateau phase. The primary quantities that we consider are the plateau luminos-ity at day 50 ( L ), the plateau duration ( t p ), and the photo-spheric velocity at day 50 ( v ). These quantities are easilydetectable by current and next generation facilities withoutthe need for late time observations or particularly high ca-dences, acknowledging that the photosperic velocity will notbe as easily observable for most sources. This will allowfor a relationship to be obtained between these quantities andproperties of the core of the progenitor that is both robust andeasily detectable with standard measurements.3.1. Comparison with thermal bomb models
Here we present global trends in photometric properties totest the impact of our explosion calculation on light curvefeatures. In Section 3.2, we will demonstrate the ability ofour light-curves and ejecta velocities to reproduce observa-tions.In order to test the effect of our explosion model proce-dure coupling STIR and SNEC, we compare with two setsof thermal bomb models that we simulated for our pro-genitor subset. The first, which we call bomb fixed E ,uses a simple thermal bomb with E fin = 10 erg, where E fin = E dep − E initial is the bomb deposition energy withthe progenitor binding energy subtracted. For this set ofmodels we use a simple 1.4 M (cid:12) mass cut for every progen-itor. These models have bomb energies that increase withprogenitor binding energy to acheive a constant final kineticenergy E kin with a nearly constant E kin /M ej ratio, as inDessart et al. (2020) ( M ej is simply approximated here as M preSN − M PNS and assumes no fallback). The second set,which we simply call bomb , takes the asymptotic explosionenergies and mass cuts from STIR and uses that to set up thethermal bomb with E dep = E
STIRexpl . The fiducial set of mod-els which couples STIR and SNEC is referred to as “STIR+ SNEC,” and has energetics determined robustly in STIRdescribed in Section 2.2.These comparisons assess the importance of having mean-ingfully chosen explosions energies, which is impossiblewithout more robust physics than can be captured in a ther-mal bomb explosion. Secondly, comparisons between thefiducial runs and the bomb models highlight the effects themechanism for driving the explosion – even with the “same”energetics – has on the resulting light curves. We considerthe response of the light curves to these variations in energet-ics and explosion models by examining several key features –the plateau luminosity, plateau duration, photospheric veloc-ity, and time to shock breakout. These tests underscore theneed for physically realistic models in light curve studies.Figure 3 shows comparisons for select bolometric lightcurves for STIR + SNEC versus bomb (top) and SNEC +STIR versus bomb fixed E (bottom). We compare lightcurves for 9, 12, 15.2, and 25 solar mass progenitors. In B
ARKER ET AL . Time [days] L b o l [ e r g s − ] bombSTIR + SNEC9M (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) Time [days] L b o l [ e r g s − ] bomb fixed ESTIR + SNEC9M (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) Figure 3.
Bolometric light curves for 9 (teal), 12 (purple), 15.2 (or-ange), and 25 (black) ZAMS mass models. The top panel showsSTIR + SNEC (solid lines) alongside the bomb models (dashedlines) which used the same energy and mass cuts. The bottom panelshows STIR + SNEC (solid lines) alongside the bomb fixed E models (dot dashed lines) which all used 10 ergs and 1.4 M (cid:12) masscuts. the top panel, the thermal bomb driven explosions – evenwith the energy informed by the STIR + SNEC runs theyare compared to – have a tendency to be dimmer and longer.This is especially evident for the 15.2 M (cid:12) progenitor, whereit is nearly indistinguishable from the 12 M (cid:12) progenitor atearly times. This is due to the discrepancy between explo-sion energy definitions used in high fidelity modeling worksand thermal bomb light curve modeling works as mention inSection 2.2. In the bottom panel the bomb fixed E mod-els, which all used 10 ergs, are brighter than the STIR+ SNEC models by an order of magnitude. This is by nomeans surprising – recent trends in high fidelity CCSNe mod-elling efforts tend to have explosion energies under 10 ergs(Couch et al. 2020; Murphy et al. 2019; Vartanyan et al. 2019;Sukhbold et al. 2016).Looking now at the full set of progenitors and models,Figure 4 shows the bolometric luminosity at day 50 (on theplateau for all progenitors) for all masses for SNEC + STIR(black), bomb fixed E (blue), and bomb (red). Despitehaving the thermal bomb energies equal to the STIR explo-sion energies, the bomb models consistently undershoot theplateau luminosity across the set until the highest mass pro-genitors, around 25 M (cid:12) , where they are roughly the same.
10 15 20 25 30 M ZAMS [M (cid:12) ] . . . . . . l o g ( L [ e r g s − ]) bombbomb fixed ESTIR+SNEC Figure 4.
Log of the plateau luminosity at day 50 for the STIR+ SNEC models (black), bomb fixed E models (blue), and bomb models (red).
