The Nickel Mass Distribution of Stripped-Envelope Supernovae: Implications for Additional Power Sources
Niloufar Afsariardchi, Maria R. Drout, David Khatami, Christopher D. Matzner, Dae-Sik Moon, Yuan Qi Ni
DD RAFT VERSION S EPTEMBER
16, 2020Typeset using L A TEX twocolumn style in AASTeX63
The Nickel Mass Distribution of Stripped-Envelope Supernovae: Implications for Additional Power Sources N ILOUFAR A FSARIARDCHI , M ARIA
R. D
ROUT ,
1, 2 D AVID
K. K
HATAMI , C HRISTOPHER
D. M
ATZNER , D AE -S IK M OON , AND Y UAN Q I N I David A. Dunlap Department of Astronomy and Astrophysics, University of Toronto,50 St. George Street, Toronto, Ontario, M5S 3H4 Canada The Observatories of the Carnegie Institution for Science, 813 Santa Barbara St, Pasadena, CA, 91101, USA Department of Astronomy, University of California, Berkeley, CA, 94720 (Received; Revised; Accepted)
Submitted to ApJABSTRACTWe perform a systematic study of the Ni mass ( M Ni ) of 27 stripped envelope supernovae (SESNe) withboth well-constrained rise times and late-time coverage ( >
60 days) by modeling their light-curve tails. Basedon this sample, we find that using “Arnett’s rule” with observed peak times ( t p ) and luminosities ( L p ) willoverestimate M Ni for SESN by a factor of ∼
2. Recently, Khatami & Kasen (2019) presented a new analyticmodel relating t p and L p of a radioactive-powered SN to its M Ni that addresses several limitations of Arnett-like models, but depends on a dimensionless parameter β , which is sensitive to details of the progenitorsystem and explosion mechanism. Using the observed t p , L p , and tail-measured M Ni values for the sampleof SESN, we observationally calibrate β for the first time—finding 0.0 < β < β values yields a significantly improved measurement of M Ni when only photospheric data isavailable. However, these observationally-constrained β values are systematically lower than those inferredfrom numerical simulations, due primarily to the observed sample having significantly higher (0.2-0.4 dex) L p for a given M Ni . We investigate this discrepancy and find that while effects due to composition, mixing,and asymmetry can increase L p none can explain the systematically low β values. However, the discrep-ancy with simulations can be alleviated if ∼ L p for the observed sample comes from sources otherthan the radioactive decay of Ni. Either shock cooling or magnetar spin down could provide the requisiteluminosity, with the former requiring that a substantive fraction of SESN undergo late-stage mass loss orenvelope inflation. Finally, we find that even with our improved measurements, the M Ni values of SESN area factor of ∼ Keywords:
Supernovae: general INTRODUCTIONStripped Envelope Supernovae (SESNe) are core-collapse supernovae (SNe) whose progenitors shed a sig-nificant fraction of their H envelope before the explosion(Clocchiatti et al. 1996; Woosley et al. 2002). It is widelythought that the light curves of SESNe are predominantlypowered by the radioactive decay of Ni synthesized inthe explosion (Arnett 1982). In this picture, while shock
Corresponding author: Niloufar [email protected] cooling emission following the often-undetected shockbreakout (SBO) may also contribute to the observed lumi-nosity of SESNe during the first few days post-explosion,the main peak of the bolometric light curve is poweredby Ni → Co radioactive decay. Following the peak, thelight curves of SESNe rapidly decline and subsequently en-ter a phase of linear (magnitude) decay, which is poweredby the Co → Fe chain. This phase typically begins atepochs (cid:38)
60 days (Clocchiatti & Wheeler 1997). The re-sulting shape of the light curve is not only sensitive to thetotal mass of Ni, but also to the total ejecta mass ( M ej ),the distribution of M Ni within the ejecta, and the degree towhich Ni deposition is asymmetric (Utrobin et al. 2017). a r X i v : . [ a s t r o - ph . H E ] S e p A FSARIARDCHI ET AL .There exists significant diversity within SESNe. Spectro-scopically, they are divided into distinct sub-types: IIb, Ib,Ic, and Ic-BL SNe (See Filippenko 1997, for a review). Thefirst three sub-types are generally thought to to be pro-duced by increasingly more stripped progenitors (Maund2018). Type IIb SNe have signatures of both H and He lines,although their H lines are weak and usually disappear af-ter the light curve peak, indicative of a small H mass. TypeIb SNe are SESNe that are H-deficient but exhibit He linesin their spectra, while SNSNe that exhibit neither H norHe lines are categorized as Type Ic SNe. Type Ic-BL SNeare also H- and He-deficient , but are categorized by broadspectral lines that are indicative of extremely high veloc-ity ejecta ( (cid:38) − ; Modjaz et al. 2014). They arethe only SN sub-type that is associated with long-durationgamma-ray bursts ( l GRBs; Woosley & Bloom 2006).The progenitor systems of SESNe remain a matter of ex-tensive debate. While they are H-poor, their envelopescould, in principle, be removed either via strong stellarwinds or via stripping through interaction with a close bi-nary companion (Woosley et al. 1995). In the former case,the progenitors of SESNe would predominately be Wolf-Rayet (WR) stars, with initial masses above 25–30 M (cid:175) (e.gBegelman & Sarazin 1986). In the latter case, many SESNecould be produced by stars with lower initial masses of-ten associated with H-rich Type II SNe (e.g. 10 − M (cid:175) ),but that have lost their envelopes via Roche Lobe Overflow(RLOF) prior to explosion (e.g. Podsiadlowski et al. 1992).In recent years, a number of pieces of observational ev-idence have pointed towards binary stars being a signifi-cant contributor to the observed sample of SESNe. First,binary interaction should be common among stars that areexpected to be CC SNe progenitors (e.g. Sana et al. 2012)and SESNe constitute about one-third of all core-collapseSNe in volume-limited samples (Li et al. 2011; Shivverset al. 2017). This is higher than the predicted fraction ifSESNe solely originate from high-mass WR stars (Smithet al. 2011). Second, unlike H-rich Type II SNe for whichdozens of Red Supergiants (RSGs) have been identified inpre-SN images (Smartt et al. 2009), direct progenitor de-tections of SESNe are scarce (Yoon et al. 2012; Eldridgeet al. 2013), indicating the progenitors are relatively faint.While a number of Type IIb progenitors have been iden-tified, they are Yellow Supergiants (YSGs). YSGs are notpredicted to explode in standard single star evolution mod-els, and thus may indicate close binary progenitor systems(Yoon et al. 2017; Sravan et al. 2019). For completely H-stripped SNe, results are even less conclusive. The only re-ported detections to date are of the progenitors for Type Throughout this paper, Type Ic-BL are not included within Type Ic class.
Ic SN2017ein (Van Dyk et al. 2018; Xiang et al. 2019) andType Ib iPTF13bvn (Cao et al. 2013; Kim et al. 2015; El-dridge & Maund 2016), the former of which has yet to beconfirmed. The non-detection of Type Ib/c progenitors inpre-SN images is seemingly in line with the binary scenariowhere the progenitors are likely to be dim He stars strippedby a companion (Eldridge et al. 2013; Van Dyk et al. 2016).Lastly, the reported ejecta masses of SESNe are almost ex-clusively in the range 2–4 M (cid:175) (Drout et al. 2011; Lymanet al. 2016). These values are lower than those predictedby models of massive single stars stripped by strong stellarwinds ( (cid:38) M (cid:175) for stars with initial masses of 25-150 M (cid:175) ;e.g. Eldridge et al. 2008), but consistent with expectationsfor lower initial mass stars stripped in binaries .However, the conclusion that most SESN are producedby stars from a similar initial mass range as H-rich TypeII SNe—simply stripped by a close binary companion—ispossibly in tension with other findings. The analyses of H α emission in SN host galaxies reveals that SESNe are morepreferably found in star-forming regions compared to H-rich Type II SNe (Anderson et al. 2012). Further studiesof stellar populations in the vicinity of SESNe sites indi-cate that Type IIb, Ib, and Ic SNe are progressively foundin younger stellar populations, suggesting that they arisefrom more massive progenitors (Maund 2018). In addition,a key piece of evidence that has been particularly prob-lematic for the binary scenario is the reported Ni massesof SESNe, which are systematically larger than those of H-rich Type II SNe (Anderson 2019; Meza & Anderson 2020).This may suggest that the progenitors of SESNe are initiallymore massive that those of H-rich Type II SNe, which ismore naturally predicted by the evolution of single stars.Statistical studies of SESNe have reported the average M Ni for SESNe > M (cid:175) (Drout et al. 2011; Lyman et al.2016; Prentice et al. 2016, 2018; Sharon & Kushnir 2020).Recently, Anderson (2019) compiled the M Ni of 115 H-richType II SNe and 141 SESNe reported in the literature. Theyfound the average value of M Ni for SESNe is 0.293 M (cid:175) which is a factor of ∼ M Ni values from SN lightcurves that differ between Type II and SESNe.Indeed, the accuracy of the M Ni estimates for SESNe hasbeen disputed in recent years (Dessart et al. 2016; Sukhboldet al. 2016; Khatami & Kasen 2019; Meza & Anderson 2020).Unlike H-rich SNe for which M Ni is estimated by model- Although these results should be interpreted with caution since ejectamasses are often obtained from Arnett-like models, for which some as-sumptions break down in the case of SESNe as discussed in this paper.
ICKELOF S TRIPPED E NVELOPE SN E M Ni of SESNeis commonly obtained from the peak of their bolometriclight curves using the models of Arnett (1980, 1982). Theseare a series of widely-used analytical models for radioac-tive heating/diffusion based on self-similar assumptionsthat provide bolometric SN light curves and a consequen-tial rule. This “Arnett’s rule” states that, for SNe powered ex-clusively by radioactive decay, the radioactive heating rateand the observed bolometric luminosity at the peak of thebolometric light curve are equal. Although Arnett’s ruleroughly holds for Type Ia SNe, the self-similarity conditionbreaks down when the SN ejecta has a centralized Ni de-position, calling into question its efficacy when applied toSESNe (Khatami & Kasen 2019). Thus, alternate means ofmeasuring M Ni in SESNe may be required.Most directly, M Ni for SESNe can be measured by mod-elling the late-time light curve tail, when the ejecta is opti-cally thin and the luminosity is determined by the instanta-neous heating rate. However, these epochs have only beenobserved for a fraction of known SESN. Katz et al. (2013)proposed a “Luminosity Integral” technique for measuring M Ni from radioactively powered SNe, which was recentlyemployed by Sharon & Kushnir (2020) on a dozen SESNe.Although this method does not suffer from many of thesimplifying assumptions of Arnett’s models, it relies on thetemporally well-sampled observations of SN from the ex-plosion epoch to the tail, and will require the addition ofan extra parameter if any other power source significantlycontributes to the observed luminosity over this timescale.Alternatively, Khatami & Kasen (2019, hereafter, KK19)recently proposed a new analytical model that relates thepeak bolometric luminosity and its epoch to the radioac-tive heating function in order to address the limitations ofArnett’s models. However, this model fundamentally de-pends on the choice of a dimensionless parameter β thatis sensitive to several physical effects including the spa-tial distribution of Ni, the envelope composition, poten-tial explosion asymmetries and extra power sources. Meza& Anderson (2020) recently applied the model of KK19 toa sample of SESN, adopting a set of β values that werederived from the simulated SESNe light curves of Dessartet al. (2016). However, to ascertain if those β values arerealistic, they must be directly constrained from observedSESN light curves with independent M Ni estimates. Theseobservationally calibrated β values would then offer an in-dependent probe of the progenitors and explosion mech-anisms of SESN. In addition, if there exists a robust β foreach SESN sub-type, then KK19’s model can be used, as analternative to Arnett’s rule, to give accurate M Ni estimatesfor a large sample of SESNe.In this paper, we present a systematic analysis of nickelmass distribution for 27 well-observed SESNe derived by modeling their radioactive light curve tails, accounting forpartial trapping of γ -rays. The resulting M Ni values arethen compared against their counterparts measured un-der Arnett’s rule. We also provide a systematic compari-son between the nickel masses of SESNe and H-rich TypeII SNe, both obtained from the radioactive light curve tail,hence minimizing the biases that originated from the mod-eling methods in previous studies. In addition, we employthe model of KK19 on the light curves of observed SESNeto 1) calibrate the β parameter using the peak light curveproperties and our independent tail M Ni measurements,and 2) constrain the progenitor and explosion propertiesof SESNe using our calibrated β in comparison to that ob-tained from numerical simulations.This paper is organized as follows. In §2, we describe an-alytical models that aim to constrain the amount of syn-thesized Ni from light curve observables. §3 presentsour criteria for selecting a sample of well-observed SESNeand a systematic procedure for obtaining their distances,extinction values, bolometric light curves, and explosionepochs. We provide the Ni masses and calibrated β val-ues for each SN in our sample in § 4. We discuss the im-plications of our results for understanding their progenitorsystems and heating sources in §5, and conclude in §6. ANALYTICAL MODELS OF M Ni To constrain the M Ni of SESNe, we employ three analyt-ical models: an optically-thin radioactive decay model forthe light curve tail, Arnett’s rule for the light curve peak,and KK19’s model for the light curve peak. Here, we brieflyreview their formulation and observational dependencies,as this will influence our SN sample selection in § 3.2.1. Radioactive Decay Modelling of the Light Curve Tail
