19 95MNRAS.277. .945T 12,7345 4 6 2 2 6 5 1 1 67 Mon. Not.R.Astron.Soc.277,945-958(1995) evolution oftheGalaxy,LMCandSMC Relative frequenciesofTypelaandIIsupernovaeinthechemical T. Tsujimoto,K.Nomoto,Y.Yoshii,M.Hashimoto,S.Yanagidaand DepartmentofPhysics,FacultyScience,KyushuUniversity,Fukuoka810,Japan InstitutfürtheoretischePhysik,UniversitätBasel,Switzerland InstituteofAstronomy,FacultyScience,UniversityTokyo,Mitaka,Tokyo181,Japan DepartmentofAstronomy,SchoolScience,UniversityTokyo,Bunkyo-ku,Tokyo113,Japan F.-K. Thielemann DepartmentofEarthScience,FacultyIbarakiUniversity,Mito,310,Japan ResearchCenterfortheEarlyUniverse,SchoolofScience,UniversityTokyo,Bunkyo-ku,Tokyo113,Japan NationalAstronomicalObservatory,Mitaka,Tokyo181,Japan fied intosubclassesofTypela,lbandIc(e.g.Branch, Type IandII,supernovaearefurtherclassi- Nomoto &Filippenko1991).Thesedifferenttypesofsuper- galaxies. Thereexisttwomajortypesofsupernovae,namely Supernovae arethesitesofheavy-elementproductionin heavy elementsondifferenttime-scalesduringthechemical novae havedifferentprogenitors,thusproducing time oftheirmassiveprogenitorsisabout10"yr,much Accepted 1995June23.Received9;inoriginalform1993July23 Ic) iftheybelongtoclosebinarysystems.Becausethelife- if theyaresinglestars,orasTypeIb/Icsupernovae(SNelb/ massive than10MexplodeasTypeIIsupernovae(SNeII) evolution ofgalaxies.Weassumethatstarsinitiallymore heavy-element enrichmentin theearlyphasesofgalactic shorter thantheageofgalaxies,SNeIIandIb/Iccause elements onamuchlongertime-scale, inthelaterphasesof I INTRODUCTION genitors iseither relatedtothelifetimeof thelow-mass galactic evolution.Theevolutionary time-scaleoftheirpro- yields fromSNeIIwiththose SNeIb/Ic. evolution. Inthispaper,we associatetheheavy-element ©1995 RAS 0 Type lasupernovae(SNela), bycontrast,produceheavy © Royal Astronomical Society • Provided by the NASA Astrophysics Data System ABSTRACT heavy elementsandtheirisotopes,alsowiththeabundancesofin The predictednucleosynthesisproductsofTypelaandIIsupernovaeare the LMCandSMC.Aidedbyareasonablemodelofgalacticchemicalevolution, ratio ofthetotalnumbers(ofalltime)TypelatoIIsupernovaethatbest combined withvariousparameterratiosandcomparedthesolarabundancesof Type lasupernovaeintheMCs. larger thanthatfortheGalaxy,yieldingA/=0.2-0.3.Wediscussseveralpossible Galaxy, inagreementwithcurrentobservations.FortheMCs,however,thisratiois reproduces theobservedabundancesisdeterminedtobeA/=0.15for Magellanic Clouds. Key words:supernovae:general-galaxies:abundancesevolution star formationhistoryscenariosthatmayaccountforsuchanenhancedfrequencyof Ian Ian the initialseparationofdoublewhitedwarfs,ifamerging companion inabinarysystem,ifRochelobeoverflow replenishes thewhitedwarfbyaccretion,oritdependson the evolutionarytime-scaleofSNlaprogenitors,whichisas neighbourhood starshasimposedastringentconstrainton scenario isadopted.Anincreasingbodyofdataforsolar their rolesinthechemicalevolutionofgalaxiesarecon- Branchetal. (1991). For detailsoftheprogenitor-supernovaconnection,see result ofthermonuclearexplosionsaccretingwhitedwarfs. element yieldsfromSNela,weassumethatlaare