Spectral modelling of the "Super-Chandra" Type Ia SN 2009dc - testing a 2 M_sun white dwarf explosion model and alternatives

0.97 MB·English

by  Stephan Hachinger

Mon.Not.R.Astron.Soc. (2012) (MNLATEXstylefilev2.2)
Spectral modelling of the “Super-Chandra” Type Ia SN 2009dc –
testing a 2 M white dwarf explosion model and alternatives
⊙
Stephan Hachinger1,2, Paolo A. Mazzali1,2, Stefan Taubenberger2, Michael Fink3,2
Ru¨diger Pakmor4,2, Wolfgang Hillebrandt2, Ivo R. Seitenzahl3,2
2
1 1IstitutoNazionalediAstrofisica-OAPd,vicolodell’Osservatorio5,35122Padova,Italy
0 2Max-Planck-Institutfu¨rAstrophysik,Karl-Schwarzschild-Str.1,85748Garching,Germany
2 3Universita¨tWu¨rzburg,Emil-Fischer-Str.31,97074Wu¨rzburg,Germany
4HeidelbergInstituteforTheoreticalStudies,Schloss-Wolfsbrunnenweg35,69118Heidelberg,Germany
p
e
S
arXivv1,2012Sep06.Thedefinitiveversionwillbeavailableatwww.blackwell-synergy.com.
6

]
R ABSTRACT
Extremely luminous, “super-Chandrasekhar” (SC) Type Ia Supernovae (SNe Ia) are as yet
S
an unexplainedphenomenon.We analyse a well-observed SN of this class, SN 2009dc, by
.
h modelling its photospheric spectra with a spectral synthesis code, using the technique of
p “Abundance Tomography”.We present spectral models based on different density profiles,
- correspondingtodifferentexplosionscenarios,anddiscusstheirconsistency.First,weusea
o
r densitystructureofasimulatedexplosionofa2M⊙rotatingC-Owhitedwarf,whichisoften
t proposed as a possibility to explain SC SNe Ia. Then, we test a density profile empirically
s
a inferredfromthe evolutionof line velocities(blueshifts).This modelmay be interpretedas
[ a core-collapse SN with an ejecta mass of ∼3M . Finally, we calculate spectra assuming
⊙
an“interactionscenario”.Insuchascenario,SN2009dcwouldbeastandardWDexplosion
1
withanormalintrinsicluminosity,andthisluminositywouldbeaugmentedbyinteractionof
v
9 the ejecta with a H-/He-poorcircumstellar medium.We find that noneof the models tested
3 easilyexplainsSN2009dc.Withthe2M⊙WDmodel,ourabundanceanalysispredictssmall
3 amountsof burningproductsin the intermediate-/high-velocitypartof the ejecta (v&9000
1 kms−1).However,intheoriginalexplosionsimulations,wherethenuclearenergyreleaseper
. unitmass is large,burnedmaterialis presentat highvelocities. Thiscontradictioncan only
9
0 beresolvedifasymmetriesstronglyaffecttheradiativetransferorifC-Owhitedwarfswith
2 massessignificantlyabove2M⊙exist.Inacore-collapsescenario,lowvelocitiesofFe-group
1 elementsareexpected,buttheabundancestratificationinSN2009dcseems“SNIa-like”.The
: interaction-basedmodellookspromising,andwehavesomespeculationsonpossibleprogen-
v
itor configurations. However, radiation-hydrodynamicssimulations will be needed to judge
i
X whetherthisscenarioisrealisticatall.
r Keywords: supernovae:individual(SN2009dc)–supernovae:general–techniques:spec-
a
troscopic–radiativetransfer
1 INTRODUCTION dependently of distance. Empirical calibration procedures exploit
this,allowingfortheconstructionofaccurateSNHubblediagrams.
TypeIasupernovae(SNeIa)aresubjecttovigorousresearchow- The fact that SNe Ia constitute a relatively homogeneous
ingtotheirrelevancetodifferentfieldsofastrophysics.Theirpro- SN subclass is usually explained by the homogeneity of their
duction via different paths of binary evolution is investigated in progenitor systems, which are supposedly carbon-oxygen white
detail (e.g. Ruiteretal. 2009; Claeysetal. 2010; Podsiadlowski dwarfs (WDs) in binary systems. In the “classical” single-
2010),asistheirimpactongalaxies(e.g. Scannapiecoetal.2008; degenerate Chandrasekhar-mass scenario, one WD explodes af-
Tangetal. 2009). Most prominently they are used today in cos- ter having accreted matter from a companion star. A thermonu-
mological studies (e.g. Perlmutteretal. 1997; Riessetal. 1998; clear runaway occurs when the WD is close to the stability
Perlmutteretal.1999;Astieretal.2006;Wood-Vaseyetal.2007) limit(Hillebrandt&Niemeyer2000),i.e.itsChandrasekhar mass
tomeasureluminositydistances.SNeIashowdifferencesintheir (MCh,non-rot∼1.4M⊙ withoutrotation).Numericalsimulationsof
intrinsicluminosity.Observationshave,however,shownthatthelu- such explosions have been successful in explaining the “leading-
minosityofeachobjectcanbeestimatedfromitslightcurveshape order” homogeneity in the observations, and also part of the di-
(e.g. Phillips 1993; Phillipsetal. 1999), which is measurable in- versityamongtheobjects(Mazzalietal.2007;Kasenetal.2009).
©2012TheAuthors.Journalcompilation©2012RAS
2 Hachingeret al.
ThemostimportantvariationinthepropertiesofSNeIaiscaused Hachingeretal.2009)fromdatatakeninthephotosphericphase,
byadifferentefficiencyinproducing56Ni,whichpowerstheop- whenthecoreoftheejectaisopaquetoopticalradiation.Assuming
tical light curve through the radioactive decays 56Ni → 56Co → differentdensityprofilesandrisetimes,weinferabest-matching
56Fe. abundance structure,respectively, byfittingtheobservations with
Despite the success of standard explosion models, peculiar synthetic spectra. Comparing models based on different assump-
SNe Ia, discovered in increasing numbers (e.g. Filippenkoetal. tions, we assess the applicability of different explosion scenarios
1992; Phillipsetal. 1992; Lietal. 2003; Howelletal. 2006), are byjudgingthefitqualityandthephysicalconsistencyofthemod-
difficult to explain thus far. Meanwhile, the precision of cosmo- els.
logical studies based on SNe Ia has significantly increased. In Below (Sec. 2), we first give a relatively extended overview
this situation, we have to clarify what mechanisms can produce ofourmethodology asitisrelevanttothepresentwork.Wethen
SNe Ia in order to avoid errors in SN cosmology which could showatomographymodelbasedonadensityprofilerepresenting
be caused by populations of peculiar SNe (cf. e.g. Foleyetal. theexplosionofa2.0M⊙rotatingwhitedwarf,andanothermodel
2010). Within the “classical” single-degenerate Chandrasekhar- basedonanempiricallyconstructed 3.0M⊙ densityprofile(Sec-
mass scenario, there is the possibility of having an “supermas- tions3and4).Finally,wepresentathirdtomographyexperiment
sive”whitedwarfasprogenitor,whichisstabilisedbyrotation(e.g. with a more speculative set-up: we model the spectra assuming
Steinmetzetal. 1992; Yoon&Langer 2005; Howelletal. 2006; thattheSNisaChandrasekhar-massexplosion(ofanon-rotating
Pfannesetal. 2010a; Fink 2010; Hachisuetal. 2012, Fink et al. WD)where some light is“externally” generated through interac-
2012 in prep.). Also other explosion scenarios are re-considered tionoftheejectawithasurroundingmedium(Sec.5).Wediscuss
toproduce peculiar and even normal SNeIa–most prominently, allourmodelsintermsofconsistencyandtheoreticalinterpretation
thedouble-degenerate/WD-merger scenario(Pakmoretal.2010a) (Sec.6)beforeweconclude(Sec.7).
andthesingle-degeneratesub-Chandrasekhar scenario(Finketal.