This again highlights the differences in conventions used todefine explosion energy – ultimately a larger energy in thethermal bomb paradigm is needed to reach the same en-ergy as in the self-consistent CCSN simulation framework.Again, the 10 erg bomb fixed E models overestimatethe plateau luminosity for nearly every progenitor by nearlyan order of magnitude, except for a small region between 20and 25 solar masses and fail to reflect the non-monotonicityof the coupled STIR + SNEC models. Within the contextof light curve modeling and progenitor property estimation,these differences cannot be ignored. Without a meaningfullydetermined distribution of explosion energetics, the distribu-tion of observables cannot be meaningfully extracted.Figure 5 shows the plateau duration for the STIR + SNECmodels (top), bomb fixed E models (bottom), and bomb models (center). We follow Valenti et al. (2016) and Gold-berg et al. (2019) and compute the plateau duration by fittingpart of the light curve near the end of the plateau to a com-bined Fermi-Dirac – linear function of the form f ( t ) = − a t − t p ) /w ) + ( p t ) + m . (3)The physical significance of the various fitting parametersis described in detail in Valenti et al. (2016) and Goldberget al. (2019). Importantly, the parameter t p is taken to bethe plateau duration and tends to be placed about halfwaythrough the drop off of the plateau. Also of interest are a and w which describe the luminosity drop at the endof the plateau and the width of the drop, respectively. Fit-ting was done using Python’s scipy.optimize.curvefit packagestarting shortly before the end of the plateau. For a few ofthe high mass STIR + SNEC and bomb models between 27and 28 M (cid:12) , timestep restrictions made it difficult to simulatethe explosions into the radioactive tails. Most made it to the YPE
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10 15 20 25 30 M ZAMS [M (cid:12) ] t p [ d a y s ] bombbomb fixed ESTIR+SNEC Figure 5.
Plateau duration for the STIR + SNEC models (top), bomb fixed E models (bottom), and bomb models (center). Forall models, two progenitors between 27 and 28 M (cid:12) have been re-moved for fair comparison, as some of them did not reach the ra-dioactive tail in the simulation time. end of the plateau and began drop off, but two progenitorswere unable to reach the end of the plateau. For the formercase, the fitting is unable to work properly and the plateauduration is set by hand in a way that was consistent with thefitting routine. For the two progenitors that could not reachthe end of the plateau – 27.4 M (cid:12) and 27.5 M (cid:12) – we omit themin comparisons involving the plateau duration.The bomb models tend to have slightly longer plateausthan their STIR + SNEC counterparts, indicative of thedifferences between the energy definitions used. The bomb fixed E models, on the other hand, have a nearlyconstant plateau duration of 100 days until the progenitorsreach the mass-loss dominated regime around 23 M (cid:12) and thedepleted H envelopes shorten the plateaus. Clearly, the dis-tribution of the explosion energies imparts a resulting mor-phology on the plateau durations that cannot be reproducedwithout energetics informed by neutrino-driven explosions.The previous figures highlight a strong dependence on theset of explosion energies used to drive the explosion. Firstly,there are small, but consistent, differences between the fidu-cial STIR + SNEC light curves and the bomb light curves, in-dicating a fundamental difference in these energy definitions.Simply using the explosion energy from high fidelity model-ing as the input to thermal bomb driven explosions does notaccount for the binding energy of the material between thePNS and stalled shock. While usually small, this differencecan have large impacts on plateau features in some cases.All of this directly impacts the ability to reliably extract pro-genitor features from light curves. Without a distribution ofexplosion energies that is set by a physically realistic explo-sion model, any sort of arbitrary distribution of light curveproperties may be recovered, even with the same diversity ofprogenitors used.
10 15 20 25 30 M ZAMS [M (cid:12) ] t s b [ d a y s ] bombbomb fixed ESTIR+SNEC Figure 6.
Time for shock breakout for the STIR + SNEC models(black), bomb fixed E models (blue), and bomb models (red).
Another quantity of interest – albeit not a directly observ-able one – is the time to shock breakout. Figure 6 shows thetime for the shock to breakout from the stellar surface forthe STIR + SNEC models (black), bomb fixed E models(blue), and bomb models (red). This is particularly impor-tant, as the time to shock breakout sets the on source win-dow for electromagnetic follow-ups of gravitational waveand neutrino events from core-collapse supernovae (Abbottet al. 2020). Using the bomb fixed E energetics, the timeto shock breakout may be underestimated by as much asnearly 3 days.With the next galactic CCSNe and prospects for detect-ing their gravitational wave and neutrino signals, the time toshock breakout becomes a measurable quantity through thedifference between GW or neutrino detection time and firstlight from the SNe. The SuperNova Early Warning System(SNEWS) (Adams et al. 2013; Al Kharusi et al. 2020) willalert observatories to trigger an EM followup after a neu-trino detection, and knowing the shock breakout time will bean important factor for the followup study. Combined withconstraints from the GW detection (Abbott et al. 2020) andconstraints from other EM observations, the time to shockbreakout could help to place additional constraints on theSNe progenitor – provided that adequate energetics are used.Similarly, constraints on the shock breakout time after an EMsignal may be used to look back at GW and neutrino data, as-suming a nearby event.3.2.