a long as¿«1.5Gyr(Yoshii,Tsujimoto&Nomoto1995), and weadoptthisvaluethroughoutpaper.Fortheheavy- was highlightedbythefactthat areasonablemixtureofthe Greggio 1986;Matteucci1991a). Theimportanceoftreating to theirongroup.Thefirst qualitative workthatdemon- explain thesolarabundances of heavyelementsfromoxygen heavy-element yieldsfromSNe laandSNeIIisableto SNe laseparatelyfromII inmodellinggalacticevolution siderably different(forareviewsee,e.g.,Matteucci& strated thiswas byNomoto,Thielemann&Wheeler (1984a). Ia The nucleosynthesisproductsofSNelaandII 19 95MNRAS.277. .945T Yanagida, Nomoto&Hayakawa(1990),etal. works, theexplosionmodelofa25-Mstar(Nomotoetal. extended thisapproachandobtainedtheratioofSNelato (1990) andNomoto,Shigeyama&Tsujimoto(1991) 946 T.Tsujimotoetal for awiderangeofprogenitormasswasavailable(e.g. isotopes oftheelementsfromoxygentonickel.Inthese SNe IIthatreproducesthesolarabundancesofpossible products ofSNen,becausenoextensivesetcalculations Artnett 1978;Woosley&Weaver1986). al. 1990,1991)wasusedtorepresentthenucleosynthesis from SNeIIforprogenitormassesintherangeof13to Nomoto &Hashimoto(1990,1994,1995)haverecently al. (1993a,1994,1995,inpreparation)andThielemann, to galacticchemicalevolution;particularlythemassrange presented detailedcalculationsofnucleosynthesisproducts 1984a) orofa20-Mstar(Yanagidaetal.1990;Nomoto the ironyieldfromSNeII,wereconstrainedbysolar- neighbourhood observations.Theirstudiesenablean and slopeoftheinitialstellarmassfunction(IMF),butalso 70 M©.Tsujimotoetal.(1994,1995b)appliedtheseresults which canthenbecomparedwiththeobservedratioin the IMF),andthereforeafairestimateofratioSNela II (averagedovertheprogenitormasswithaweightingfor estimate tobemadeofthenucleosynthesisproductsSNe François 1989;Matteucci1991b)usedeightelements(C,N, Arnett, Schramm&Truran(1989)usedtwoelements(Oand based ononlyalimitednumberofelements.Forexample, to SNeIIcanbefound(A^/Nn~0.15;seeSection3.2), 0 Fe) andobtainedaslightlylowerratiothanourown,Af/7V Galaxy (e.g.vandenBergh&Tammann1991). the bestfittoalltheirsolarabundances,wehaveobtained boundary conditionofthemodel.Inthispaper,however, Matteucci andhercollaboratorsfittedtheabundanceratios using 14elementsaswelltheirisotopesandallowingfor their individualabundanceswiththesolarasa O, Ne,Mg,Si,S,Fe)andobtainedahigherratioA/7V~ among theelementstoobservationsbutdidnotcompare Dopita 1990,1992).Wenotethattheabundancepatterns being accumulated(e.g.Russell&Bessell1989; present. o observed fortheMCsarequitedifferentfromsolar observations ofabundancesvariousheavyelementsare abundance patterncanalsobeappliedtotheLargeand the Galaxy.SincenucleosynthesisargumentsindicatethatFe of differentratiosfortheMCsandGalaxy, abundance pattern(seethereferencesabove,butalsoPagel Small MagellanicClouds(LMCandSMC),forwhichthe Aia/An -0.15fortheGalaxy,whichismostrealisticat understanding thatA/would beenhancedintheLMC is mainlyproducedbySNela whileOismainlyproducedby concluded that7Vi/AfortheLMCissmallerthan because theobservedO/Feratio fortheLMCissmallerthan Ian that fortheGalaxy.Underthese circumstances,inSection