Stellarcollapse 10
Webeginourstudyofastrophysicalsourcesofgravitationalwaves(GWs) withachapterdevotedtostellarcollapse.FromthepointofviewofGW physics,thisisinterestingforatleasttwodifferentreasons.First,stellarcollapsethroughsupernovaexplosionisitselfapotentiallyinteresting sourceofGWproduction.Second,stellarcollapsecanleaveasremnant acompactobject,suchasawhitedwarf(WD),aneutronstar(NS)or astellar-massblackhole(BH).Aswewillseeindetailinlaterchapters, thesecompactobjectsareamongthemostinterestingsourcesfromthe pointofviewofGWastrophysics.
Supernovae(SNe)areamongthemostspectaculareventsintheUniverse.Aswewilldiscussindetailinthischapter,therearetwovery differentmechanismsleadingtoSNexplosions:(1)Thegravitational collapseofthecoreofastar,oncethenuclearfuelthatfeedsthethermonuclearreactionsinsidethecoreisexhausted.AswewillseeinSection10.2.1,dependingonthepropertiesoftheprogenitor,thisleadsto eventsclassifiedastypeIb,IcortypeIISNe,andleavesbehindacompactremnant,usuallyaneutronstar(whichissometimesobservableasa pulsar)orpossiblyablackhole(BH).1 (2)Thethermonuclearexplosion
ofawhitedwarfthataccretesmassfromacompanion,goingbeyondits Chandrasekharlimit.ThisgivesrisetotypeIaSNe.Inthiscasethe starthatexplodesisdispersedinspaceanditsremnantisnotacompact object.Atypicalcore-collapseSNcanreleaseanenergy ∼ 1053 erg.Of thisenergy,99%isemittedinneutrinos,about1%goesintokineticenergyoftheejectedmaterial,andlessthan0.01%,i.e.about1049 erg,is releasedinphotons.Thecorrespondingpeakluminosityinphotonscan beoforderafewtimes109L orhigher.Thus,atypicalcore-collapse SNatitspeakhasanopticalluminositythatrivalsthecumulativelight emittedbyallthestarsinitshostgalaxy.Aswewillseeindetailinthis chapter,typeIaSNehavesimilarelectromagneticluminosities.Such events,whentheytakeplaceinourGalaxy(barringobscurationfrom dustintheGalacticplanebeyondafewkpc),canleadtotrulyimpressiveopticaldisplaysthathavebeenobservedbymankindsinceancient times.Anumberofmilestonesinastronomyareassociatedwithnearby SNexplosions.Tycho’sSNin1572andKepler’sin1604markedanew epochinastronomy,whilerecentdiscoveriessuchasthepulsarinthe remnantofthe1054CrabSNandthedetectionofneutrinosfromthe 1987ASNinthenearbyLargeMagellanicCloudrankamongthemilestonesofmodernastronomy.Wethereforefinditappropriatetobegin thischapterwithanintroductiontohistoricalSNe.
GravitationalWaves,Volume2:AstrophysicsandCosmology.MicheleMaggiore. c MicheleMaggiore2018.Publishedin2018byOxfordUniversityPress. DOI10.1093/oso/9780198570899.001.0001
HistoricalSupernovae4 10.2
PropertiesofSupernovae10 10.3
Thedynamicsofcore collapse21 10.4
GWproductionby self-gravitatingfluids35 10.5
Complements66
GWsfromstellarcollapse46 10.6
1
Therearealsoothermechanismsthat cantriggertheexplosion,asinelectroncaptureSNe,aswellasamorerefined classificationofSNtype,aswewilldiscussinmoredetaillaterinthechapter. Itisalsoinprinciplepossiblethatthe collapseproducesnovisibleSNevent andallthematterisswallowedbythe finalBH.