The “light curve tail” refers to the late-time evolutionof the SN light curve once it enters a phase of linear de-cline in magnitude vs. time. For SESNe, the light curvetail typically begins at an earlier epoch ( t (cid:38)
60 days post-explosion) compared to H-rich Type II SNe, for which thetail is observable only after the H-recombination plateauphase ends ( t (cid:38)
90 days post-explosion). It is widelythought that the tail of core-collapse SNe is powered bythe Co → Fe radioactive decay chain (Colgate & McKee1969). At this stage, the ejecta become transparent to thestored radiative energy; therefore, the observed luminos-ity traces the instantaneous heating rate. The γ -rays pro-duced by the radioactive decay heat the ejecta, making thetail of the light curve an appropriate probe for measuringthe amount of Ni produced. The observed luminosity ofthe tail can be then modeled as: L (cid:39) L γ (cid:161) − e − ( t / T ) − (cid:162) + L pos , (1) A FSARIARDCHI ET AL .(Wygoda et al. 2019), where t is time since the explosion, L γ is the luminosity produced by the radioactive decay ofCo and Ni , and L pos is the total energy release rate ofpositron kinetic energy. The term in parenthesis is a de-position factor, which represents the incomplete trappingof γ -rays with T denoting the partial trapping timescale ofthe tail. The deposition factor is proportional to 1 − e − t − for an explosion in homologous expansion (Sutherland &Wheeler 1984; Clocchiatti & Wheeler 1997). The luminos-ity terms in Equation 1 can be expressed as: L γ = M Ni (cid:179) ( (cid:178) Ni − (cid:178) Co ) e − t / t Ni + (cid:178) Co e − t / t Co (cid:180) (2) L pos = M Ni (cid:178) Co (cid:179) e − t / t Ni − e − t / t Co (cid:180) , (3)where (cid:178) Ni = × erg g − s − and (cid:178) Co = × erg g − s − are the specific heating rates of Ni and Codecay, respectively, and t Ni = t Co = γ -rays is commonly assumed for H-rich Type II SNe due to their large ejecta masses and cor-respondingly long T , it is important to determine the T from the slope of light curve tail for SESNe since their ejectamasses are smaller and T is usually comparable to the on-set time of the radioactive tail. If the bolometric luminosity L can be ascertained observationally, the only unknownsin Equations 1 and 2 are M Ni and T which can be deter-mined by fitting the slope and overall normalization of theradioactive tail of the light curve.2.2. Arnett’s Rule
While robust, the “light curve tail” method is not alwaysaccessible because the late-time radioactive tails are of-ten faint, and thus more difficult to observe. As a result,the M Ni of SESNe are typically obtained with Arnett’s rule,which states that the instantaneous heating rate from theradioactive decay of Ni and Co is equal to the bolomet-ric luminosity of the SN at the light curve peak. This can berewritten as: L p = M Ni (cid:179) ( (cid:178) Ni − (cid:178) Co ) e − t p / t Ni + (cid:178) Co e − t p / t Co (cid:180) , (4)where t p and L p are the peak time and peak bolomet-ric luminosity, respectively. Arnett-like models make sev-eral assumptions to solve the thermodynamic differentialequation, including homologous expansion of the ejecta,radiation-dominated pressure, spherical symmetry, and aself-similar energy density profile and also adopt a radia-tion diffusion approximation (Arnett 1980, 1982).2.3. KK19’s model
KK19 showed that the assumption of self-similarity forthe energy density profile will limit the accuracy of theArnett-like models, especially for centrally-located heatingsources, due to the time-dependent evolution of the diffu-sion wave through the ejecta. Instead, they propose a newrelationship between the peak time, t p , and peak luminos-ity, L p , without assuming self-similarity: L p = β t (cid:90) β t p t (cid:48) L heat ( t (cid:48) ) d t (cid:48) (5)where L heat ( t ) denotes a generic heating function and β is a dimensionless parameter of an order of unity. When L heat ( t ) is powered by Ni → Co → Fe radioactive de-cay, Equation 5 becomes: L p = (cid:178) Ni M Ni t β t (cid:183)(cid:179) − (cid:178) Co (cid:178) Ni (cid:180)(cid:179) − (1 + β t p / t Ni ) e − β t p / t Ni (cid:180) + (cid:178) Co t (cid:178) Ni t (cid:179) − (1 + β t p / t Co ) e − β t p / t Co (cid:180)(cid:184) . (6)For this specific form of L heat ( t ), the following relationshipshold: The M Ni required to reproduce a fixed { t p , L p } pairwill be directly proportional to the β value adopted. In con-trast, if M Ni is known, then the value of Lp or tp required toreproduce a given { t p , M Ni } or { L p , M Ni } pair, respectively,will be inversely proportional to the value of β adopted (ifthe light curve is powered entirely by radioactive decay).The parameter β incorporates the fact that L p does notnecessarily trace the radioactive heating rate as the storedinternal energy of ejecta may lag or lead the observed lumi-nosity, L ( t ), at the time of peak. The choice of β criticallydepends on several physical effects such as the spatial dis-tribution of Ni, the envelope composition, asymmetriesin the heating source or ejecta, and all power sources con-tributing to the observed luminosity along with their exactheating functions. Using Equation 6, β can be derived fromthe light curve of SESNe with known L p and t p , if there isan independent constraint on M Ni . We can then observa-tionally calibrate the appropriate values of β using a sam-ple of SESNe of various sub-types. With a sample of cali-brated β values, one can potentially apply KK19’s model toa wide range of SESNe with only photospheric data cover-age to constrain their M Ni . In addition, comparing the β values obtained from observed SESN light curves to thoseinferred from numerical light curve models calculated withdifferent input physics can inform us about the explosiondetails of SESNe. SN SAMPLE AND METHODS3.1.
Sample Selection
Our SESN sample should consist of those SESNe forwhich a measurement of the M Ni can be made from both ICKELOF S TRIPPED E NVELOPE SN E M Ni ofSESNe obtained from the Arnett model and the radioactivetail and also provides the means to produce a data-drivencalibration of the KK19 β values for SESN. Therefore, wecompiled the photometry of well-observed SESNe in theliterature and select SESNe that meet the following criteria:1. well-sampled coverage of the early rise (i.e., multi-ple observations before 5 days pre-maximum in atlist one band) or the observation of an accompany-ing GRB/X-ray flash, since a constraint on the epochof explosion is needed to derive M Ni from Equations1 and 2,2. multiple photometric measurements on the tail ofthe light curve, i.e., epochs (cid:38)
60 days, to be able toobtain M Ni from the radioactive tail,3. reasonable coverage around the light curve peak,which is required for both computing M Ni using theArnett model (Equation 4) and calibrating the β pa-rameter using KK19’s model (Equation 6),4. light curves in at least two bands over the light curvetail and peak, so that the bolometric luminosity andhost galaxy reddening can be computed. (See § 3.5for the method.)We identified 27 SNe from the literature that satisfythe above criteria and downloaded their photometric datafrom The Open Supernova Catalog (Guillochon et al. 2017).Our sample consists of 8 IIb, 8 Ib, 4 Ic, and 7 Ic-BL SNe.These SNe are listed in Table 1 along with their basic prop-erties, including SN type, the host galaxy name, distanceestimate, extinction, and the epoch of explosion.3.2. Distances
The distances we adopt throughout our analyses arelisted in Table 1. We adopt up-to-date host galaxy distancesreported in NASA/IPAC Extragalactic Database (NED) . Weprioritize distances obtained by Cepheids and Tip of RedGiant Branch methods when available and otherwise usecosmology-dependent values. For redshift-dependent dis-tances, we adopt the standard Λ CDM cosmology with aHubble constant H = − Mpc − , matter den-sity parameter Ω M = Ω Λ = https://ned.ipac.caltech.edu/ given in Drout et al. (2011), which is based on a host galaxyredshift reported in ATel 854 (Antilogus et al. 2006).3.3. Galactic and Host Galaxy Extinction
We adopt the value for galactic extinction along the lineof sight to each SN reported in NASA/IPAC Infrared Sci-ence Archive based on the extinction model of Schlafly &Finkbeiner (2011) and assuming an A V / E ( B − V ) = E ( X − Y ) host = ( X − Y ) obs − ( X − Y ) int , where X and Y are the measured magnitudescorrected for the Galactic extinction in two different filters.When computing the extinction, we take the average of thecolor difference between the observed data and the tem-plates of Stritzinger et al. (2018) from 5 days to 10 days post-maximum. When determining this average, time of maxi-mum is defined based on the observed filter that we adoptas the “ X ”-band in the above expression.Whenever available, we use X − Y = V − R / r / i color in-dices. Since there is no template provided for V − R intrin-sic color in Stritzinger et al. (2018), we convert observedJohnson R -band photometry to Sloan r -band using thecolor transformation relation of Jordi et al. (2006) when re-quired. E ( X − Y ) is then converted to the standard redden-ing E ( B − V ) using the bandpass coefficients of Schlafly &Finkbeiner (2011). For those SNe for which photometricdata is not available in any of the R / r / i filters, we adopt B − V color index instead. Furthermore, we find that ourobtained reddening is not robust to the choice of filters X and Y for several Type IIb SNe (i.e., SN1993J, SN2011dh,and SN2013df). For these SNe, we take the average of E ( B − V ) values derived using different color indices suchas V − r , V − i , and B − V . The final host galaxy extinctionsused in our analyses are listed in Table 1.3.4. Epoch of Explosion
The estimated epochs of explosion for each SN are pre-sented in Table 1. For several of Type IIb SNe with double-peaked light curves, the epoch of explosion is adopted fromthe reported values obtained from by modeling the shockcooling emission. For SN1998bw, which is a Type Ic-BL SNassociated with GRB 980425, we take the GRB epoch as theexplosion epoch. Similarly, for SN2008D, the epoch of theobserved X-ray flash XRO080109 is taken as the explosionepoch. Since the shock velocities of these SNe are high, we https://irsa.ipac.caltech.edu/applications/DUST/ A FSARIARDCHI ET AL . Table 1.
SESN sample with their basic parameters
SN name Host Type d (Mpc) Galactic E ( B − V ) (mag) Host E ( B − V ) (mag) t0 (MJD)SN1993J M81 IIb 3.6 (0.2) a c SN1994I M51 Ic 8.6 (0.1) a d SN2002ap M74 Ic-BL 9.8 (0.5) a b SN2008D NGC 2770 Ib 31.4 (2.2) 0.0193 (0.0002) 0.47 (0.04) 54474.6 (0.0) e SN2008ax NGC 4490 IIb 9.2 (0.6) 0.0188 (0.0002) 0.25 (0.04) 54528.3 (1.0)SN2009bb NGC 3278 Ic-BL 40.1 (2.8) 0.0847 (0.0010) 0.40 (0.08) 54912.9 (1.1)SN2009jf NGC 7479 Ib 33.8 (2.4) 0.0970 (0.0013) 0.07 (0.06) 55099.5 (4.2)SN2011bm IC 3918 Ic 99.2 (6.8) 0.0285 (0.0005) 0.00 (0.15) 55645.5 (0.5)SN2011dh M51 IIb 8.6 (0.1) a c iPTF13bvn NGC 5806 Ib 23.9 (1.7) 0.0436 (0.0006) 0.15 (0.04) 56458.3 (0.8)SN2013df NGC 4414 IIb 17.9 (1.0) a c SN2013ge NGC 3287 Ib 23.7 (1.6) 0.0198 (0.0002) 0.10 (0.10) 56602.3 (4.7)SN2014ad PGC 37625 Ic-BL 26.7 (1.9) 0.0380 (0.0012) 0.10 (0.07) 56724.5 (3.0)SN2016coi UGC 11868 Ic-BL 18.1 (1.3) 0.0737 (0.0021) 0.27 (0.08) 57533.2 (2.1)SN2016gkg NGC 613 IIb 19.7 (1.4) 0.0166 (0.0002) 0.20 (0.17) 57655.2 (0.0) c a Redshift-independent distances. SN1993J and 2013df (Gerke et al. 2011); SN1994I and 2011df (McQuinn et al. 2016); SN2002ap (McQuinn et al. 2017) b Distance from the value reported in Drout et al. (2011) c Epoch of explosion from the shock cooling emission d Epoch of explosion from the GRB emission e Epoch of explosion from the X-ray emissionN
OTE —References: SN1993J (Richmond et al. 1994, 1996a); SN1994I (Richmond et al. 1996b); SN1996cb (Qiu et al. 1999); SN1998bw (Galama et al. 1998;McKenzie & Schaefer 1999); SN2002ap (Pandey et al. 2003; Yoshii et al. 2003); SN2003jd (Valenti et al. 2008); SN2004aw (Taubenberger et al. 2006); SN2004gq(Bianco et al. 2014; Stritzinger et al. 2018); SN2005hg (Drout et al. 2011); SN2006T (Stritzinger et al. 2018); SN2006el (Drout et al. 2011; Bianco et al. 2014);SN2006ep (Bianco et al. 2014; Stritzinger et al. 2018); SN2007gr (Hunter 2007); SN2007ru (Sahu et al. 2009); SN2007uy (Bianco et al. 2014); SN2008D(Bianco et al. 2014); SN2008ax (Pastorello et al. 2008); SN2009bb (Pignata et al. 2011); SN2009jf Sahu et al. (2011); SN2011bm (Valenti et al. 2012); SN2011dh(Tsvetkov et al. 2012); iPTF13bv (Folatelli et al. 2016; Fremling et al. 2016); SN2013df (Morales-Garoffolo et al. 2014; Shivvers et al. 2019); SN2013ge (Droutet al. 2011); SN2014ad (Sahu et al. 2018); SN2016coi (Prentice et al. 2018); SN2016gkg (Bersten et al. 2018); can assume that the GRB or X-ray flash occurs shortly afterthe explosion time; therefore, GRB 980425 and XRO080109provide accurate estimates of the explosion epochs. For therest of SNe in our sample, we estimate the explosion timeby fitting a power-law with the form: f = f ( t − t ) n t > t t ≤ t , (7)to the observed fluxes, f , in the band with the best earlylight curve coverage. We carry out least-square regressionto fit for the power index n , scaling coefficient f , and epoch of explosion t . For the fitting, we only considerepochs that are pre-maximum-light and within 5 days ofthe first reported detection as well as any publicly availablenon-detection upper limits. The uncertainties on the ex-plosion epoch quoted in Table 1 come directly from the fit-ting process. The consequences of a possible “dark phase”(Piro & Nakar 2013) between the explosion epoch and theepoch of first light will be discussed in § 5.1.1.3.5. Bolometric Light Curves
The relative paucity of SESN with extensive coverage inUVOIR bands from early to late times is a challenge for
ICKELOF S TRIPPED E NVELOPE SN E Table 2.