SNe II,herconclusionseems to betheinverseofourgeneral 1/4. InobtainingthesevaluesofAf/A,Arnettetal.and have determined A/fortheMCsthrough acomparison 4.2, aidedbyreasonablemodels ofchemicalevolution,we 1992). Matteucci(1991b)explainedthisdifferenceinterms Ian ~ 1/10,whileMatteucciandhercollaborators(Matteucci& Ian an Ian Ian Hashimoto, Nomoto&Shigeyama(1989),Hashimotoet To date,similarattemptstoestimate7V/7Vhavebeen Our methodofconstrainingtheNJAratiofroman Ian Xn © Royal Astronomical Society • Provided by the NASA Astrophysics Data System between thepredictedandobservedabundancesof10 that A^ia/NforboththeLMCandSMCislargerthan elements fortheLMCand12SMC.Wefind Nucleosynthesis productsofSNeIIarethosefoundafter Galaxy, insharpcontrasttoMatteucci’sconclusion. have beencalculated(Hashimotoetal.1989,1993a,1994, masses ofsynthesizedheavyelementsin13-70M©stars explosive nuclearburningbymassiveprogenitorstars.The 2 NUCLEOSYNTHESISPRODUCTSOFTYPE tion). Inthepresentstudy,weassumethatlowermass bound oftheprogenitorsSNeII(oruppermass and theresultsforvariousmassesofprogenitorstarsare of thewhitedwarfprogenitors)ism=10M©andthat summarized inTable1(Hashimotoetal.1995,prepara- heavy-element productionfromastarofmassmis the mass-lossrateduringAGBphaseof8-10M©stars, negligible. Infact,theexactvalueofmstronglydependson undergo supernovaexplosions(Hashimoto,Iwamoto& n Nomoto 1993b). elements from8-10M©starsisnegligibleevenifthese and isthushighlyuncertain,theproductionofheavy 1995, inpreparation;Thielemannetal.1990,1994,1995), corresponds toacriticalmassmabovewhichstarsform Tsujimoto etal.(1994,1995b)foundthatm=50±10M© black holeswithoutejectingheavyelementsintospace. where M^m)istheithheavy-elementmassproducedina Salpeter’s IMF,thatis, averaged overSNeIIprogenitorstarswithaweightof II ANDTYPEIASUPERNOVAE x H] diagramforthesolar-neighbourhoodobservations.Table is reasonabletoreproducethebreakin[O/Fe]versus[Fe/ star ofmain-sequencemassm.Theupperlimitm x of ra=50and70M©;theformerisbestestimatem their isotopes(atotalof42species)fortworeferencevalues x nucleosynthesis calculationshavebeenperformed.Thetabu- lated resultsareusedtocalculatetheabundancepattern 2 givestheaveragesynthesizedmassesof18elementsand per unitmass(Anders&Grevesse1989).InFig.1weshow and thelatterisuppermassendofstarsforwhich the normalizedpatterndefinedasxjx^O)form=50M©. Xi =M/Yi,whichisnormalizedtothesolarx((D)Z / Yokoi 1984b;Thielemann,Nomoto &Yokoi1986),which carbon deflagrationmodelW7(Nomoto,Thielemann& BH has beenupdatedwiththeuse ofthelatestnuclearreaction rates (Thielemann,Nomoto & Hashimoto1993).Table2 BH Fig. 1.Notice thatx/jc(0)<$Cx ). Thisclearly pattern normalizedtosolarvalues inthesamemanneras the updatedW7model,and Fig.2showstheabundance gives themassesof18elements andtheirisotopesbasedon u uBH u iJ i 0Fe For ourlateruse,wedefinetheheavyelementmass,, The nucleosynthesisproductsofSNelaarethosefromthe n where Zistheobservedabundanceofithelement ¿ * m u 10M© (1+x) M(m)~d / (1+Ar) m d ©1995 RAS,MNRAS 277,945-958 19 95MNRAS.277. .945T an are ta indicates thatSNelaenhancetheironabundancerelative to oxygenduringthechemicalevolutionofgalaxies. the Galaxy,andwbemassfractionofsynthesized where M=X!