Comparisons with observations
In this section, we compare our light-curves to observa-tions of Type IIP SNe both through global properties ofmany SNe and fits to the light-curves of individual SNe IIPthat have M ZAMS determined through pre-explosion imagingdata. 3.2.1.
Comparison with a large observational sample
ARKER ET AL . .
00 41 .
25 41 .
50 41 .
75 42 .
00 42 .
25 42 . log (L [erg s − ]) v [ k m s − ] τ Sob = 1Observational Data . . . . . . . . . M Z A M S [ M (cid:12) ] Figure 7.
Photospheric velocity at day 50, v , versus the log ofthe bolometric luminosity of the plateau at day 50, L for all of theexploding progenitors. Simulated data are colored by the zero-agemain sequence mass. Points with error bars are observational datafrom Guti´errez et al. (2017a,b). Apart from photometric observations, spectroscopic ob-servations may also be used to constrain progenitor prop-erties. While we have not computed full synthetic spectrain this work, we can approximate standard line velocities.Figure 7 shows photospheric velocity at day 50 ( v ) versusplateau luminosity at day 50 ( L ) for all progenitors that ex-ploded as Type IIP CCSNe. Also plotted are data presented inGuti´errez et al. (2017a,b) . All photospheric velocities hereare inferred from the Fe II ( ˚ A ) line. In our models, thisvelocity is calculated in post-processing as the velocity of theejecta at the point where the Sobolev optical depth ( τ Sob ) isunity, with τ Sob = πq e m e c n Fe η i f t expl λ (4)where q e and m e are the electron charge and mass, n F e isthe number density of Fe (or, in general, whatever speciesis being considered), η i is the ionization fraction relevant forthe transition of interest, f = 0 . is the atomic oscillatorstrength, t expl is the time since explosion, and λ is the wave-length associated with the transition. For material in homolo-gous expansion, this measures the strength of a particular line(Mihalas et al. 1978; Kasen et al. 2006) and the point where τ Sob = 1 has been shown to match better to observationalmeasurements than the τ = 2 / electron scattering photo-sphere (Goldberg et al. 2019; Paxton et al. 2018). Ultimatelywe are able to reproduce the range of observables fairly wellwithout needing to tune to any observations. Bolometric luminosity data were calculated from M V measurements atday 50 provided by C. Guti`errez (private communication). This approximation relies on the material being in homol-ogous expansion. We calculated the total relative error inthe velocity profile at day 30, v , from the velocity profileassuming homologous expansion at day 30, ˜ v , above thephotosphere. In calculating this deviation, the outermost fewcells were omitted due to boundary condition effects. We ob-serve a deviation of 4 – 8 % for most models with the largestaverage deviation of about 8 % occuring for only a handfulof models around the cusp of transitioning to the mass-loss-dominated regime. By day 50 most models are within 4 % .This justifies our use of the Sobolev approximation for linevelocities, as the material is sufficiently close to homologousexpansion.The sample of luminosities and velocities from our mod-els matches well with the observational sample, but reachhigher in luminosity than the observed set. These high lu-minosity events are from some of the higher pre-supernovamass stars around the transition to the mass-loss dominatedregime (see Figure 1). These high mass stars are less com-mon than their lower mass companions. The highest ZAMSmass stars, dominated by mass-loss, dip back down and leftin luminosity- and velocity-space. Ultimately, we are ableto reproduce observed distributions quite well without hav-ing to tune to observations, instead following the explosionsfrom self-consistent simulations.3.2.2. Determination of progenitor properties for individualevents
It is commonplace to estimate supernova progenitor pa-rameters using a grid hydrodynamical models (i.e., codessimilar to SNEC using a thermal bomb) with varying ini-tial masses, thermal bomb energies, and other parameters,and determining the best fitting model (see, e.g., Utrobin& Chugai 2008, 2009; Morozova et al. 2018; Martinez &Bersten 2019; Martinez et al. 2020; Eldridge & Xiao 2019).We do this with our set of explosions for 7 observed bolo-metric light curves from Martinez & Bersten (2019); Mar-tinez et al. (2020) . We calculate bolometric luminosities us-ing the bolometric correction method of Bersten & Hamuy(2009), which requires only BVI photometry to estimate thebolometric correction.Figures 8 and 9 show observed bolometric light curves(left) and Fe II λ A line velocities (right) for (top to bot-tom) SN 2004A, SN 2004et, SN 2005cs, SN 2008bk, SN2012aw, SN 2012ec, and SN 2017eaw. Dark blue lines showbolometric luminosity and velocity evolution for best fit pro-genitors from our sample using the STIR + SNEC modelusing the fitting described in Section 2.5. Gold lines arefor ZAMS mass models corresponding to estimates frompre-explosion imaging. We use the ZAMS mass estimates Observational data were provided by L. Martinez (private communication).