The fit parameters for the SESN sample
SN name Type BC bands log L p (erg s − ) t p (days) Tail M Ni ( M (cid:175) ) T (days) Arnett M Ni ( M (cid:175) ) Calibrated β KK19 M Ni ( M (cid:175) ) f SN1993J IIb V − I V − I V − R V − I V − I V − R V − I B − V V − R B − V V − r B − V V − I V − I B − V SN2008D Ib V − r SN2008ax IIb V − R V − I V − I V − I V − R V − I V − I B − V V − I V − I V − I M Ni values obtained from KK19’s model assuming the median values of calibrated β reported in Table 4 (see § 4.4).2 Since the BCs provided by Lyman et al. (2014) are given in Johnson bands, magnitudes in Sloan r are first converted to Johnson R using the transformationsof Jordi et al. (2006). computing bolometric light curves that are needed to ob-tain M Ni . Here, we focus on obtaining the bolometric lu-minosities for epochs around the light curve peak and thelate-time tail. In order to leverage the multi-band pho-tometric data available for our SESNe sample, we adoptthe bolometric correction (BC) coefficients of Lyman et al.(2014, 2016). These color-dependent coefficients weremeasured by fitting the SEDs of a sample of SESNe thathave coverage in ultra-violet, optical, and infrared wave-lengths, and can be utilized as long as light curves for a SNof interest are available in a minimum of two bands.We first compute the absolute magnitude light curves forall SN in our sample in the pair of bands indicated in Ta-ble 2 (column “BC bands”). We correct for the distancesand total line-of-sight extinction described above. Next,we fit the multi-band absolute magnitude light curvesaround the peak and over the radioactive tail with a spline-smoothing function and linear function, respectively. Weperform a Monte Carlo (MC) analysis to propagate the un- certainties in the measured magnitudes and distance es-timate. The fitted absolute magnitude light curves, whichtogether also provide intrinsic color as function of time, arethen used to calculate a bolometric magnitude light curveby applying the color-dependent BC polynomials of Lymanet al. (2014, 2016). Specifically, M bol = M X + BC, where theBC is computed using the color indices listed in column“BC bands” of Table 2, and X denotes the first indicatedband listed in that column. Finally, we convert bolomet-ric magnitudes to luminosities assuming M bol, (cid:175) = L bol, (cid:175) = × erg s − .Figure 1 illustrates this process. It presents the abso-lute magnitude (top panel) and the resulting bolometric(bottom panel) light curves for two SNe in our sample:SN2008ax and SN2007ru. These two objects were specifi-cally chosen to span the range of light curve coverage avail-able during the early rise and late-time tail for SN in oursample. The spline and linear fits to the absolute magni-tude light curves are shown in the top panel. The x-axis A FSARIARDCHI ET AL . − − − − M a b s ( m ag ) SN2008ax V fit R fit VR MJD − L b o l ( e r g s − ) M Ni ’ M (cid:12) T ’ L p t p t Ni model − − − − M a b s ( m ag ) SN2007ru V fit I fit VI MJD − L b o l ( e r g s − ) M Ni ’ M (cid:12) T ’ L p t p t Ni model
Figure 1.
Extinction-corrected absolute magnitude (top panel) and bolometric luminosity (bottom panel) light curves for SN2008ax (leftpanel) and SN2007ru (right panel). The green and red solid curves represent fits to the absolute magnitudes in V and R / I bands, respec-tively. The cyan vertical line indicates the epoch of explosion t , while the vertical and horizontal orange lines denote the peak time t p andpeak luminosity L p of the bolometric light curves, respectively. The 1- σ confidence level in t , t p , and L p are shown with cyan and orangestrips. The dot-dashed red curve in the lower panels represents the best-fit Ni model of Equation 1 to the bolometric radioactive tails (seeannotation for fit parameters). Note when error bars are not visible in the top panel they are smaller than the plotted points. represents time since the inferred epoch of explosion de-rived in § 3.4. Gray regions indicate the uncertainties in thebolometric luminosity obtained at each epoch. These un-certainties stem from (in decreasing order of importance):error in the distance estimate, BC error, and photometricerror. We also mark the epoch of explosion t , the peak lu-minosity L p and peak time t p of the bolometric light curvein the bottom panel, with shaded regions representing theuncertainty on each parameter.Derived values of L p and t p for each SN are listed in Ta-ble 2, and plotted in Figure 2. Note that the final error in t p is a combination of the error in the t and bolometriclight curve. Overall, the peak luminosities for our samplespan 10 –10 erg s − and rise times span 8.2–34.6days (SN1994I and SN2011bm, respectively). As seen inFigure 2, no correlation is apparent between L p and t p forthe SESNe in our sample.Comparing our L p estimates with previous studies, wefind that our derived peak luminosities are a factor ∼
10 20 30 t p (days) L p ( e r g s − ) M N i ( M (cid:12) ) Figure 2.
Peak time, t p , versus peak luminosity, L p , for our sampleof SESNe. Markers are color-coded based on their tail M Ni value. L p estimates are consistent within our quoted errors withthose of Lyman et al. (2016), who also adopt the BC poly-nomial fits of Lyman et al. (2014). ICKELOF S TRIPPED E NVELOPE SN E RESULTS4.1.
Nickel Masses from the Radioactive Tail
To constrain M Ni of our SESNe sample, we model theirradioactive light curve tails using the analytic model ofWygoda et al. (2019) discussed in § 2. This model is sim-ilar to those of Valenti et al. (2008) and Drout et al. (2013)with one minor modification: the positrons’ escape is ne-glected. Since positrons’ escape occurs on a time scale of afew thousand days, it should not affect our results.By fitting the bolometric luminosity and slope of the ra-dioactive tail for the SESN sample, we can constrain thetwo unknown parameters in Equation 1: the nickel mass, M Ni , and partial trapping timescale of the tail, T . The fit-ting is done in an MC fashion: we run 1000 trials drawingfrom the distribution of possible luminosities and epochsof explosion. This allows us to propagate the uncertain-ties in these quantities when obtaining M Ni and T . Weonly consider epochs of ≥
60 days post-explosion, whenthe ejecta of SESNe are expected to be optically thin, suchthat the bolometric luminosity will be set by the instan-taneous heating rate. In Figure 1, we display the best-fitradioactive tail models for SN 2008ax and SN 2007ru (dot-dashed red curves; bottom panels). As shown, the modelclosely matches the evolution of the bolometric radioactivetail. The best-fit parameters, “tail M Ni ” and T , for each SNare listed in Table 2. Our best-fit tail M Ni values range from ∼ M (cid:175) to ∼ M (cid:175) with a median value of 0.08 M (cid:175) . T is in the range ∼ M Ni values. Objects with larger M Ni values also exhibit brighter peak luminosities, as expectedfor SNe powered predominately by radioactive decay.We report the basic statistics of our results (mean, me-dian, and standard deviation) for both the full sample andseparated by SESN sub-type in Table 3. However, we notethat our sample size is relatively small when SNe are cat-egorized by sub-types; especially normal Type Ic SNe, forwhich only 4 events met all of our sample criteria outlinedin § 3.1 and whose distribution may be skewed by the ex-treme event SN 2011bm. Therefore, we conduct Analysis ofVariance (ANOVA) test to check whether the reported dif-ferences between the mean M Ni of SN sub-types are sta-tistically significant. The result of ANOVA test indicatesthat the pairwise comparison of M Ni between SN sub-types is not generally statistically significant. One excep-tion for Type Ic-BL SNe for which the reported mean M Ni was found to be higher than that of the combined sampleof all other SESN sub-types with p-value <0.05. This is con-sistent with previous studies which have typically foundsystematically higher M Ni for Type Ic-BL events (e.g. Droutet al. 2011; Lyman et al. 2016; Prentice et al. 2016). . . . . . O v e r a ll C D F ArnettTailKK19 . . . . . T a il C D F Ic-BLIcIbIIb M Ni ( M (cid:12) ) . . . . . A r n e tt C D F Ic-BLIcIbIIb . . . . M Ni ( M (cid:12) ) . . . . . . KK C D F Ic-BLIcIbIIb
Figure 3.
Cumulative Distribution Functions of M Ni . Top:
The M Ni CDFs obtained using the radioactive tail modeling (bluecurve), Arnett’s rule (olive curve), and KK19 model (pink curve).
Middle top:
The tail M Ni CDFs categorized into the SN types: TypeIc-BL (yellow curve), Ic (red curve), Ib (blue curve), and IIb (greencurve).
Middle bottom & bottom: same as the middle top panelbut for Arnett and KK19 CDFs, respectively. KK19 M Ni values areobtained using the median values of calibrated β (see § 4.4). Thevertical lines show the mean of each distribution. The hatchedregions represent the uncertainties in CDFs. Figure 3 displays Cumulative Distribution Functions(CDFs) of the derived M Ni for our sample of SESNe. Inthe top panel of Figure 3, the M Ni CDFs are provided forthe entire SESN sample obtained using multiple methods:radioactive tail modeling (blue), Arnett’s rule (green), and0 A
FSARIARDCHI ET AL . Table 3.
Table of Ni Mass Statistics
Tail M Ni ( M (cid:175) ) Arnett M Ni ( M (cid:175) ) KK19 M Ni ( M (cid:175) )SN Type Mean Median Std Mean Median Std Mean Median StdIIb 0.06 0.06 0.02 0.13 0.13 0.04 0.07 0.07 0.02Ib 0.11 0.06 0.11 0.20 0.11 0.19 0.12 0.08 0.1Ic 0.20 0.10 0.22 0.26 0.16 0.22 0.15 0.11 0.11Ic-BL 0.15 0.15 0.07 0.31 0.29 0.16 0.15 0.15 0.07All 0.12 0.08 0.12 0.22 0.16 0.17 0.12 0.09 0.09 KK19 model (pink). (See 4.2 and 4.5 for Arnett and KK19methods, respectively.) In order to account for the errorsin individual M Ni measurements when plotting the CDFs,we run 1000 MC trials in which we sample each M Ni valuebased on the distribution defined by its uncertainly andconstruct a new CDF. These sampled CDFs are over-plottedin Figure 3, forming hatched regions that represent the un-certainties associated with the obtained CDFs.In the second panel of Figure 3 we present the CDFs ofthe tail M Ni values for each SESN sub-types separately. Weconduct Kolmogorov-Smirnov (K-S) tests on the CDFs oftail M Ni estimates for each sub-type. A K-S test on theCDF of Type Ic-BL and Ib/c SNe rejects the null hypothe-sis that these SN types are drawn from the same groups ofexplosions with a p-value = = = M Ni values reported inthe recent work of Meza & Anderson (2020) are lower limitsas they do not take the partial trapping of γ -rays into ac-count. Our tail M Ni estimates provided in Table 2 are con-sistent with these lower limits for SNe that are shared be-tween both samples. Similarly, our M Ni and T estimatesare consistent with (within the margin of error) those ob-tained from the Katz Integral method (Sharon & Kushnir2020) for 8 SESNe in common between the samples.4.2. Comparison to Arnett Model
For comparison, we also measure M Ni using Arnett’s rule,described in § 2, which has been extensively employed inthe literature. For each SN in our sample, we fit for M Ni inEquation 4 assuming the t p and L p values listed in Table 2.Similar to the procedure of deriving tail M Ni , we run 1000MC trials to take into account the uncertainties in t p and L p when obtaining Arnett M Ni values. Results for individual SN are provided in Table 2, while basic statistics of both thefull Arnett distribution and SESN sub-types are reported in3. The Arnett M Ni values span 0.04 M (cid:175) to 0.67 M (cid:175) with amean value of 0.22 M (cid:175) . The third panel of Figure 3 displaysArnett M Ni CDFs for different SESN sub-types.Figure 4 (top panel) presents a comparison between thetail and Arnett M Ni for our sample of SESNe. The re-sults highlight the systematic discrepancy between the twomethods. The M Ni values obtained from the radioactive tailmodeling are, on average, a factor of ∼ M Ni for everySESN in our sample. The overestimation of M Ni by Arnettmodel is also illustrated in Figure 3 (top panel), where theCDF of the Arnett M Ni distribution is below that of the taildistribution with a relatively large margin.The means and standard deviations of our Arnett-derived M Ni values for different SN types closely match thevalues reported in Lyman et al. (2016), but our median val-ues are lower than those of Prentice et al. (2016) for TypeIb, Ic, and Ic-BL SNe by ∼ M (cid:175) . This discrepancy isprimarily due to different approaches in deriving t p , whichis estimated in Prentice et al. (2016) by measuring the risetime from the half-maximum luminosity to L p (denoted by t − ) and using a linear empirical correlation for translat-ing t − to t p . We also note the Arnett M Ni values of Meza &Anderson (2020) are, on average, 50% lower than our Arnettestimates. This difference can be traced to their anoma-lously lower peak luminosities as discussed in § 3.5, above.The inaccuracy of M Ni values obtained from Arnett mod-els has been also shown in several radiative-transfer nu-merical simulations of SESNe. For example, Dessart et al.(2015, 2016) found that the Arnett’s rule overestimated the M Ni of SESNe by 50% and attributed this discrepancy tothe fixed electron scattering opacity assumption of Arnett’smodels. Similarly, Sukhbold et al. (2016) pointed out thatArnett’s rule does not hold for their simulations of TypeIb/c SNe evolved from massive single star progenitors.We note that the discrepancy we find between our Arnett ICKELOF S TRIPPED E NVELOPE SN E − A r n e tt M N i ( M (cid:12) ) Ic-BLIIbIbIc
SN1993JSN1994ISN1996cbSN1998bwSN2002apSN2003jdSN2004awSN2004gqSN2005hgSN2006TSN2006elSN2006epSN2007grSN2007ruSN2007uySN2008DSN2008axSN2009bbSN2009jfSN2011bmSN2011dhiPTF13bvnSN2013dfSN2013geSN2014adSN2016coiSN2016gkg − − Tail M Ni ( M (cid:12) ) − − KK M N i ( M (cid:12) ) Figure 4.