2007,2010;Simetal.2010),whereaHeshellaroundtheWDdet-
onatesandtriggerstheexplosionofthestar.Furthermore,thereare
relativelynew,somewhat“exotic”SNIamodels(e.g.Bravoetal. 2 METHODANDDATA
2009).
2.1 Radiative-transfercode
On the observational side, one prominent SN Ia subclass
waiting to be explained are the “super-Chandrasekhar mass” ob- We use a 1-D stationary Monte-Carlo radiative-transfer code
jects [SC SNe Ia – Howelletal. (2006); Hickenetal. (2007); (Abbott&Lucy1985,Mazzali&Lucy1993,Lucy1999,Mazzali
Scalzoetal. (2010), and references below; the designation refers 2000andStehleetal.2005)tocalculatesyntheticSNspectrafrom
totheChandrasekharmassfornon-rotatingWDs].Theearly-time agivendensityandabundanceprofile.
spectraoftheseSNeresemblethoseofotherSNeIawhiletheirlu- The code computes the radiative transfer from an assumed
minosityisabouttwicetheaverage(Howelletal.2006).According photospherethroughtheSNejectaatagivenepoch.Aninitialden-
toArnett’srule(Arnett1982),56NimassesofmorethanaChan- sityprofileisusedtocalculatethedensitieswithintheejecta,as-
drasekhar massarerequiredtoexplaintheluminosityofsomeof suming homologous, force-free expansion. This expansion phase
theseobjects.Aluminositypredictionfromthelight-curveshape, commencesshortlyafterexplosioninmostSNmodels[e.g.Ro¨pke
usingtherelationofPhillipsetal.(1999),failsatleastforsomeSC (2005);cf.however Sec.5.1],sothat r=v×t holdsforeach
SNe(Taubenbergeretal.2011).Possibly,partoftheluminosityof particleatalltimesrelevanttothisworkingoodapproximation(r:
SC SNe comes from energy sources other than 56Ni decay, such distancefromthecentre,t:timefromexplosion,v:velocityatthe
asinteraction of theejectawith circumstellar material. Themore onsetofhomologousexpansion).Radiusandvelocitycanthenbe
conventionalparadigm,however,isthatSCSNeIaaremoremas- usedinterchangeablyasspatialcoordinates.
sivethannormalobjects(possiblytheresultofarotatingprogenitor Fromthephotosphere, whichislocatedat anadjustablev ,
ph
WD), and produce more 56Ni than a Chandrasekhar-mass explo- continuousblackbodyradiation[I+=B (T ),whereI+ isthe
ν ν ph ν
sioncoulddo(Howelletal.2006).Inanycase,in-depthanalyses specific intensity in outward directions, and B (T ) the specific
ν ph
ofobservationswithradiativetransfermodelsareneededtobetter intensity according to the Planck law at temperature T ] is as-
ph
understandSCobjects. sumedtobeemittedintotheatmosphere.Notabledeviationsfrom
In this work, we study the recent SC SN 2009dc, which thisapproximationtothefluxintheinnerlayersappearinthered
reached a peak M ∼ −20 and exploded in a tidal bridge be- andinfrared,whereadiscrepancyinthefluxlevelofsyntheticto
bol
tweentwogalaxies(UGC10063/64,typesS0/SBd).Observations observedspectrathereforeissometimesunavoidable.
withanextraordinarilygoodtimecoverageareavailableforthisSN The photon packets simulated undergo Thomson scattering
(Yamanakaetal. 2009; Tanakaetal. 2010; Silvermanetal. 2011; and interactions with lines, which are treated in the Sobolev ap-
Taubenbergeretal.2011).Atmaximumlight,SN2009dchasspec- proximation. A downward branching scheme ensures a good ap-
tralpropertiessimilartoSN2003fg(Howelletal.2006),andthere- proximationtothebound-boundemissivity.Radiativeequilibrium
fore is representative at least for part of the SC objects. Other isenforcedbyconstruction(Lucy1999)oftheMonte-Carlosimu-
SC SNe are different to some degree. For example, SN 2007if lation.Theexcitationandionisationstateofthematteriscalculated
(Scalzoetal. 2010) shows higher-temperature spectra and some- fromtheradiationfieldstatisticsusingamodifiednebularapprox-
whathigherlinevelocities(asalsoSN2006gz,Hickenetal.2007). imation(Mazzali&Lucy1993;Mazzali2000).Inthisapproxima-
Thereasonsfor thisdiversity areunclear, asisthetheoreticalin- tion,thegasstateineachradialgridcellismostlydeterminedfrom
terpretationofSCSNe.Weusearadiative-transfercodetomodel aradiationtemperatureT andadilutionfactorW.T corresponds
R R
theobserved spectraofSN2009dc, inferringejectadensitiesand tothemeanfrequencyoftheradiationfieldandW parametrisesits
abundances. The method we employ (Abundance Tomography, energydensity(forgivenT ).Weiterateexcitation,ionisationand
R
Stehleetal.2005)hasproved suitableforinferringtheproperties theradiationfieldinturnuntiltheT valueswithintheatmosphere
R
ofquitediverseSNe(e.g.Tanakaetal.2011,Mazzalietal.2008, areconvergedtotheper centlevel.Withintheseiterations,T is
ph
©2012TheAuthors.Journalcompilation©2012RAS,MNRAS
Spectroscopicanalysisof SN2009dc 3
automatically adjusted in order to match a given bolometric out- thefreedomtheseconstraintsgiveus(roughly±1000kms−1),we
putluminosityL .Thus,thephotospheric luminosityisadapted choosev suchthatweobtainanoptimumfit.
bol ph
so as to compensate for reabsorption of radiation, which occurs During the fitting process, we assess and take into account
whenpacketsre-enterthephotosphere.Afterthetemperatureitera- additional effectsof L and v onthestrength of spectral lines
bol ph
tions,theemergentspectrumiscalculatedbyformalintegrationof viatheplasmastate.Alowerv tendstomaketheradiationfield
ph
thetransferequation(Lucy1999),usingasourcefunctionderived bluer at least in parts of the atmosphere (cf. above). This results
fromtheMonteCarlostatistics. inhigher radiation temperatures and an increased ionisation (and
occupationofexcitedlevels).AhigherluminosityL makesthe
bol
radiationfieldstrongerandbluer,withthesameresult.
2.2 Spectralmodels
To summarize, a “SN model” from which our code calculates a
syntheticspectrumisspecifiedbythedensityprofile,theabundance
2.2.3 Timet–sensitivityofthemodelontherisetime
stratification,theluminosityL ,thephotosphericvelocityv and
bol ph
thetimefromexplosiont. Thetimefromexplosiontmustbedeterminedfromtherespective
Spectral modelling means adjusting thismodel toobtain the observational epoch [usually given relative to B-band maximum
bestpossiblematchofsyntheticandobservedspectrum;themodel (B max.)]andtheassumed1 risetimetr,inwhichtheSNrisesto
parameters will then represent the SN properties. Usually, a spe- Bmax.afterexplosion.
cificdensityprofileandrisetimeisassumedbeforestartingtofit When the density distribution in velocity space is kept con-
thespectra. Below, webriefly discuss how thevarious remaining stant2, and tr is changed, the spectrum shows an overall shift of
parametersinfluencetheradiativetransferandthespectra,andwe linevelocities(meanblueshifts)forthefollowingreasons:
describeourgeneralstrategyforfittingtheobservations,including
• Modelswithasmallert(smallert)usuallyhavephotospheres
thetomographytechnique. r
athigherv .Withthemorecompactejecta,thehigherv is
ph ph
necessaryinordertoavoidexcessivebackscatteringandatoo
2.2.1 Abundancesandtheirimprintonthespectrum bluespectrumoftheoutgoingradiationatthelowerboundary
(whenahighluminosityisemittedfromasmallphotosphere).
