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DRAFTVERSIONJANUARY26,2012 PreprinttypesetusingLATEXstyleemulateapjv.5/2/11 NORMALTYPEIASUPERNOVAEFROMVIOLENTMERGERSOFWHITEDWARFBINARIES R.PAKMOR HeidelbergerInstitutfürTheoretischeStudien,Schloss-Wolfsbrunnenweg35,69118Heidelberg,Germany M.KROMER,S.TAUBENBERGER Max-Planck-InstitutfürAstrophysik,Karl-Schwarzschild-Str. 1,85741Garching,Germany 2 1 S.A.SIM 0 ResearchSchoolofAstronomyandAstrophysics,MountStromloObservatory,CotterRoad,WestonCreek,ACT2611,Australia 2 n F.K.RÖPKE a UniversitätWürzburg,Emil-Fischer-Str.31,97074Würzburg,Germany J 4 2 W.HILLEBRANDT Max-Planck-InstitutfürAstrophysik,Karl-Schwarzschild-Str. 1,85741Garching,Germany ] DraftversionJanuary26,2012 E H ABSTRACT . One of the most important questions regarding the progenitor systems of Type Ia supernovae (SNe Ia) is h whether mergers of two white dwarfs can lead to explosions that reproduce observations of normal events. p Herewepresentafullythree-dimensionalsimulationofaviolentmergeroftwocarbon-oxygenwhitedwarfs - o withmassesof0.9M⊙ and1.1M⊙ combiningveryhighresolutionandexactinitialconditions. Awell-tested r combinationofcodesisusedto studythe system. We startwiththedynamicalinspiralphaseandfollowthe t subsequent thermonuclear explosion under the plausible assumption that a detonation forms in the process s a of merging. We thenperformdetailed nucleosynthesiscalculationsandradiativetransfersimulationsto pre- [ dict synthetic observables from the homologouslyexpandingsupernova ejecta. We find that synthetic color lightcurvesofourmerger,whichproducesabout0.62M of56Ni,showgoodagreementwiththoseobserved 1 ⊙ fornormalSNeIainallwavebandsfromUtoK.Linevelocitiesinsyntheticspectraaroundmaximumlight v alsoagreewellwithobservations. Weconclude,thatviolentmergersofmassivewhitedwarfscancloselyre- 3 2 semblenormalSNeIa. Therefore,dependingonthenumberofsuchmassivesystemsavailablethesemergers 1 maycontributeatleastasmallfractiontotheobservedpopulationofnormalSNeIa. 5 Subjectheadings:stars: supernovae:general–hydrodynamics–binaries:close-radiativetransfer . 1 0 1. INTRODUCTION (e.g.Badenesetal. 2007) seem to favor the doubledegener- 2 ate scenario. In addition, first studies of SN 2011feseem to 1 Despite many years of dedicated research, the progenitor disfavorasingledegenerateprogenitor(see,e.g.Bloometal. : systems and explosion mechanisms of SNe Ia remain un- v 2011). There is, however, no unambiguous proof for any clear. It is generally accepted that SNe Ia originate from i progenitorscenarioyet. Foradetaileddiscussionaboutcon- X thermonuclear explosions of massive carbon-oxygen white straintsontheprogenitorscenariosseeHowell(2011). dwarfs in binary systems. Depending on the nature of the r Todate,mosttheoreticalworkonSNeIahasconcentrated a companion star, two different progenitor systems have been onthesingledegeneratescenario,asmergersofwhitedwarfs proposed. Inthesingle degeneratescenario(Whelan&Iben were thought not to lead to thermonuclearexplosions. This 1973) a carbon-oxygen white dwarf accretes from a non- wasmainlybasedonthepicturethatmergerswouldleavebe- degeneratecompanionstaruntilitreachestheChandrasekhar- hindthemoremassivewhitedwarfwithahotenvelopemade massandexplodes(butnotethatanexplosionbeforereaching upofthematerialofthelessmassivewhitedwarf.Fastaccre- theChandrasekharmassmayalsobepossible,e.g.Finketal. tionfromtheenvelopewillthenturnthecarbon-oxygenwhite 2007, 2010). In contrast, in the double degenerate sce- dwarf into an oxygen-neon white dwarf (Nomoto&Iben nario(Iben&Tutukov1984;Webbink1984)amergeroftwo 1985;Saio&Nomoto1998)whichcollapsestoaneutronstar carbon-oxygen white dwarfs causes a thermonuclear explo- asit approachesthe Chandrasekharmass (Nomoto&Kondo sionofthemergedsystem. 