A reddening-free method to estimate the $^{56}$Ni mass of Type Ia supernovae

0.5 MB·

by  S. Dhawan

Astronomy&Astrophysicsmanuscriptno.main (cid:13)c ESO2016
January20,2016
A reddening-free method to estimate the 56Ni mass of Type Ia
supernovae
SuhailDhawan1,2,3,B.Leibundgut1,2,J.Spyromilio1,andS.Blondin4
1 EuropeanSouthernObservatory,Karl-Schwarzschild-Strasse2,D-85748GarchingbeiMu¨nchen,Germany
e-mail:[email protected]
2 ExcellenceClusterUniverse,TechnischeUniversita¨tMu¨nchen,Boltzmannstrasse2,D-85748,Garching,Germany
3 PhysikDepartment,TechnischeUniversita¨tMu¨nchen,James-Franck-Strasse1,D-85748GarchingbeiMu¨nchen
4 AixMarseilleUniversite´,CNRS,LAM(Laboratoired’AstrophysiquedeMarseille)UMR7326,13388Marseille,France
Received;accepted
6
1
Abstract
0
2
TheincreaseinthenumberofTypeIasupernovae(SNeIa)hasdemonstratedthatthepopulationshowslargerdiversitythanhasbeen

n assumedinthepast.Thereasons(e.g.parentpopulation,explosionmechanism)forthisdiversityremainlargelyunknown.Wehave
a investigatedasampleofSNeIanear-infraredlightcurvesandhavecorrelatedthephaseofthesecondmaximumwiththebolometric
J peakluminosity.Thepeakbolometricluminosityisrelatedtothetimeofthesecondmaximum(relativetotheBlightcurvemaximum)
9 asfollows:Lmax(1043ergs−1)=(0.039±0.004)×t2(J)(days)+(0.013±0.106).
1 56NimassescanbederivedfromthepeakluminositybasedonArnett’srule,whichstatesthattheluminosityatmaximumisequal
to instantaneous energy generated by the nickel decay. We check this assumption against recent radiative-transfer calculations of

] Chandrasekhar-massdelayeddetonationmodelsandfindthisassumptionisvalidtowithin10%inrecentradiative-transfercalcula-
R tionsofChandrasekhar-massdelayeddetonationmodels.
S TheLmax vs.t2 relationisappliedtoasampleof40additionalSNeIawithsignificantreddening(E(B−V) >0.1mag)anda
. reddening-freebolometricluminosityfunctionofSNeIaisestablished.Themethodistestedwiththe56Nimassmeasurementfrom
h thedirectobservationofγ−raysintheheavilyabsorbedSN2014Jandfoundtobefullyconsistent.
p Super-Chandrasekhar-massexplosions,inparticularSN2007if,donotfollowtherelationsbetweenpeakluminosityandsecondIR
- maximum.Thismaypointtoanadditionalenergysourcecontributingatmaximumlight.
o
TheluminosityfunctionofSNeIaisconstructedandisshowntobeasymmetricwithatailoflow-luminosityobjectsandarather
r
t sharphigh-luminositycutoff,althoughitmightbeinfluencedbyselectioneffects.
s
a Keywords.supernovae:general–supernovae:individual:2014J,2006X,2007if
[

1
v 1. Introduction al.2013;Patatetal.2015).Duetointerstellardustacorrection
4 forreddeningintheMilkyWayandthehostgalaxyneedstobe
7 Type Ia supernovae (SNeIa) exhibit diverse observable proper- applied.Ourgoalistoestablisharelationbetweenthebolomet-
8 ties.Inadditiontothespectralandcolourdifferences,thepeak ricpeakluminosityandthe56Nimassindependentofreddening.
4 luminosity of SNeIa range over several factors (e.g. Suntzeff
The Near Infrared (NIR) light curve morphology of SNeIa
0 1996, 2003; Li et al. 2011). The amount of 56Ni, derived
. is markedly different from that in the optical. In particular, the
1 fromthebolometricluminosity,(Contardo,Leibundgut&Vacca
lightcurvesstarttorebrightenabout2weeksafterthefirstmaxi-
0 2000) and the total ejecta mass (Stritzinger et al. 2006; Scalzo
mum,resultinginasecondpeak.Recentstudies(e.g.Biscardiet
6 etal.2014)alsoshowawidedispersion.TheM distribution
56Ni al.2012;Dhawanetal.2015)foundthatmoreluminousSNeIa
1 providesinsightintothepossibleprogenitorchannelsandexplo-
reach the second maximum in NIR filters at a later phase. This
:
v sionmechanismsforSNeIa(seeHillebrandt&Niemeyer2000; waspredictedbyKasen(2006)whoalsoindicatedthatthephase
Xi Livio2000;Truran,Glasner,&Kim2012). of the second maximum (designated in the following as t2 and
Theuncertaintyinthereddeningcorrectiondirectlyimpacts measured relative to the B-band light curve maximum) should
ar the ability to derive accurate bolometric luminosities and 56Ni beafunctionofthe56Nimassintheexplosion.Weexpectthat
massesderivedfromthepeakluminosity.Thetotaltoselective thephaseofthesecondNIRmaximumcanbeusedtodetermine
absorption (RV) appears systematically and significantly lower bolometricpeakluminosityLmax andtheamountof56Nisyn-
intheSNhoststhanthecanonicalMilkyWayRV valueof3.1. thesizedintheexplosion.
Nobili & Goobar (2008) use a large sample of nearby SNeIa
In the following, we investigate the link between the peak
to derive an average R which is significantly lower than 3.1.
V bolometricluminosity(L )andthephaseofthesecondmax-
max
Takingintoaccountspectroscopicfeaturesthatcorrelatewithlu-
imum in the NIR light curves (t ). We use a sample of nearby
2
minosity,Chotardetal.(2011)foundanR of2.8±0.3which
V SNeIawithlowhost-galaxyextinction(describedinSection2)
is consistent with the Milky Way value. However, objects with
todetermineL andthenemploydifferentmethodstoderive
max
highextinctionareseentohaveanunusuallylowR (Phillipset
V M (Section3).ThisrelationcanthenbeusedtoderiveL
56Ni max
and M for all SNeIa with a measured t , since the timing
56Ni 2
Sendoffprintrequeststo:S.Dhawan parameter is free of reddening corrections and allows us to in-
1
S.Dhawanetal.:NickelmassinSNeIa
We add to this sample objects from the literature. We only in-
cluded SNeIa with observations near maximum from U to H
filters. The full description of the selected SNeIa can be found
inDhawanetal.(2015).