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IGHT C URVES AND P ROGENITORS M (cid:12) – well belowthe minimum mass we consider to produce a CCSN – so weuse the estimate from Smartt (2015). Finally, we use the massestimate for SN 2017eaw from Eldridge & Xiao (2019). Inall cases we use the optimal value of the initial mass whenpossible, or the closest value within the reported range thatwas both on our mass grid and produced an explosion.We determine the best fit progenitor by minimizing the to-tal relative error as discussed in Section 2.5. We also triedminimizing χ , as was done in Morozova et al. (2018), butfound unsatisfactory performance compared to our method.We did not consider the errors associated with the observa-tions in our fitting. The inverse variance weighting typicallyused in χ minimization gave stronger significance to the ra-dioactive tail, as this region has much smaller error comparedto the plateau. The result was the selection of models that fitthe tail nicely, but fit the plateau very badly . We do not con-sider data before 30 days post shock breakout, as very earlytime bolometric luminosities are heavily influenced by inter-actions with circumstellar meterial (CSM) (Morozova et al.2018) and we have not included CSM effects in this work.An alternative approach to light curve fitting is to fit toband magnitudes, as in Morozova et al. (2018). For diffu-sion codes such as SNEC, this approach is limited to justthe plateau, as this approximation to radiative transport is nolonger valid in later phases (see, e.g., Morozova et al. 2018).Using the full bolometric light curve allows us to bypass thislimitation while providing informaiton about the radioactivephase.We do not expect to find close fits for all observed CCSNe.In this work, we have progenitors that cover a wide rangeof ZAMS masses with realistic explosions, but may be lim-ited in scope in other regards, such as rotation, metallicity, Ni mass and distribution, and possible effects of binarity.Moreover, we do not have models with masses lower then9 M (cid:12) , which may contribute to CCSNe. For example, SN2000bk is very underluminous with low photospheric veloc-ities as is very likely a lower mass progenitor than we havein our set (Mattila et al. 2008; Van Dyk et al. 2012; Martinez& Bersten 2019; O’Neill et al. 2021). With these limitationsin mind, we still find good fits for a number of observed lightcurves. Our best fit progenitors tend to have larger ZAMSmasses than those estimated from pre-explosion imaging –by as much as 14 M (cid:12) . The differences highlighted in Fig- This was avoided in Morozova et al. (2018), as they did not fit beyond theplateau phase. ures 8 and 9 show the inherent degeneracy involved in ex-tracting CCSNe progenitor properties. As shown in Gold-berg et al. (2019); Dessart & Hillier (2019), there are familesof progenitor properties that can lead to a given light curve.Many of our best fit progenitors, such as those of SN 2012awand SN 2017eaw, highlight the high mass solutions to thesefamilies of light curves.In the current work, we do not use velocity evolution in de-termining the best fit progenitor. We explored selecting mod-els that minimize some combination of the errors for both lu-minosity and velocity evolution, but saw little-to-no impacton the best fit models. Despite this, most of the progenitorsthat fit the luminosities reasonably well also fit the velocitiesfairly well. While we did not fit to velocity evolution, wechoose to present approximated Fe II λ A velocities forour best fit models. We opted to present the iron line velocityinstead of the typical electron scattering photosphere, as theelectron scattering photosphere is not directly observable andis systematically lower than the iron line velocities (Goldberget al. 2019; Paxton et al. 2018; Martinez et al. 2020).3.3. Correlations
In this section, we address the primary goal of this study,which is to connect light curve properties to progenitor prop-erties using a statistically significant sample of simulations.Figure 10 shows the Spearman’s correlation matrix for theobservable quantities and progenitor properties that we con-sider for the STIR + SNEC models. Our goal is to assessdirect correlations between individual quantities, and for thisreason we do not consider correlations with ZAMS mass be-cause it does not correlate with any single quantity. In manycases, we are simply recovering well-known correlations,which provide a sanity check on our methods. For example,relationships between photospheric velocity and luminosityhave been used in Type IIP supernova cosmology (Hamuy2005; Nugent et al. 2006; Poznanski et al. 2009). Relation-ships between photometric and spectroscopic observables, L , v , and t p and properties of the progenitor, such as R (the pre-supernova progenitor radius in units of 500 R (cid:12) )in addition to the explosion energy are used in scaling rela-tionships, such as those in Popov (1993); Kasen & Woosley(2009); Sukhbold et al. (2016); Goldberg et al. (2019).We first consider some typical observables of Type IIPlight curves – the plateau luminosity ( L ), plateau dura-tion ( t p ), and photospheric velocity measured through the Fe5169 ˚ A line during the plateau phase ( v ). These observ-ables correlate with, of course, each other, and are expectedto correlate with properties of the progenitors, such as thepresupernova radius ( R ) and envelope mass ( M env ). Weobserve significant correlations between t p , L , and R .Correlations with R tend to be non-monotonic (see, e.g.,Figure 1), which is why they tend to have weaker values2 B ARKER ET AL . Time [days] . . . . . l o g L b o l [ e r g s − ] (cid:12) (cid:12) SN2004A
Time [days] v F e II [ k m s − ] (cid:12) (cid:12) SN2004A
Time [days] . . . . . l o g L b o l [ e r g s − ] (cid:12) (cid:12) SN2004et
Time [days] v F e II [ k m s − ] (cid:12) (cid:12) SN2004et
Time [days] . . . . . . . l o g L b o l [ e r g s − ] (cid:12) (cid:12) SN2005cs
Time [days] v F e II [ k m s − ] (cid:12) (cid:12) SN2005cs
Time [days] . . . . . . . . l o g L b o l [ e r g s − ] (cid:12) (cid:12) SN2008bk
Time [days] v F e II [ k m s − ] (cid:12) (cid:12) SN2008bk
Figure 8.