1991).Waystoavoidthetransformationofthecarbon-oxygen Many recent findings including SN rates from population whitedwarfintoanoxygen-neonwhitedwarfhavebeenpro- synthesisstudies(Ruiteretal.2009),studiesofthedelaytime posed(e.g.Yoonetal.2007),butwithoutconclusiveresults. distribution of observed SNe Ia (e.g. Maozetal. 2010), the Recently, however, we demonstrated that violent mergers lack of radio emission of SNe Ia (e.g. Hancocketal. 2011), of two carbon-oxygen white dwarfs could directly lead to the lack of hydrogen emission in nebular spectra of SNe Ia a thermonuclear explosion while the merger is still ongoing (Leonard2007),thelackofX-rayemissioninellipticalgalax- (Pakmoretal. 2010). We also showed that the observables ies(Gilfanov&Bogdán2010)andstudiesofSNIaremnants 2 R.Pakmoretal. log ρ [g cm 3] − 4.0 5.0 6.0 7.0 2.0 00s 150s 300s 2.0 0.0 0.0 2.0 2.0 − − ] 2.0 450s 600s 605s 2.0 ] m m c c 9 9 0 0 1 1 [ 0.0 0.0 [ y y 2.0 2.0 − − 1.9 610s 612s 620s 30.0 0.0 0.0 30.0 − 1.9 − 1.9 0.0 1.9 3.0 0.0 3.0 30.0 0.0 30.0 − − − x [109 cm] FIG.1.—Snapshotsofthemergerofa1.1M⊙ anda0.9M⊙ carbon-oxygenwhitedwarfandthesubsequentthermonuclearexplosion. Atthestartofthe simulation thebinarysystem hasanorbital periodof≈35s. Theblack crossindicates thepositionwhere thedetonation isignited. Theblack lineshows thepositionofthedetonationfront. Color-codedisthelogarithmofthedensity. Thelasttwopanelshaveadifferentcolorscalerangingfrom10- 4gcm- 3 to 106gcm- 3and104gcm- 3,respectively. forsuchanexplosionwithtwowhitedwarfsof0.9M show 0.9M carbon-oxygenwhitedwarf. Wefollowtheevolution ⊙ ⊙ goodagreementwiththeobservedpropertiesofsubluminous of the binary system through the merger phase, thermonu- 1991bg-likeSNeIa.Furthermore,wefoundthatforaprimary clear explosion and nucleosynthesis. Finally we use three- massof0.9M a massratioofatleastabout0.8isrequired dimensionalradiativetransfersimulationstoobtainsynthetic ⊙ forthescenariotowork(Pakmoretal.2011). lightcurvesandspectra. Lately, Danetal. (2011) showed that using exact initial 2. MERGERANDEXPLOSION conditionscanchangethepropertiesofthemerger. Inpartic- ular,thisleadstoasignificantlylongerinspiralintheirsimu- The inspiral and merger is modeled using a modified ver- lations. However,Danetal.(2011)wereonlyabletorunthe sion of the GADGET code (Springel 2005). Modifications simulationwitharesolutionof2×105particles(forcompar- include the Helmholtz equation of state (Timmes&Swesty ison, the violentmergercalculationsbyPakmoretal. (2010, 2000)anda13isotopenuclearreactionnetworkthatcontains 2011)used2×106particles). all α-elements from 4He to 56Ni. Radiative cooling effects In this work, we combine high resolution merger simula- arenotincludedinoursimulation. Adetaileddescriptionof tions with exact initial conditions. We present the results the modifications will be given in a forthcoming paper. In of a simulation of the massive merger of a 1.1M and a additionthemaximumsmoothinglengthofaparticlewasre- ⊙ stricted to 108cm. This affects only particles ejected from 3 ρ [gcm−3] Xi 10−310−210−1 1.0 10−3 10−2 10−1 1.0 TABLE1 ANGLE-AVERAGEDLIGHTCURVEPARAMETERSFORSELECTEDBANDS. ρ C O Bolometrica U B V R tmax 18.6 18.0 20.8 23.2 21.6 ∆m15 0.74 1.30 0.95 0.67 0.42 M(tmax) -19.2 -19.6 -19.0 -19.2 -19.2 M(tmax(B)) -19.1 -19.5 -19.0 -19.2 -19.2 −2S0i000 0 20000−2F0e000 0 20000−25060N0i0 0 20000 aNotethatthisisnotthetruebolometriclightcurveofourcalculations.Forcomparabil- itytoobservedbolometriclightcurves,themodellightcurvewasreducedtoUBVRIJHK bolometric. temperature and follow its propagation through the merged objectuntilmostofthematerialisburned. Fig.1showsthat −2·104 0 2·104−2·104 0 2·104−2·104 0 2·104 theprimarywhitedwarfandmostpartsofthesecondaryare v [kms−1] already burned 2s after the detonation formed. The energy releasefromnuclearburningunbindstheobject.Usinganex- FIG.2.