The sample of low-reddening SNeIa is defined to circum-
1.6 Y
vent the uncertainties of host galaxy extinction. The 18 objects
1.4 arepresentedinTable1.WeuseE(B−V)hostvaluesfromthe
literature. Only objects with E(B − V) < 0.1 mag were
1.2 host
included.Sinceweconsideronlyobjects,whichdisplaythesec-
1.0 ond maximum in their NIR light curves this implies that most
low-luminositySNeIa,especiallySN1991bg-likeobjectswere
0.8
excluded.
0.6 At maximum light the UV-optical-IR integrated luminosity
represents >90% of the true bolometric luminosity (Blondin,
Dessart,&Hillier2015).WeconstructedUBVRIJH bolomet-
1)1.6 J riclightcurvesforobjectswithsufficientphotometrynearmax-
−
s1.4 imumlightintheopticalandtheNIR.TheK filterdatawasex-
g
r cludedsinceonlyfewSNIahavewell-sampledK lightcurves.
e1.2 We calculated the fraction of the flux emitted in K for a few
3
401.0 well-observed SNe Ia with sufficient data and determined it to
1 bearound1−3%oftheUVOIRluminosityatmaximum.The
(x0.8 exclusionoftheK-fluxresultsinonlyaminoruncertaintyinthe
a
m0.6 finalUVOIRluminosity.
L
Priortothederivationofabolometricfluxforthelowextinc-
tionsample(seeTable3)weapplyacorrectionforthemeasured
1.6 H extinctionfollowingCardelli,Clayton&Mathis(1989).Theas-
sumeddistancesandtheirreferencescanbefoundinTable1.
1.4
1.2
3. Results
1.0
0.8 Based on our previous work (Dhawan et al. 2015), where we
foundstrongcorrelationsbetweenvariousderivedparametersof
0.6 SNeIa with t in the Y and J filters, we argued that the bolo-
2
metric maximum luminosity should also correlate with t . The
2
10 15 20 25 30 35 40 sample of low-reddening SNeIa described in Section 2 is used
t (days) toestablishtherelationbetweent andL .Thet parameter
2 2 max 2
hastheadvantagethatisisessentiallyindependentofreddening
anddistance(relativetothecalibrationsample).Withsuchare-
Figure1.ThebolometricmaximumluminosityL isplotted lationwewillbeinapositiontoderivetheluminosityfunction
max
againstthephaseofthesecondmaximumt inYJH filterlight ofSNeIaatmaximum.
2
curves. A strong correlation is observed in Y and J, whereas
a weaker correlation is seen in the H band. Best fit lines are
3.1. CorrelationbetweenL andt
overplottedinblack.Thefitincludeserrorsonbothaxes. max 2
Figure 1displaysastrongcorrelationbetweent fortheY andJ
2
filterlightcurvesandthebolometric(UVOIR)luminosityL
max
cludeheavilyreddenedobjects.Wecheckourderivationagainst (determinedbyfittingasplineinterpolationtotheUVOIRlight
independentmeasurementsofM56NiwiththenearbySN2014J curve) with Pearson coefficients r = 0.88 and r = 0.86, re-
inM82andSN2006X(Section4).Withthereddeningindepen- spectivelyforthelow-reddeningsample.Amuchweakertrend
dentmethodwecanestablishtheluminosityfunctionofSNeIa isobservedintheH filterlightcurvewithr≈0.60.
at maximum and also derive the distribution of nickel masses
The slope of the L vs. t relation appears to flatten for
max 2
amongSNIaexplosions(Section5).Wefinishbydiscussingthe objects with t (cid:38) 27d. This is most prominent in the Y band.
2
implications of this determination of the M distribution in
56Ni However,wewouldrequirealargersampletoconfirmthistrend
theconclusions(Section6).
amongstthemostluminousobjects.
Wefitasimplelinearrelationtothedata
2. Data
L =a ·t +b (1)
max i 2,i i
Our SNIa sample is constrained to objects, which have NIR
observations at late times (t > 50 days after B maximum) whichleadstotheentriesinTable 2(forYJH filters).Thecor-
with well-sampled optical and NIR light curves to construct respondingfitsareshowninFigure1.Wecompareourobserved
a (pseudo-)bolometric light curve and measure t . The main valuestotheL andt fromtheDDCmodelsofBlondinetal.
2 max 2
source of near-infrared photometry of SNeIa is the Carnegie (2013). Model spectra and light curves published in Blondin et
Supernova Project (CSP; Contreras et al. 2010; Burns et al. al.(2013)basedondelayeddetonationexplosionsshowsimilar
2011; Stritzinger et al. 2011; Phillips 2012; Burns et al. 2014). correlationstothosedescribedherein.
2
S.Dhawanetal.:NickelmassinSNeIa
Table1.ThesampleofSNeIawithlowreddeningE(B−V) < 0.1.ThereferencesfortheSNeIaarepresentedalongwith
host
theextinctionvaluesandthedistancesemployedforcalculationofthe(pseudo-)bolometricluminosityatmaximum.