Comparison between STIR + SNEC light curves (blue lines) and observations (squares) for bolometric luminosity (left) and Fe II λ A line velocities (right). Gold lines show light curves for ZAMS masses obtained from pre-explosion imaging (Smartt 2015; Davies &Beasor 2018; Eldridge & Xiao 2019). Grey shaded region shows the first 30 days that we omitted from fitting. From top to bottom : SN 2004A,SN 2004et, SN 2005cs, and SN 2008bk.
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Time [days] v F e II [ k m s − ] (cid:12) (cid:12) SN2012aw
Time [days] . . . . . . . . l o g L b o l [ e r g s − ] (cid:12) (cid:12) SN2012ec
Time [days] v F e II [ k m s − ] (cid:12) (cid:12) SN2012ec
Time [days] . . . . . . . l o g L b o l [ e r g s − ] (cid:12) (cid:12) SN2017eaw
Time [days] v F e II [ k m s − ] (cid:12) (cid:12) SN2017eaw
Figure 9.
Comparison between STIR + SNEC light curves (blue lines) and observations (squares) for bolometric luminosity (left) and Fe II λ A line velocities (right). Gold lines show light curves for ZAMS masses obtained from pre-explosion imaging (Smartt 2015; Davies &Beasor 2018; Eldridge & Xiao 2019). Grey shaded region shows the first 30 days that we omitted from fitting. From top to bottom : SN 2012aw,SN 2012ec, and SN 2017eaw
ARKER ET AL . M Fe R M preSN M env E expl v L t p M Fe R M preSN M env E expl v L t p − . − . − . − . . . . . . Figure 10.
Correlation matrices for observable quantities and prop-erties of the progenitors for STIR + SNEC. Here we considerthe following quantities: iron core mass ( M Fe ), progenitor radius( R ), explosion energy ( E expl ), photospheric velocity at day 50( v ) as determined from the Fe II ( ˚ A ) line, log of the plateauluminosity at day 50 ( L ), and plateau duration ( t p ). The lowerleft half of the matrix shows the Pearson correlation coefficient foreach pair of quantities. of the correlation coefficient. There is a moderate correla-tion between the L and v and the presupernova mass( M preSN ). Interestingly, we do not observe this correlationin the bomb fixed E models.The explosion energy ( E expl , see Section 2.2) is expectedto correlate with both progenitor properties and observableproperties. Correlations between E expl and observable prop-erties are almost perfect monotonic relationships, for exam-ple with a correlation coefficient of 0.97 for L – E expl . Thisis because in the self-consistent STIR + SNEC models, theexplosion energies are the total positive energies of unboundmaterial as liberated by neutrino heating and is thus corre-lated with properties of the core (and thus, the rest of theprogenitor properties through stellar evolution) of the pro-genitor.Finally, we turn our attention to connections between prop-erties of the core of the progenitor and observable quanti-ties. Motivated by connections between explosion energyand the compact remnant, we explore correlations with theiron core mass ( M Fe ). Progenitors with more massive ironcores tend to liberate more gravitational binding energy, havehigher neutrino luminosities, and ultimately are associatedwith more energetic explosions for progenitors that success- . . . . . . . . L [erg s − ] × . . . . . M F e [ M (cid:12) ] + 1.2987 Figure 11.