Top: M Ni obtained using the radioactive tail modeling(x-axis) and Arnett’s rule (y-axis) for our sample of SESNe. Ar-nett’s rule yields M Ni values which are systematically a factor of ∼ Bottom: the same but with M Ni values calculated us-ing the model of KK19 and our empirically-calibrated β values(see § 4.5) displayed on y-axis. Substantially better agreement isfound. The markers are color-coded to represent the SESN sub-types with yellow, green, red, and blue indicating SNe Ic-BL, IIb,Ic, and Ib, respectively. The dashed black line denotes equality. and tail M Ni values is approximately twice as large as thatquoted by Dessart et al. (2016).Despite these limitations, Arnett models have beenwidely used for deriving M Ni as well as ejecta masses andkinetic energies of SESNe (Drout et al. 2011; Lyman et al.2016; Prentice et al. 2016, 2018). A few observationalstudies have also indicated contrasts between results frommodelling the early and late-time light curves of SESNe.For example, Valenti et al. (2008) evoke a “two-zone” modelto try to resolve an inconsistency between the explosionparameters derived from early- and late-time light curvesof SN2003jd, which they fit with Arnett and radioactivemodels, respectively. In another study, Wheeler et al. (2015)estimate T values for dozens of SESNe by an analytical re-lation that depends on M ej and kinetic energy, which wererewritten in terms of the observed rise time and photo- spheric velocity, assuming Arnett’s model. The estimated T values were found to be in tension with the values mea-sured directly from the light curve tails, which likely is dueto the limitations of Arnett’s model. More recently, Meza& Anderson (2020) measured M Ni values for a sample ofSESNe using a variety of methods. While their tail M Ni val-ues are lower limits, they confirm that Arnett values areconsistently higher than those derived via other methods.For the rest of our analyses, we assume that our tail M Ni estimates are more realistic than those of the Ar-nett’s model. This is because the ejecta are expected tobe transparent to optical photons over the tail. Therefore,the bolometric luminosity traces the instantaneous heat-ing rate without any further assumption regarding the self-similarity of the energy density profile, which is a funda-mental assumption in the Arnett-like models (KK19).4.3. Comparison of Stripped-Envelope and Type II SN M Ni As described § 1, by comparing measurements of M Ni for 115 H-rich Type II SNe and 145 SESNe previously pub-lished in the literature, Anderson (2019) identified a dis-crepancy in their distributions, with SESNe displaying amean M Ni that was a factor of ∼ M Ni directly for a smaller sample of SESNe, using anumber of methods (Arnett’s rule, KK19, and radioactivetail modeling) in a uniform manner, demonstrating that astatistically significant discrepancy remains. However, thetail M Ni values presented in Meza & Anderson (2020) arestrictly lower limits to the true M Ni , as they assume com-plete trapping of γ -rays, while the Arnett and KK19-basedvalues may each contain systematic biases (in the lattercase because they adopt β values which have yet to be ob-servationally calibrated; see § 4.4). Thus, while sufficient torobustly demonstrate that SESN have a different M Ni distri-bution than Type II SNe, the magnitude of this discrepancyremains somewhat uncertain.Here, we compare the CDF of M Ni for SESNe derivedfrom our radioactive tail measurements to that for the 115H-rich Type II SNe from Anderson (2019). M Ni for most ofthis sample of Type II SNe were calculated using the bolo-metric luminosity of the radioactive tail of the light curveassuming full trapping of the γ -rays. Figure 5 illustrates the M Ni CDF of our sample of SESNe (orange curve) and the H-rich Type II SNe (green curve). For reference, we also showthe original sample M Ni values of SESNe compiled from theliterature by Anderson (2019, pink curve)—most of whichwere obtained using Arnett’s rule—and the lower limits of M Ni from Meza & Anderson (2020, light blue curve). We seethat our distribution of M Ni for SESNe measured from theradioactive tail lies between that of the Arnett-based val-2 A FSARIARDCHI ET AL . . . . . . . M Ni ( M (cid:12) ) . . . . . . C D F H-rich Type II (Anderson19)SESN (Anderson19)SESN (this work, Tail)SESN (Meza20, Tail Lower Limit)
Figure 5.
Cumulative Distribution Functions of M Ni for SESN vs.H-rich Type II SNe. The green curve represents tail-based M Ni values for Type II SNe compiled Anderson (2019), while red, lightblue and orange curves represent three different distributions forSESNe: the primarily Arnett-based M Ni values compiled from theliterature by Anderson (2019), lower limits on tail M Ni computedby Meza & Anderson (2020), and the tail M Ni values derived in§ 4. The mean value of the tail-based M Ni values found in thiswork are a factor of ∼ ues of Anderson (2019) and the tail upper limits of Meza &Anderson (2020), as expected.Overall we find that our sample of SESNe have a meanvalue ( ∼ M (cid:175) ; Table 3) which is a factor of ∼ ∼ M (cid:175) ). This is a fac-tor of ∼ M Ni CDFs of H-rich Type II SNe (An-derson 2019) and SESNe in this work. The test gives D-value = = − , meaning that the CDFsare inconsistent with being drawn from the same distribu-tion. By excluding Type Ic-BL SNe from the test, we findD-value = = × − , which similarly con-firms that Type IIb/Ib/c SNe and H-rich Type II SNe are in-consistent with being drawn from the same distributions.As in Meza & Anderson (2020) we find that a majority ofthis discrepancy come from the lack of SESNe in our sam-ple with low M Ni values. The lowest tail M Ni in our sam-ple is 0.03 M (cid:175) , while an incredible ∼
48% of Type II SNhave M Ni lower than this value. If we recompute the K-Stests described above, but considering only Type II SN with M Ni > M (cid:175) , we find a p-value = = M Ni Type II SNe. − − Tail M Ni ( M (cid:12) ) . . . . . . . . . C a li b r a t e d β Ic-BLIIbIbIc
SN1993JSN1994ISN1996cbSN1998bwSN2002apSN2003jdSN2004awSN2004gqSN2005hgSN2006TSN2006elSN2006epSN2007grSN2007ruSN2007uySN2008DSN2008axSN2009bbSN2009jfSN2011bmSN2011dhiPTF13bvnSN2013dfSN2013geSN2014adSN2016coiSN2016gkg
Figure 6.
Values for the β parameter given in Equation 6 for theSESNe in our sample, calculated using the observed t p , L p , andtail-based M Ni as inputs. The results are color-coded based theSN sub-type. β is a dimensionless parameter defined by KK19 andis correlated with different physical effects such as composition,asymmetries, and the radial extent of Ni within ejecta. The hor-izontal lines indicate the median β value Type IIb (green), Type Ib(green), Type Ic (red), and Type Ic-BL (yellow) SNe. Calibration of β values from KK19 In § 4.2 we demonstrated that Arnett-based models yield M Ni values that are a factor of 2 larger than those foundfrom modelling the radioactive tail. While obtaining tail-based M Ni measurements for all SESNe would be ideal,in practice the requisite photometric data exists for onlya subset of events. Thus, another means to estimate M Ni from photospheric data alone would be beneficial.As discussed in § 2, KK19 proposed an analytical modelthat relates the peak luminosity and its epoch to a generalheating function without relying on some of the simpli-fying assumptions adopted by Arnett’s models. This newmodel, described in Equation 6, depends on a dimension-less parameter β in addition to M Ni , t p and L p . KK19 sug-gested β = β = β canbe obtained from the observed sample of SESNe with inde-pendent M Ni values measured from their radioactive tails.We use Equation 6 to calculate the value of β inferred foreach SESN in our sample given their tail M Ni , t p and L p provided in Table 2. The uncertainty in the derived β val-ues has contributions from the error in tail M Ni , L p , and t p . ICKELOF S TRIPPED E NVELOPE SN E Table 4.
Table of Derived Parameter Statistics β ∗ t p (days) Log L p (erg s − ) f † Log f L p (erg s − )SN Type Mean Median Std Mean Median Std Mean Median Std Mean Median Std Mean Median StdIIb 0.78 0.77 0.19 20.2 21.5 2.5 42.37 42.34 0.21 0.24 0.26 0.12 41.87 41.78 0.21Ib 0.66 0.79 0.21 17.4 16.8 3.0 42.61 42.39 0.30 0.29 0.24 0.10 42.03 41.94 0.29Ic 0.88 0.90 0.61 17.0 12.7 10.5 42.67 42.67 0.18 0.10 0.13 0.29 41.97 41.62 0.32Ic-BL 0.56 0.54 0.33 14.4 15.0 2.5 42.87 42.84 0.19 0.32 0.36 0.17 42.49 42.47 0.27All 0.70 0.70 0.34 17.4 16.6 5.2 42.67 42.55 0.30 0.26 0.29 0.18 42.17 41.94 0.36 ∗ The parameter β is discussed in § 2 and obtained in § 4.4.† The excess power factor f is defined in § 5.1.5. In Figure 6 we plot the derived β values versus tail nickelmass for individual SNe. The results exhibit a significantscatter, with β ranging from ≈ β = β value for each SESN sub-type. Table 4 providessummary information on the mean, median and standarddeviation of the derived β values for each SN sub-type. Themedian values of β for Type IIb, Ib, and Ic SNe are roughlysimilar, but the standard deviation of Type Ic SN is a fac-tor ∼ β value of0.54, which is ≈
30% smaller than that of other SESN types.Two SNe in our sample, SN1994I and SN2007ru, have β close to zero, which may suggest that the derived tail M Ni is inadequate to produce the observed peak luminosity, L p .Recall that for a fixed M Ni and t p , a lower β value will yielda higher peak luminosity (see § 2.3). Both of these SNe arefast declining and will be discussed further in § 5.4.5. Improved Photospheric M Ni Estimates from theMedian Calibrated β Values
Using the results from § 4.4 we now assess whether, inpractice, the model of KK19 can be used to obtain morereliable M Ni estimates than Arnett for SESNe from photo-spheric data alone. In Table 2 we list M Ni values for eachSN that have been calculated using their observed L p and t p in conjunction with the median β value for each SN sub-type listed in Table 4. Errors listed in Table 2 account onlyfor the errors in L p and t p and do include the impact of thestandard deviation in the distribution of β values. Despitethe significant scatter in β values found for individual SNe,we find that the procedure of calculating M Ni assuming theKK19 model and the median β value for each SN sub-typeoffers a significant improvement over Arnett-based mea-surements, both for the overall distribution of M Ni valuesfor SESN and for individual objects. These two effects aredemonstrated in Figures 3 and 4, respectively. In the top panel of Figure 3 we present the CDF of M Ni calculated using KK19 with the median calibrated β incomparison to that of the radioactive tail and Arnett meth-ods. As shown, not only is the mean value of the KK19 M Ni distribution the same as that from the radioactive tail mea-sured M Ni (shown by a vertical lines; see also Table 3), butthe overall CDF of KK19-measured M Ni values closely ap-proximates that of the radioactive tail M Ni measurements.In the bottom panel of Figure 3 we also display the CDFsof KK19 M Ni estimates separated by SN sub-type. As listedin Table 3, the median values of these distributions are allwithin ≈
10% of those calculated from the radioactive tail.In Figure 4 we demonstrate that this agreement extendsto individual objects. The KK19-measured M Ni values foreach SNe (bottom panel) are much closer to their tail coun-terparts compared to the Arnett-derived ones (top panel).We find that, on average, the KK19 M Ni values are within ∼
17% of the tail-derived values. The largest variations oc-cur for the Type Ic SN 1994I and SN 2011bm for which thenickel mass is overestimated by ∼
65% and underestimatedby ∼ M Ni by a factor of ∼ β values listed in Ta-ble 4 should be used to calculate M Ni for SESNe.4.6. Inferred β Values for Theoretical SESN Light Curves
In addition to providing improved estimates for M Ni from photospheric data alone, the β values calculated forour observed SESNe encode information on the explosionproperties and progenitors of the population. Effects suchas composition, asymmetry and additional power sourceswill impact the degree to which the internal energy of theejecta lags or leads the observed luminosity at the time ofpeak. In order to assess if the observed population of SESNmatches expectations from theory, and to gain insight intothe physical processes that dictate β in observed events, wecalculate the β values for a set of analytical and numericallight curves models available in the literature.4 A FSARIARDCHI ET AL .4.6.1.
Arnett Models
First, as a baseline, we derive β for a grid of light curvescalculated using an analytic Arnett model. We take t p and M Ni in the ranges 5–40 days and 0.02–0.5 M (cid:175) , respectively,which correspond to the approximate ranges found for ourobserved sample . Given a pair of t p and M Ni , Arnett’s rulegives L p ; we then compute β from Equation 6 using t p , L p ,and M Ni . The resulting values of β for this grid are plot-ted as a grey shaded region in Figure 7. As expected giventhe inconsistency between Arnett and tail-derived nickelmasses shown above, these β values are inconsistent withthose of our observed population. In particular, the Ar-nett models occupy a parameter space with high β valuesin the range of 1.55–1.95, while all but one observed SESN(SN 2011bm) has a calibrated β < Large Grids of Numerical SESN
Next, we calculate the implied β values for two largesuites of simulated SESN light curves from Dessart et al.(2016) and Ertl et al. (2019). Both sets of models considerthe explosion of a grid H-poor stars, but utilize differentpre-SN stellar structures, explosion assumptions, and hy-drodynamic/radiative transfer codes. Dessart et al. (2016)consider a subset of the SN progenitors stripped via closebinary interaction that were evolved in Yoon et al. (2010).These models have final pre-explosion masses between 3.0and 6.5 M (cid:175) (initial masses between 16 and 60 M (cid:175) ) and finalcompositions chosen to span the range of SESN sub-types:Type IIb (defined as >
50% He plus some residual H in theouter envelope), Type Ib ( ≈
35 % He), and Type Ic (H andHe deficient). Dessart et al. (2016) uses a piston in order toproduce four different explosion energies for each pre-SNstructure and also consider two different levels of mixing ofradioactive materials. The purpose was to investigate howthese physical properties map onto observables, ratherthan ascertaining what explosion energy and 3D effectswould be achieved for a given pre-SN structure a priori. Fi-nal SN light curves were calculated with the 1D non-localthermodynamic equilibrium (non-LTE) radiative-transfercode CMFGEN (Dessart & Hillier 2010), and thus accountfor time and wavelength-dependent opacity variations.In contrast, Ertl et al. (2019) consider the explosion ofthe He star models of Woosley (2019), which are assumedto have lost their H envelopes due to binary interactionsprior to the onset of He-ignition, and are evolved to core-collapse in the KEPLER hydrodynamic code (Weaver et al.1978). Thus, all pre-SN models are H-deficient, but likelylead to a combination of Type Ib and Type Ic SN, with fi-nal surface He mass fractions spanning 0.16 to 0.99. Un-like in Dessart et al. (2016) the SN explosions are carriedout in a neutrino-hydrodynamics code P-HOTB (Janka &Mueller 1996), giving constraints on explosion energies, − − M Ni ( M (cid:12) ) . . . . . . . . . β t p β = 1 . β = 1 . β = 0 . IIbIbIcIc-BLErtl19 (Ib/c)Kleiser18 (Ib/c)Barnes18 (Ic-BL)Dessart16 (IIb & Ib/c)
Figure 7.