SN µ E(B−V) E(B−V) Reference t (Y) t (J) t (H) L
host MW 2 2 2 max
(d) (d) (d) (1043erg/s)
SN2002dj 32.93±0.30 0.096±0.030 0.010±0.003 P08 ... 31.1±1.8 23.0±0.9 1.25±0.26
SN2002fk 32.59±0.15 0.009±0.044 0.035±0.003 C14 ... 29.5±0.2 25.8±0.3 1.42±0.23
SN2005M 35.01±0.09 0.060±0.021 0.027±0.002 B14 28.9±3.8 30.9±0.7 ... 1.19±0.20
SN2005am 32.85±0.20 0.053±0.017 0.043±0.002 B14 21.7±0.1 21.3±0.7 19.7±0.7 1.10±0.20
SN2005el 34.04±0.14 0.015±0.012 0.098±0.001 B14 25.0±0.1 24.6±0.6 24.3±0.7 1.01±0.11
SN2005eq 35.46±0.07 0.044±0.024 0.063±0.003 B14 37.5±0.1 35.0±0.7 25.1±0.1 1.32±0.20
SN2005hc 36.50±0.05 0.049±0.019 0.028±0.001 B14 37.5±0.1 36.5±2.5 ... 1.36±0.30
SN2005iq 35.80±0.15 0.040±0.015 0.019±0.001 B14 27.7±0.1 24.2±0.7 25.0±0.1 1.07±0.21
SN2005ki 34.73±0.10 0.016±0.013 0.027±0.001 B14 26.8±0.1 25.2±1.7 20.5±1.7 1.03±0.27
SN2006bh 33.28±0.20 0.037±0.013 0.023±0.001 B14 25.0±0.3 22.9±0.3 21.0±0.6 0.86±0.15
SN2007bd 35.73±0.07 0.058±0.022 0.029±0.001 B14 28.3±0.1 ... ... 1.22±0.13
SN2007on 31.45±0.08 <0.007 0.010±0.001 B14 18.7±0.4 18.2±0.1 14.1±1.4 0.60±0.09
SN2008R 33.73±0.16 0.009±0.013 0.062±0.001 B14 15.5±0.7 14.1±0.7 ... 0.53±0.10
SN2008bc 34.16±0.13 <0.019 0.225±0.004 B14 32.9±0.3 33.3±0.2 31.0±1.4 1.24±0.19
SN2008gp 35.79±0.06 0.098±0.022 0.104±0.005 B14 33.5±1.2 35.7±0.8 34.4±0.7 1.29±0.14
SN2008hv 33.84±0.15 0.074±0.023 0.028±0.001 B14 25.0±0.3 24.7±0.3 21.9±0.5 1.08±0.16
SN2008ia 34.96±0.09 0.066±0.016 0.195±0.005 B14 24.0±0.7 25.6±0.2 19.2±0.9 1.13±0.14
SN2011fe 28.91±0.20 0.014±0.010 0.021±0.001 P13 ... 30.0±0.8 24.3±0.6 1.10±0.15
E(B-V)references:P08:Pignataetal.(2008);C14:Cartieretal.(2014)B14:Burnsetal.(2014);P13:Patatetal.(2013)
Table 2. Values of the coefficients for correlations between tion between explosions (Branch 1992; Khokhlov, Mueller, &
L andt intheindividualfilters Hoeflich 1993). These early papers found rather large ranges
max 2
with 0.75 < α < 1.4 depending on the exact explosion model
and the amount of assumed mixing Branch (1992); Khokhlov,
Filter ai bi Mueller,&Hoeflich(1993).MorerecentlyBlondinetal.(2013)
Y 0.041±0.005 −0.065±0.122 foundarangeofαwithin10%of1fordelayeddetonationmod-
J 0.039±0.004 0.013±0.106
els.Thesemodelsarenotapplicableforlow-luminositySNeIa.
H 0.032±0.008 0.282±0.174
Should α systematically depend on explosion characteristics
thenthederivednickelmassesmaysufferfromasystematicdrift
notcapturedinourtreatment.Theseuncertaintiesmustbetaken
intoaccountfortheinterpretationofthederived56Nimass.
Intheinterestofacleanlowextinctionsample,wehavere-
moved7objectswithE(B−V) <0.1buttotalE(B−V)≥
host
3.2.1. Arnett’srulewithindividualrisetimes
0.1. Interestingly, several of the excluded objects are amongst
themostluminousSNeIainthesample.Evenaftertheremoval Arnett’srulestatesthattheluminosityoftheSNatpeakisgiven
of these 7 objects we do not derive a significant correlation for bytheinstantaneousrateofenergydepositionfromradioactive
theH bandlightcurvesfromoursample.Itwillhavetobeseen, decays inside the expanding ejecta (Arnett 1982; Arnett et al.
whether future data will reveal a correlation or whether the H 1985).
light curves are not as sensitive to the nickel mass as the other Thisissummarizedas(Stritzingeretal.2006):
NIRfilters.Therelationsareidenticalforthefullandrestricted
sample within the uncertainties listed in Table 2. We combine L (t )=αE (t ), (2)
max R 56Ni R
therelationsfromthetwobandsforextrapolatingthevaluesof
Lmaxinthefollowinganalysis.WeassumetheY bandestimate where E56Ni is the rate of energy input from 56Ni and 56Co
tobeequivalenttothevalueintheJ bandandcalculatetheslope decaysatmaximum,tR istherisetimetobolometricmaximum
andinterceptwiththephotometryofbothfilters,whichleadsto and α accounts for deviations from Arnett’s Rule. The energy
improvedstatistics. outputfrom1M(cid:12)of56Niis(α=1):
3.2. DerivingM56Ni fromLmax (cid:15)Ni(tR,1M(cid:12))=(6.45·1043e−tR/8.8+1.45·1043e−tR/111.3)ergs−1
(3)
WepresentthreedifferentmethodstoderiveM fromL ,
56Ni max Weusetherelationforestimatesusingdifferentrisetimesin
namelyusingArnett’srulewithanindividualrisetimeforeach
theBfilterforeachSNfollowing,
SN Ia, using Arnett’s rule with an assumed constant rise time
applied to all SNe Ia and by calculating Lmax from delayed tR,B =17.5−5·(∆m15−1.1) (4)
detonation models with different M yields (Blondin et al.
56Ni
2013). Arnett’s rule states that at maximum light the bolomet- fromScalzoetal.(2014)whichcoversthet –∆m param-
R,B 15
ricluminosityequalstheinstantaneousrateofenergyinputfrom eter space of Ganeshalingam, Li, & Filippenko (2011). Like
theradioactivedecays.Anydeviationsfromthisassumptionare Scalzo et al. (2014) we apply a conservative uncertainty esti-
encapsulated in a parameter α below. It is quite possible that mate of ±2 days. The bolometric maximum occurs on average
αdependsontheexplosionmechanismandshowssomevaria- 1daybeforeB (Scalzoetal.2014).
max
3
S.Dhawanetal.:NickelmassinSNeIa
Table 3. M measurements for low reddening SNe Ia. The components of the error from L and rise time are given along
56Ni max
withthetotalerror.