Table10.1 SummaryofthehistoricalSNe,andthesourceoftheirrecords,adapted fromGreenandStephenson(2003).RemnantsupdatedfromFerrandandSafi-Harb (2012).(Theidentifieroftheremnants,asforexampleinG120.1+01.4,referstoits Galacticcoordinates).WehaveclassifiedSN1604astypeIa,followingforexample Blair etal. (2007),Reynolds etal. (2007)andreferencestherein.Thenatureofthe CrabSN(corecollapseorelectroncapture)isdebated;seetheFurtherReading.
DateLengthofRemnantClassificationHistoricalrecords visibilityChineseJapaneseKoreanArabicEuropean
AD1604(Kepler’s)12monthsG004.5+06.8typeIafew–many–many AD1572(Tycho’s)18monthsG120.1+01.4typeIafew–two–many AD11816monthsG130.7+03.1?–fewfew–––AD1054(Crab)21monthsG184.6 05.8debatedmanyfew–one–AD10063yearsG327.6+14.6typeIamanymany–fewtwo AD3938monthsG347.3 00.5–one––––AD386?3monthsG011.2 00.3–one––––AD369?5months––one––––AD1858or20monthsG315.4 02.3typeIa?one––––
Thereadereagertoplungeintomore technicalissuescansimplyskipthis section
10.1HistoricalSupernovae
AswewillseeinSection10.2.1,inagalaxylikeourstheestimatedrate ofSNexplosionsisoforderoftwopercentury.However,intheGalactic planetheextinctionofvisiblelightsignificantlylimitsourview;for instance,theextinctionofvisiblelightfromtheGalacticcenterisabout 30magnitudes.Thus,aGalacticSNvisibletothenakedeyeisavery rareevent.However,whenanearbystarbecomesaSN,theeffectsare quitespectacular.Inthehistoricalperiod,thishashappenedahandful oftimes.
2Novaearisewhenawhitedwarf(WD) inabinarysystemaccretesmassfrom acompanionatarateofabout10 9 10 8M /yr.Thematerialaccreted isrichinhydrogenandaccumulates onthesurfaceoftheWD,whereit iscompressedbyfurtheraccretionand heated.Whenalayerofabout10 5 10 4M ofhydrogenhasbeenaccreted,arunawaythermonuclearreactiontakesplace,releasinganenergyof order1045 erg,whichisthereforeseveralordersofmagnitudesmallerthanin SNexplosions.TheWDthengradually coolsdownandgoesbacktoitsquiescentstate,wheretheaccretionprocess canstartagain,leadingtorecurrent novaexplosions.Acleardistinctionbetweenclassicalnovaeandsupernovae wasfirstmadebyBaadeandZwicky in1934.
EvidencefortheoldestSNeobservedbymankindisbasedonhistoricalrecords.SinceaGalacticSNremainsvisibleformonths,and sometimesuptoafewyears,onecanfocusonhistoricalrecordsofstars thatsuddenlyappearedandremainedvisibleforatleastfourmonths, inordertoeliminatemostnovae2 andthepossibilityofconfusionwith
comets(cometsbeingeliminatedalsobecauseoftheirevidentproper motion).
Table10.1givesasummaryofSNethathavebeenseenbythenaked eyeinhistoricaltimes,andforwhichwehavewrittenrecords,inthe last2000years.
SN185
TheoldestrecordedSNisSN185,whichwasfirstobservedonDecember7,185attheimperialobservatoryofLo-Yang,incentralChina. TheChineseastronomersrecordeditsappearanceanditsgradualfading,providingtheoldestplausiblehistoricalaccountofaSN.Itfinally disappearedaftereither8or20months(dependingontheinterpretationofasentenceintherecordtomean“nextyear”or“yearafter next”).Theidentificationoftherecordedpositionoftheeventwith
theregionbetween α and β CensuggeststhattheremnantofSN185 couldbeidentifiedwiththeSNremnantRCW86(G315.4 02.3),atan estimateddistanceofabout2.8kpc.RecentobservationswithChandra andXMM-Newtonhaveindeedstrengthenedthecaseforthisidentification.ThestudyofitsX-raysynchrotronemissionhasinfactsuggested anestimatefortheageofthisremnantconsistentwiththeexplosion date,withintheuncertaintiesofthedetermination.Theregularshape oftheremnantshell,togetherwiththeabsenceofapulsar,wouldpoint towardatypeIaSN,whichisalsosuggestedbytheChandraX-ray observations.