/^,iadMi XuikenfromTable2. Let NbethetotalnumberofSNethathaveeveroccurredin in low-massstars.Letrbethemassfractioncontributedby supernovae The abundance patternx¡tobecompared withthesolar we defineras elements thathavebeenejectedfromSNeandnotlockedup 3.1 RelativecontributionsofTypelaandII 3 THESOLARABUNDANCEPATTERN SNe laperunitmassofallheavyelementsinthegas.Then ©1995 RAS,MNRAS 277,945-958 r= , (2) Ia w iaMiNi+wM anu wMN laia © Royal Astronomical Society • Provided by the NASA Astrophysics Data System 20 21 30 24 22 32 26 25 23 35 34 33 28 27 36 37 29 39 38 46 44 40 41 48 47 50 49 52 50 54 53 62 60 38 59 57 56 54 55 Species Ne Ne i*o Table 1.NucleosynthesisproductsofSNeIIforvariousprogenitormasses. Si Mg Ne 18 s 31 p Mg Mg Na cit s s Si A1 Ar cit Si Kf Ar Tif Caf Ca Kf Tif Tif Tit Tif Cr Cr Cr Cr involved intheirabundancesTypeIIsupernovae(seeSection2). Ni Ni Ni Cof Fe Fe Fe Mn f Thesespeciesarenotusedinminimizingg(r)equation(3)becauseoftheuncertainties 0 m=13 Mq 9.44E-09 2.25E-02 2.08E-04 1.51E-01 8.96E-04 9.23E-03 7.27E-04 6.68E-02 2.95E-04 7.99E-04 4.85E-04 1.01E-04 2.36E-03 6.73E-06 3.70E-Ö5 1.04E-03 1.38E-03 2.56E-06 2.53E-03 1.46E-02 1.87E-03 3.56E-10 5.13E-06 1.19E-Ô4 2.30E-05 3.45E-06 1.83E-03 4.86E-03 3.65E-04 3.35E-08 9.34E-05 3.72E-03 5.82E-03 2.10E-03 1.95E-05 1.68E-04 1.22E-04 1.42E-06 1.15E-03 1.50E-01 1.05E-03 1.39E-04 3.55E-01 m= 15Mq 3.93E-05 2.08E-02 4.01E-03 3.16E-02 2.03E-03 2.55E-03 3.01E-02 4.04E-03 7.16E-02 1.35E-02 9.60E-05 6.55E-04 3.25E-03 1.25E-02 1.53E-04 6.49E-04 5.63E-03 3.45E-05 5.29E-03 3.31E-05 9.60E-06 1.49E-03 6.26E-06 7.49E-05 2.37E-06 4.74E-04 4.09E-08 6.10E-06 3.75E-06 4.90E-03 4.49E-03 5.15E-05 9.50E-04 3.36E-03 7.50E-03 1.21E-09 1.58E-04 1.35E-04 1.36E-03 1.22E-04 1.44E-01 8.67E-03 7.92E-01 m=18 Mq 2.19E-03 2.74E-02 7.25E-03 4.11E-04 8.69E-02 5.44E-03 5.94E-03 3.62E-02 3.76E-02 3.33E-03 7.54E-03 1.61E-01 8.95E-05 6.13E-03 6.29E-04 1.76E-03 6.72E-06 3.66E-05 1.89E-03 1.48E-04 8.59E-05 3.11E-07 5.11E-03 4.82E-05 2.53E-08 7.49E-05 7.54E-06 2.23E-06 1.04E-05 8.71E-04 7.57E-02 6.04E-03 5.48E-04 2.52E-04 3.08E-03 2.17E-03 1.43E-05 1.50E-04 1.44E-03 1.17E-10 Synthesized isotopicmass(Mq) Relative frequenciesofTypelaandIIsupernovae947 8.68E-03 m=20 Mq 2.29E-01 2.93E-02 3.03E-04 1.48 2.29E-02 7.19E-03 8.50E-02 4.96E-06 8.84E-05 9.80E-03 1.85E-02 1.47E-01 1.15E-03 6.05E-05 1.55E-02 1.74E-02 3.24E-05 1.05E-03 6.81E-06 9.15E-05 3.25E-03 3.78E-03 1.26E-03 4.89E-06 3.25E-04 6.26E-09 8.64E-04 3.54E-05 7.12E-05 2.27E-04 7.26E-04 2.18E-03 3.71E-03 7.32E-02 1.28E-06 3.07E-03 2.52E-03 1.12E-10 1.85E-04 1.73E-06 1.31E-04 x =rMJM^(l-r)M/,(3) where irunsovertheheavyelementsandtheirisotopes ing thefollowingfunction(Yanagidaetal.1990;Nomoto and themostprobablevalueofrisdeterminedbyminimiz- jc, (O)isthereforewrittenas theoretical valuesofx¿forsomeparticularelementsshow g(r)='Z [log*,■-logx¡(O)f/n,(4) al. 1990,1991): chosen intheminimizationprocedure.Wenotethat relatively largedeviationsfrom thesolarvalues.Someof products duringcorehelium burning (Prantzos,Hashimoto these valueswouldbelarger ifs-processnucleosynthesis tions (Nomoto&Hashimoto 1988).Itisalsothecasethat & Nomoto1990)andshell carbon burning(Raiterietal. 