SN M −Arn err(L ) err(risetime) M −Arn(fixedrise) err(L ) err(risetime) M −DDC
Ni max Ni max Ni
(M(cid:12)) (M(cid:12)) (M(cid:12)) (M(cid:12)) (M(cid:12)) (M(cid:12)) (M(cid:12))
SN2002dj 0.59±0.16 0.12 0.10 0.63±0.16 0.13 0.10 0.61±0.13
SN2002fk 0.68±0.16 0.11 0.12 0.71±0.17 0.12 0.12 0.76±0.13
SN2005M 0.59±0.14 0.10 0.10 0.60±0.14 0.10 0.10 0.59±0.11
SN2005am 0.47±0.13 0.08 0.10 0.55±0.14 0.10 0.10 0.52±0.11
SN2005el 0.45±0.10 0.05 0.09 0.51±0.11 0.06 0.09 0.48±0.07
SN2005eq 0.67±0.15 0.10 0.11 0.66±0.15 0.10 0.11 0.67±0.11
SN2005hc 0.69±0.19 0.15 0.12 0.68±0.19 0.15 0.12 0.71±0.16
SN2005iq 0.48±0.13 0.09 0.09 0.54±0.14 0.11 0.09 0.51±0.10
SN2005ki 0.45±0.14 0.11 0.09 0.51±0.17 0.14 0.09 0.49±0.14
SN2006bh 0.37±0.10 0.06 0.08 0.43±0.11 0.08 0.07 0.40±0.07
SN2007bd 0.55±0.13 0.06 0.11 0.61±0.12 0.07 0.10 0.59±0.10
SN2007on 0.23±0.06 0.03 0.05 0.30±0.07 0.05 0.05 0.28±0.05
SN2008R 0.20±0.06 0.04 0.05 0.27±0.07 0.05 0.05 0.25±0.06
SN2008bc 0.60±0.14 0.09 0.11 0.62±0.15 0.10 0.11 0.63±0.11
SN2008gp 0.62±0.13 0.06 0.11 0.65±0.11 0.07 0.09 0.64±0.09
SN2008hv 0.48±0.11 0.07 0.09 0.54±0.12 0.08 0.09 0.52±0.09
SN2008ia 0.50±0.12 0.06 0.10 0.57±0.11 0.07 0.09 0.55±0.09
SN2011fe 0.50±0.12 0.07 0.10 0.55±0.12 0.08 0.09 0.52±0.10
3.2.2. Arnett’srulewithafixedrisetime
Originally M was determined from L for a fixed rise
56Ni max
time of 19 days for all SNe Ia (Stritzinger et al. 2006). Similar 9 var
totheseanalyseswepropagateanuncertaintyof±3daystoac-
countforthediversityintherisetimes. 6
Thepeakluminositythenbecomes(Stritzingeretal.2006)
L =(2.0±0.3)·1043(M /M )ergs−1. (5) 3
max 56Ni (cid:12)
Asdescribedabove,weassumedα=1(seeStritzingeretal. 0
2006;Mazzalietal.2007),whichistheanalyticalapproximation 9 fixed
ofArnett(1982).FortheDDCmodelsofBlondinetal.(2013)
αiswithin10%of1forallbuttheleastluminousmodel. N6
S
N
3.2.3. Interpolatingusingdelayeddetonationmodels 3
WeinterpolatetherelationbetweenL (inagivenfilterset,u
max
0
→Hinthiscase)andM foundfromagridofChandrasekhar
56Ni 9 DDC
massdelayeddetonationmodelsofBlondinetal.(2013)tode-
rivea56Nimassfromtheobservedpeakluminosityforthesam-
plepresentedinTable1.Theresulting56Nimassestimatesare 6
presented in the bottom panel of Figure 2. For all but the least
luminousofthesemodels,αiswithin10%of1(Blondinetal. 3
2013).
0
M
56Ni
3.3. Comparisonofdifferentmethods
InFigure2,weplotthedistributionsoftheM ,inferredfor
56Ni
thelow-reddeningsample,fromthedifferentmethods. Figure2.Thehistogramsshowthedifferentmethodstoestimate
Similar to previous studies we find that there is a large dis- theM56Ni fromtheLmax.ThevaluesfoundfromArnett’srule
tributionintheM valuesforthesampleinTable1.Wenote with fixed and individual rise times are plotted in the top and
56Ni
a over a factor of 2 difference between the lowest and highest middle panels. The bottom panel displays the values estimated
M56Ni values(afactorof∼3forthevariablerisetimeformal- by usingthe relation between Lmax and M56Ni found fromthe
ism).Unlikepreviousstudies,thissampledoesn’tincludefaint, DDCmodels.
91bg-like objects, since their NIR light curves do not display a
secondmaximum.Theseobjectsarefoundtohaveamuchlower
M ∼0.1M (Stritzingeretal.2006;Scalzoetal.2014)from higher and lower masses. A further difference can be seen in
56Ni (cid:12)
their peak luminosities. There is clearly a majority of objects Fig.2wherethemassdistributionbetweenthecaseofindivid-
withnickelmassesbetween0.4and0.7M withextensionsto ual and the fixed rise times is slightly different due to the fact
(cid:12)
4
S.Dhawanetal.:NickelmassinSNeIa
that observed rise times often are shorter than the assumed 19 relation of the second maximum in the NIR light curves is en-
days. couraging.
The individual errors clearly dominate over the differences As a second case, we determine the bolometric peak lu-
between the methods and the results are not influenced by the minosity L and the nickel mass M based on t to
max 56Ni 2
chosenmethod.Thereappearsasmallsystematicoffsetbetween the heavily extinguished SN 2006X. Wang et al. (2008) de-
the 56Ni masses derived from DDC models and the ones with rived a peak luminosity for this SN from multi-band photom-
Arnett’s rule and fixed rise time. The 56Ni masses from the etry and a correction for dust absorption in the host galaxy.
DDC models are about 0.05 M smaller, however, well within TheydeterminedabolometricpeakluminosityforSN2006Xof
(cid:12)
the overall uncertainties, which are typically around 0.15 M (1.02±0.1)·1043ergs−1,whichcompareswellwithourmea-
(cid:12)
(Tab.3). surementof(1.14±0.16)·1043ergs−1.Wangetal.(2008)de-
For SN2011fe Pereira et al. (2013) report a rise time of terminedM56Ni =0.50±0.05M(cid:12),whichshouldbecompared
16.58days. Using this rise time, we obtain an M56Ni of 0.49 to M56Ni = 0.57 ± 0.11 M(cid:12) found from t2 using the fixed
M(cid:12) whichisa0.06M(cid:12) shiftfromthevalueusinga19drise. rise time formalism. The measured rise time for SN 2006X is
Thisshiftissmallerthantheuncertaintyonthe56Nimass.For tR(B)=18.2±0.9d,whichleadstoM56Ni =0.55±0.10M(cid:12).
the low-reddening sample we note that the average difference Table5presentsseveraladditionalhighlyreddenedSNeIa,
betweenthefixedriseandvariableriseformalismsis0.04M . which had a previous determination of the nickel mass. The
(cid:12)
Forthefollowinganalysis,wecalculatetheM56Ni usingt2. M56Ni fortheseobjectswerecalculatedinthesamewayasfor
BysubstitutingtherelationderivedbetweenL andt (equa- SN2014JandSN2006X.
max 2
tion(1)andequation(3)),weobtain FromTable 5,wecanseethat1986Ghasalowervalueof
M than the other heavily reddened objects. This is consis-
56Ni
M a ·t (i)+b tent with the observed optical decline rate and lower B band
56Ni = i 2 i . (6) luminosity (Phillips et al. 1987). Using nebular spectra, Ruiz-
M α·(cid:15) (t ,M )
(cid:12) Ni R (cid:12) Lapuente&Lucy(1992)calculatetheM forSN1986Gand
56Ni
Wemostlywillusethefixedrisetimeformalisminthefol- findavalueof0.38±0.03M(cid:12).Thisisfullyconsistentwiththe
estimatefromt .
lowinganalysis,althoughinspecialcases,wewillalsomakeuse 2
Scalzo et al. (2014) give M for SN 2005el and
ofthemoreaccuratelyknownrisetime. 56Ni
SN 2011fe. The comparison for SN 2011fe shows M =
56Ni
0.52±0.15M(cid:12)fromtheNIRlightcurves,whereasScalzoetal.