Anotherpossibleremnantcandidatehasbeenproposed,G320.4 01.2 (RCW89),whichcontainsthepulsarPSRB1509-58,andtherefore wouldcorrespondstoacore-collapseSN.Thetimingmeasurementof thispulsararealsoconsistentwiththeageofSN185.
SN1006
AnumberofotherpossibleSNewererecordedbeforeAD1000;see Table10.1.However,thefirsteventforwhichwehaveextensivehistoricalrecordsisaSNthatexplodedinAD1006inthedirectionofthe Lupisconstellation,andwasrecordedinChina,Japan,Europe,Egypt andIraq.Itdisappearedafirsttimefromviewafter17months,and remainedoccasionallyvisibleatdawnfor3years.
TheidentificationofthelikelyremnantofthisSNcamein1965,by searchingradiocataloguescoveringpartoftheregionofskysuggested bythehistoricalrecords.Theremnantisnowidentifiedwiththeradio sourcePKS1450-51(whoseGalacticcoordinatesareG327.4+14.6).Its distancefromus,aswenowinferfromtheremnant,wasabout2.2kpc.
FromthespectrumoftheremnantitisbelievedthatitwasatypeIa SN.UsingthestandardluminosityoftypeIaSNetogetherwiththe knowndistancetotheremnant(andplausibleassumptionsaboutabsorption)allowsustoestimatethatitreachedanapparentvisualmagnitude V −7 5.3 Bycomparison,thefullMoonhasamaximumappar- 3Thestandardastronomicalnotionsof luminosity,magnitudesandcolorindex ofstarsarerecalledintheComplement Section10.6.
entmagnitude V −12 94,andthelimitingbrightnessforanobjectto bevisiblewiththenakedeyewhentheSunishighis V −4,dropping to V −2 5whentheSunislessthan10degreesabovethehorizon. ComparingwiththevisualmagnitudesgiveninTable10.5onpage70, weseethat,atitsmaximumbrightness,SN1006wasbyfarthebrightest objectinthenightskyaftertheMoon,andeasilyvisibleduringdaytime.Thehistoricalrecordsconfirmthatitwasindeedvisibleduring theday,anditwasevenbrightenoughtoreadatnightbyitslight!The mostdetailedreportsbyfararefromChineseastronomers,whodeterminedthepositionofthis“gueststar”togoodaccuracy.Twoaccounts ofthisSNappearedalsoinEurope,inchroniclesofthemonasteriesof St.Gallen,inSwitzerland,andofBenevento,inItaly.
4Thesubjectisquitecontroversial amonghistoriansofscience.SomeEuropeandocumentshavebeensuggested asreferringtoSN1054,butlookquite imprecise,andoveralltheevidencethat theyactuallyrefertotheSNisnotvery convincing.Ithasbeensuggestedthat thelackofwrittendocumentswasdue tocensorshipfromtheChurch(given thatthechroniclesoftheepochwere compiledinmonasteries),possiblyconnectedwiththefactthattheSNappearedjustatthetimeoftheEastWestSchismthatgaverisetotheseparationoftheChurchoftheRomanEmpireintowhatlaterbecametheRoman CatholicChurchandtheEasternOrthodoxChurch.Infact,thedateof theexcommunicationofthePatriarch ofConstantinopleMichaelICerularius isJuly16,1054.Theusuallyaccepted datefortheappearanceoftheSNis July4,sobyJuly16itwasjustnear itsmaximumluminosity. Therehavealsobeensuggestionsthat thisSNisdepicted,togetherwiththe Moon,incavepaintingsfromnative americansinArizona.Ithasbeenproposedthatthepaintingsrepresentsa conjunctionbetweentheMoonandthe SN,madepossiblebythefactthatsoon afteritappeared,onJuly5,theSN asseenfromEarthwasindeedonthe planeoftheeclipticandinadirection closetothatoftheMoon.However, thedatingofthepaintingsisquiteimprecise(betweenthe10thand12thcenturies),andonlyoneofthemshowsthe crescentmoonwiththecorrectorientationinrelationtotheSN,soitisdifficulttomakedefinitestatements.