Iron core mass M Fe versus plateau luminosity at day 50 L . fully explode. This correlation, therefore, once again high-lights the need for realistic physics in explosion models evenin 1D. Equipped with this correlation, and the previouslymentioned relationships between explosion energy and ob-servables, one might expect some imprint of the iron coremass on the observables. Indeed, for the STIR + SNEC mod-els we observe a very strong, linear relationship between ironcore mass and plateau luminosity. We note that the com-pactness parameter ξ . (O’Connor & Ott 2011) produces astronger correlation. This, however, is of little practical use,as the 9-12 M (cid:12) progenitors have nearly zero compactness,breaking the trend for the most common progenitors, and theiron core mass is a more physical quantity (i.e., does not de-pend on the exact choice of mass coordinate for the mea-surement). The compactness parameter and iron core massare very tightly correlated and both provide a measure of thegravitational binding energy available in the explosion.A relationship between iron core mass and supernova ob-servables helps constrain stellar evolution models and char-acterize the diversity of supernova light curves. Figure 11shows iron core mass versus plateau luminosity at day 50.Higher luminosity events tend to originate from progenitorswith more massive iron cores. Ultimately, more massive stel-lar cores collapse to form more massive proto-neutron stars,liberating more gravitational binding energy in the processand resulting in higher neutrino luminosities emanating fromthe PNS surface. All of this results in a more energetic ex-plosion and a brighter supernova. In Table 1 we report thefits coefficient for the M Fe - L relationship and the associ-ated variances and covariances for a linear fit of the form y = ax + b .This correlation, though simple, has a profound implica-tion that we can constrain core structure from optical pho-tometry alone. While not necessarily providing a precise measure of the iron core mass for individual events due to ob- YPE
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Type IIP CCSNe simulta-neously. Furthermore, these parameter estimates can be usedto constrain stellar evolution models for CCSN progenitors.We find a similar, although slightly weaker, correlation be-tween the photospheric velocity at day 50, v , as well, butmost LSST sources won’t have a spectroscopic follow-up sothis is of limited use.For any relationship of this type to be useful, error mustbe taken carefully into account. The optimal fit parameterswere obtained with a least squares method. However, it isknown that the covariances provided by least squares meth-ods are not appropriate for a wide range of problems, includ-ing those with a non-Gaussian intrinsic scatter among othercriteria (see, e.g., Clauset et al. 2009, and references therein).For this reason, we resort to a bootstrapping method (Efron1979) to obtain the errors on the fit parameters. This methodhas the advantage of making no assumptions about the under-lying distribution of the data. Instead, bootstrapping operatesby resampling the data M times with replacement. For eachresampling, a new fit is made and those fit parameters stored.Then, estimates of the variance and covariance of parameters u and v are given by σ u = 1 M M (cid:88) j =1 ( u j − u ) (5) σ uv = 1 M M (cid:88) j =1 ( u j − u ) ( v j − v ) (6)where u and v are the optimal fit parameters and each of u j , v j are the fit parameters for each of the M resamples. Theseerror estimates tend to be, for this application, somewhatsmaller than parameter errors obtained through a simple leastsquares method. The full set of fit parameters, variances, andcovariances are supplied in Table 1. We note that the fit pre-sented uses the non-log plateau luminosity as its independentvariable, as opposed to the log luminosity presented in otherparts of the paper. Then, given errors on the fit parameters itis straightforward to compute the error on an iron core massestimate. For a linear fit, we propagate the combined obser-vational – fit parameter uncertainty in the following way: σ Fe = σ a L + σ L a + σ b + σ + 2 L σ ab , (7)where L is the luminosity at day 50 in erg s − and wherewe have included explicitly the covariance of the fit parame-ters a and b . In order to further account for intrinsic scatterin the relationship, we have included σ res which is the 67 % percentile on the residual distribution r i = | M Fe − ˆ M Fe | ,where ˆ M Fe is computed from the fit. As an example, using Table 1.
Linear fit paramaters for iron core mass ( M Fe ) to plateauluminosity ( L ) for successfully exploding models. The first tworows shows the optimal fit parameters. The next two rows showsthe error on each parameter. The final row shows the covariance be-tween the parameters and the residual error accounting for intrinsicscatter. M Fe = aL + ba × − b σ a × − σ b × − σ ab -2.38 × − σ res × − SN 1999em and the data in Guti´errez et al. (2017a,b), weestimate an iron core mass of about 1.42 ± DISCUSSION AND CONCLUSIONSWe present synthetic bolometric light curves for 136 so-lar metallicity, non rotating CCSNe progenitors and considerstatistical relationships for those with ZAMS masses rang-ing from 9 M (cid:12) to 31 M (cid:12) . These light curves, as well as theSNEC initial profiles and necessary parameters, are providedonline . We also include the necessary binding energy ofour progenitors to offset STIR’s explosion energy to produceidentical results with a thermal bomb explosion (see Sec-tion 3.1). In the online resources, we furthermore provide thelight curves for the M ZAMS > (cid:12) models that success-fully explode. These progenitors were exploded in sphericalsymmetry with the self-consistent, high-fidelity CCSNe sim-ulation framework FLASH with the STIR explosion model(Couch et al. 2020). STIR includes all of the physics nec-essary for following gravitational collapse and the resultingexplosion robustly – approximate general relativistic gravity,state-of-the-art M1 neutrino transport, modern hydrodynam-ics schemes, approximate effects of turbulence and convec-tion, and