4. Test with well observed SNe Ia (2014)findM56Ni =0.42±0.08M(cid:12).Thedifferenceismostly
intheadoptedvalueofα,1.2inScalzoetal.(2014)comparedto
DustinthehostgalaxyandtheMilkyWaymakesthedetermina- 1inthisstudy.RescalingthevaluefromScalzoetal.(2014)to
tionofthepeakluminosityuncertain.ManynearbySNeIahave α=1,weobtainM56Ni=0.50±0.08M(cid:12),whichisfullyconsis-
shownmarkeddeviationsinthehostgalaxydustpropertiesfrom tentwithourvalue.Pereiraetal.(2013)reportnickelmassesfor
thoseobservedintheMilkyWaymostlyfavouringasmallerR SN2011fefordifferentvaluesofα.Theirnickelmassforα=1
V
value (Goobar 2008; Phillips et al. 2013). The extinction cor- isM56Ni = 0.53±0.11M(cid:12) ,nearlyidenticaltoourdetermi-
rectionsarenotoriouslyuncertainanddirectlyaffectourability nation. For SN 2005el, Scalzo et al. (2014) obtain an M of
56Ni
to measure peak bolometric luminosities of SNe Ia. Since t is 0.52±0.12M .Scaledtoanα = 1,thisgivesM =0.62.
2 (cid:12) 56Ni
independentofreddening,wecanusethederivedcorrelationto WefindM =0.51±0.11M ,whichisbroadlyconsistent
56Ni (cid:12)
determine the peak luminosity and estimate the 56Ni mass for withthevaluefoundinScalzoetal.(2014).
heavilyreddenedSNeIa. FromthecomparisonsinTable 5,weconcludethatthereis
WetestthisrelationonSN2014J,whichhasadirectγ−ray good agreement between our values and those published in the
detection from the 56Ni → 56Co decay chain (Churazov et al. literature. For SN 2001el we see that the error in the estimate
2014; Diehl et al. 2015). Using the best fit relation for the from t2 is substantially smaller than from the bolometric light
reddening-freesample,weobtainM =0.64±0.15M for curve.
56Ni (cid:12)
at = 31.99±1.15daysandarisetimeof19days.Sincethe One significant outlier is SN2007if. This was presented as
2
error on the rise time is taken as ±3 days, we expect the error asuper-Chandrasekhar-massexplosion(Scalzoetal.2010)with
onM todecreasewithalessconservativeerrorestimateon atotalluminosityof3.2·1043 ergs−1.Thereddeningfromthe
56Ni
t .Goobaretal.(2015)usedPalomarTransientFactory(PTF) host galaxy is somewhat unclear. There is no indication of Na
R
andKilodegreeExtremelyLittleTelescope(KELT)datatomea- foreground absorption, while the colour evolution and the Lira
sure the rise time of SN 2014J. They find t = 17.25 days. lawwouldindicatesomereddening.Anyreddeningwouldonly
R
Weplaceaconservativeerrorestimateof1dayandevaluatethe increase the luminosity and the derived nickel mass based on
M56Ni =0.60±0.10M(cid:12)whichhasalowererrorbarthanfrom Arnett’srule.TheM56Ni estimatefromt2 forSN2007ifissig-
thefixedrisetimeformalism. nificantly lower than the mass estimate through the bolometric
The direct measurement of M for SN 2014J through peak luminosity by Scalzo et al. (2010). If we recalculate the
56Ni
theγ−raydetectiongivesanindependentandfairlysecureesti- M56Ni fromthebolometriclightcurvepresumingnoextinction
mateofthenickelmass.Churazovetal.(2014)derive56Ni = fromthehostgalaxy,weobtainM56Ni =1.6M(cid:12).Thisisafac-
0.62±0.13M .Diehletal.(2015)findaslightlylowermassof torof∼2largerthanourestimate.Wediscussthissupernovain
(cid:12)
M =0.56±0.10M . Section6.
56Ni (cid:12)
Adetailedcomparisonofthederived56Nimassesisgivenin
Table4.Thedifficultyoftheextinctioncorrectionandtheadvan-
5. The luminosity function of SNe Ia at maximum
tageofthemethodpresentedhereareobvious.Theuncertainty
in the γ−ray determination is due to the weakness of the sig- We are now in a position to derive L for all SNe Ia with a
max
nalandleadstoslightlydifferentinterpretations.Theverygood reliably measured t (as given in Tables 1 and 6) and establish
2
correspondencebetweenthedirectM measurementandour thebolometricluminosityfunctionofSNeIaatmaximumlight.
56Ni
5
S.Dhawanetal.:NickelmassinSNeIa
Table 4. Comparison of different methods to estimate M for SN 2014J. All measurements assume a distance modulus of
56Ni
27.64±0.10.
M (inferred) σ Method Reference
Ni
0.62 0.13 γraylines Churazovetal.(2014)
0.56 0.10 γraylines Diehletal.(2015)
0.37 ... BolometriclightcurveA =1.7mag Churazovetal.(2014);Marguttietal.(2014)
V
0.77 ... BolometriclightcurveA =2.5mag Churazovetal.(2014);Goobaretal.(2014a)
V
0.64 0.13 NIRsecondmaximum thiswork(combinedfit)
0.60 0.10 NIRsecondmaximum+measuredrise thiswork
Table5.M estimatesforobjectswithhighvaluesofE(B−V) .Comparisonwithindependentestimatesfromtheliterature
56Ni host
aregivenwhereavailable.
SN t M (inferred) M (Lit.Val.) PercentDifference Referencea
2 56Ni 56Ni
(d) (M(cid:12)) (M(cid:12))
SN1986G 16.4±1.4 0.33±0.08 0.38±0.03 15.15 RL92
SN1998bu 29.9±0.4 0.58±0.12 0.57 1.7 S06b
SN1999ac 27.0±2.0 0.53±0.12 0.67±0.29 26.4 S06a
SN2001el 31.2±0.7 0.62±0.12 0.40±0.38 33.8 S06a
SN2002bo 28.9±0.7 0.56±0.12 0.52 7.1 St05
SN2003cg 30.2±1.5 0.59±0.13 0.53 10.1 ER06
SN2003hv 22.3±0.1 0.43±0.11 0.40±0.11 6.9 L09
SN2006X 28.2±0.5 0.57±0.11 0.50±0.05 12.2 W08
SN2007if 32.3±0.8 0.65±0.16 1.6±0.1 158.3 S10
a ThereferencesfortheM measurementsareRL92:Ruiz-Lapuente&Lucy(1992),S06a:Stritzingeretal.(2006),S06b:Stritzingeretal.