1993) wereincludedinpre-supernova evolutionarycalcula- iulull some oddZelements andneutron-richspecies areproduced i =l 5.94E-01 2.99 m=25 Mq 3.22E-03 3.39E-02 6.69E-03 3.17E-02 3.92E-02 6.81E-03 6.97E-03 3.84E-02 9.02E-04 1.59E-01 2.77E-03 2.20E-04 1.03E-01 1.81E-02 6.15E-03 3.47E-05 6.72E-05 1.95E-02 2.79E-06 6.71E-03 6.84E-06 7.24E-04 2.11E-05 4.81E-03 5.90E-10 6.01E-06 8.98E-05 9.11E-07 6.67E-04 5.24E-02 2.41E-08 5.01E-05 1.32E-05 5.02E-04 2.19E-05 1.31E-03 1.70E-04 1.33E-03 1.16E-03 1.39E-04 9.11 6.58E-01 m=40 Mq 5.66E-02 2.36E-03 4.29E-01 4.81E-02 3.54E-01 2.37E-02 5.99E-03 4.32E-02 8.05E-02 1.79E-06 5.43E-02 3.11E-02 4.75E-04 7.49E-04 9.14E-03 1.07E-01 2.56E-02 3.43E-05 3.83E-04 1.77E-01 2.77E-03 3.56E-05 2.00E-05 1.14E-02 2.81E-08 9.74E-07 3.56E-04 2.00E-10 2.17E-05 1.17E-04 8.41E-04 2.51E-05 2.29E-03 7.50E-02 9.17E-03 3.88E-04 3.31E-03 1.49E-04 1.58E-04 1.11E-04 2.14E+01 2.00 3.80E-03 m=70 Mq 6.98E-02 5.23E-02 2.05E-01 2.91E-01 7.87E-01 7.55E-01 2.57E-02 1.14E-02 2.92E-02 2.14E-02 2.84E-05 3.84E-04 6.16E-03 1.98E-02 1.44E-01 1.01E-01 2.97E-04 1.02E-03 1.00E-01 1.08E-01 6.26E-07 2.56E-10 6.97E-06 1.01E-04 1.76E-03 3.64E-04 6.86E-04 7.50E-02 7.61E-08 1.44E-05 9.25E-03 3.83E-03 5.81E-03 1.42E-04 1.00E-04 1.01E-04 1.77E-03 1.59E-04 1.28E-03 19 95MNRAS.277. .945T 948 T.Tsujimotoetal. very sensitivetotheneutronexcessofthinlayer,and Thielemann etal.1993,1995.)Theisotopesofthese in thedeepestlayerofejecta,amountswhichare for 14elements(O,Ne,Na,Mg, Ar,Si,P,S,Ca,Cr,Mn, Table 2aretakenasastandard inputandareusedtorepro- detailed discussion,seeHashimotoetal.1993a,1994; not usedintheminimizationprocedure. elements areshownbyopen circles inFigs1and3are are thereforesubjecttolargeuncertainties.(Foramore Fe, Ni)andtheir isotopes(atotalof31species). Fig.3shows duce thesolarabundancepattern (Anders&Grevesse1989) Theoretical valuesofMand Mforra=50Min l Ia / nuo 21 20 30 23 22 33 32 28 27 26 25 24 46 37 35 34 29 39 38 36 49 48 47 44 40 41 50 53 52 50 62 60 57 56 58 59 54 55 54 Table 2.NucleosynthesisproductsofSNIIand la. their abundancesinTypeIIsupernovae(see to massumingaSalpeterIMF. * Averageoverthemassrangefromra=10M Section 2). equation (3)becauseofuncertaintiesinvolvedin f Thesespeciesarenotusedinminimizingg(r) 1«0 Species Ne Ne 31 p Si Na Ne s s Si A1 Mg Mg Mg i8 u 0 Tit cit cit s Si Kf Ar Ar Tif Tif Tif Caf Ca Kf Cr Cr Cr Tit Ni Ni Fe Fe Ni Cof Fe Mn Cr 0 © Royal Astronomical Society • Provided by the NASA Astrophysics Data System , 4.61E-03 m=50Mo‘ 6.51E-03 2.12E-01 8.83E-02 8.99E-03 2.01E-02 1.80 6.62E-03 8.05E-03 2.62E-03 3.84E-02 1.08E-03 1.83E-02 4.64E-05 5.98E-06 5.53E-05 5.77E-03 5.07E-06 6.23E-05 1.05E-01 1.48E-02 1.44E-02 5.09E-04 8.44E-02 3.62E-03 3.86E-04 2.33E-08 3.81E-10 2.11E-06 7.48E-06 1.21E-03 3.63E-03 7.27E-05 2.72E-03 1.78E-04 1.37E-03 1.88E-05 1.01E-04 ti 1.15E-03 1.16E-04 1.75E-03 1.19E-04 Synthesized mass(Mq) Type 11 , 4.51E-03 2.69E-01 2.47 m=70Mo■ 4.54E-02 8.56E-03 2.11E-04 2.92E-02 3.25E-03 1.39E-03 