a high fidelity nuclear EoS (SFHo) – and in agree-ment with results of 3D CCSNe simulations. For progenitorsthat explode with STIR, we follow the explosions in SNECto produce bolometric light curves, forming a large, statis-tically significant set of CCSN light curves followed fromhigh-fidelity explosions allowing us to address relationshipsbetween progenitor properties and properties of the explosionin a statistical way. We consider the full shape of these lightcurves, but also reduce them to characteristic quantities suchas the plateau luminosity, plateau duration, and photosphericvelocity. https://doi.org/10.5281/zenodo.4477095 ARKER ET AL .Our first conclusion is that global trends in light curveproperties – such as plateau duration and plateau luminos-ity – depend sensitively on the explosion model and requireexplosion energies set by robust physics. To demonstratethis, we compute bolometric light curves for the same setof progenitors using two different thermal bomb models withSNEC. The distribution of explosion energies plays a lead-ing role in setting the distribution of observables across alarge sample of progenitors. Thus, the ability to identifyglobal trends in light curve properties and extract progeni-tor features from them depends sensitively on the determi-nation of explosion energy, underscoring the need for explo-sions driven with high-fidelity multi-physics models.The second result of our study is to present a simple best-fitprocedure to individual, observed CCSN light curves (Mar-tinez et al. 2020). The usual procedure for estimating pro-genitor properties of observed CCSNe is to construct a largegrid of “hydrodynamical models” – usually in ZAMS mass,explosion energy, and perhaps Ni mass and distribution –and find a best fit model. This approach results in known de-generacies, for example, as shown by Goldberg et al. (2019);Dessart & Hillier (2019) wherein there are certain familiesof progenitor and explosion parameters (such as ejecta mass,explosion energy, and photospheric velocity) that produce agiven light curve, though pre-explosion radius measurementsmay help to resolve this degeneracy (Goldberg & Bildsten2020). Our approach differs in that we do not control theexplosion properties, instead following a dense set of var-ious ZAMS mass progenitors from self-consistent neutrinodriven explosions. While this does not solve the light curvedegeneracy problem, it could reduce the size of the family ofexplosion properties for a given light curve, as some combi-nations of explosion energy and stellar mass are not realiz-able. Although the explosions are not calibrated to observeddata we still find great agreement both when comparing tolarge samples of events and for some individual cases. In-triguingly, we find best-fit ZAMS masses that are greater byas much as 13 M (cid:12) (i.e., double) than those estimated frompre-explosion imaging in tandem with stellar evolution mod-eling. The fact that hydrodynamic models have tended to findZAMS masses in agreement with pre-explosion imaging es-timates for these CCSNe (Morozova et al. 2018; Martinez &Bersten 2019; Martinez et al. 2020) may indicate the dangerof exploring too large a parameter space instead of know-ing which regions are physically realizable, though we notethat some hydrodynamic models have also found noticeablyhigher masses in better agreement with our conclusions (e.g.,Utrobin & Chugai 2008, 2009). Ultimately, the set of solu-tions for matching a given observed light curve is degenerate,with many progenitors being capable of producing a givenlight curve. Despite the progenitors and explosions in this study not be-ing crafted to reproduce specific events, we find good agree-ment with several observed CCSNe. Notably, the luminosityevolution of SN 2012aw is fit by our 21.5 M (cid:12) progenitor re-markably well. The best fit progenitors for the observed lightcurves in this study are not necessarily the progenitors thatthese explosions originated from – they simply reproduce theobservables (or don’t). We have demonstrated that beyondthe now understood light curve degeneracies, there are ad-ditional degeneracies inherited from the choice of explosionmodel. This result is complementary to the recent findingsby Farrell et al. (2020) where they showed that a star’s finaltemperature and luminosity cannot be reliably traced back tothe star’s ZAMS mass – that very different mass stars mayend up at the same temperature and luminosity. These resultstogether show that much more work is needed before a star’sZAMS mass can be reliably determined – the path from stel-lar birth to death is not a one-to-one function.The light curves we present here present avenues for futurework to explore the discussion surrounding explosion energy.There is tension between explosion energies realized in 3DCCSN simulations and energies inferred from fitting hydro-dynamical models to observations. The energies from thesetwo methods differ, with those inferred from hydrodynam-ical modeling being significantly larger (see Murphy et al.2019, which discusses this tension in detail). On one hand,3D simulations of very massive progenitors have often sim-ply not asymptoted to their final values within the simulatedtime. There is also still physics left to include, such as therecently demonstrated affects of magnetic fields on neutrino-matter interactions (Kuroda 2021) and improved neutrinopair-production rates (Betranhandy & O’Connor 2020) onthe explosion mechanism, neutrino mixing, among other af-fects, all of which will likely play a role in setting the finalenergy. On the other hand, solutions using thermal bombmodels have been shown to be degenerate, and these studiesaccess a very large area of this degenerate parameter spaceand may not necessarily find physically realizable solutions.The methods described here could illuminate or even weakenthe tension between these energies by limiting the parameterspace spanned by hydrodynamical modeling studies and byusing physically-motivated explosions.The final aim of this study is to leverage the large numberof light curves to perform a statistical investigation of rela-tionships between progenitor and explosion properties. Fo-cusing our investigation to Type II SNe, 136 light curves,a number of correlations between the light curves and theirprogenitors are found. We find a robust relationship betweenthe iron core mass of the progenitor and the luminosity on theplateau of the SNe. Simply, more massive iron cores liber-ate more binding energy, have higher resultant neutrino lumi-nosities, and produce more energetic and brighter SNe. This YPE