56Ni
(2006),St05:Stehleetal.(2005),ER06:Elias-Rosaetal.(2006),L09:Leloudasetal.(2009),W08:Wangetal.(2008),S10:Scalzoetal.(2010)
Forobjectsinthelow-reddeningsample,weusetheL deter- 6. Discussion and Conclusion
max
minedfromt andthebest-fitlinearrelation(greenhistogramin
2
Figure 3).Sincethephaseofthesecondmaximuminthenear Using the relation derived from the low-reddening sample we
infrared is independent from the reddening we can derive the extrapolateanL valuefor58SNeIaobjectshavingamea-
max
reddening-freedistributionoftheluminosityfunctionofSNeIa suredt .Theestimateoft ,alongwiththisrelation,providesa
2 2
(Fig. 3). We show here the histogram of 58 SNe Ia as derived method to deduce the bolometric peak luminosity, independent
fromtheY andJ lightcurves.Theluminosityscaleisbasedon of a reddening estimate, distance measurement (relative to the
thecalibrationsampleoflow-reddeningobjects(Section3). calibrationofourlow-absorptionsample)andwithoutrequiring
multi-bandphotometry.Wehencehaveestablishedareddening-
freeluminosityfunctionofSNeIaatpeak(Fig.3).
The luminosity function of SNe Ia is clearly not symmet-
ric. The luminosity range spans slightly over a factor of 2. We We established an intrinsic luminosity function and 56Ni
findnoobviousdifferencebetweenthefullsampleandthelow- massdistributionforallSNeIawithat measurement(Tab.5).
2
reddening sample used to calibrate the relation between t2 and The distribution of Lmax has a standard deviation of 0.2 ·1043
Lmax.Ifanythingthecalibrationsamplehasaflatterdistribution ergs−1 andM56Ni hasastandarddeviationof0.11M(cid:12).Scalzo
withmostSNearound0.9·1043 ergs−1,whilethefullsample et al. (2014) find a similar distribution of M with a σ of
56Ni
includes more luminous objects. This could be an effect of the 0.16M .WetestourmethodonSN2014J,aheavilyreddened
(cid:12)
magnitudelimitofthesearches.Theexactbiasesinoursample SN Ia in the nearby galaxy M82 and find good agreement be-
aredifficulttodefineasitisnotvolumelimited. tween the estimates from the γ−ray observations (Churazov et
al.2014;Diehletal.2015,seeTable4).Faint,91bg-likeSNeIa,
Thebolometricluminosityfunctioncanbecomparedtothe whichshowtypicallylowerluminosities(Filippenkoetal.1992;
R filter luminosity function derived by Li et al. (2011) based Leibundgut et al. 1993), do not display a second maximum in
on 74 SNe Ia including the low-luminosity objects missing in theirNIRlightcurvesandarenotinoursample.Therefore,the
our sample. The Li et al. (2011) magnitude-limited luminosity true dispersion, in peak luminosity and M56Ni, for SN Ia will
function(theirFig.10)peaksatanabsolutemagnitudeof≈−19 likelybelargerthanwhatisderivedhere.Stritzingeretal.(2006)
withafewobjectsabove−19.5andatailtofainterobjectsdown findadispersionofafactorof∼10,sincetheirsampleincluded
to−17.Thisisalsoreflectedinourluminosityfunction(Fig.3), peculiarSNeIalikeSN1991bgandSN1991T.
whereweobserveaclearpeakatL =1.3·1043ergs−1with
max Our reddening-free estimate of the M can be compared
56Ni
some more luminous objects and a tail to fainter objects. The to independent 56Ni mass estimates, e.g. from the late-time (≥
rangeisalsocomparabletotheonefoundbyLietal.(2011).
200d)pseudo-bolometriclightcurve.Itshouldalsobepossible
todeterminetheamountofradiationemittedoutsidetheUVOIR
In the next step we derive the distribution of M for all region of the spectrum at late phases and a bolometric correc-
56Ni
SNeIawithsufficientinfraredlightcurvedatausingequation6 tion (e.g. Leloudas et al. 2009). There are very few objects for
andafixedrisetimeandα = 1.Table6andFig.3presentthe which both NIR data to measure t and nebular phase pseudo-
2
SNIanickelmassfunction. bolometricobservationsarepresent,makingaquantitativecom-
6
S.Dhawanetal.:NickelmassinSNeIa
Table 6. M and L measurements for the
M 56Ni max
56Ni completesampleofobjectswitht2measurements
0.3 0.4 0.5 0.6 0.7
21 LFouwll -SRaemddpelening SN M56(NMi(cid:12)) σ L(m10a4x3erg/σs)
1980N 0.42 0.10 0.84 0.21
1981B 0.63 0.13 1.26 0.21
1986G 0.33 0.07 0.66 0.18
18 1998bu 0.58 0.12 1.16 0.20
1999ac 0.53 0.12 1.05 0.20
1999ee 0.68 0.15 1.36 0.21
2000E 0.62 0.14 1.24 0.22
15 2000bh 0.65 0.14 1.30 0.22
2001bt 0.55 0.12 1.10 0.20
2001cn 0.58 0.13 1.19 0.20
2001cz 0.67 0.14 1.33 0.22
2001el 0.61 0.13 1.22 0.21
12
N 2002bo 0.56 0.11 1.12 0.21
NS 2003cg 0.64 0.13 1.19 0.22
2003hv 0.43 0.10 0.84 0.17
2004ey 0.57 0.14 1.14 0.20
9
2004gs 0.43 0.11 0.85 0.18
2004gu 0.71 0.17 1.42 0.23
2005A 0.56 0.13 1.12 0.18
2005al 0.49 0.13 0.97 0.21
6 2005na 0.64 0.15 1.28 0.22
2006D 0.49 0.13 0.98 0.19
2006X 0.57 0.11 1.13 0.19
2006ax 0.62 0.15 1.24 0.21
3 2006et 0.64 0.16 1.27 0.22
2006gt 0.39 0.09 0.77 0.18
2006hb 0.41 0.11 0.81 0.19
2006kf 0.47 0.12 0.94 0.19
2007S 0.71 0.16 1.41 0.22
0
0.6 0.8 1.0 1.2 1.4 2007af 0.57 0.14 1.16 0.20
L (1043ergs 1) 2007as 0.47 0.14 0.94 0.25
max −
2007bc 0.55 0.14 1.09 0.20
2007bm 0.54 0.13 1.08 0.20
Figure3.HistogramdistributionofL derivedfromtherela-
max 2007ca 0.66 0.16 1.29 0.22
tionsforthefullsampleofobjects.Green:EstimatesofLmaxfor 2007if 0.65 0.16 1.30 0.22
thelow-reddening,calibrationsample.Yellow:Estimatesforall 2007jg 0.53 0.14 1.06 0.20
objectswithat measurementinthefullsample.Theaxislabels 2007le 0.61 0.15 1.21 0.20
2
ontopcorrespondtotheM estimate.Weusethecombined 2007nq 0.46 0.13 0.92 0.20
56Ni
fittoobtainthefinalvalues. 2008C 0.63 0.16 1.26 0.23
. 2008fp 0.62 0.13 1.24 0.21
2014J 0.64 0.13 1.28 0.22
parison for a sample of objects extremely difficult. Thus, we
stronglyencouragemorelate-timeobservationsofSNIa.