6.54E-03 7.67E-03 1.99E-02 6.14E-05 7.67E-05 7.67E-05 1.95E-02 1.74E-02 1.12E-01 5.24E-04 3.78E-03 7.43E-05 2.75E-03 8.40E-02 3.77E-03 3.93E-04 1.98E-03 1.12E-02 1.25E-02 1.29E-01 1.53E-04 1.53E-04 1.94E-04 1.94E-04 1.63E-03 1.73E-03 1.22E-04 1.22E-04 1.17E-03 1.17E-03 1.94E-04 1.94E-04 1.94E-04 u 2.02E-03 4.05E-05 2.49E-03 8.46E-06 8.25E-10 9.86E-04 8.50E-03 6.32E-05 4.50E-04 4.18E-04 8.61E-04 3.18E-05 8.41E-02 3.98E-05 1.43E-01 2.03E-04 6.04E-07 7.44E-06 8.52E-05 2.66E-03 2.55E-02 6.13E-01 8.23E-03 7.85E-04 5.15E-03 2.71E-04 8.86E-06 1.74E-03 1.50E-01 1.90E-03 1.49E-02 1.34E-04 Type la 1.05E-02 1.28E-01 1.90E-04 1.26E-05 1.69E-05 1.71E-05 1.23E-02 1.06E-03 1.02E-03 1.04E-01 W7 n r [0/Fclll W written as The contributionofSNelatoeachelementabundanceis in theinsetofthisfigureg{r)isplottedasasequencer. the normalizedabundancepatternx,/*,(O)calculatedfrom equation (3)withthemostprobablevaluer=0.09,and found thatthemostprobablevalueofrinthiscaseis limit asfarra^30M.Thevalueofrdoesnotdepend the 14elementschosen,weobtainedr=0.08asmost on becauseheavy-elementproductionfrom8-to10-M and istabulatedinTable3. function g{r)intheinset.Furthermore,werepeated this casewithr=0.08,isshowninFig.4,togetherthe probable value.TheresultingabundancepatternO),in of elements.Byaddingtheisotopicabundanceseach depend onm.Weexaminedhowrdependsourchoice rp/M+(1—r)/M’ P pMiJM stars isnegligible,sothatM/inequation(3)doesnot than 10percentonly.Thus,consideringthestandardmodel changing theslopeindexfromx=0.5to2changesrbyless calculations fordifferentIMFslopesandfoundthat r =0.10,andthatitisveryinsensitivetotheuppermass and itsvariantsabove,thevalueofrisconstrainedtobe p Table 2,wecanestimatetherelativefrequencyofoccurrence r =0.09±0.01againstpossibleuncertaintiesintheanalysis. of SNelaandIIfromequation(2): u0p where /and1-/arethemassfractionsofinterstellar where wandvvrepresentthemassfractionofheavy p o respectively, wewrite elements ejectedintotheinterstellargasfromSNelaand p xp Iapn iyla heavy-element abundanceaveragedoverthepresentmetal- gas andofstars,respectively.Here,Zisthepresentheavy- and oxygen andironaremostlyproducedbySNeIIla, SNe II,respectively.Assumingthatthisfractionisnot / n the ironabundance.Thiscontribution isestimatedfromthe licity distributionofstars.Inequation(8)thefactorcisintro- element abundanceinunitmassofthegas,andZis selective amongejectedelementsandrememberingthatthe p p duced tocorrectforthenon-negligible SNIIcontributionto p correction factoriswrittenas O/Fe ratioformetal-poorstars, becausetheirOandFe abundances exhibitgenuine products ofSNeII.Now,the Wla^la. rM w,= p w„=- c =1-io~ (Z/)(Z, g Ian g s \\N\\ (l—r)M pn g 0FegQ pldi Using Mform=70Masanotherinput,wehave UIuo Using therthusobtained,andtakingMfrom pIan (1 -/g)cZ+/c’ ss>FeggjFe l-/g)Z,o+/gZ sgi0 /gZ, C g^g>Q fggZ,F g 0.184, ©1995 RAS,MNRAS 277,945-958 (6) (8) (7) 19 95MNRAS.277. .945T |o/Fe| Figure 1.AbundancepatternfromTypeIIsupernovaexplosions.Relativeabundancesofsynthesizedheavyelementsandtheirisotopes, minimizing g(r)inequation(3),becauseofuncertaintiesinvolvedtheirabundancesTypeIIsupernovae(seeSection2). normalized