Thepart oftheabundance structurerelevant fortheSNspectrum Thehigherv thenleadstosomeincreaseoflinevelocities.
ph
varieswiththeepoch(seealsoSec.2.2.5).Foreachmodel,onlythe
• The ejecta are more compact for a smaller t , since
abundancesabovethephotosphere(i.e.atv>v )arerelevant. r
ph
r=v×t, where t is the sum of t and the epoch (relative
The abundances of intermediate-mass elements (IME, e.g. r
toB maximum).Therefore,forasmallert theenergyden-
Mg,Si,S,Ca)normallyinfluencethestrengthofindividualspectral r
sityoftheradiationfieldinsidetheejectatendstobelargerat
features.Incontrast,mostFe-groupelementsdonotleavedistinct
anygivenvelocityv(withL keptconstant).Thezonewhere
featuresintheopticalspectra.Theyratherinfluencethespectrum bol
ionisationislowenoughforlineformation(i.e.triply-andes-
bymodulatingthelineblockingintheUVandbya“transfer”of
pecially doubly-ionised species dominate) will be located at
fluxtothered[viabranching,seeMazzali(2000)].Thelineblock-
higherv.Thisthenreflectsinhigherlinevelocities.
ing effect has the consequence of backwarming within the atmo-
sphere(steepeningofthetemperatureprofile),exertinganindirect
Whenreducingt belowrealisticvalues,lineformationwould
influence on line strengths of all elements via the ionisation and r
havetooccurintheoutermostzonesoftheejecta.Thelowdensities
excitationstateoftheplasma. Thisstateisnot fixedbyinput pa-
(andthestrongionisationduetothelowdensities)inthesezones
rametersinourapproach,butisdeterminedsuchthatitisconsistent
howeverdisfavourtheformationofprominentfeaturessuchasSiII
withtheradiationfield.
λ6355. As a result, the spectra of an observed object can not be
explainediftoolowarisetimeisassumed.
2.2.2 InfluenceofL andv
bol ph
L istheparametercontrollingthefluxlevelinthesyntheticspec-
bol
trum.Foreachepoch,itisadaptedduringthefittingprocesssoas 2.2.4 Fittingobservedspectra
to match the overall flux in the optical part of the observed (and
Theprocessofspectralfittingbeginswithchoosingadensitypro-
flux-calibrated) spectrum. Therefore, it is easily constrained to a
fileandarisetime,whichsubsequentlyremainunchanged.Wethen
reasonableprecision.
iteratively determine optimum values of those abundances which
Thephotosphericvelocityvph hasvarious,morecomplicated influencefeaturesontheonehand,andparametersthatcontrolthe
effectsonthemodel.First,itsetsalowerlimittotheradiiatwhich
temperaturestructureandthelinevelocitiesontheother.Wetryto
lineabsorptioncanoccurinthesimulation.Second,itdetermines
matchthespectralfeaturesaswellastheoverallflux,butifthisis
theintegratedopticaldepthoftheatmosphere,whichshouldbeap-
not possible simultaneously, we prefer a better fit tothe lines. In
propriate(τ & 23 intherelevantwavelengthrange)eveniftheno- the present case, we sometimes allow the synthetic spectra to be
tionofasharpphotosphereemittingablackbodyisquiteapproxi-
tooredifotherwisethemodelatmosphereswouldbecometoohot.
mativeinTypeISNe(Saueretal.2006).Foroursimulations,itis
important thatthephotosphere isassumeddeepenough suchthat
theassumptionofablack-bodylikeemissionatthatdepthissatis-
fiedaswellaspossible.Averylowvph,however,generallyleads 1 Therisetimetrcanonlytosomedegreebeconstrainedfromtheavailable
toaveryblueradiationfieldatthelowerboundary,astheemitting earlylightcurvedata[cf.Taubenbergeretal.(2011)andSec.2.4].
surfaceshrinks.Whenthisisnotfullycompensatedbyattenuation 2 Here,wemeanthatthetime-invariant densitydistribution dm(v), i.e.
dv
above thephotosphere, the model spectrum will be bluer. Within theexplosionmodel,iskeptconstant.
©2012TheAuthors.Journalcompilation©2012RAS,MNRAS
4 Hachingeret al.
2.2.5 AbundanceTomography 2.4 ObservationsofSN2009dc
The method of Abundance Tomography (Stehleetal. 2005) ex- We analyse the luminosity-calibrated spectra of SN 2009dc of
tendstheapproachoffittingonespectrum(Mazzali&Lucy1993). Taubenbergeretal. (2011). This data set samples SN 2009dc ex-
ItaimsatinferringtheabundanceprofileofaSNstepbystepfrom tremelywellfrom9.4dbeforeB maximumtolatetimes.Wedo
theoutertotheinnerlayers(assumingadensitystructureandarise notmodelspectralaterthan36.4dpastBmaximum.Atthisepoch
time).Tothisend,onefitsatimeseriesofphotosphericspectra,in –lateforaSNIa–thephotosphererecedesdeepintothe56Ni-rich
whichdifferentlayersoftheejectaleavetheirimprint.Inthepho- zoneandourassumptionofradiativeequilibriuminthesimulated
tospheric phase, some core of the ejecta is optically thick at UV atmosphereeventuallybreaksdown.
andoptical wavelengths. Aspectrum isthenonlysensitive tothe Asthespectraonlyshow aslowevolutionoflinevelocities,
optically thin part of the ejecta. As time progresses, a larger and weexpectaverymoderatephotosphericrecessionforallourmod-
largerfractionoftheejectabecomesvisible.Therefore,laterspec- els(whichisconfirmedbyouractualcalculations).Thishasanim-
traaresensitivetomorecentrallayers, whiletheinfluence ofthe pact on the tomography method: if the abundance zone between
outerlayersonthemissmaller. two subsequent photospheres is too thin, the zone has little in-
Inordertocreateamodelfortheoutermostejectaofanob- fluenceon thespectrum, whichimpliesalargeuncertainty inthe
ject,wefittheearliestspectrumavailable.Thephotosphericveloc- abundancedetermination.Inordertoavoidthis,weonlymodelthe
ity,theluminosityandtheabundancesareoptimised.Inthecaseof spectraat−9.4d,−3.7d,+4.5d,+12.5d,+22.6dand+36.4d
SN2009dc,weusethreeabundancezonesabovetheearliestpho- withrespecttoBmaximum,leavingouttheotheronesinbetween.
tosphereinordertohavecompositiongradientsintheouterejecta, FollowingTaubenbergeretal.(2011),wegenerallyassumean
allowingforanoptimumfit(cf.Sec.3.1). extinctiontowardsSN2009dcof
Thespectrumatthenextepochcarriestheimprintofthemate-
E(B−V) ∼E(B−V) +E(B−V) ∼0.17mag.
rialintheouterenvelopeandadditionallythatofthelayerswhich tot host Gal
the photosphere has receded into in the meantime. As the outer BecauseoftherelativelyshortdistancetotheSN,wecanaddup
abundance structure isalready constrained, the new photospheric thereddeningvalueswithouttakingredshiftintoaccounthere.The
velocity and the abundances of the newly-visible layers are now GalacticextinctiontakenintoaccountisE(B−V) =0.07mag
Gal
theprimaryfittingparameters.Iftheabundancesoftheouterlayers (Schlegeletal.1998),whileBurstein&Heiles(1982)givealower
have a significant impact on the quality of the fit, and no decent value E(B−V) =0.04mag. The reddening due to the host
Gal
fitispossiblewiththevaluesinferredearlier,thosevaluesarere- galaxy carries an error of 0.08mag (Taubenbergeretal. 2011).
vised(normallybylessthan30%oftheirinitialvalue)toequally Therefore,thelower-limitreddeningwithintheerrorbarsis
optimisethefittoallobservations.Theprocedureiscontinuedwith
laterspectrauntilthecompletetimeseriesisfitted. E(B−V)tot >0.06mag.