TheobservedL andM distributionsdirectlyconnect servationsforSNewitharangeofpeakluminosities.Theyfinda
max 56Ni
tothephysicaloriginofthediversityamongstSNeIa.Apossi- verygoodagreementoftheirmodelswithphotometricandspec-
ble explanation is the difference in the explosion mechanism. troscopic observations at maximum. The range of M pro-
56Ni
Pure detonations of M WDs (Arnett 1969) were seen to be ducedbytheirmodelscorrespondswellwiththeobservationsin
ch
unfeasiblesincetheyburntheentirestartoirongroupelements Figure3,makingthesemodelsastrongcandidatetoexplainthe
anddonotproducetheintermediatemasselements(IMEs)ob- observeddiversity.
servedinSNIaspectra.Puredeflagrations(e.g.Travaglioetal. M explosion models can possibly account for the ob-
Ch
2004)canreproduceobservedpropertiesofSNewithM ≤ serveddistributioninM .Recentstudies(e.g.vanKerkwijk,
56Ni 56Ni
0.4M . Deflagration models however, cannot account for SNe Chang, & Justham 2010) on the other hand posit sub-
(cid:12)
withhigherM andhence,cannotexplaintheentiredistribu- Chandrasekhar mass explosions as a progenitor scenario for
56Ni
tioninFigure3. SNe Ia (for e.g., see Woosley & Weaver 1994). This sce-
Delayed-detonation models (e.g. Khokhlov 1991; Woosley nario is attractive since it can account for the progenitor statis-
1990)aremoresuccessfulinproducinghigherM .Inthisex- tics from population synthesis (see Livio 2000; Ruiter et al.
56Ni
plosionmodelasubsonicdeflagrationexpandsthewhitedwarf 2013).Moreover,studieslikeStritzingeretal.(2006)andScalzo
to create low densities for IMEs to be produced in a super- et al. (2014) find a significant fraction of SNe Ia to have
sonic detonation phase which is triggered at a deflagration-to- M < 1.4M , providing observational evidence for the sub-
ej (cid:12)
detonationtransitiondensity(ρ ). M progenitor scenario. We compare the luminosity function
tr Ch
Recent1DstudiesbyBlondinetal.(2013)confrontasuiteof in Figure 3 to the one obtained by Ruiter et al. (2013), using
Chandrasekharmass(M )delayeddetonationmodelswithob- theirviolentmergermodels.Theypresentarelationbetweenpri-
Ch
7
S.Dhawanetal.:NickelmassinSNeIa
mary white dwarf mass (MWD) and peak brightness for a grid ofS.B.toGarching.WewouldliketothankRahmanAmanullahforproviding
of sub-M models. For objects in the lowest two bins of our publishedphotometryofSN2014Jinthenearinfrared.
Ch
luminositydistribution,theM correspondsto1to1.1 .For
WD (cid:12)
thehighestluminosityobjects,themodelsindicateanM of
WD
References
1.28M . Thus, the luminosity function corresponds to a range
(cid:12)
of sub-Chandrasekhar MWD, which provides further evidence ArnettW.D.,1969,Ap&SS,5,180
fortheplausibilityofsub-M explosionsasaprogenitorsce- ArnettW.D.,1982,ApJ,253,785
Ch
nario. The 56Ni mass distribution (Fig. 3) is comparable to the ArnettW.D.,BranchD.,WheelerJ.C.,1985,Nature,314,337
BiscardiI.,etal.,2012,A&A,537,A57
yields from the models of Sim et al. (2010). Our L and
max BlondinS.,DessartL.,HillierD.J.,KhokhlovA.M.,2013,MNRAS,429,2127
M distributionsdonotallowustodistinguishwhichexplo-
56Ni BlondinS.,DessartL.,HillierD.J.,2015,MNRAS,448,2766
sionmechanismisresponsiblefortheobservedvariety. BranchD.,1992,ApJ,392,35
We note that our sample includes one peculiar, super- BurnsC.R.,etal.,2011,AJ,141,19
M event, SN 2007if (Scalzo et al. 2010), with an estimated BurnsC.R.,etal.,2014,ApJ,789,32
Ch CardelliJ.A.,ClaytonG.C.,MathisJ.S.,1989,ApJ,345,245
M56Ni = 0.65±0.16M(cid:12) usingourtechnique.Thisissignifi- CartierR.,etal.,2014,ApJ,789,89
cantly lower than the value estimated in Scalzo et al. (2010) of ChotardN.,etal.,2011,A&A,529,L4
1.6±0.1M .Thet estimateforthisobjectisnotexceptionally ChurazovE.,etal.,2014,Nature,512,406
(cid:12) 2
high,indicatingasubstantialbutnotexceptionalamountof56Ni ChurazovE.,etal.,2015,ApJ,812,62
ContardoG.,LeibundgutB.,VaccaW.D.,2000,A&A,359,876
(similar to 91T-like SNe). One of the possible reasons for this
ContrerasC.,etal.,2010,AJ,139,519
discrepancycouldbethatthepeakluminosityisnotjustaprod-
DadoS.,Dar,A.,2015,ApJ,809,32
uct of 56Ni decay. This idea has been entertained in theoretical Dhawan S., Leibundgut B., Spyromilio J., Maguire K., 2015, MNRAS, 448,
modelsforthesesuper-M SNIa.Themodelsadvocateasce- 1345
Ch
narioofejectainteractionwithcircumstellarmaterial(CSM;see DiehlR.,etal.,2015,A&A,574,A72
Elias-RosaN.,etal.,2006,MNRAS,369,1880
Hachingeretal.2012;Dado&Dar2015).Thereisalsoanindi-
FilippenkoA.V.,etal.,1992,AJ,104,1543
cationofashellinteractioninthissupernova(Scalzoetal.2010) FriedmanA.S.,etal.,2015,ApJS,220,9
and if this interaction results in increased peak luminosity then GaneshalingamM.,LiW.,FilippenkoA.V.,2011,MNRAS,416,2607
the 56Ni mass through Arnett’s rulewould be overestimated. It GoobarA.,2008,ApJ,686,L103
GoobarA.,etal.,2014,ApJ,784,L12
could well be that additional energy is emitted in these super-
GoobarA.,etal.,2015,ApJ,799,106
M objects. A significant, but not extreme, amount of 56Ni
Ch HachingerS.,MazzaliP.A.,TaubenbergerS.,FinkM.,PakmorR.,Hillebrandt
producedintheexplosionalongwithinteractionwiththeCSM W.,SeitenzahlI.R.,2012,MNRAS,427,2057
couldthenexplaintheobservedproperties,e.g.lowerejectave- HillebrandtW.,NiemeyerJ.C.,2000,ARA&A,38,191
locities(∼9000kms−1)andhighpeakluminosity.InHachinger KasenD.,2006,ApJ,649,939
KhokhlovA.M.,1991,A&A,245,114
etal.(2012),thelowerlimitonM56Niis∼0.6M(cid:12)whichagrees KhokhlovA.,MuellerE.,Ho¨flichP.,1993,A&A,270,223
wellwithourestimate. LeibundgutB.,etal.,1993,AJ,105,301
The literature for such super-M objects with NIR light LeloudasG.,etal.,2009,A&A,505,265
Ch
curves is still limited. Using the data in Taubenberger et al. LiW.,etal.,2011,MNRAS,412,1441
Livio M., 2000, in: Type Ia Supernovae, Theory and Cosmology, ed. J. C.