tothecorrespondingsolarabundances,Xy/x^O),areshownbycircles.Thespeciesindicatedopencirclesnot usedin Figure 2.AbundancepatternfromTypelasupernovaexplosions. Therelativeabundancesofsynthesizedheavyelementsandtheirisotopes, normalized tothecorrespondingsolarabundances,x,/x,(G),areshown bycircles. where [0/Fe]standsfortheobservedoxygenexcessrelative or to ironformetal-poorstarswith[Fe/H]^-1. formation rateisnotconstant overtheageofGalaxyand depend onthestarformationhistory. Ifstarformationoccurs continuously inthesolarneighbourhood (Gallagher,Hunter has apeakasinferredfrom the metallicitydistributionof & Tutukov1984),wewould expect thatw~vv.Ifthestar c =l-lO-"(Z/)(Z/Z,(9) solar-neighbourhood Gdwarfs, theefficiencywmightbe ©1995 RAS,MNRAS 277,945-958 slightly larger than w.Thisnaiveargument givesarough n Ian soFe0 Ia u It isapparentfromequations(7)and(8)thatw Ian © Royal Astronomical Society • Provided by the NASA Astrophysics Data System Relative frequenciesofTypelaandIIsupernovae therefore of/V/yV,needmodelsgalacticchemicalevolu- tion, aswediscussbelow. estimate ofA/^0.184.Preciseestimatesw,and the inputparameterssummarized inTable4,thetime-scale We havemadeasimplified model ofchemicalevolution (Yoshii etal.1995)andwedo notrepeatthemhere.Among which isfairlystandard,allowing materialinflowfrom outside theconsideredzone (cf.Tinsley1980).Technical 3.2 Chemicalevolutionmodelforthesolarneighbourhood details ofthemodelarediscussed fullyinaseparatepaper t ofinfall,the lifetimetofSNlaprogenitors, thepower- Ian Ianlau m Vd 949 19 95MNRAS.277. .945T uncertainties involvedintheirabundancesTypeIIsupemovae(seeSection2).Theinsetshowstheminimizingfunctiong(r) forwhich Figure 3.Solarabundancepatternbasedonsynthesizedheavyelements,fromacompositeofTypelaandIIsupernovaexplosionswith abundances, Xy/x^O),areshownbycircles.Thespeciesindicatedopencirclesnotusedinminimizingg{r)equation(3), because of the mostprobableratoofr.Therelativeabundancessynthesizedheavyelementsandtheirisotopes,normalizedtocorresponding solar 950 T.Tsujimotoetal r =0.09. fraction/ ofgasistakenfrom Young&Scoville(1991),and various references(Fig.5a). the oxygenexcess[0/Fe]„for metal-poorstarsistakenfrom Fe abundancesinthegas,Zand,areadjustedto given inTable 4 andthefeaturesofmodel areshownin tionary behaviourofOand Fe abundancesinthegasand reproduce thebreakin[O/Fe]versus[Fe/H]diagram(Fig. law indexkofthestarformationrate,andpresentO G dwarfs(Fig.5c).Ontheotherhand,presentmass stars. Thecalculatedquantities relevanttoourdiscussionare 5a) andthemetallicitydistributionofsolar-neighbourhood p p g g 0Fe element (*)r-p=0.09r=0.08 Table 3.RelativecontributionofSNlatotheabundanceeach species. p Note. Theresultsforisotopicabundancesareshowninthe are given. second column;otherwise,onlyresultsforelementabundances Using theseinputparameters, wecalculatetheevolu- Mn 0.800.77 Mg 0.02/0.00/0.000.01 m 11.8770.52/0,490.79 Na 0.00 Ca 0.280.25 Ne 0.00/0.00/0.020.00 Cr 0.45/0.45/0.55/0.550.44 Ar 0.29/0.120.24 Al 0.01 Fe 0.84/0.57/0.630.57 Si 0.21/0.02/0.040.17 O 0.01/0.000.01 P 0.060.05 S 0.29/0.32/0.120.25 © Royal Astronomical