Degeneracies,i.e.equallygoodfitswithdifferentparameters,
Whilewegenerallyusethestandardvalueof0.17mag,werepeat
arethemostimportantsourceofuncertaintyinthefittingprocess.
someanalysesforavalueof0.06magtotesttheinfluenceonthe
Abundancesnotwellconstrainedbyanearlyspectrumcansome-
results.
times be determined when fitting a later spectrum. The respec-
The rise time of SN 2009dc has been observationally es-
tive values may then undergo significant revision (> 30%). In a
timated to be shorter than ∼30d and longer than ∼22d [we
fewcases,thisa-posteriorideterminationdoesnotwork.Then,we
follow Taubenbergeretal. (2011) here who give a larger, more
assume the unknown abundances to match typical nucleosynthe-
conservatively-estimatedrangethanSilvermanetal.(2011)].
sispatternswithinSNIaexplosionmodels(Iwamotoetal.1999).
Mostimportantly,whenFe-groupelementsdonotleadtothefor-
mationofindividualfeatures,themixofFe-groupelementsisset
soastoresemblethatintheouter,intermediateorinnerzoneofthe 3 TOMOGRAPHYASSUMINGANEXPLOSIONOFAN
Iwamotoetal. (1999) models as appropriate. Furthermore, in the SUPERMASSIVEWD
intermediatezoneoftheejecta,Sihasbeenassumedtobethemost
Ourfirstsetofmodelsisbasedonadensityprofilerepresentative
abundant element, evenwhenthesezonescontributedlittletothe
of an explosion of a rotating WD: we adopt the profile resulting
formationofthespectralfeatures.
fromthe“AWD3det”simulationofFinketal.[2012,inprep.;see
alsoFink(2010)],whore-calculatedthe“AWD3detonation”model
of Pfannesetal. (2010b) with improved detonation physics. The
AWD3det model can be regarded prototypical for explosions of
rotating, massive (2M⊙) white dwarfs. Thethermonuclear flame
in AWD3det propagates as a pure detonation (shock-driven, su-
2.3 StudyofSN2009dc:concept
personic combustion wave) from the very beginning. A pure de-
SN2009dcisinmanyrespectsdifferenttootherSNewhichAbun- flagration(subsoniccombustionflame)inamassive,rotatingWD
dance Tomography has been applied to. In particular, as it is un- wouldbelesslikelytoexplainSN2009dc,asitdoesnotproduce
knownwhichexplosionmodelapplies,thedensityprofileandthe much56Ni(∼0.7M⊙),andleadstoastronglymixedcomposition
risetimetrconstitutemajorelementsofuncertaintyinouranalysis. (Pfannesetal. 2010a). Delayed-detonation models for these pro-
Wereflectthisinourmodellingapproach:weperformAbun- genitors,inwhichtheflameinitiallyproceedsasadeflagrationand
dance Tomography three times, using different density profiles laterasadetonation(cf.Khokhlov1991),produceroughlysimilar
whichrepresent different explosion types. Theaimistocompare outcomesasAWD3det,astheinitialdeflagrationinarotatingWD
thedifferentmodelsintheendandtoassesstheirconsistency.Be- tendstobeweakandburnslittlematerial(Fink2010).
fore conducting our final tomography, respectively, we decide on Inorder toconduct atomography analysisinspherical sym-
anoptimumrisetimeforeachdensityprofile. metryasusual,wehadtoreducetheAWD3detdensityfieldtoan
©2012TheAuthors.Journalcompilation©2012RAS,MNRAS
Spectroscopicanalysisof SN2009dc 5
Table 1. Rise time estimates from our spectral fits using the AWD3det
W7 (reference)
AWD3-det densityprofiledescribed inthetext,fordifferent values ofthereddening
3m] at t=100s (after explosion) 0 0.10 .1011 0w97dec0-.e7xp tFfcshEerioar,tao(ovlyptuBmeutmprbf−reoaneorVefilaginenln)ieadvec,caeaahnttsrlhhcddfieetuhmetlfnoeatoeotsbuetwisatdtreyhla,lrvveivapcaene∆rilltuodedyefiλn.tsoglhT−enteo.hhefcetdor∆tsherreerveλceliorsaa=ipnttsiiodeooλnnnatdsi,nymibwndneeg−etthwtvcirrλeapdhelfocnobciunsroltalhw(tuhtweemheiissatncheynhsnmλogtohpioopvebtdteitsimei,mc=lfsuoi.Ssmr6Tei1edhIra6Iiecms5λhef.oo66tdudi3Aem˚re5ntl)h5es-.
ρ [g/c ρprofile [tdr] [kmvps−h1] ∆[A˚λ] t[r,do]pt
0.001
0 5000 10000 15000 20000 standard:E(B−V)=0.17mag,prog.metallicityZ∼0
velocity [km/s]
AWD3det 27.5 9440 -24.9
Figure1.Densityprofiles usedforAbundance Tomography(Sections 3, 30.0 8640 -3.7
4and 5), and W7profile as a reference. The AWD3det model has been 35.0 7120 20.8
40.0 5950 42.1 31.5
converted to1D(cf.Sec.3);the09dc-expmodelisshownwithitsslope
adaptedtoarisetimeof29d(cf.Sec.4.1). E(B−V)=0.06mag,prog.metallicityZ∼0
AWD3det 22.5 10610 -42.9
25.0 9100 -26.8
averaged1-Ddensityprofilebyaddingupthecellmassesintora- 27.5 7860 1.9
dialvelocitybins(Fig.1).Asphericitiesaretosomedegreeinherent 30.0 6850 17.0 27.8
inarotatingexplosionmodel(Fink2010).Wekeepthisinmindas E(B−V)=0.17mag,solarprog.metallicity
acaveatforthediscussionofourresults.
AWD3det 27.5 10070 -28.5
30.0 9200 -8.0
35.0 7680 19.1
3.1 Risetimeestimate 40.0 6560 38.7 32.1
WedetermineanoptimumrisetimeforourAWD3det-basedmod-
elsfromthe−9.4dspectrumofSN2009dc.Theearliestobserva-
aregiveninTable1.Thesevaluessampletherelationbetweent
tionismost useful for thispurpose, asit ismost sensitiveon the r
and∆λ,towhichwecalculatealinearfit(least-squaresmethod).
assumedrisetime(therelativedifferenceint,thetimefromexplo-
Wedemand∆λ=0andobtainfromthelinear-fitrelationanopti-
siononset,islargestatearlyepochs).
mumvaluet (seeagainTable1).