SN1054(theCrabsupernova)
Shortlyafter,in1054,theCrabSNexplodedandwasrecordedby Arab,ChineseandJapaneseastronomers.ItgaverisetotheCrabnebula,whoseremnantneutronstarweobservetodayastheCrabpulsar, PSRB0531+21.Itsdistancefromusis2.0 ± 0.5kpc.
Theidentificationoftheremnantofthe1054SNwiththeCrabnebula, basedontheexpansionspeedofthecloudmeasuredspectroscopically,as wellasonvariousconcordanthistoricalrecords,isquitefirm.Thefirst suggestionthattheCrabnebulawastheremnantofSN1054wasdue toHubble.In1928,whenthenatureofnebulaewasstillunknown,he observedthattheCrabnebulawasexpandingradiallyanddeducedthat itwasmostprobablytheremnantofanexplosion.Fromtheexpansion ratehecouldinferthattheexplosiontookplaceninecenturiesearlier, consistentwithSN1054.Thisanalysiswasrefinedandstrengthenedby MayallandOortin1939and1942.Fromtheanalysisofthehistorical records,itisbelievedthatitreachedanapparentmagnitudebetween 7and 4 5andagainitwasvisibleduringdaylight.Itremained visibletothenakedeyeforaboutayearandahalf.Itispuzzlingthat, forsuchanimpressivephenomenon,thereisnounambiguousEuropean record,particularlyconsideringthat,halfacenturyearlier,SN1006was recordedinEurope,soEuropeanchroniclersofthatepochdidnotlack interestinsuchphenomena.4
Today,afteralmost1000years,theCrabnebulastillhasaluminosity of8 × 104L ,mostlyintheformofpolarizedsynchrotronradiation, indicatingthepresenceofhighlyrelativisticelectronsspiralingaround magneticfieldlines.Thesourceofthisenergy,solongaftertheexplosion,remainedapuzzleuntilthediscoveryofthepulsar.Aswewill discussinSection11.1.1,ultimately,thishugeluminositycomesfrom thepulsar’sspindown.TheCrabnebulawasfirstdetectedinradio wavesin1963andinX-raysin1964.Thediscoveryofthepulsarinside theCrabnebula,in1968,wasamilestoneinastronomyandmadethe CrabthemoststudiedandfamousSNremnant,togetherwiththerecent SN1987A.
SN1181
ThenextvisibleGalacticSNappearedinAD1181,andwasrecordedin ChinaandJapan.Itremainedvisibleforsixmonths.TheSNremnant 3C58,withGalacticcoordinatesG130.7+03.1,atadistanceofabout 3.2kpc,hasbeenproposedastheremnantofthissupernova.Within thisnebulahasbeendiscoveredtheradioandX-raypulsarJ0205+6449. Recentwork,however,hasquestionedthisidentificationoftheremnant.Iftheidentificationwerecorrect,itsyoungageoflessthan900 yearswouldsuggestarapidexpansionofthenebula,whiletheobserved expansionseemsconsiderablylower,andrathersuggeststhattheSN remnant3C58couldbeatleast2700yearsold.
SN1572(Tycho’ssupernova)
positionremainedfixed,withoutadailyparallaxwithrespecttothe fixedstars,allowedBrahetoinferthattheobjectwasfarbeyondthe Moon;furthermore,theabsenceofapparentpropermotionoveraperiod ofmonthsshowedhimthatitwasmuchfurtherawaythantheplanets, andwasindeedastar.Thiswasahighlynon-trivialconclusionfor theepoch,whichcontradictedtheacceptedAristoteliandoctrinethat changesintheskycouldonlytakeplaceinthesublunarregion,and ultimatelyledtothenotionoftheimmutabilityoftheheavensbeing abandoned.Italsoopenedthewaytomodernastronomy,revealingthe importanceofperformingaccurateastrometricmeasurements.