Values for the β parameter given in Equation 6 foundfor the observed sample of SESNe in comparison to those calcu-lated from a variety of theoretical models. The gray region rep-resents the parameter space that Arnett light curves take for var-ious pairs of t p and M Ni . The numerical models of Dessart et al.(2016), Barnes et al. (2018), Kleiser et al. (2018a,b), and Ertl et al.(2019) are shown with yellow, red, magenta, and green markers,respectively. The blue markers denote β obtained for our sam-ple of SESNe. The diamond, inverted triangle, circle, and squareblue markers represent SN types IIb, Ib, Ic, and Ic-BL, respectively.Overall, the observed population of SESNe possess lower β valueswith more scatter than the numerical models. Only the modelsof Kleiser et al. (2018a,b), in which shock cooling contributes asignificant fraction of the peak luminosity, overlap with the bulkof the observed population. The horizontal dashed lines repre-sent β = {0.82,1.125,1.6} suggested by KK19 for Type IIb, Ib/c, andType Ia SNe, respectively. nickel masses, and remnant masses. The progenitor mod-els that lead to a successful SN have initial He star masses inthe range 3.3–19.75 M (cid:175) , which roughly translates to ZAMSmass range of 16–51 M (cid:175) . For these events, bolometric lightcurves are calculated by post-processing the P-HOTB re-sults in KEPLER. While KEPLER treats electron scatteringdirectly, a constant additive opacity must be adopted to ac-count for the effects of atomic lines. Ertl et al. (2019) chosethis ‘line’ opacity to match that of SESN near peak.For each light curve published in Dessart et al. (2016) andErtl et al. (2019), we compute β from the published M Ni , t p ,and L p and Equation 6. The results are presented in Fig-ure 7. The β of Ertl et al.’s models (green) span then range1.31–1.64 with more massive initial He stars having rela-tively higher nickel masses and β values. These are largerthan the β values found for all of the of models of Dessart ICKELOF S TRIPPED E NVELOPE SN E β values of the observed SESNe areconsiderably smaller and the scatter in the observed β val-ues much larger than those of either set of numerical mod-els. In addition, while the observed SESNe span a similarrange of M Ni as the models of Dessart et al. (2016), ∼ M Ni higher than any any of the models ofErtl et al. (2019), which were designed to self-consistentlydetermine the radioactive material that can be synthesizedby neutrino-driven explosions. We discuss the implica-tions of these results in § 5. For comparison, in Figure 7we also mark the values β = {0.82,1.125,1.6} that are rec-ommended for Type IIb, Ib/c, and Ia SNe, respectively, byKK19. While β = β value of 0.78 obtained for the observed Type IIb SNe, β = β values forType Ib and Ic SNe (see Table 4).4.6.3. Specialized SESN Models
Finally, we also examine the light curve models from twospecialized models, which were each designed to probe aspecific physical effect that may be present in SESN. Barneset al. (2018) performs a 2D relativistic hydrodynamic sim-ulation with radiative transport in order to model a singlejet-driven explosion. They adopt an analytic pre-SN modelwith a mass of 3.9 M (cid:175) and inject an engine with an engineof ∼ × ergs. The resulting explosion would be classi-fied as a Type Ic-BL, and synthesizes 0.24 M (cid:175) of Ni. Bymodelling in multiple dimensions Barnes et al. (2018) findthat both the ejecta density profile and distribution of ra-dioactive material are aspherical, and generate light curvesfor different viewing angles. We compute the β that wouldbe inferred from each of these angles and plot the resultsas red stars in Figure 7. We find β in the range 1.35–1.65with models viewed from directions more aligned alongthe polar axis having progressively higher β . These resultslie close to those of the observed Type Ic-BL SN 2009bb ( β = M Ni = (cid:175) ), but yield significantly larger β val-ues than observed for most of the Type Ic-BL in our sample( 〈 β 〉 = (cid:38) (cid:175) ) and the subsequent cooling of shock deposited en-ergy can lead to substantial luminosity beyond that pro-vided by Ni. Using a combination of the MESA stellarevolution code, hydrodynamic simulations, and the Se-dona radiative transport code Kleiser et al. (2018a,b) modelthe light curves that would result from the explosion ofsuch systems, finding luminosities of log L = −
20 days. Originally proposed as a means to explain the class of rapidly evolving Type I SN (e.g.SN2010X; Kasliwal et al. 2010), a majority of the models ofKleiser et al. (2018a,b) are computed without contributionsfrom Ni. However, Kleiser et al. (2018a) also provide sixfiducial models in which they add 0.01, 0.05, and 0.1 M (cid:175) of Ni to one of their models with two levels of mixing. Wecalculate β for the three “strongly” mixed models—whichyield relatively smooth, as opposed to strongly double-peaked, light curve morphologies most similar to observedType Ib/c SN—and plot the results in Figure 7 (magenta tri-angles). We find β values of ∼ lower end of observed SESNe. Implications of these re-sults are discussed below. DISCUSSIONIn the sections above, we calculated Ni masses for 27SESNe based on their late-time tails. We confirm thatthese masses are systematically lower than those derivedby Arnett-like analytical models. These masses allow usto observationally calibrate the β value introduced in KK19based on their observed rise times and peak luminosities.Despite scatter, we demonstrate that calculating M Ni us-ing the medians of our empirically calibrated β values of-fers a significantly improved estimation when only photo-spheric light curve data is available. However, in doing sowe find that (a) the β values inferred for SESNe are system-atically lower than those found from most numerical sim-ulations of SESN explosions and (b) a systematic discrep-ancy remains between the Ni masses for SESNe and TypeII core-collapse SNe. In the sections below, we discuss thepossible origins for each of these discrepancies, and theirimplications for the progenitors and explosion mechanismof stripped envelope core-collapse SN.5.1.
Possible Origins of Low β Values
In § 4.6, we presented the β values inferred for differentnumerical models of SESNe. The results show that mostnumerical models give higher β values compared to obser-vations. In order to disentangle the origin of this discrep-ancy, in Figure 8 we present the pairwise dependence andhistograms of the three quantities that determine β , i.e., L p , t p , and M Ni , for both the numerical models detailed in § 4.6and observed SESNe. This figure illustrates that:1. While both the observed sample and model SESNshow a correlation between M Ni and L p , the ob-served objects exhibit considerably ( ∼ M Ni .2. The observed SESNe tend to have shorter rise timescompared to the models. The median rise time forthe entire sample is 16.6 days, as compared to 19.5and 26.8 days for the Ertl et al. (2019) and Dessartet al. (2016) models, respectively.6 A FSARIARDCHI ET AL . C o un t C o un t . . . . Log ( L p ) (erg s − ) C o un t . . . . . . M N i ( M (cid:12) ) t p (days) . . . . L og ( L p )( e r g s − ) . . . M Ni ( M (cid:12) ) Barnes18 (Ic-BL)Dessart16 (IIb & Ib/c)Ertl19 (Ib/c)Kleiser18 (Ib/c)Observed SESNe
Figure 8.
Pairwise relationship of log L p , t p , and M Ni for numerical models of Dessart et al. (2016) (yellow upper triangles), Barnes et al.(2018) (red stars), Kleiser et al. (2018a,b) (magenta left triangles), Ertl et al. (2019) (green pentagons) and our sample of SESNe (blue circles).Diagonal panels display the histogram of the three parameters. M Ni for the observed sample are those derived from modelling the late-time tail (§ 4.1). Overall the observed population of SESNe display shorter rise times and have substantially higher peak luminosities for agiven M Ni than the numerical models. As described in § 2.3 both rise time and peak luminos-ity are inversely proportional to β . Thus, shorter rise timeswould primarily act to increase β . Indeed, it appears thatthe main driver between the different β values of the Ertlet al. (2019) and Dessart et al. (2016) models is that Ertlet al. find shorter rise times for a given M Ni . This effect wasdiscussed in Ertl et al. (2019) and is primarily due to theiradoption of a constant line opacity. In contrast, the higherluminosity for a given M Ni would act to lower β , and this istherefore likely the origin of the discrepancy in β displayedin Figure 7. Here we investigate the possible physical ori-gins of this discrepancy, as well as the scatter in effective β displayed by the observed sample.5.1.1. Dark Period
The light curves of some SESNe are expected to have a“dark period” between the explosion epoch and the first observable light if they lack prominent cooling envelopeemission and their Ni is deposited deep within the ejecta(Piro & Nakar 2013). This dark period is roughly the timethat takes for the diffusion front to move inward (in a La-grangian sense) and reach the shallowest regions of theejecta that contain Ni. KK19 use numerical simulationsto show that for a completely central heating source, thedark period could be as large as 20 days, while the modelsof Dessart et al. (2016) typically have dark periods (cid:46)
ICKELOF S TRIPPED E NVELOPE SN E Ni → Co → Fe decay chain would need to reproducethe same tail luminosity at a longer time post-explosion.Both effects could alleviate some of the discrepancies be-tween the observed and model SESN in Figure 8.To quantify the effect of a possible dark period on ouranalysis in § 4, we increase the rise time by 5 days and re-compute both tail M Ni and β for our sample of SESNe. Theresults show that, on average, the tail M Ni values would in-crease by ∼ β values would actuallyfurther decrease by ∼
8% compared to those listed in Ta-ble 2. We therefore conclude that while a dark period couldexplain some of the discrepancy between the rise times ofobserved SESNe and numerical models, the subsequent in-crease in inferred M Ni is insufficient to offset this effect,and an even larger discrepancy between the β of the ob-served SESNe and numerical models would result.5.1.2. Composition, Opacity, and Recombination
Composition can influence the morphology of SESNlight curves, primarily through its influence on the opacityof the ejecta. In practice, the opacity will also depend bothon the age of the SN and the spatial location of of the dif-fusion front, as effects such as ionization, recombination,and line blanketing will modify the opacity compared toconstant pure electron scattering. Notably, while ionized,the opacity of a given material will be dominated by elec-tron scattering and will subsequently fall to significantlyonce recombined (e.g. KK19, Piro & Morozova 2014). KK19investigate the impact of ion recombination on light curverise times, peak luminosities and β values for ejecta withvarying compositions. For ejecta with higher recombina-tion temperatures, the opacity will fall at an earlier time.This leads to a shorter dark period, shorter observed risetime, and higher peak luminosity, which combine to yielda lower β value. KK19 find that for a central heating sourceand ejecta with recombination temperatures of ∼ β values of 0.70, 0.94, and 1.12 re-sult. β = β values of the observedSESN sample if the Ni is primarily diffusing through
He-rich ejecta. However, we note that the models Dessart et al.(2016) which include full non-LTE radiation transport andwavelength dependent opacities, all display β around 1.12,despite the fact that over 60% of their models have compo-sitions that are >
50% He. This implies that the Ni synthe-sized in the explosions is primarily diffusing through thedenser CO cores, whose opacities remains high long afterthe He envelopes. In this case, the surface He would have recombined at earlier times and would be effectively trans-parent near maximum light, consistent with the low black-body temperatures observed for many SESN near maxi-mum ( ∼ β values of observed SESN if a significant frac-tion of their M Ni is mixed out into a He-rich envelope. Themodels of Dessart et al. (2016) currently implement twomixing schemes. Thus, stronger or more directed mixing,such as that described in Hammer et al. (2010), may be re-quired. However, while such effects may reconcile observa-tions of some Type IIb and Ib SNe, it is unclear if they cansimilarly explain the trends observed in Type Ic and Ic-BLSNe—which also display low β values, but do not have anydetectable He in their spectra. While the presence of He inthe progenitors of Type Ic SN is still debated (e.g. Hachingeret al. 2012), arguments rely on the He being transparent.Mixing of Ni into a He envelope would significantly in-crease the likelihood of non-thermal excitation and thusobserved spectroscopic features, making this explanationless plausible (Dessart et al. 2012).5.1.3.
Mixing of Radioactive Material
The mixing of radioactive material within SN ejecta isgenerally difficult to model due to its inherent 3D nature(e.g. Joggerst et al. 2009; Hammer et al. 2010; Wongwatha-narat et al. 2015). While it is generally believed that the Nidistribution of SESN is more centrally concentrated than inType Ia SN, there is also evidence that at least some mixingis required to reproduce SESNe observations (Dessart et al.2012). The distribution of Ni inside the ejecta can alterthe shape of the light curve and thus impact the β param-eter. In particular, for smoothly stratified models, more ex-tended Ni distributions (corresponding to stronger mix-ing) will lead to both shorter rise times and higher lumi-nosities for a given M Ni (e.g. Dessart et al. 2016, KK19).However, KK19 find that these two effects combine to pro-duce a higher β value for more strongly mixed models.They find that the lowest β that can be achieved for a con-stant opacity model is β = β values of the observed SESNe.5.1.4. Asymmetry
There is growing evidence from a combination of spec-tropolarimetry, nebular spectroscopy, and resolved SNremnants that some SESN may be asymmetric (e.g. Valentiet al. 2011; Milisavljevic & Fesen 2015; Tanaka 2017). As8 A
FSARIARDCHI ET AL . = cos Figure 9.