—Densityandcompositionofthefinalejectainhomologousexpan- pandinggrid(Röpke2005)wefollowthedynamicejectauntil sion100saftertheexplosionofasliceinthex-zplane.Themassfractionis shownforcarbon,oxygen,silicon,stableironandradioactive56Ni. theyreachhomologousexpansionabout100safterthedeto- nation was ignited. They have an asymptotic kinetic energy thebinarysystemduringthemergerbutleadstoasignificant of1.7×1051erg. speedupofthecode.Sincetheseparticlesareatverylowden- sitiesandcontainonlylessthanonepercentofthetotalmass, 3. NUCLEOSYNTHESIS they have no noticable influence on the explosion dynamics Inordertoobtaindetailedisotopicabundancesoftheejecta andobservables. weadd106 tracerparticlestothesimulationoftheexplosion Theinitialbinarysystemconsistsofa1.1M⊙anda0.9M⊙ that record their local temperature and density. In a post- carbon-oxygenwhitedwarfconstructedfromatotalof1.8× processing step we run a detailed nuclear network contain- 106equal-massparticles. Bothwhitedwarfsaresetupiniso- ing384isotopesonthesetrajectories(Travaglioetal.2004). lationandrelaxedwith anadditionalfrictionforcefor100s. Tomimictheeffectofsolarmetallicitywechoosetheinitial We then apply the method described in Danetal. (2011) to compositionofthetracerparticlesas47.5%12C,50%16Oand slowlymovethetwo white dwarfsclosetogether. When the 2.5%22Nebymass. first particle of the less massive white dwarf crosses the in- Inthe explosion,a total of0.7M of irongroupelements ⊙ ner Lagrange-point we stop and start the actual simulation. are synthesized. They consist predominantly of radioactive Atthistime,thebinarysystemhasanorbitalperiodofabout 56Ni(0.61M )withasmallfractionofstable58Ni(0.03M ) ⊙ ⊙ 35s. andstable54Fe(0.02M ). Inaddition,0.5M ofintermedi- ⊙ ⊙ TheevolutionofthebinarysystemisshowninFig.1. The atemasselementsareproducedin theexplosion. Theejecta mass transfer is stable for more than 15 orbits. After about contain about 0.5M of oxygen and about 0.15M of un- ⊙ ⊙ 600s the secondary white dwarf becomes dynamically un- burnedcarbon. stable and is disrupted on a timescale of one orbit. As the Thespatialcompositionanddensitystructureoftheejecta material of the secondary is accreted violently onto the pri- in homologous expansion are shown in Fig. 2. Its inher- mary, material is compressed and heated up on the surface entlythree-dimensionalstructureisaresultofthestateofthe oftheprimarywhitedwarf. Asaconsequencehotspotsform merged object at the time the detonation forms. Since the in which carbon burning is ignited. When the first hotspot detonation propagatesfaster at higher densities, the primary reaches a temperature larger than 2.5×109K at a density whitedwarfisburnedfirstanditsashesexpand. Astheyex- of about 2×106gcm- 3 we assume that a detonation forms pand they sweep around the material of the partially intact (Seitenzahletal. 2009). Note that despite the high resolu- secondarywhite dwarf that is still being burned. Therefore, tion we use, we still tend to underestimate the temperature theashesoftheprimaryhavealreadyexpandedsignificantly in the hotspot compared to even higher resolution simula- before burning of the secondary is completed (roughly one tions(Pakmoretal.2011).Onlyfuturedetailedinvestigations second later), meaningthat the ashes of the secondarycom- might be able to decide whether or not a detonation really pletely dominate the center of the ejecta. Hence, when the formsbuttheconditionsinourSPHsimulationssuggestthat ejectareachthehomologousexpansionphaseseveraltensec- itisplausible. onds later, the very