(2011)forSN2009dc,weobtainat (J)of31.7±6.2 dwhich
2 Niemeyer&J.W.Truran,Cambridge:CambridgeUniversityPress,33
corresponds to an M of 0.65 ± 0.18M . Taubenberger et
56Ni (cid:12) MarguttiR.,ParrentJ.,KambleA.,SoderbergA.M.,FoleyR.J.,Milisavljevic
al.(2013)alsoargueforlessextremeM56Nibasedonlatephase D.,DroutM.R.,KirshnerR.,2014,ApJ,790,52
photometry and spectroscopy, although they prefer a compara- MazzaliP.A.,Ro¨pkeF.K.,BenettiS.,HillebrandtW.,2007,Science,315,825
tivelyhigherM (∼1M )thanourinferredvalue.Onepos- NadyozhinD.K.,1994,ApJS,92,527
56Ni (cid:12) NobiliS.,GoobarA.,2008,A&A,487,19
sible reason could be that the high ejecta densities lead to an
PatatF.,etal.,2013,A&A,549,A62
earlier onset of the recombination wave than expected for nor- PatatF.,etal.,2015,A&A,577,A53
malIa’sandhenceanearliert thanisexpectedforagiven56Ni PereiraR.,etal.,2013,A&A,554,A27
2
mass. This would lead to an inference of lower M from t PhillipsM.M.,2012,PASA,29,434
56Ni 2
PhillipsM.M.,etal.,1987,PASP,99,592
forsuper-M SNe.
Ch PhillipsM.M.,etal.,2013,ApJ,779,38
If we assume that the inferred 56Ni mass from t indi-
2 PignataG.,etal.,2008,MNRAS,388,971
cate the core 56Ni for all SNeIa the peak luminosity of super– RuiterA.J.,etal.,2013,MNRAS,429,1425
M SNeIa would be boosted by an additional energy source, Ruiz-LapuenteP.,LucyL.B.,1992,ApJ,400,127
Ch
like shell interaction within the explosion. A good indicator ScalzoR.A.,etal.,2010,ApJ,713,1073
ScalzoR.,etal.,2014,MNRAS,440,1498
couldbethelatebolometricdeclinephaseandluminosity.This
SimS.A.,Ro¨pkeF.K.,HillebrandtW.,KromerM.,PakmorR.,FinkM.,Ruiter
comparison would be much closer to the 56Ni determitation of A.J.,SeitenzahlI.R.,2010,ApJ,714,L52
thesecondpeakthanthepeakbolometricluminosity. StehleM.,MazzaliP.A.,BenettiS.,HillebrandtW.,2005,MNRAS,360,1231
Larger samples of well-observed SNe (e.g. Friedman et al. StritzingerM.,LeibundgutB.,WalchS.,ContardoG.,2006,A&A,450,241
StritzingerM.,MazzaliP.A.,SollermanJ.,BenettiS.,2006,A&A,460,793
2015)willhelpinimprovingthestatisticsofsuchastudy.Future
StritzingerM.D.,etal.,2011,AJ,142,156
investigationswithadetailedcomparisonbetweenobservations
Suntzeff N. B., 1996, in: Supernovae and supernova remnants, ed. Richard
andasuiteofsub-MCh detonationmodelswillhelpshedmore McCray&ZhenruWang,Cambridge:CambridgeUniversityPress,41
light on the nature of the progenitor scenario and explosion Suntzeff,N.B.2003,in:FromTwilighttoHighlight,ThePhysicsofSupernovae,
mechanismofSNIa.Moreover,futuretheoreticalstudiesofpe- ed.W.Hillebrandt&B.Leibundgut,Heidelberg:Springer,183
TaubenbergerS.,etal.,2011,MNRAS,412,2735
culiar, super-M SNe will help in deciphering the nature of
Ch TaubenbergerS.,etal.,2013,MNRAS,432,3117
theseextremeexplosions. TravaglioC.,HillebrandtW.,ReineckeM.,ThielemannF.-K.,2004,A&A,425,
1029
Acknowledgements. This research was supported by the DFG Cluster of TruranJ.W.,GlasnerA.S.,KimY.,2012,JPhCS,337,012040
ExcellenceOriginandStructureoftheUniverse’.B.L.acknowledgessupportfor vanKerkwijkM.H.,ChangP.,JusthamS.,2010,ApJ,722,L157
thisworkbytheDeutscheForschungsgemeinschaftthroughTRR33,TheDark WangX.,etal.,2008,ApJ,675,626
Universe.WeallaregratefultotheESOVisitorProgrammetosupportthevisit WoosleyS.E.,1990,BAAS,22,1221
8
S.Dhawanetal.:NickelmassinSNeIa
WoosleyS.E.,WeaverT.A.,1994,ApJ,423,371
9