Theabundance structureoftheearly-timemodelscomprises r,opt
Two example models, where one can clearlysee theshift in
threeabundanceshells.Thesetupallowsoptimisation,butavoids
theλ6355positionwiththeassumedrisetime,areshowninFig.
anoverparametrisationandremainssensibleintermsofthechem-
ical structure: the models have a zone of thickness 600kms−1 2 together with the observed spectrum of SN 2009dc. A detailed
discussionoftheSNspectrumandourfinaloptimummodelbased
above the photosphere with some Fe-group elements (up to 15%
onAWD3detisgiveninthenextSection(Sec.3.2).
bymass;higherfractionsareprobablynotrealistic)andhighIME
We first performed our rise time experiment assuming a to-
massfraction.Abovethiszone,thereisalayerdepletedinFe-group
elementsbutstillrichinIME,withathicknessof∼2000kms−1.It talextinctionofE(B−V)=0.17magandnegligibleprogenitor
metallicity.Thelatterassumption, whichprovedoptimum forthe
causesrelativelylittlebackscattering,suchthattemperaturedrops
fitquality,hastwomainimplicationswhenmodellingtheinterme-
quickly with radius and becomes favourable for the formation of
diateandouterejecta:First,therearenolowerlimitstothemetal
prominent linesduetosingly-ionised IME.Stillabove, theatmo-
abundancesintheprogenitorWD(whichwewouldhavetorespect
sphereisassumed toconsist ofaC-Omixcontaining onlytraces
whendetermining theoptimumabundance structure).Second, no
ofotherelements(massfractionsgenerally.10%ofthoseinthe
stableFeisproducedintheouterlayerswhichundergoincomplete
zone below). The photospheric velocitiesareselected such that a
Si-burning in the explosion, as a pure C/O mix provides no ex-
reasonable temperature structure (i.e. a large enough strength of
cessneutrons(Iwamotoetal.1999).Hence,thereisnozonewhere
SiII lines) results and less than two thirds of the radiation pack-
stableFeisthedominantiron-groupelementdirectlyaftertheex-
etsarere-absorbedduetobackscattering. Wheneverindoubt,we
plosion. When the Fe-group mix cannot be determined from the
choose the lowest possible photospheric velocity in order not to
spectra, we therefore always assume amix of Fe-group elements
artificiallysuppresstheformationoflinesdeepinsidetheejecta.
whichisdominated56Nianditsdecayproductsand/orby52Cr(cf.
AsdescribedinSec2.2.3,thelinevelocitiesinthesynthetic
Sec.2.2.5).
spectrachangewitht.Wesetupmodelsfordifferentt andcom-
r r
Afterwards,werepeatedtheanalysisassumingsolarmetallic-
pare the positions of the synthetic and the observed SiII λ6355
feature3(measuredasinHachingeretal.2006).Precisely,therise ityandalower-than-standardreddeningE(B−V)tot∼0.06mag
(seeSec. 2.4),respectively. Thisenables us toestimate theinflu-
timeswehavetestedaret =21d,22.5d,25d,27.5d,30d,35d,
r
enceoftheseassumptionsonourstudy.Therespectiveresultsare
and40d(onlythemostpromisingmodelshavebeenfinalised).For
showninTable1aswell.
thefourmodelswhichshowtheleastmismatch∆λintheposition
For AWD3det, withstandard assumptions, the optimum rise
oftheobservedandsyntheticSiIIλ6355feature,trand∆λvalues
timeturnsouttobe31.5d(Table1).Evidently,optimumrisetimes
frommeasured∆λvalueswillalwayscarrysomeuncertainty,from
3 SiIIλ6355velocitiesinnormalSNeareknowntobewellfittedbyour themeasurementsaswellasthemodellingmethods.Withonestep
spectralmodels(e.g.Stehleetal.2005). inour tr grid, theshiftinlineposition(Table1) is,however, rel-
©2012TheAuthors.Journalcompilation©2012RAS,MNRAS
6 Hachingeret al.
SN 2009dc: −9.4d
Model AWD3det, t =27.5d
) r
nits Model AWD3det, tr=40.0d
u
y SiII
ar λ6355
r
bit
r
a
(
λ
F
3500 4000 4500 5000 5500 6000 6500 7000
λ [ Å ]
Figure2.AWD3det-basedmodelsforthe−9.4dspectrumofSN2009dcfornegligibleprogenitormetallicity andE(B−V)=0.17mag.Weshowthe
modelsforthemostextremetrvalueslistedinTable1.AnoptimummodelwouldfitthevelocityoftheSiIIλ6355line(marks;inset).Withaveryshortrise
time,thevelocity(blueshift)ofthesyntheticfeatureistoohigh(bluegraph);withaverylongrisetime,thevelocityistoolow(orangegraph).
atively large, so that we can crudely estimate the error in our t elements(Simassfraction:15%,Fe-groupmassfraction:9%),re-
r
determinationtobeequalorsmallerthananaveragestepinourtr spectively.CIIλ6580appearsasaprominentlineinthespectra.It
grid(3d).Wethusgivethefollowinglimitontherisetime: isreproducedusingsurprisinglylowmassfractionsofC(3%inthe
outermostzone,2%everywhereelse),asthehighluminosityofthe
t &28.5d.
r,09dc/AWD3det SNleadstoanionisationstatefavouringCIIoverCI.
A very similar limit is found for solar progenitor metallic- Our synthetic spectra are generally too red. A bluer colour
ity.IfoneassumesaweakerreddeningofE(B−V)∼0.06mag, wouldhaveimpliedahighT throughouttheatmosphere.Wecan-
R
the optimum rise times for our models are lower. This is due to notimplementthis,asalowenoughT iscrucialforareasonable
R
thelowerluminosity,reducingtheionisationandallowinglinesto ionisationbalance,whichisneededtomatche.g.theratiobetween
form further inside in the ejecta (i.e. line velocities as low as in theSiIIIλ4563andSiIIλ6355features.
the observations of SN 2009dc can be explained by models with Withinthefirstsixdayscoveredbytheobservations,thespec-
relativelyshort risetimes, cf. Sec. 2.2.3). FromTable1,we con- trumofSN2009dc doesnotevolveverymuch.Forbothspectra,
clude that for E(B−V)∼0.06mag our rise time limit would the photospheric velocities are low (9050kms−1 at −9.4d and
be tr,09dc/AWD3det & 24.8d. However, at present we see no com- 8300kms−1 at−3.7d)comparedtonormalSNeIabeforemaxi-
pellingreasonforpreferringthelowreddeningovertheonegiven mum.ThemostprominentlinesduetoSiIIandSIIaresomewhat
byTaubenbergeretal.(2011). stronger at −3.7d, but are still formed in the same atmospheric
layersasbefore.Thismeansthatareduction ofIMEintheouter
layershasnot onlyaneffectonthe−9.4dspectrum, butalsoon
3.2 Tomography
laterones.