Inferred value of β for the set of 2D radiative transfermodels, depending on viewing angle µ = cos θ , where µ = ± µ = A = v r / v z (i.e. degree of asymmetry), where A = β when averaged over all viewingangles. We find that while line-of-site effects can lead to signifi-cant scatter in observed β , asymmetry will increase the average β found for a population. shown in Figures 7 and 8, the β values of the mildly asym-metric simulations of Barnes et al. (2018) depend on theobserver’s viewing angle. This is primarily due to a varia-tions in the observed peak luminosity, with viewing angleswith larger L p leading to lower β values. Thus, dependingon their nature, asymmetries in Ni mixing or ejecta distri-bution can be reflected both in the mean value and scatterin the β parameters observed for a population of SESNe.To test the degree to which asymmetry can modify ob-served β values for a population, we run a set of light curvesimulations with varying degrees of ejecta asymmetry us-ing the multi-dimensional radiative transfer code Sedona(Kasen et al. 2006). We assume an axisymmetric homol-ogously expanding ejecta profile consisting of a brokenpower-law in density following Chevalier & Soker (1989)and Kasen et al. (2016). To account for deviations fromspherical symmetry, we vary the semi-major axis as inDarbha & Kasen (2020) paramterized by A ≡ v r / v z , where v r and v z are the outer ejecta velocities at the equator andpole, respectively. In total, we run four radiative transfersimulations with A ≤
1, i.e., prolate ejecta configurations.We choose fiducial values of M ej = M (cid:175) , v z = km s − for our simulations. To account for the heating, we set theinnermost 0.1 M (cid:175) to consist of Ni. Finally, we assumea constant grey opacity of κ = g − . The resulting light curve is then calculated at ten different viewing angles µ = cos θ , in the range µ ∈ { − µ = µ = ± L p ( µ , A ) and t p ( µ , A )for the output bolometric light curves, which we then maponto an inferred β based on Equation 6 and the model pa-rameter M Ni = M (cid:175) . In Figure 9, we show the inferredvalues of β for the different set of asymmetric ejecta con-figurations and viewing angles. As expected, β does notvary with viewing angle for the case A =
1, i.e. no ejectaasymmetry. However, increasing the degree of asymme-try results in lower inferred β when viewed along the equa-tor, and higher β when viewed at the poles. This is due to L p being larger when viewed along the equator, where theprojected surface area is largest; similarly, L p is decreasedalong the poles for asymmetric ejecta due to a smaller pro-jected surface area (Darbha & Kasen 2020). This is in agree-ment with the results found in Barnes et al. (2018).While the total spread in β values observed for ourastymmetric simulations is (cid:38) asymmetry acts to increase themean inferred value of β . This is opposite to the direc-tion that has been observed, where the average β is sys-tematically lower than the spherically symmetric models ofDessart et al. (2016); Ertl et al. (2019) (as well as the A = sys-tematically lower inferred values of β . However, we notethat when asymmetry is strong other effects such as thedevelopment of non-radial flows (Matzner et al. 2013; Af-sariardchi & Matzner 2018) and the ejection of nickel-richclumps to high velocities (Drout et al. 2016) could furtherinfluence the light curve morphology.5.1.5. Additional Power Sources
In § 5.1 we demonstrated that the main driver of the low β values for our observed SESN was their high L p for a given M Ni (Figure 8). Thus, another plausible explanation for theorigin of the discrepancy between the β distribution of themodels and the observed SESNe is that additional powersources beyond the radioactive decay of Ni contribute tothe peak luminosity of SESNe. This was previously pro-posed by Ertl et al. (2019), who noted that their numericalsimulations were unable to reproduce the brighter half ofobserved Type Ib/c SNe luminosity function (Figure 8). Inaddition, when modeling a sample of SESN with the lumi-nosity integral method of Katz et al. (2013), Sharon & Kush-nir (2020) required an additional model parameter, whichthey interpret as non-negligible amount of emission pro-
ICKELOF S TRIPPED E NVELOPE SN E Ni. The presence of andadditional luminosity source near peak could also explainwhy the observed SESNe show an even larger discrepancybetween Arnett and tail-measured M Ni than the theoreticalmodels of Dessart et al. (2016).Within our sample, the need for additional powersources is particularly conceivable for SN 1994I andSN 2007ru, for which we derived a negative and close tozero β , respectively. In practice, a negative β is not physi-cal in the general definition given by KK19 (see Equation 5).Rather, this implies that the version of this equation whichassumes pure Ni heating (Equation 6) is incapable of pro-ducing such a bright peak luminosity on the observed risetime when coupled with the M Ni measured from the ra-dioactive tail. While these are the most extreme cases,other observed SESN may also have extra power sourcescontributing to the observed luminosity. In this case, at-tributing the observed peak luminosity solely to the ra-dioactive decay of Ni will result in smaller β values thatexpected based on their composition and Ni distribution.Besides the radioactive decay of Ni, power sources thatcan contribute to the light curves of CCSN include shockcooling emission, ejecta interaction with circumstellar ma-terial (CSM), and energy from a central engine. Here, weassess the viability of each of these sources in explainingthe discrepancy between observed and model SESNe, andimplications thereof.
Luminosity Required:
We begin by evaluating how muchexcess luminosity would be required to reconcile the β val-ues we derive in § 4.4 with those of the theoretical mod-els in § 4.6. To do so, we assume that the average valueof β =1.125 found by the models of Dessart et al. (2016)is accurate for SESN powered only by radioactive decay.Given their full treatment of radiative transfer/opacity, thisis equivalent to assuming that the composition, energet-ics, and mixing of radioactive material included in Dessartet al. (2016) reflect reality. Then, using β = M Ni and t p listed in Table 2, and Equation 6, we calculate theluminosity that Ni decay can produce at the peak time ofthe SN. From this, we define an “excess luminosity factor”, f , as the fraction of peak luminosity that is in excess overwhat is expected from a β = f for each SN are listed in Table 2and the mean, median and standard deviation in Table 4.In Figure 10 we plot the excess luminosity factor, f , versusthe excess luminosity, f × L p . We emphasize that these “ex-cess luminosity” values should be taken as order of magni-tude estimates only, as they (a) neglect any variations from β = − . . . . f . . . . . . . . . L og f L p ( e r g s − ) IIbIbIcIc-BL C o un t . . Count
Figure 10.
Excess power factor, f , versus logarithm of excess peakluminosity f L p for our SESN sample. Histograms of f and f L p are displayed on x- and y-axis, respectively. Overall we find thatreconciling the observed SESNe with current numerical simula-tions would require 7–50% of their peak luminosity to come frompower sources other than Ni. This corresponds to excess lumi-nosities of 41.4 (cid:46) log( f L p ) (cid:46) the observed light curve; depending on the nature of theexcess luminosity source this need not be the case. Never-the-less, they provide a useful diagnostic.Overall, we find f values in the range of − f values, reflecting the fact that they had mea-sured β > require additional powersources. For the remaining 24 events, we find that if themodels of Dessart et al. (2016) and our tail M Ni are accu-rate, we require that ∼ Ni. This translates intoconsiderable excess luminosity in the range of 2.5 × –5.5 × erg s − or, equivalently, peak bolometric magni-tudes for the excess power source of − > M bol >− fraction of the peak luminosityto come from other sources, are mixed between sub-types. Shock Cooling and CSM Interaction:
Both shock cool-ing and CSM interaction face challenges in explaining thisrequired excess emission. First, shock cooling emissionis predicted to be both faint and short-lived for the com-pact progenitors (R ∼ R (cid:175) ) typically evoked for H-poor SESN(Nakar & Sari 2010; Rabinak & Waxman 2011). Second, thesubstantial luminosity required and lack of narrow emis-sion lines in the majority of SESNe spectra limit any poten-0 A FSARIARDCHI ET AL .tial CSM to dense and confined shell or disk-like configu-rations (Chevalier & Irwin 2011; Moriya & Tominaga 2012;Smith et al. 2015), which are not predicted from standardmodels of stellar evolution (Smith 2014). However, recentprogress may change this picture: models show that par-ticularly low mass He stars ( (cid:46) (cid:175) ) can undergo substan-tial inflation (achieving radii (cid:38)
100 R (cid:175) ; e.g. Yoon et al. 2010,Kleiser et al. 2018a, Woosley 2019) and there is increasingobservational evidence that many CCSN—of all varieties—undergo a period of enhanced mass loss shortly beforecore-collapse (e.g Margutti et al. 2015; Drout et al. 2016;Bruch et al. 2020). Thus, a significant fraction of SESN pro-genitors may have large effective radii ( (cid:38)
20 R (cid:175) ) in whichcase shock deposited energy can contribute substantiallyto their observed luminosity.As described in § 4.6.3, Kleiser et al. (2018a,b) modelthe light curves that would result solely from the diffu-sion of shock deposited energy in both of these scenarios.The set of O/He-rich CSM shells modeled in Kleiser et al.(2018b) have masses of 1 − (cid:175) and are located at radii of ∼ (cid:175) , designed to mimic an intense final mass-lossepisode. They find transients which rise to peak magni-tudes of −
15 mag < M r < −
18 mag on timescales of ∼ Niis added, the models of Kleiser et al. (2018a,b) are able toreproduce the low β values of the observed population.While the particular theoretical models plotted in Fig-ure 7 show slight double-peaked morphology in the their optical light curves—which are not typically observed—they were created by adding Ni to a shock cooling curvethat reaches −
17 mag and contributes (cid:38)
50% of the lumi-nosity near peak. In contrast, we expect the SESN in oursample to still be dominated by the radioactive decay of Ni, with a median excess luminosity factor of f = narrow high-velocity absorption features, which may be indicative ofa shell-like CSM structure (Drout et al. 2016; Kleiser et al.2018b). However, the lack of prominent double-peakedstructure in many Type Ib/c SNe combined with the needfor excess luminosity near maximum light implies that: (i)the He/O-rich material which leads to the large effective ra-dius cannot be too tenuous, in which case it would becomeoptically thin on a timescale of ∼ days (Dessart et al. 2018;Woosley 2019) and (ii) the Ni synthesized in the explosionmust be well-mixed to avoid a significant dark-period andsubsequently large offset in time between the two emissioncomponents (Kleiser et al. 2018b). We therefore conclude that shock cooling emission is aviable source for the excess luminosity required to recon-cile SESN observations and models. While low mass Hestars can reach the radii required through “natural” stellarevolution processes, such events are predicted to eject verylittle radioactive Ni (Kleiser et al. 2018a; Woosley 2019).Thus, reproducing the full observed population via thismechanism likely requires a significant number of SESNto undergo intense late-stage mass loss due to instabilities(Smith & Arnett 2014; Woosley 2019), internal gravity waves(Quataert & Shiode 2012; Fuller & Ro 2018), or some otherphysical process during the final nuclear burning stages.We emphasize that this shock cooling emission will rapidlyfade once the ejecta cools to the recombination tempera-ture of O/He-rich material ( t <
40 days), and thus M Ni mea-sured at >
60 days post-explosion should be unaffected.
Central Engines:
On the other hand, a central enginecould provide the additional energy source required topower the light curve around peak. We note, in partic-ular, that the we found a lower mean β value and re-quire a higher mean excess luminosity for Type Ic-BLSNe (Table 4), for which central engines are commonlyevoked. Both magnetars and collapsars can provide a natu-ral source of extra luminosity, in the form of spin-down en-ergy and fallback accretion (Dexter & Kasen 2013), respec-tively. Ertl et al. (2019) investigate the former as a powersource for SESNe in general, arguing that even the forma-tion of a more moderate millisecond pulsar (e.g., Yoon et al.2010) may be sufficient for rotational energy to impact theSN light curve without impacting the overall energetics.We use the magnetar spin-down energy and timescaleof Kasen (2017) together with SN timescale and ejecta ve-locity of Kasen et al. (2016) to estimate the general phasespace of magnetar properties required to provide the ex-cess luminosity found above. In Figure 11 we plot risetime vs. excess luminosity for our sample of SESNe. Alsoshown are lines which which represent the peak luminos-ity and time achieved by magnetar models with a fixed pe-riod but varying magnetic field (solid) and fixed magneticfield but varying periods (dotted). All models assume anopacity of κ = g − , explosion energy of 10 erg,and were calculated both for M ej = M (cid:175) (top panel) and M ej = M (cid:175) (bottom panel)—chosen to span the range ofSESNe ejecta masses from Lyman et al. (2016). For M ej = M (cid:175) , P values of 10–116 ms and B ( = B /10 G) val-ues of 7–59 are yield luminosities consistent with require-ments. For M ej = M (cid:175) , similar magnetic field strengths butshorter periods are necessary with P = = P and B found here over-lap with—but extend to longer periods and higher mag- ICKELOF S TRIPPED E NVELOPE SN E . . . . . . . . . . . . . L og f L p ( e r g s − ) M ej = 2 M (cid:12) P = m s P = m s P = m s P = m s P = m s P = m s B = B = B = B = B = IIb Ic Ic-BL Ib . . . . . . . t p (days) . . . . . . L og f L p ( e r g s − ) M ej = 5 M (cid:12) P = m s P = m s P = m s P = m s P = m s P = m s B = B = B = B = B = Figure 11.
Logarithm of excess peak luminosity log( f L p ) versuspeak time t p for our sample of SESNe (excluding SNe with nega-tive excess factor f ). The diamond, inverted triangle, circle, andsquare orange markers represent SN types IIb, Ib, Ic, and Ic-BL,respectively. Also plotted are lines which which represent thepeak luminosity and time achieved by magnetar spin-down mod-els with a fixed period but varying magnetic field strength (solidpurple) and fixed magnetic field but varying periods (dotted cyan)for ejecta mass of 2 M (cid:175) (top panel) and 5 M (cid:175) (bottom panel). netic field strengths—than those of magnetar fits to super-luminous SN light curves by Nicholl et al. (2017).Figure 12 displays two representative magnetar modelsfor the excess peak luminosity of SN2008ax. The excessemission factor is 0.29, corresponding to a luminosity of5.90 × erg s − (dashed line). The blue curve illustratesa model with B = P =
32 ms, and M ej = 5 M (cid:175) , whilethe orange curve represents a magnetar with B = P =
116 ms, and M ej = 2 M (cid:175) . Both models peak at thelevel of the excess luminosity calculated above, but havehave different magnetar properties and light curve mor-phologies. Figure 12 highlights that, unlike shock coolingemission, if a magnetar contributes to the light curve nearpeak it can also power a non-negligible portion of the tailluminosity. In this case, tail-based measurement of M Ni would be overestimated and, as a result, the fraction of thepeak luminosity which must come from sources other thanradioactive decay underestimated . While we find that fitsover 60–120 days post-explosion, as performed in § 3.5, are Time (days) L b o l ( e r g s − ) SN L bol Magnetar M ej = 5 M (cid:12) , B = 36 , P = 32 ms Magnetar M ej = 2 M (cid:12) , B = 19 , P = 116 ms Figure 12.
The bolometric light curve of SN2008ax in comparisonwith two magnetar models. The dashed red horizontal line indi-cates the excess emission in the L p of SN2008ax (i.e, ∼
29% of thepeak luminosity). If this power is contributed to the light curveby sources other than the radioactive decay, then β increases tothe same level as predicted by numerical models, i.e., β (cid:39) t p and 0.29 × L p of SN2008ax. not sufficient to distinguish between the L ( t ) ∝ t − power-law decline of the magnetar model and the exponentialform of the radioactive decay of Ni (Equation 1) futuremodelling of a subset of SESNe with data covering a longerbaseline ( (cid:38)
200 days) could potentially break this degener-acy. If the slope of the tail is shallower than Co → Feconversion rate this could also be an indication that otherpower sources are contributing to the light curve tail (e.g.,Ertl et al. 2019). However, none of the SESNe in our samplehave such a shallow tail.5.1.6.