Society • Provided by the NASA Astrophysics Data System Solar Neighborhood CO co co jcg o »>=0.16 LMC 0.03 0.01 0.03 0.90 0.76 0.65 0.44 0.89 0.43 0.44 »>=0.19 SMC 0.91 0.01 0.03 0.78 0.68 0.48 0.46 0.35 0.03 0.00 0.90 0.48 135 4.1 RelativecontributionsofTypelaandIIsupernovae from thesolarabundancepattern; forexample,theO/Fe heavy elementsintheLMCandSMCcompiledbyRussell& Fig. 6showsasummaryoftheobservedabundances with ourestimatebasedonthenucleosynthesisarguments. Analyses oftheobservedratessupernovaexplosionsgive novae. production isdominatedby SNe IIandFeproductionis Dopita (1992).Theheavy-elementabundancesfortheMCs PATTERNS the associatedSNeIb/Ic)occurenceratesinrecentpast. here wouldbeclosetotheratioofSNelaII(and different relativefrequencybetween thesetypesofsuper- dominated bySNela,thedifferent O/Feratiosuggestsa ratio intheMCsissmallerthan thesolarratio.AsO are deficientbyafactorof2-4relativetotheirsolar in theGalaxy.Ifstarformationratewerealmostconstant, total numbersofSNelaandIIthathaveeveroccurred from themodelthatwisslightlylargerthanvv,andwe abundances. TheMCabundance patternsarealsodifferent 4 THELMCANDSMCABUNDANCE 0.10 inSbc-Scgalaxies(Tammann1993),goodagreement ^ia/Ai/ib/ic ~0.15(vandenBergh&Tammann1991)and as inthesolarneighbourhood,numberratioobtained normalization inMaccordingtoequations(1)and(6).For (8/10) =0.11.Wenotethatthisistheratiobetween example, ifm,=8M,theratiowouldbe0.15x obtain, finally,7V/7V=0.15.Thisratiowouldbeslightly obtained fromequations(6)and(7).Wehaveconfirmed Fe abundances,Zand,thenwvvcanbe Figs 5(a)-(d).ThemodelOandFedistributionsofstars(Figs smaller ifm,werethan10M,duetothedifferent 5c andd)canbeusedtocomputethestellaraverageO Ian n 0 Ian s 0FeIan 0 ©1995 RAS,MNRAS 277,945-958 19 95MNRAS.277. .945T the mostprobableratioof/*.AsFig.2,butforabundancesheavyelementsbyaddingtheirisotopicandr=0.08. Figure 4.Solarabundancepatternbasedonsynthesizedheavyelements,fromacompositeofTypelaandIIsupernovaexplosionswith p? function g{r)andreproducetheMCabundancepatterns, input ofSNIIproductsbyaddingtheisotropicabundances Ni) andx^SMC)for12elements(O,Ne,Na,Mg,Si,S,Ar, of eachtheelements.AsinSection3.1,weminimize x,(LMC) for10elements(O,Ne,Mg,S,Ar,Ca,Cr,Mn,Fe, with themostprobablevalue r =0.16,andFig.8showsthe used toobtainr(Section3.1), therelativefrequencyw^N^/ Ca, Cr,Mn,Fe,Ni). in Section4.3, we retainsuchanIMFdependence ofMin of Minequation(1).Untilwe discusstheIMFforMCs same fortheSMC,withr=0.19. AlthoughtheIMFisnot ©1995 RAS,MNRAS 277,945-958 wN dependsontheIMFparameters throughthedefinition p p n u p u We adoptMforra=50fromTable2asastandard Fig. 7showsthefittedabundance patternfortheLMC, / nu0 © Royal Astronomical Society • Provided by the NASA Astrophysics Data System CO _co CO z CO z i5 o + between tandhasbeenstopped. Note. t,iandareinunitsofGyr.Intheburstmodels,starformation calculated quantities. input parameters.. * Thisvalueistheinputparameter. Table 4.Theinputparametersandcalculatedquantitiesinthechemicalevolution models forthesolarneighbourhood,LMCandSMC. x2 mIax2 [O/Fejn NiJNn [Fe/H], [Fe/H], [O/H], [O/H], h-h tjall Wla tun