Chineseobserversrecordedthatitwasvisibleindaylight,whileKoreandocumentscompareditsbrightnesswiththatofVenus.ThissuggeststhatatitsmaximumtheSNwasbrighterthanthethreshold V −4forvisibilityduringdaylight,butnotbymuch.Theremnantis identifiedwiththeradioandX-raysource3C10(G120.1+01.4).6 Today
ThenextSNvisibletothenakedeyeappearedafteraboutfourcenturies, inAD1572,inthedirectionoftheconstellationofCassiopea,andwas observedinAsiaandEurope.TheSNwasprobablyfirstdetectedin EuropeonNovember6(orpossiblyafewdaysearlier)bytheabbotof MessinaandbyotherobserversinEurope.Verydetailedobservations ofitweremadebytheDanishastronomerTychoBrahe,whorealized thatitwasanewstarandbegunobservingitonNovember11. Hecarefullyfolloweditoverthefollowingyear,establishingthatits positionwasfixed,anddeterminingittowithinafewarcminutes.He wasalsotheonlyastronomertomonitorcarefullythedeclineofits brightnessinthefollowingmonths.ThisSNisthusoftenreferredto asTycho’sSN.5 Itremainedvisiblefor18months.Thefactthatits 5AsTychoreports,“Onthe11thday ofNovemberintheeveningaftersunset,Iwascontemplatingthestarsina clearsky.Inoticedthatanewandunusualstar,surpassingtheotherstarsin brilliancy,wasshiningalmostdirectly abovemyhead;andsinceIhad,from boyhood,knownallthestarsofthe heavensperfectly,itwasquiteevident tomethattherehadneverbeenany starinthatplaceofthesky,eventhe smallest,tosaynothingofastarsoconspicuousandbrightasthis.Iwasso astonishedofthissightthatIwasnot ashamedtodoubtthetrustworthiness ofmyowneyes.ButwhenIobserved thatothers,onhavingtheplacepointed outtothem,couldseethattherewas reallyastarthere,Ihadnofurther doubts.Amiracleindeed,onethathas neverbeenpreviouslyseenbeforeour time,inanyagesincethebeginningof theworld.”(FromBurnham,1978).
6Beautifulimagesofthisand otherSNremnantsinX-rays havebeentakenbyChandra,see http://chandra.harvard.edu/photo/2011 /tycho/ theremnantisashellofangulardiameter8arcmin(bycomparison,the fullMoonhasanangulardiameterbetweenapproximately29and34 arcmin,dependingonitsexactdistancefromEarthalongitsorbit).
HistoricalrecordsofthelightcurvesuggestatypeIaSN.Nocompact remnanthasbeendetectedatitscenter,whichalsopointstowarda typeIaSN.Finally,theclassificationastypeIahasbeenbeautifully confirmedthankstothedetectionofalightechofromtheSN,dueto scatteringandabsorption/re-emissionoftheSNflashbyinterstellardust neartheremnant.Inthiswayithasbeenpossibletoobservesomeof thelightemittedbytheSNnearmaximumbrightness,whichhasarrived morethanfourcenturiesafterthedirectflash,andithasbeenpossible toperformaspectroscopicanalysis.Thespectrumhasconfirmedthat SN1572wasatypicaltypeIaSN.Itsdistancefromushasusually beenquotedintherange2 3 2 8kpc,althoughtheabsolutebrightness inferredfromthelightecho,togetherwiththehistoricalinformation thatithad V −4,rathergivesadistance3 8+1 5 1 1 kpc.