inner parts of the ejecta do not contain Atthistimewemapthewholestateofthesimulationona materialfromtheprimarywhitedwarfandthereforenoiron- uniformCartesiangridwitharesolutionof7683gridcellsand groupelements. aboxsizeof4×109cm. About0.03M ofmaterialislostby ⊙ themappingasitisoutsidethebox.Sincethismaterialmakes 4. COMPARISONWITHOBSERVATIONS uplessthantwopercentofthetotalmassandhasadensitytoo Using the three-dimensionaldensity structure from explo- lowtocontributesignificantlytonuclearburning(i.e. itstays sionmodelingandthecorrespondingspatialabundancedistri- unburned)itdoesnotaffectthedynamicsoftheejectaorthe butionfromthetracerparticlesweapplytheMonteCarlora- syntheticobservablesderivedfromthemodel. diativetransfercodeARTIS(Kromer&Sim2009;Sim2007) With these initial conditions we use the LEAFS code tocalculatesyntheticspectraandlightcurvesforourmodel. (Reineckeetal.1999a)thatappliesthelevel-settechniqueto Fig. 3 shows angle-averaged and line-of-sight depen- model detonation flames (Reineckeetal. 1999b; Finketal. dent lightcurves of our model compared with several well- 2010). We ignite the detonation at the cell with the highest observed normal SNe Ia. The angle-averaged lightcurves 4 R.Pakmoretal. FIG.3.—Lightcurvesofourmodel. ThepanelsfromtoplefttobottomrightcontainUBVRIJHKbolometricandbroad-bandU,B,V,R,I,J,H,Klightcurves. Theblack line corresponds tothe angle-average ofthe model. Grey histograms showlightcurves along seven different lines-of-sight representative forthe scattercausedbydifferent(100)viewinganglesincludingthemostextremelightcurves. ThetimeisgivenrelativetoB-bandmaximum.Theredsymbolsshow observationaldataofthreewell-observednormalSNeIa,SN2001el(Krisciunasetal.2003),SN2003du(Stanishevetal.2007),andSN2005cf(Pastorelloetal. 2007). B-band rise time of 20.8 days, a peak brightness of - 19.6, - 19.0, and - 19.2in the U, B, and V band, respectively, and a light curve decline rate in the B band of ∆m = 0.95). 15 These values are well within the range of normal SNe Ia (Hickenetal.2009). Moredetailedvaluesforselectedbands oftheangle-averagedlightcurvesaregiveninTable1. Inparticular,theangle-averagedlightcurvesintheU andR bandagreeverywellwiththoseobservedfornormalSNeIa. The angle-averagedsynthetic B-bandlightcurveis about0.3 magnitudesfainteratmaximumthanthethreesupernovaewe comparewith andslightly brighterfrom25daysaftermaxi- mumonwards. Theangle-averagedV-bandlightcurveofour modelagreeswellwiththedatauptoabout30daysaftermax- imum,butdeclinesslightlymoreslowlyafterwards. Due to the asymmetric ejecta structure, our model FIG.4.—Maximumlightspectrumofourmodel. Theredlineshowsthe spectrumofourmodelonedayaftermaximumlightintheB-band.Theblack lightcurvesshow a non-negligiblesensitivity to line-of-sight lineshowstheobservedspectrumofSN2003du(Stanishevetal.2007)atthe effects. In the B band, for example, we find peak magni- sametime. tudes between -19.5 and -18.7. At the same time ∆m (B) 15 showgoodagreementwith observationsin theopticalbands variesbetween0.5and1.4,roughlyalongthePhillipsrelation and reproducegeneralpropertiesof normalSNe Ia havinga (Phillipsetal.1999).FortheUband,thescatterisevenlarger 5 whileitdecreasesintheredderbands. Forlowerphotonen- plosion indirectly. The metallicity of the two white dwarfs ergies,theasymmetryoftheejectaislessimportant,sincethe hasonlyasmallimpactonthefinalcompositionoftheejecta opticaldepthsaresmallerandphotonsprobealargerfraction by changingthe mixtureof iron-groupelementssynthesized of the total ejecta, thereby making the observablesless sen- (Simetal.2010). sitive to line-of-sighteffects (compare Kromer&Sim 2009; The momentat which the detonationforms is an artificial Kromeretal.2010). parameterofourmodel. Physicallyitwill