IIP CCSN L
IGHT C URVES AND P ROGENITORS
FLASH using the STIR model. Notably, STIR requires no tuning toobservations, eliminating the potential for biases when simu-lating progenitors different than the one used for tuning. Im-portantly, the results from STIR are consistent with 3D simu-lations. The explosion energies, explodability, and the shapeof each as a function of ZAMS mass differ non-trivially forSTIR and PUSH (see Couch et al. 2020; Ebinger et al. 2019)and this could have impacts on global trends in explosionproperties. On the other hand, Curtis et al. (2020) obtainedtheir Ni distributions using a nuclear reaction network inconjunction with their CCSN simulations. Our Ni yieldswere fit from Sukhbold et al. (2016) who exploded the sameprogenitors with an expansive reaction network coupled tothe evolution. This is sufficient for the current work, and fu-ture work with
FLASH will include detailed nucleosynthesiscalculations. Curtis et al. (2020) also have a larger diversityof supernova types through their inclusion of sub-solar andzero metallicity progenitors. To keep the scope of the cur-rent work contained, we have not produced synthetic spectrafor these explosions, whereas Curtis et al. (2020) calculatedspectra for their supernovae.Similarly, Sukhbold et al. (2016) present a sample of syn-thetic light curves of the same statistical size and originatingfrom the same progenitors using a different parametrized,neutrino-driven explosion mechanism. Using these simula-tions they present scaling relations to determine explosionand progenitor properties from obervables. The outcomes ofthese simulations – both the explosions and resulting lightcurves – differ non-trivially from STIR and this work. Itwould be interesting, for future work, to investigate the affectof these differences in explosion mechanism when applied topopulations of observed CCSNe and implications for inferredproperties such as explosion energy.This work is part of a larger context to understand and predict full multi-messenger signals from realistic CCSNe. Understanding how variations in progenitors properties tieinto variations of different observables will ultimately helpto constrain real populations. This work, in tandem withthe work of Couch et al. (2020) and Warren et al. (2020),gives us explosion fates, energies, neutron star mass distri-butions, neutrino signals, approximate GW signals, and nowEM signals for a massive suite of neutrino driven CCSNe.It is only through advanced methods – studying in detail allmessengers from first principles simulations – used in tan-dem with growing observational data that we can truly un-derstand these phenomena.
Software:
FLASH (Fryxell et al. 2000; Dubey et al.2009), SNEC (Morozova et al. 2015, 2016), Pandas (McK-inney 2010), NumPy (Harris et al. 2020), SciPy (Jones et al.2001) ACKNOWLEDGMENTSWe thank E. H. Miso for many constructive discussions.BLB is supported by the National Science Foundation Gradu-ate Research Fellowship Program under grant number DGE-1848739. C.E.H. is grateful for support from NSF throughAST-1751874 and AST-1907790, and from the PackardFoundation. MLW was supported by an NSF Astronomyand Astrophysics Postdoctoral Fellowship under award AST-180184. EOC is supported by the Swedish Research Coun-cil (Project No. 2018-04575 and 2020-00452) SMC is sup-ported by the U.S. Department of Energy, Office of Sci-ence, Office of Nuclear Physics, Early Career Research Pro-gram under Award Number DE-SC0015904. This material isbased upon work supported by the U.S. Department of En-ergy, Office of Science, Office of Advanced Scientific Com-puting Research and Office of Nuclear Physics, ScientificDiscovery through Advanced Computing (SciDAC) programunder Award Number DE- SC0017955. This research wassupported by the Exascale Computing Project (17-SC-20-SC), a collaborative effort of two U.S. Department of Energyorganizations (Office of Science and the National NuclearSecurity Administration) that are responsible for the planningand preparation of a capable exascale ecosystem, includingsoftware, applications, hardware, advanced system engineer-ing, and early testbed platforms, in support of the nation’sexascale computing imperative. This work was supportedin part by Michigan State University through computationalresources provided by the Institute for Cyber-Enabled Re-search. We collectively acknowledge that MSU occupies theancestral, traditional and contemporary lands of the Anishi-naabeg – Three Fires Confederacy of Ojibwe, Odawa andPotawatomi peoples.8 B
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IGHT C URVES AND P ROGENITORS A. COMPOSITIONAL DEPENDENCEFor our light curves, we modified the compositional profile in the FLASH part of the domain to be pure He, as full compositionis not currently tracked in the output. In this appendix, we provide comparisons of select light curves using thermal bombs withFLASH explosion energies for both the modified compositional profile and the original compositional profile. Figure 12 showslight curves with the unaltered (orange) and modified (blue) compositional profiles for 9, 15.2, 25, and 30 M (cid:12) progenitors. Forthe cases considered here, the difference in luminosity on the plateau is bounded above by 0.1 dex, which has no meaningfulaffect on the iron core mass estimates and distributions of Section 3.3. Time [days] l o g ( L b o l [ e r g s − ]) Time [days]
Time [days] l o g ( L b o l [ e r g s − ]) Time [days]
Figure 12.
Light curves using a thermal bomb driven explosion with STIR explosion energies using the modified compositional profile (blue)and unaltered profile (orange). We show light curves for 9, 15.2, 25, and 30 M (cid:12)(cid:12)