ThesyntheticspectrabasedonAWD3detareshowninFig.3.The
risetimewehaveusedfor thecalculationsis30d.Theoptimum
rise time inferred above is a bit longer, but 30d is the strict up-
perlimitallowedbyobservations (Taubenbergeretal.2011).The
3.2.2 +4.5dmodel
code-inputparametersofourtomographymodelsarecompiledin
AppendixB. Thespectrumandthemodelhavenowchangedconsiderably.Lines
producedbyIMEstillgainmorestrength,astemperaturesdropin
theouterlayersoftheatmosphere.Thecoresofthelinesofsingly-
3.2.1 −9.4dand−3.7dmodels
ionisedIME(suchasSiII)remainatrelativelyhighvelocities(as
The observed −9.4d spectrum of SN 2009dc extends down to at the early epochs). Only the low-velocity wings of the absorp-
3000A˚,wherethefluxisunusuallyhighforaSNIa.Despitethe tionsare caused by the lower layers of theejecta. InSiII λ6355
highluminosityandbluecolour,theopticalspectrumshowsstrong andintheSIIW-feature(observedaround∼ 5400A˚),theselow-
signaturesofsingly-ionisedFe-groupandIMEspecies.Thesimi- velocitywingscanunfortunatelynotbereproduced, regardlessof
larlyluminousSN2007ifdoesnotshowclearSiIIorSIIlinesat theabundancesassumed.Thismayindicateatoostrongionisation
this epoch (Scalzoetal. 2010). This points towards smaller IME inthelowerlayersofthemodel,oratoohighphotosphericveloc-
abundances or perhaps towards a higher degree of ionisation in ity, which however is required in order not to obtain a hot lower
SN 2007if [cf. SN 1991T – Mazzalietal. (1995) vs. SN 1999ee boundaryspectrum.
–Hamuyetal.(2002),wherevariationsinionisationarecrucial]. TheCII λ6580featureintheobserved spectrumhasshifted
In the case of SN 2009dc, an optimum fit to the spectra is tomuchlower velocitiesbythisepoch. Thisclearlyindicatesthe
achieved with three abundance zones in the outer ejecta (just as presenceofCinthelowerlayers.Theline’sstrengthathighveloc-
described in Section 3.1). From the outside inwards, these zones ities,atthesametime,isautomaticallyreducedbecause oflower
areunburned(i.e.depletedinFe-groupelementsandalsoIMEto densities and temperatures (the line originates from a highly ex-
avoidCaandSihigh-velocityabsorption),somewhatricherinIME citedlevel).AnotherfeatureindicatingadropintemperatureisOI
(Si mass fraction 8% inthis model) and finally in IME/Fe-group λ7773,whichbecomesdeeperintheobservationsandinthemodel.
©2012TheAuthors.Journalcompilation©2012RAS,MNRAS
Spectroscopicanalysisof SN2009dc 7
CaII, SiII SiII(MgII, FeIII)III SANW D2030d9edt−cb:a−s9e.4dd model
Si
SII (SiII) SiII CII CII[t=E2(0B.60−dV, l)g=(L0/L.81)=79].,90, vph=9050km/s
CoIII,FeIIICoIII,CrIII

SN 2009dc:−3.7d
AWD3det−based model,
t=26.40d, lg(L/L8)=10.01, vph=8300km/s
...
nits) FeIII, SII SiII SANW D2030d9edt−cb:a+s4e.5dd model,
y u SiII II t=34.50d, lg(L/L8)=9.98, vph=7900km/s
bitrar SiII C OI,MgII
F (arλ CoIII,FeIIICoIII SiIICaII (MgII,)FeIIISiIII
SN 2009dc:+12.5d
AWD3det−based model,
t=42.50d, lg(L/L8)=9.82, vph=7500km/s
y SiIICaIICoII,...CrII,...CoII,FeII,CrII,MgII mostlyFeII (NaI, SiII)? SiII SAt=5NW2. 6D2003d,0d lg9e(Ldt/−Lc8b:)a+=9s2.6e25d., 6v pmdh=o72d0e0lk,m/s
mostlCoII OI,MgII MgII CaII MgII
SN 2009dc:+36.4d
AWD3det−based model,
t=66.40d, lg(L/L8)=9.39, vph=4700km/s
3000 4000 5000 6000 7000 8000 9000
λ [ Å ]
Figure3.Sequenceofspectralmodels(redgraphs)forSN2009dc,basedontheAWD3detdensityprofile,andobservations(blackgraphs).Identificationsare
givenforthemostprominentfeatures.
©2012TheAuthors.Journalcompilation©2012RAS,MNRAS
8 Hachingeret al.
velocity [km/s]
3.2.3 +12.5dmodel 3000 5000 8000 11000 15000
100
a)
The+12.5dspectrumshowsaconsiderabledropinUVflux.Pho-
tospherictemperaturesarelower,but thelineblocking intheUV
10
also increases. The Fe-group abundances at the photosphere are
hntniioaogtwnihoedenreffgotehrfceaCtenivoifesoIlIrioIntwahsneeudrpptpCrhreraevnsIisIoaIiuntisngthtsotephetpehcrfletervuasixi.onEuagsrslopyeue-picnooidnaclih∼ls,ye3fdCa5vso0to0aIutIAre˚ia.n:nDgtdhereCsepciriootInemIiatsbhraiee-- mass fraction [%] 1 AEBW−DV=3COMS0dig.e1t7−based,
decreasing ionisation, the synthetic FeIII feature at ∼4300A˚ is 0.1 S
Ca
deepenoughtoreproducetheobservedline,assignificantamounts Ti+Cr
of56Nihavedecayedinto56Fe.Noadditional54Feisassumedto F56eN0i0
bepresentinthemodels. 0.01
0 0.5 1 1.5 2
Theobservedfeaturesareallinallreproduced,withsomeex- enclosed mass [Msun]
ceptions:at∼4500A˚,thereisamarkedabsorptionandre-emission
featureintheobservations,whichisreproducedonlyatlaterepochs 100
b)
in our models. The other exception is SiII λ5972, which is too
shallow.Wesuggest thatNaI Dstartsinfluencingtheλ5972fea-
turearound thisepoch. Naisnot included inour models, aspast 10
attemptstofitthefeaturehavesufferedfromdeviationsintheioni- %]
saantdiodnTahtoaef,twShiihsIiIcehlλe6imn3ce5rn5eta(vsMeelsoawzcziitatyhliseehptooawclh.s.1a9T9mh7ei)so.mbsaetcrvhebdeltiwneeemnomveosdteols- mass fraction [ 1 AEBW−DV=3COMS0dig.e1t7−based,
wardsthered(lowervelocities)astimeprogresses,whilethecentre 0.1 S
ofthesyntheticlinedoesnotchangethatmuch.Wehavealready Ca
Ti+Cr
rpeemrmovite.dPaSritforfomthethveeloouctietyrmdorostplainyethrseaosbfsaerrvaesdthsepeecatrrlaiemstasypaeccttura- 0.01 F56eN0i0
allybecausedbyafeatureformingbluewards,whichgetsstronger 0 5000 10000 15000
velocity [km/s]
withtimeandemitsintotheSiIIλ6355region.Judgingfromour
linelist,thisisprobablyaFeIIfeature,butwedonotreproduceit
withourmodels. 100
c)
3.2.4 +22.6dmodel 10
%] W7
Artlriincuthem2si2n(a.m6rFeaeddr-kgupereaodstutoipnBseFilnimeggm.lay3xe-n)iim.otsTnu.himTseeh,dbetahFmleaeon-psgchterpooortuoofpsmtpheihelneseemerneletinrnfeetescasetwuidsrietemshsoivinnsettrtolyhyeaasstzmrpooeannctge-- mass fraction [ 1 nsyunctlehCOMSoei−sgis
teroftemperatureanddensitystructure. 0.1 S
Ca
Ti+Cr
F56eN0i0
3.2.5 +36.4dmodel 0.01
0 5000 10000 15000
Remarkably,SN2009dcstillshowsaphotosphericspectrumlong velocity [km/s]
aftermaximum,withav of4700kms−1at+36.4d.Thequality Figure4.AbundanceTomographyofSN2009dcbasedontheAWD3det
ph
ofthespectralfitsisrelativelygoodgiventhelateepoch.Theslow densityprofile.The“56Ni0”and“Fe0”linesrepresent the56Niandsta-
evolution into the nebular phase indicates higher densities in the bleFeabundances directlyafterexplosion, respectively (cf.AppendixB,
TableB1).Panela):abundancesinmassspace.Panelb):same,inveloc-
intermediateandinnerpartcomparedtonormalSNeIa.