bedeterminedby The angle-averagedlightcurveof our model in the I band the properties of the binary system discussed above. Since agreeswellwiththeobservationsuptomaximumlight.After- wecannotresolvetheformationofthedetonationmicroscop- wardsitisbetween0.2and0.7magnitudesbrighterthanour ically, however, we have to infer the most likely place and comparisonSNeIa.Thisoffset(intheIbandaftermaximum) timeforittoformfrommacroscopicproperties. Onceweas- can be attributed to a flux excess in the CaII NIR triplet in sumethatadetonationformsonthesurfaceoftheprimaryits thesyntheticspectra. Thiscouldpointtoanover-abundance exact place and time are only secondary effects: the choice of calcium in the model. However, it is more likely to be a for the moment of detonation affects the densities at which shortcoming of our radiative transfer treatment, which uses thematerialofthesecondarywhitedwarfisburned(sincethe the simple van Regemorter approximation (vanRegemorter detonationoccurswhilethesecondaryisbeingdestroyed)but 1962)totreatcollisionalexcitation. Thuswelikelyunderes- itdoesnotstronglyaffecttheburningoftheprimarybecause timatetheeffectivenessofcoolingbyforbiddentransitionsof itisnotdynamicallyaffectedbythemerger. heavy elements and therefore predict that too much cooling Compared to the merger of two 0.9M white dwarfs ⊙ occursviathestrongdipoletransitionsofCaII. (Pakmoretal. 2010) the mergerwe presenthere mainly dif- There is good agreement between model and data in the fersin themassof theprimarywhite dwarf. Since itiscon- NIRbands(J,H,K). Inparticular,ourmodelreproducestime siderably more massive, its central density is higher and its and brightness of the second peaks and even the light curve materialis burnedpredominantlyto iron groupelements. In declineatmorethan40daysaftermaximumquiteaccurately. addition,themassratioofthebinarysystemwemodelhereis However,highprecisionmodelingoftheNIRlightcurvesre- wellbelowunity.Therefore,themorecompactprimaryisnot quiresan extensiveatomic data set to properlysimulate flux subjecttonoticeabletidalforcesfromthesecondary. redistribution by fluorescence (Kasen 2006; Kromer&Sim In addition, although exact initial conditions may weaken 2009). Here,however,wehaverestrictedourselvesforcom- the merger, we show that it still leads to the formation of putational reasons to a simplified atomic data set (cd23_gf- hot spots on the surface of the primary, in which densities 5 of Kromer&Sim 2009) with only ∼400,000 lines. This and temperatures are sufficiently high that a detonation is has been shown to give reliable results in the optical bands plausible. This is consistent with the propertiesof hotspots butslightlyunderpredictstheNIRbrightness(Kromer&Sim seen in previous studies with less relaxed initial conditions 2009)betweentheprimaryandsecondarypeaks. (Pakmoretal.2010,2011)andalsowithveryrecentsimula- Fig.4showstheangle-averagedspectrumofourmodelone tions by Raskinetal. (2011) who found similar hot spots in dayafterB-bandmaximum. Forcomparisonwe overplotan calculations with relaxed initial conditionsand only slightly observedspectrumofthenormalSN2003du(Stanishevetal. smaller resolution than our simulation. Note that Danetal. 