Possible Limitations of Tail M Ni Values
Throughout the analyses of § 4 and § 5, and specificallyin the model comparisons of Figures 7 and 8, we assumethat the M Ni values measured from radioactive decay mod-eling of SESNe light curve tails are reliable estimates forthe actual M Ni . In § 2 we utilize the tail luminosity modelof Wygoda et al. (2019), which relies on a number of as-sumptions. In particular, the simple scaling form of the γ -ray deposition factor, f dep = − e − ( t / T ) − , only holds if theejecta is in homologous expansion and if the γ -ray opacityis constant and purely absorptive. However, both are stan-dard assumptions: ejecta should reach a phase of homol-ogous expansion after several expansion doubling times—i.e., a few days—while we measure M Ni over epoches > γ -ray opacity is typically assumed to be con-stant (Sutherland & Wheeler 1984; Clocchiatti & Wheeler1997; Wygoda et al. 2019). We note that other assump-tions on the ejecta density distribution or nickel mixing will2 A FSARIARDCHI ET AL .chiefly change pre-factors of T , while the scaling relationof f dep —and therefore M Ni —will remain unchanged.Thus, we conclude that any error in M Ni is due to thelate-time luminosity that we attribute to radioactive decaynot being accurate. This could occur if either the bolomet-ric corrections utilized in § 3.5 do not adequately describethe behavior of our observed sample or if power sourcesother than radioactive decay (e.g., CSM interaction, mag-netar spin down; see above) contribute to the luminosityon the light curve tail. In the latter case, our tail M Ni valueswould be overestimated. However, we emphasize that thiseffect can not resolve the tension with theoretical modelsshow in Figures 7 and 8. Rather, lower M Ni values would in-crease the discrepancy, with the observed sample of SESNeshowing even larger L p values for a given M Ni .5.2. Consequences of M Ni Discrepancy with Type II SNe
The discrepancy in Ni mass distributions for SESNeand Type II SN was first identified using Arnett-based mea-surements of M Ni for SESNe (Anderson 2019). In § 4.2we demonstrated that Arnett’s rule over-predicts M Ni forSESNe by roughly a factor of 2—likely due both to limita-tions in Arnett’s model (KK19) and to possible contribu-tions from additional power sources to the peak luminos-ity of SESN (§ 5.1.5). However, in § 4.3 we find that evenwhen tail-based M Ni values are used, our population ofSESNe have a mean M Ni value (0.12 M (cid:175) ) which is a factorof ∼ M (cid:175) ). Therefore a crit-ical question remains: what makes the M Ni distribution ofSESNe skew to larger values than Type II SNe? Are the M Ni values for the observed population of SESNe biased? If not,does the discrepancy with Type II SNe come about becauseSENe originate from higher ZAMS mass stars? Or are theZAMS masses of SESNe and H-rich Type II SNe are some-what similar, but other physical mechanisms are respon-sible for the observed difference in the M Ni distribution?Here, we consider each of these questions in turn. Does the distribution of M Ni derived accurately representthe true distribution of M Ni synthesized in the core-collapseof H-poor stars? As highlighted by Meza & Anderson (2020),the discrepancy between SESNe and Type II SNe is primar-ily due to a lack of observed SESNe with low M Ni . Whilethe light curves of Type II SNe—powered predominately byH recombination—remain luminous for (cid:38)
100 days regard-less of M Ni , low- M Ni SESN may be faint and/or rapidly-evolving. In particular, as described in § 5.1.5, low-massstripped He stars (M (cid:46) (cid:175) ; corresponding to ZAMS (cid:46) (cid:175) ) can inflate to large radii prior to core-collapse.Stars with these initial masses likely dominate the popula-tion of Type II SNe, due to the initial mass function. How-ever, the explosion of their stripped counterparts may bedominated by bright and rapidly-fading cooling envelope emission (Dessart et al. 2018; Kleiser et al. 2018a; Woosley2019), with minimal contributions from Ni. Observa-tionally, these could manifest as rapidly-fading Type I SN(Kasliwal et al. 2010; Drout et al. 2013), Type Ibn SNe (Hos-seinzadeh et al. 2017), or the broader class of fast blue opti-cal transients (Drout et al. 2014) rather than “traditional”SESNe. Such events were not explicitly included in oursample, and have rarely been followed to late enough timesto constrain the M Ni ejected. While the rates of rapidly-evolving transients ( ∼ M Ni distribution shown in Figure 5 maynot accurately represent reality if the light curves of SESNeare not solely powered by the radioactive decay of Ni andthe timescale of the additional power source(s) is (cid:38)
60 days(see § 5.1.5). In this case, attributing the full tail lumi-nosity to Ni would lead to an overestimate of the truevalues. Within this context, it is notable that while sim-ulations of neutrino-driven core-collapse SNe (Sukhboldet al. 2016; Ertl et al. 2019) are able to self-consistently pro-duce the range of M Ni values observed in H-rich Type IISN ( ∼ M (cid:175) ; Müller et al. 2017, Afsariardchi et al.2019), they are unable to produce M Ni values as high asthose derived for the upper ∼
30% of our SESN sample (seeFigures 7 and 8). It was for this reason that Ertl et al. (2019)invoked magnetars to explain the observed light curvesof SESNe. While this may resolve the M Ni discrepancy, itsubsequently requires that magnetars influence SESN at ahigher rate than Type II SNe. This may be a natural conse-quence of stripped stars retaining a larger fraction of theirangular momentum, which in H-rich stars is lost primar-ily due to rotational breaking when the star expands to theRSG phase (e.g., Ertl et al. 2019). Do SESNe originate from higher ZAMS mass stars thanType II SNe?
If observational biases cannot explain the rel-ative lack of low M Ni SESNe, the discrepancy could indicatethat SESNe preferentially form from higher ZAMS massstars—which are expected to synthesize higher amountsof M Ni —than Type II SNe. While on face value this mayfavor the single star progenitor channel, this is in tensionwith the observed occurrence rate of SESNe, which is muchhigher than the explosion rate of stars with ZAMS mass (cid:38) M (cid:175) that eventually become WR stars (Smith et al.2011). In addition, the mass-loss rate of massive stars isstill uncertain, and it is not clear whether all massive starswith ZAMS mass (cid:38) M (cid:175) can strip their H envelope (Smith2014). Another possible explanation is that SESNe do formstripped binaries and span the same overall ZAMS massesas Type II SNe. However, while the relative rates of Type IISNe are dominated by the IMF, SESNe are skewed to higherrelative masses. This may be a natural consequence of the
ICKELOF S TRIPPED E NVELOPE SN E Do additional physical mechanisms modify the M Ni syn-thesized in SESN? Alternatively, if the M Ni distribution forSESNe is accurate, and SESNe originate from similar ZAMSmasses as H-rich Type II SNe, then there must be somephysical processes that make the M Ni of SESNe larger.While it is often assumed stripping of the H and even Heenvelope via binary interaction should leave the inner corestructure of the primary star intact (e.g., Fryer & Kalogera2001)—in which case the M Ni distributions of SESN andType II SNe should be indistinguishable—this picture maynot be complete. In particular:(i) In close binaries, fast orbital rotation, tides, magneticbreaking, and angular momentum transport can in-fluence the convective core sizes profoundly (e.g.,Song et al. 2018). Therefore, changes in the corestructure may impact the M Ni production.(ii) A fraction of SESNe may originate from the mergerof binary stars (Zapartas et al. 2017). In this case,a more massive core capable of producing a largeramount of Ni may result. Although the rate of thismerger channel seems to be relatively small ( ∼ M Ni of SESNe produced via the binary channel.Additional analysis is required to distinguish the contri-butions of each of the above scenarios towards explainingthe discrepancy in observed M Ni for H-poor and H-richcore-collapse SNe. SUMMARY AND CONCLUSIONSIn this paper we measure the Ni masses for a sam-ple of 27 stripped-envelope core-collapse SNe with well-constrained explosion epochs and late-time photometriccoverage by modeling their radioactive tails. We both com-pare these results to Arnett-based M Ni measurements anduse them, in conjunction with the observed rise times andpeak luminosities for the sample, to observationally cali-brate the β parameter in the new analytic light curve modelof Khatami & Kasen (2019). This parameter β allows the in-ternal energy of the ejecta to lag or lead the observed lu-minosity at the time of peak (in contrast to Arnett models),and is hence a function of the ejecta composition, mixing,asymmetry, and total power sources. Here we summarizeour main conclusions. 1. We find Ni masses for measured from the radioac-tive tail of 0.03 M (cid:175) < M Ni < M (cid:175) , with a medianvalue of 0.08 M (cid:175) . Type Ic-BL SNe show higher M Ni on average, with a median value of 0.15 M (cid:175) .2. M Ni values measured via Arnett’s rule are systemat-ically larger than those found from the radioactivetail by a factor of ∼
2. While limitations in Arnett’srule when applied to SESNe had previously been dis-cussed, this discrepancy is approximately a factor of2 larger than that found in recent numerical simula-tions (Dessart et al. 2016).3. Using our observed rise times, peak luminosities,and tail-based M Ni values we find KK19 β valueswhich range from 0.0 < β < β values show signifi-cant spread with a standard deviation of 0.34. Twoobjects exhibit β ≈
0, which may indicate that the ra-dioactive decay of Ni is incapable of powering theirentire peak luminosity.4. Despite the observed scatter, we demonstrate thatusing the model of KK19 with the median values ofour calibrated β (see Table 4) yields significantly im-proved measurements of M Ni in comparison to Ar-nett’s rule when only photospheric data is available.5. When comparing our calibrated β values to those ofinferred from a range numerical light curve models(e.g. Dessart et al. 2016; Ertl et al. 2019), we find thatthe simulations significantly overestimate β , on av-erage. This is primarily due to the observed sampledisplaying dramatically larger ( ∼ M Ni than the numerical mod-els. The observed population also exhibits shorterrise times, on average.6. We investigate a number of physical mechanisms toexplain this observed discrepancy. Effects due tocomposition and the mixing of radioactive elementscan lead to brighter peak luminosities and shorterrise times while the impact of line-of-site variationsdue to explosion asymmetries can lead the observedscatter in β . However, all of these mechanisms havedifficulties explaining systematically low β values forthe entire population.7. Alternatively, we demonstrate that the discrepancywith numerical models can be resolved if an ad-ditional power source contributes between ∼ × –5.5 × ergs − . Both diffusion of shock deposited energy andmagnetar spin-down are capable of providing the re-quired luminosity over appropriate timescales.4 A FSARIARDCHI ET AL .8. Finally, we demonstrate that recently identified dis-crepancy between the observed M Ni distribution ofSESNe and H-rich Type II SNe (Anderson 2019; Meza& Anderson 2020) persists in our sample. The me-dian tail M Ni value of our SESNe is a factor of ∼ M Ni SESN may primarily manifest as rapidly evolv-ing transients as opposed to “traditional” SESN, thatthe close binary fraction increases for higher massstars leading to SESN forming from a distribution ofZAMS masses skewed relative to the IMF, and thatadditional physical effects may impact the M Ni pro-duction in SESNe.ACKNOWLEDGMENTSWe thank Daniel Kasen, Katelyn Breivik, and JenniferHoffman for helpful comments and discussions, TuguldurSukhbold for providing numerical simulation results andSiva Darbha for providing code used to setup the 2D radia-tive transfer models.M.R.D. acknowledges support from the Natural Sci-ences and Engineering Research Council (NSERC) of Canada through a Discovery Grant (RGPIN-2019-06186),the Canada Research Chairs Program, the Canadian Insti-tute for Advanced Research (CIFAR), and the Dunlap Insti-tute at the University of Toronto. This research benefitedfrom interactions made possible by the Gordon on BettyMoore Foundation through grant GBMF5076.D.K.K. is supported by the National Science Founda-tion Graduate Research Fellowship Program. This researchused resources of the National Energy Research ScientificComputing Center, a DOE Office of Science User Facilitysupported by the Office of Science of the U.S. Departmentof Energy under Contract No. DE-AC0205CH11231.D.S.M. was supported in part by a Leading Edge Fundfrom the Canadian Foundation for Innovation (projectNo.30951) and a Discovery Grant (RGPIN-2019-06524)from the Natural Sciences and Engineering ResearchCouncil (NSERC) of Canada.REFERENCES Afsariardchi, N., & Matzner, C. D. 2018, ApJ, 856, 146,doi: 10.3847/1538-4357/aab3d4Afsariardchi, N., Moon, D.