ityspace. Inpanelc),theabundances oftheSNIaexplosion modelW7
The photospheric velocity at +36.4d is much lower than at
(Iwamotoetal.1999;cf.Stehleetal.2005)fornormalSNeIaareplotted
+22.6d. This jump is, however, probably not physically signifi-
forcomparison.Whenassumingazero-metallicityprogenitor[modelW70,
cant,andratheranartefactofthephotosphericapproximationfor
Iwamotoetal.(1999)],themostsignificantchangeistheabsenceof“Fe0”
suchlateepochs:anunusuallylowbackscatteringrateinthelatest- intheouterlayers,representedbythedottedpartoftherespectivecurve.
epochmodelshowsthatthisapproximationbeginstobreakdown
here.
fractions of some per cent suffice to fit the observed CII λ6580
line,althoughitismuchstrongerthaninotherSNeIa.Cmustbe
3.2.6 Abundances
present downto∼ 7500kms−1 inorder toexplaintheobserved
TheabundancestratificationoftheAWD3det-basedejectamodels lowvelocityinthepost-maximumλ6580feature.Themajorityof
isshowninFig.4. thematerialintheweaklyburnedzones,however,consistsofO.
The outer zone (v&9650kms−1) only contains small Between∼9000and7000kms−1 IMEarehighlyabundant.
amounts of IME and Fe-group elements. This corresponds to the ThemassfractionofFe-groupelementsinthislayer,between12%
weaklineblockingandtherelativelyshallowfeaturesintheearly- and58%,isconstrainedbylineblockingoftheUVflux.
time spectra. Due to the relatively high ionisation, carbon mass Although our model sequences extend to late epochs, we
©2012TheAuthors.Journalcompilation©2012RAS,MNRAS
Spectroscopicanalysisof SN2009dc 9
mostly explore regions of incomplete burning. At velocities
100
<7500kms−1, finally, Fe-group elements start to dominate. a)
These zones are sampled by the +22.6d and +36.4d spec-
tra. Due to degeneracy, the data can be fitted with different Fe- 10
group abundances. Wechoose rather high massfractions, consis- %]
ttt(heiavnebetul−ynw)d9iatt.ohn4gctdeehtsehsoepfrfeaccc5tot6rnNuthsmitaia.ttunwTtdehes9ets3aemb%elaesbsoFsymemferdaaicFsresteicao-tgtnlrytsohaueofp+ftee“r3l56ee6x.m4Npeldion0p”stsihoaoanntl,ordersaep“dshFpyeeer0icen”-. mass fraction [ 1 AEW(BD−V3COMSd)ig=e0t−.0b6asmeadg,
0.1 S
“Fe ” is only present deep inside our model ejecta, as our mix Ca
0
Ti+Cr
obfleFthe-eglroowup-meelteamlliecnittsyWhas7-bbeaesendsneutculepos(cyfn.thSeesci.s2c.a2lc.5u)lattoiorneWsem70- F56eN0i0
0.01
(Iwamotoetal.1999). 0 5000 10000 15000
velocity [km/s]
WithrespecttotheW7/W70nucleosynthesis(seeFig.4c),all
burningproductsarefoundatmuchlowervelocitiesinSN2009dc.
100
Asafurtherdifference,the“abundancemixing”isbitstrongerthan b)
thatofW7,ashasalsobeenfoundintomographystudiesofother
SNeIa(Stehleetal.2005).InSN2009dc,weseeCinfairlydeep
10
layers,andneedsomeFe-groupmaterialintheouterzonestore-
%]
pbsthiurteoirvndsieuptdyceecaotnrfthadtehcFeasenps-egpacreltoscrouatrpabeealoarnrylyeeptrhorseo.nd.EIuMIxcMceEedEpmtwmafiosathsrtesftrhroiaaemcltoeiisuomtnpeorrierslesaelyidnmeotrwisit,nendt-htm.heTeixshuieunnnsg--, mass fraction [ 1 AsoWlaDr 3COMSmdigeetta−lblicaistyed,
ofO,attheexpenseof Si.StricterlimitsontheOabundances in 0.1 S
Ca
thelowerlayersmaybededuced infurther studiesmodellingthe Ti+Cr
nebularspectraofSN2009dc. F56eN0i0
Thecumulativechemicalyields(totalmassofC/O,IMEand 0.01
0 5000 10000 15000
Fe-group elements) of all our models are given and discussed in velocity [km/s]
Section6.2. Figure5.Influence ofreddening andmetallicity onthe AWD3det-based
tomography (plots in velocity space). Panel a): abundances inferred for
the lower limit reddening E(B−V)∼0.06mag and low metallicity.
3.3 Abundanceprofilesandassumptionson Panelb):sameforE(B−V)∼0.17mag(normal),butsolarmetallicity
metallicity/reddening (i.e.highermetallicitythaninourstandardmodel).TheabundancesofO,
WerepeattheAWD3det-basedtomographyforalowerreddening Si,“Fe0”and“56Ni0”inthestandardmodel[E(B−V)∼0.17mag,low
metallicity–cf.Fig.4]areplottedasthick,lighterlinesforcomparison.
E(B − V)∼0.06mag and solar progenitor metallicity, respec-
tively, in order toexamine how our resultschange withthese as-
sumptions.
When using a lower reddening, themodels have a lower lu- formthespectrallines.Thisshiftsthebordersofsomeabundance
minosityandtheradiationfieldintheirinteriorislessintense,de- zones.Still,theabundancestratificationweinferisagainqualita-
creasing the ionisation. This holds even though we use a shorter tivelysimilartothestandard,low-metallicitycase.
optimumrisetime(Sec.3.1)ofonly28d(whichtendstoincrease All in all, we see that our results are somewhat sensitive to
radiationfielddensities,cf.Sec.2.2.3).Themodelscontainmore reddeningandmetallicity,buttherespectivechangesarenotlarge
singly-ionisedmaterial,whichiseffectiveinproducinglines(IME) enoughtocompromiseourconclusions.
andblockingtheUVflux(Fe-group).Thus,wereproducethespec-
trawithsomewhatlowerabundancesofIMEintheouterlayersof
the ejecta, and lower abundances of Fe-group elements. Qualita-
tively, however, the abundance stratification in velocity space re-
4 TOMOGRAPHYWITHACORE-COLLAPSE-LIKE,
mainsthesame(Fig.5a).Thequalityofthemodelsisabitbetter
EMPIRICALLYMOTIVATEDDENSITYPROFILE
thanwiththehighstandard reddening, whichtendstoexacerbate
themodels’fluxexcessinthered. In this part, we conduct a tomography with an “empirically mo-
Ahigh(solar)metallicity,ontheotherhand,impliesthatthere tivated” density profile (“09dc-exp”). This profile is constructed
arelowerlimitstotheabundancesofFe-groupelementsintheouter (Sections4.1,4.2)fromtwoexponentials(i.e.itisapiecewiseex-
ejecta(Asplundetal.2009).Furthermore,thereisachangeinthe ponentialcurve)withaflatterslopeintheinnerpart.Theouterpart
typical nucleosynthesis patterns: significant amounts of 54Fe ap- isinferredfromtheevolutionoflinevelocitiesinthespectra,as-
pearinlayerswithincompleteburning(Iwamotoetal.1999).We suming that linesalways form at adensity roughly constant with
reflectthis,asfaraspossible, intheabundances of Fe-groupele- time(seeAppendixA).