2007)atthesameepoch. Ourmodelshowsmostofthechar- (2012)donotfindhotspotsinsimilarsystemswithexactini- acteristic features of SNe Ia, particularly the defining SiII tialconditionsbutmorethanafactoroftenfewerparticles. doubletat λλ6347,6371but also the weaker SiII featuresat Our model can be interpreted as a pure detonation of an λλ5958,5979 and λλ4128,4131, the MgII triplet at λ4481 isolatedsub-Chandrasekharmasswhitedwarfasdescribedin and the CaII H and K absorption. The SII W-feature at Simetal. (2010) with an additional componentfrom the re- ∼5400Å (which is a blend of several lines) is also visible mainsofthesecondarywhitedwarfsurroundingthesystem. though it is weaker than in SN 2003du. In the red tail of Quantitatively, however, the color lightcurves of our model thespectrumtheCaIINIRtripletisclearlyvisibleaswellas agreesignificantlybetterwithobservationsthanthetoymod- some indicationof the OI tripletλλ7772,7774,7775. More- els of Simetal. (2010). In particular, our modelalso shows over,theoverallspectralshapeandthevelocity-shiftsofmost goodagreementintheNIR-bandsandreproducestheposition of the line featuresin the observedspectrumare well repro- ofthesecondarypeaksinthesebandsverywell. duced,indicatingthatthevelocitystructureofourmodelisa Thisdifferencetothetoymodelsislikelytobeassociated goodrepresentationofthatinrealSNeIa. with a different density profile and composition structure in the inner parts of the ejecta. As discussed in Section 3 this 5. DISCUSSION is a result of the presence of the secondarywhite dwarf and The dominantparameterthat determinesthe brightnessof its interaction with ashes of the primary when they expand. the explosionin our modelis the mass of the primary white Also, the asymptotickineticenergypermassofthe ejectais dwarf. Inthe mergerthe primaryremainsmostly unaffected smallerforourmergermodelthanfordetonationsofisolated whereasthe secondary white dwarf is destroyed. Therefore, sub-Chandrasekhar mass white dwarfs, because the burning becausethedensityprofileoftheprimarywhitedwarftofirst ofthe secondarywhitedwarfis less completeand hencethe order only depends on its mass and the density stays high averageenergyreleasepermassissmaller. enoughtoburntoiron-groupelements(56Ni)onlyinthepri- Overall, our explosion reproduces observational data of mary white dwarf, the brightness of the supernova directly normalSNeIaofthesamebrightnessreasonablywell. Since correlateswiththemassoftheprimarywhitedwarf. the time span from the onset of mass transfer between the Physicalparametersofsecondaryimportancearethemass two white dwarfs until the ejecta reach homologous expan- of the secondary white dwarf and the composition of both sionisveryshort(onlyoftheorderofafewminutes)thereis whitedwarfs(C/O-ratioandmetallicity). Thematerialofthe noextendedouterenvelopetheexplosionejectainteractwith secondaryis burnedonlyto intermediate-masselementsand laterthanafewminutesaftertheexplosion,incontrasttothe oxygen and therefore only affects the brightness of the ex- modelbyFryeretal.(2010). 6 R.Pakmoretal. Observational constraints (Napiwotzkietal. 2005, 2007) ACKNOWLEDGEMENTS on the number of double white dwarf binaries significantly This work was supported by the Deutsche Forschungs- moremassivethanaChandrasekharmassarestillnotveryre- gemeinschaft via the Transregional Collaborative Research strictive. Ifviolentmergerscontributenoticeablytothetotal Center TRR 33 “The Dark Universe”, the Excellence Clus- SNe Ia rate, our calculations suggest that it will be hard to ter EXC153 “Origin and Structure of the Universe” and the distinguishthemergereventsfromthebulkofnormalSNeIa Emmy Noether Program (RO 3676/1-1). Parts of the simu- via optical/NIR lightcurves and optical spectra. Further de- lations were carried out at the John von Neumann Institute tailed work is therefore needed to investigate whether there for Computing (NIC) in Jülich, Germany (project hmu14). are other characteristic properties of SN Ia explosions from R. P. gratefully acknowledgesfinancial supportof the Klaus violentwhitedwarfmergersandtoexplorehowtheobserva- TschiraFoundation. tionaldisplaychangeswiththepropertiesoftheirprogenitor system. 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