-S., Drout, M. R., et al. 2019, ApJ, 881,22, doi: 10.3847/1538-4357/ab2be6Anderson, J. P. 2019, A&A, 628, A7,doi: 10.1051/0004-6361/201935027Anderson, J. P., Habergham, S. M., James, P. A., & Hamuy, M.2012, MNRAS, 424, 1372,doi: 10.1111/j.1365-2966.2012.21324.xAntilogus, P., Gilles, S., Pain, R., et al. 2006, The Astronomer’sTelegram, 854, 1Arnett, W. D. 1980, ApJ, 237, 541, doi: 10.1086/157898—. 1982, ApJ, 253, 785, doi: 10.1086/159681Barnes, J., Duffell, P. C., Liu, Y., et al. 2018, ApJ, 860, 38,doi: 10.3847/1538-4357/aabf84Begelman, M. C., & Sarazin, C. L. 1986, ApJL, 302, L59,doi: 10.1086/184637Bersten, M. C., Folatelli, G., García, F., et al. 2018, Nature, 554,497, doi: 10.1038/nature25151Bianco, F. B., Modjaz, M., Hicken, M., et al. 2014, ApJS, 213, 19,doi: 10.1088/0067-0049/213/2/19Bruch, R. J., Gal-Yam, A., Schulze, S., et al. 2020, arXiv e-prints,arXiv:2008.09986. https://arxiv.org/abs/2008.09986 Cao, Y., Kasliwal, M. M., Arcavi, I., et al. 2013, ApJL, 775, L7,doi: 10.1088/2041-8205/775/1/L7Chevalier, R. A., & Irwin, C. M. 2011, ApJL, 729, L6,doi: 10.1088/2041-8205/729/1/L6Chevalier, R. A., & Soker, N. 1989, ApJ, 341, 867,doi: 10.1086/167545Clocchiatti, A., & Wheeler, J. C. 1997, ApJ, 491, 375,doi: 10.1086/304961Clocchiatti, A., Wheeler, J. C., Benetti, S., & Frueh, M. 1996, ApJ,459, 547, doi: 10.1086/176919Colgate, S. A., & McKee, C. 1969, ApJ, 157, 623,doi: 10.1086/150102Darbha, S., & Kasen, D. 2020, arXiv e-prints, arXiv:2002.00299.https://arxiv.org/abs/2002.00299Dessart, L., & Hillier, D. J. 2010, MNRAS, 405, 2141,doi: 10.1111/j.1365-2966.2010.16611.xDessart, L., Hillier, D. J., Li, C., & Woosley, S. 2012, MNRAS, 424,2139, doi: 10.1111/j.1365-2966.2012.21374.xDessart, L., Hillier, D. J., Woosley, S., et al. 2015, MNRAS, 453,2189, doi: 10.1093/mnras/stv1747—. 2016, MNRAS, 458, 1618, doi: 10.1093/mnras/stw418Dessart, L., Yoon, S.-C., Livne, E., & Waldman, R. 2018, A&A, 612,A61, doi: 10.1051/0004-6361/201732363
ICKELOF S TRIPPED E NVELOPE SN E Dexter, J., & Kasen, D. 2013, ApJ, 772, 30,doi: 10.1088/0004-637X/772/1/30Drout, M. R., Soderberg, A. M., Gal-Yam, A., et al. 2011, ApJ, 741,97, doi: 10.1088/0004-637X/741/2/97Drout, M. R., Soderberg, A. M., Mazzali, P. A., et al. 2013, ApJ, 774,58, doi: 10.1088/0004-637X/774/1/58Drout, M. R., Chornock, R., Soderberg, A. M., et al. 2014, ApJ, 794,23, doi: 10.1088/0004-637X/794/1/23Drout, M. R., Milisavljevic, D., Parrent, J., et al. 2016, ApJ, 821, 57,doi: 10.3847/0004-637X/821/1/57Eldridge, J. J., Fraser, M., Smartt, S. J., Maund, J. R., & Crockett,R. M. 2013, MNRAS, 436, 774, doi: 10.1093/mnras/stt1612Eldridge, J. J., Izzard, R. G., & Tout, C. A. 2008, MNRAS, 384, 1109,doi: 10.1111/j.1365-2966.2007.12738.xEldridge, J. J., & Maund, J. R. 2016, MNRAS, 461, L117,doi: 10.1093/mnrasl/slw099Ertl, T., Woosley, S. E., Sukhbold, T., & Janka, H. T. 2019, arXive-prints, arXiv:1910.01641. https://arxiv.org/abs/1910.01641Filippenko, A. V. 1997, ARA&A, 35, 309,doi: 10.1146/annurev.astro.35.1.309Folatelli, G., Van Dyk, S. D., Kuncarayakti, H., et al. 2016, ApJL,825, L22, doi: 10.3847/2041-8205/825/2/L22Fremling, C., Sollerman, J., Taddia, F., et al. 2016, A&A, 593, A68,doi: 10.1051/0004-6361/201628275Fryer, C. L., & Kalogera, V. 2001, ApJ, 554, 548,doi: 10.1086/321359Fuller, J., & Ro, S. 2018, MNRAS, 476, 1853,doi: 10.1093/mnras/sty369Galama, T. J., Vreeswijk, P. M., van Paradijs, J., et al. 1998, Nature,395, 670, doi: 10.1038/27150Gerke, J. R., Kochanek, C. S., Prieto, J. L., Stanek, K. Z., & Macri,L. M. 2011, ApJ, 743, 176, doi: 10.1088/0004-637X/743/2/176Guillochon, J., Parrent, J., Kelley, L. Z., & Margutti, R. 2017, ApJ,835, 64, doi: 10.3847/1538-4357/835/1/64Hachinger, S., Mazzali, P. A., Taubenberger, S., et al. 2012,MNRAS, 422, 70, doi: 10.1111/j.1365-2966.2012.20464.xHammer, N. J., Janka, H. T., & Müller, E. 2010, ApJ, 714, 1371,doi: 10.1088/0004-637X/714/2/1371Hosseinzadeh, G., Arcavi, I., Valenti, S., et al. 2017, ApJ, 836, 158,doi: 10.3847/1538-4357/836/2/158Hunter, J. D. 2007, Computing in Science and Engineering, 9, 90,doi: 10.1109/MCSE.2007.55Janka, H. T., & Mueller, E. 1996, A&A, 306, 167Joggerst, C. C., Woosley, S. E., & Heger, A. 2009, ApJ, 693, 1780,doi: 10.1088/0004-637X/693/2/1780Jordi, K., Grebel, E. K., & Ammon, K. 2006, A&A, 460, 339,doi: 10.1051/0004-6361:20066082Kasen, D. 2017, Unusual Supernovae and Alternative PowerSources, ed. A. W. Alsabti & P. Murdin, 939,doi: 10.1007/978-3-319-21846-5_32 Kasen, D., Metzger, B. D., & Bildsten, L. 2016, ApJ, 821, 36,doi: 10.3847/0004-637X/821/1/36Kasen, D., Thomas, R. C., & Nugent, P. 2006, ApJ, 651, 366,doi: 10.1086/506190Kasliwal, M. M., Kulkarni, S. R., Gal-Yam, A., et al. 2010, ApJL,723, L98, doi: 10.1088/2041-8205/723/1/L98Katz, B., Kushnir, D., & Dong, S. 2013, arXiv e-prints,arXiv:1301.6766. https://arxiv.org/abs/1301.6766Khatami, D. K., & Kasen, D. N. 2019, ApJ, 878, 56,doi: 10.3847/1538-4357/ab1f09Kim, H.-J., Yoon, S.-C., & Koo, B.-C. 2015, ApJ, 809, 131,doi: 10.1088/0004-637X/809/2/131Kleiser, I., Fuller, J., & Kasen, D. 2018a, MNRAS, 481, L141,doi: 10.1093/mnrasl/sly180Kleiser, I. K. W., Kasen, D., & Duffell, P. C. 2018b, MNRAS, 475,3152, doi: 10.1093/mnras/stx3321Li, W., Leaman, J., Chornock, R., et al. 2011, MNRAS, 412, 1441,doi: 10.1111/j.1365-2966.2011.18160.xLyman, J. D., Bersier, D., & James, P. A. 2014, MNRAS, 437, 3848,doi: 10.1093/mnras/stt2187Lyman, J. D., Bersier, D., James, P. A., et al. 2016, MNRAS, 457,328, doi: 10.1093/mnras/stv2983Margutti, R., Guidorzi, C., Lazzati, D., et al. 2015, ApJ, 805, 159,doi: 10.1088/0004-637X/805/2/159Matzner, C. D., Levin, Y., & Ro, S. 2013, ApJ, 779, 60,doi: 10.1088/0004-637X/779/1/60Maund, J. R. 2018, MNRAS, 476, 2629, doi: 10.1093/mnras/sty093McKenzie, E. H., & Schaefer, B. E. 1999, PASP, 111, 964,doi: 10.1086/316404McQuinn, K. B. W., Skillman, E. D., Dolphin, A. E., Berg, D., &Kennicutt, R. 2016, ApJ, 826, 21,doi: 10.3847/0004-637X/826/1/21—. 2017, AJ, 154, 51, doi: 10.3847/1538-3881/aa7aadMeza, N., & Anderson, J. P. 2020, arXiv e-prints, arXiv:2002.01015.https://arxiv.org/abs/2002.01015Milisavljevic, D., & Fesen, R. A. 2015, Science, 347, 526,doi: 10.1126/science.1261949Modjaz, M., Blondin, S., Kirshner, R. P., et al. 2014, AJ, 147, 99,doi: 10.1088/0004-6256/147/5/99Moe, M., & Di Stefano, R. 2017, ApJS, 230, 15,doi: 10.3847/1538-4365/aa6fb6Moe, M., Kratter, K. M., & Badenes, C. 2019, ApJ, 875, 61,doi: 10.3847/1538-4357/ab0d88Morales-Garoffolo, A., Elias-Rosa, N., Benetti, S., et al. 2014,MNRAS, 445, 1647, doi: 10.1093/mnras/stu1837Moriya, T. J., & Tominaga, N. 2012, ApJ, 747, 118,doi: 10.1088/0004-637X/747/2/118Müller, T., Prieto, J. L., Pejcha, O., & Clocchiatti, A. 2017, ApJ, 841,127, doi: 10.3847/1538-4357/aa72f1
FSARIARDCHI ET AL . Nakar , E., & Sari, R. 2010, ApJ, 725, 904,doi: 10.1088/0004-637X/725/1/904Nicholl, M., Guillochon, J., & Berger, E. 2017, ApJ, 850, 55,doi: 10.3847/1538-4357/aa9334Pandey, S. B., Anupama, G. C., Sagar, R., et al. 2003, MNRAS, 340,375, doi: 10.1046/j.1365-8711.2003.06148.xPastorello, A., Kasliwal, M. M., Crockett, R. M., et al. 2008,MNRAS, 389, 955, doi: 10.1111/j.1365-2966.2008.13618.xPignata, G., Stritzinger, M., Soderberg, A., et al. 2011, ApJ, 728, 14,doi: 10.1088/0004-637X/728/1/14Piro, A. L., & Morozova, V. S. 2014, ApJL, 792, L11,doi: 10.1088/2041-8205/792/1/L11Piro, A. L., & Nakar, E. 2013, ApJ, 769, 67,doi: 10.1088/0004-637X/769/1/67Podsiadlowski, P., Joss, P. C., & Hsu, J. J. L. 1992, ApJ, 391, 246,doi: 10.1086/171341Prentice, S. J., Mazzali, P. A., Pian, E., et al. 2016, MNRAS, 458,2973, doi: 10.1093/mnras/stw299Prentice, S. J., Ashall, C., Mazzali, P. A., et al. 2018, MNRAS, 478,4162, doi: 10.1093/mnras/sty1223Qiu, Y., Li, W., Qiao, Q., & Hu, J. 1999, AJ, 117, 736,doi: 10.1086/300731Quataert, E., & Shiode, J. 2012, MNRAS, 423, L92,doi: 10.1111/j.1745-3933.2012.01264.xRabinak, I., & Waxman, E. 2011, ApJ, 728, 63,doi: 10.1088/0004-637X/728/1/63Richmond, M. W., Treffers, R. R., Filippenko, A. V., & Paik, Y.1996a, AJ, 112, 732, doi: 10.1086/118048Richmond, M. W., Treffers, R. R., Filippenko, A. V., et al. 1994, AJ,107, 1022, doi: 10.1086/116915Richmond, M. W., van Dyk, S. D., Ho, W., et al. 1996b, AJ, 111, 327,doi: 10.1086/117785Riess, A. G., Macri, L. M., Hoffmann, S. L., et al. 2016, ApJ, 826, 56,doi: 10.3847/0004-637X/826/1/56Sahu, D. K., Anupama, G. C., Chakradhari, N. K., et al. 2018,MNRAS, 475, 2591, doi: 10.1093/mnras/stx3212Sahu, D. K., Gurugubelli, U. K., Anupama, G. C., & Nomoto, K.2011, MNRAS, 413, 2583,doi: 10.1111/j.1365-2966.2011.18326.xSahu, D. K., Tanaka, M., Anupama, G. C., Gurugubelli, U. K., &Nomoto, K. 2009, ApJ, 697, 676,doi: 10.1088/0004-637X/697/1/676Sana, H., de Mink, S. E., de Koter, A., et al. 2012, Science, 337, 444,doi: 10.1126/science.1223344Schlafly, E. F., & Finkbeiner, D. P. 2011, ApJ, 737, 103,doi: 10.1088/0004-637X/737/2/103Sharon, A., & Kushnir, D. 2020, arXiv e-prints, arXiv:2004.07244.https://arxiv.org/abs/2004.07244Shivvers, I., Modjaz, M., Zheng, W., et al. 2017, PASP, 129, 054201,doi: 10.1088/1538-3873/aa54a6 Shivvers, I., Filippenko, A. V., Silverman, J. M., et al. 2019,MNRAS, 482, 1545, doi: 10.1093/mnras/sty2719Smartt, S. J., Eldridge, J. J., Crockett, R. M., & Maund, J. R. 2009,MNRAS, 395, 1409, doi: 10.1111/j.1365-2966.2009.14506.xSmith, N. 2014, ARA&A, 52, 487,doi: 10.1146/annurev-astro-081913-040025Smith, N., & Arnett, W. D. 2014, ApJ, 785, 82,doi: 10.1088/0004-637X/785/2/82Smith, N., Li, W., Filippenko, A. V., & Chornock, R. 2011, MNRAS,412, 1522, doi: 10.1111/j.1365-2966.2011.17229.xSmith, N., Mauerhan, J. C., Cenko, S. B., et al. 2015, MNRAS, 449,1876, doi: 10.1093/mnras/stv354Song, H. F., Meynet, G., Maeder, A., et al. 2018, A&A, 609, A3,doi: 10.1051/0004-6361/201731073Sravan, N., Marchant, P., & Kalogera, V. 2019, ApJ, 885, 130,doi: 10.3847/1538-4357/ab4ad7Stritzinger, M. D., Taddia, F., Burns, C. R., et al. 2018, A&A, 609,A135, doi: 10.1051/0004-6361/201730843Sukhbold, T., Ertl, T., Woosley, S. E., Brown, J. M., & Janka, H.-T.2016, ApJ, 821, 38, doi: 10.3847/0004-637X/821/1/38Sutherland, P. G., & Wheeler, J. C. 1984, ApJ, 280, 282,doi: 10.1086/161995Tanaka, M. 2017, Philosophical Transactions of the Royal Societyof London Series A, 375, 20160273, doi: 10.1098/rsta.2016.0273Taubenberger, S., Pastorello, A., Mazzali, P. A., et al. 2006,MNRAS, 371, 1459, doi: 10.1111/j.1365-2966.2006.10776.xTsvetkov, D. Y., Volkov, I. M., Sorokina, E., et al. 2012,Peremennye Zvezdy, 32, 6. https://arxiv.org/abs/1207.2241Utrobin, V. P., Wongwathanarat, A., Janka, H. T., & Müller, E. 2017,ApJ, 846, 37, doi: 10.3847/1538-4357/aa8594Valenti, S., Benetti, S., Cappellaro, E., et al. 2008, MNRAS, 383,1485, doi: 10.1111/j.1365-2966.2007.12647.xValenti, S., Fraser, M., Benetti, S., et al. 2011, MNRAS, 416, 3138,doi: 10.1111/j.1365-2966.2011.19262.xValenti, S., Taubenberger, S., Pastorello, A., et al. 2012, ApJL, 749,L28, doi: 10.1088/2041-8205/749/2/L28Van Dyk, S. D., de Mink, S. E., & Zapartas, E. 2016, ApJ, 818, 75,doi: 10.3847/0004-637X/818/1/75Van Dyk, S. D., Zheng, W., Brink, T. G., et al. 2018, ApJ, 860, 90,doi: 10.3847/1538-4357/aac32cWeaver, T. A., Zimmerman, G. B., & Woosley, S. E. 1978, ApJ, 225,1021, doi: 10.1086/156569Wheeler, J. C., Johnson, V., & Clocchiatti, A. 2015, MNRAS, 450,1295, doi: 10.1093/mnras/stv650Wongwathanarat, A., Müller, E., & Janka, H. T. 2015, A&A, 577,A48, doi: 10.1051/0004-6361/201425025Woosley, S. E. 2019, ApJ, 878, 49, doi: 10.3847/1538-4357/ab1b41Woosley, S. E., & Bloom, J. S. 2006, ARA&A, 44, 507,doi: 10.1146/annurev.astro.43.072103.150558
ICKELOF S TRIPPED E NVELOPE SN E27