mentsinourmodels(Fig.5b).Theresultingspectrahaveaslightly Although we do not assume any explosion model in the be-
worse quality: the outer layers with solar Fe-group abundances ginning,theprofileresemblesdensityprofilesfoundinsimulations
blockflux, heatinguptheatmosphere andincreasing thefluxex- ofcore-collapseSNewithC-Ostarprogenitors(e.g.Iwamotoetal.
cessinthered,wheretheradiationcanfinallyescape.Photospheric 1994,2000).Withanejectamassof∼3M⊙,ourmodelsbasedon
velocities are quite a bit higher in order to keep the backscatter- 09dc-expcanbeseenasanapproachtointerpretSN2009dc asa
ing reasonable and the atmospheric temperatures low enough to core-collapseexplosion.
©2012TheAuthors.Journalcompilation©2012RAS,MNRAS
10 Hachingeretal.
W7 (reference) Table2.Risetimeestimates fromourspectral fits,usingdifferent expo-
=100s (after explosion) 01 .101 eeeexxxxpppp11110044,,,, ttttrrrr====23235050dddd ((((vvvv✕✕✕✕====11110044000000000000kkkkmmmm////ssss,,,, ttttrrrr====23235050....0000dddd)))) Af1tntohr,eo,enwdmhtriiiofeatfawhdledrledtieehvnenneenetirasndvirogitl×fyynfE-elpyfi(rtr(ethosBtneelficidgles−ehl∆sotthlpVfyλaoe)t)r.−ostaTefhnvthetrdeheorermaeouldlpteaeedtttrniaiemoslnelnijsiutec.yimtciyttayalrp.si(rsoTsoeehcfietehliemattesnaexbgatlert)ee,rs,ofitwposetrsiaittdshenidafat,lfgroe,cagrocieonfrnu.rtecsAsvaptplaocopluuneTlednaasidtbneoildgxef
3m] at t 0.01 ρprofile [tdr] [kmvsp−h1] ∆[A˚λ] t[r,do]pt
ρ [g/c 0.001 standard:E(B−V)=0.17mag,prog.metallicityZ∼0
0.0001 exp9 25.0 9600 −9.4
5000 10000 15000 20000 27.5 10060 −8.3
velocity [km/s]
30.0 8580 12.4
Figure6.Examplesofthedensityprofilesfortheouterejectaconstructed 35.0 7210 33.7 27.8
inSec.4.1/AppendixA,andtheW7profileasreference.Allprofilesare exp10 25.0 10250 −10.3
27.5 9580 −4.5
plotted forareference timet0=100safterthe explosion, although they 30.0 8630 12.0
havebeencreatedassumingdifferentrisetimestr. 35.0 7250 30.4 27.7
exp12 25.0 10610 −36.9
27.5 9520 −16.4
30.0 8600 5.5
4.1 Empiricallyinferredouterdensityprofileandoptimum
35.0 7170 31.8 30.0
risetime exp14 27.5 10190 −28.5
30.0 9320 −5.2
4.1.1 Gridofempirically-inferreddensityprofiles 35.0 7460 24.4
40.0 6090 42.1 31.6
Wehave constructed atwo-parameter gridof exponential density
E(B−V)=0.06mag,prog.metallicityZ∼0
profiles for the outer layers of theejecta (Appendix A; examples
seeFig.6).Oneparameteristheabsolutedensityscale,whichwe exp9 22.5 11500 −10.1
25.0 8920 7.1
parametrise here in terms of the velocity v× at which the profile 27.5 7900 20.3
firstintersectstheW7model(cf.Fig.6).Forthisweallowvalues 30.0 7050 30.7 24.0
of 9000, 10000, 12000, or 14000kms−1. Theother parameter is exp10 21.0 10450 −19.5
22.5 10160 −18.3
therisetime(21d, 22.5d, 25d, 27.5d, 30d, 35d or 40d), with 25.0 8880 4.3
whichtheslopeofthedensityprofileinferredfromthelinevelocity 27.5 8000 17.0 24.7
exp12 22.5 10310 −28.8
evolutionchangessomewhat,butnotdrastically(cf.AppendixA).
25.0 9200 −0.1
The set of exponential profiles, which are given names reflecting 27.5 8310 12.9
v× (e.g.“exp9”matchesW7atv× = 9000kms−1),coverswell exp14 2370..50 97747500 −2253..81 25.9
thephysicalparameterspaceinwhichsolutionsforSN2009dcwill 30.0 8920 −6.1
befound(seebelow). 35.0 7200 22.6
40.0 5350 49.4 31.3
Foreachv×,weinferanoptimumrisetimeseparately.Inthe
end,wechooseonecombinationof(v×|tr),whichpromisesopti- E(B−V)=0.17mag,solarprog.metallicity
mumresults,inordertoconstructthefull09dc-expdensityprofile.
exp9 25.0 10200 −2.5
27.5 10920 −6.0
30.0 9190 6.5
4.1.2 Density/risetimetest 35.0 7590 27.4 27.4
exp10 25.0 10800 −29.5
27.5 10130 −8.9
The optimum rise time for each v× is inferred from the position 30.0 9040 7.2
mismatchoftheSiIIλ6355feature,comparingtheobservedspec- 35.0 7650 29.5 29.5
tratothesyntheticones.Thisprocedurehasalreadybeendescribed exp12 25.0 11040 −32.3
27.5 9980 −7.3
in Section 3.1. Again, the influence of solar metallicity, and of a
30.0 9030 6.2
lower-than-standard reddening is explored by repeating the mod- 35.0 7620 26.2 29.7
ellingforthesecases. exp14 27.5 10620 −29.8
30.0 9720 −13.9
Table2gives –for each assumed reddening, metallicityand 35.0 8020 12.1
v× separately – the measured line position mismatches between 40.0 6540 41.8 32.7
the observations and the four optimum models (for different t),
r
aswellastheresultingt .InFigure7,weplotspectraforase-
r,opt
lectionofthesemodels(forE(B−V)∼0.17magandnegligible
metallicity). withtheresultthattheSiIIλ6355linecannotbewellformed.For
Usingasmallerv× fortheempiricaldensityleadstosmaller this reason, the exp9 models allow us to reproduce the observed
densities throughout the envelope. Looking from the outer layers SiII line depths only with unrealistically high Si mass fractions
inwards,highdensitiesarereachedlater,andthezonefavouredfor & 70%(cf.Iwamotoetal.1999),ifatall(seet = 25.0dmodel
r
SiII lineformation tendstobedeeper inside (whichreducesline inFig.7).Wethereforeexpecttheactualdensitiesintheouterlay-
velocities). Thus, the t values needed to reproduce the low line ersofSN2009dctobehigherthanthoseintheexp9models.The
r
velocities of SN 2009dc are usually shorter for a low v×. If v× exp14models,ontheotherhand,needalongrisetimetoreproduce
isverylow,thezonedense enough forlineformationmaybefar theSiIIλ6355line(Table2)andhaveanexcessivelyhighopacity.
inside where theradiation fieldisstrong. Thisthen favours SiIII Thus,theyconstituteanupperlimittotherealdensities.
©2012TheAuthors.Journalcompilation©2012RAS,MNRAS