Asearchforthecompanionstarfromwhichthewhitedwarfaccreted mass,goingbeyondtheChandrasekharlimit,hasrevealedaG2star inthedirectionofthecenterofthenebula,andatadistancebetween
Fig.10.1 ThelightcurveoftheSN ofAD1604fromEuropean(◦)and Korean(•)observations,withaEuropeanupperlimitonOctober8. FromStephensonandGreen(2002).
2.5and4.0kpc,socompatiblewiththedistancetothenebula.This starhasapeculiarphase-spacevelocity,morethanthreetimesaslarge asthatofanyotherstarinthisregion,whichcouldbeinterpretedas arisingfromthekickreceivedbythecompanionintheexplosion.Other interpretations,intermsofastarunrelatedtotheSNandbelongingto thethickdiskpopulation,are,however,possible.
SN1604(Kepler’ssupernova)
ThenextSNvisibletothenakedeyeappearedin1604,andwasfirstobservedonOctober9inItaly,byastronomersinVeronaandinCosenza. ItremainedvisibleuntilOctober1605,andwasextensivelyfollowed byEuropean,ChineseandKoreanastronomers.JohannesKeplerwas amongthosewhoobservedit.DuetopoorweatherconditionsinPrague, hecouldstartobservingitonlyonOctober17.However,histreatise De StellaNovainPedeSerpentarii (“OnthenewstarinthefootofOphiuchus”,Serpentariusbeingalessfamiliarnamefortheconstellation Ophiuchus)wasthemostimportantEuropeandescription,inparticularfortheaccuratepositionalmeasurements,sothisSNisalsocalled Kepler’sSN.ThemostaccuratepositionalmeasurementsareingeneralfromEuropeanastronomers,withanaccuracyofabout1arcmin (comparedwithaprecisionofabout1degreefromChineseandKorean astronomers).ItsluminositycurvecanbeinferredbothfromEuropean observationsandfromKoreandocumentsrecordingitsluminosityona day-by-daybasisforthefirstsixmonths,andmatchingtheEuropean observations.TheSNwasdetectedabout20daysbeforemaximumluminosity,thanksalsotothefortuitouscircumstancethatatthattime MarsandJupiterhappenedtobeinconjunction.Thisconjunctionwas beingcarefullyobserved,andtheSNappearedatjust3degreesNEfrom thepositionofthesetwoplanets(and6degreesEastofSaturn).We thereforehaveadetailedrecordoftheluminositycurvefromappearance, thoroughmaximumluminosityandfading;seeFig.10.1.Accordingtoa reconstructionoftheluminositycurveduetoBaade,itreachedamaximumvisualmagnitude V −2.25,soitwasnotasspectacularas SN1006,withitsinferred V −7.5,theCrab(maximum V between 7and 4 5)orTycho’sSN(maximum V −4).Still,inthenight skyitwasbrighterthananystar,andamongtheplanetsonlyVenus wassignificantlybrighterthantheSN.WhentheSNappeareditwasas brightasMars,andthensurpassedJupiterinafewdays.Thefactthat thisSNwasrelativelyhighwithrespecttotheGalacticplanereduced significantlytheobscurationbydust,allowingtheSNtobevisibleby thenakedeye.
Theremnant(whoseGalacticcoordinatesareG004.5+06.8)wasidentifiedbyBaadein1943,andhasbeenstudiedatinfrared,optical,radio andX-raywavelengths.Itsdistancefromusisquiteuncertain,with estimatesrangingfromabout3kpctomorethan6kpc.Itislocatedin thedirectionoftheGalacticcenter,so,taking4kpcasanestimateofits distance,itisroughlyhalf-wayfromtheGalacticcenter.Itisrelatively
highabovetheGalacticplane,ataverticalheight z 590(d/5kpc)pc, where d isitsdistancefromus.
TheclassificationofthisSNhasbeencontroversialfordecades.Baade suggestedthatthehistoricallightcurvewasconsistentwithatypeIa, buthisclaimwaslaterquestioned.Thepresenceofdensecircumstellarmaterialimpliessignificantmasslossfromtheprecursorstar, whichismoresuggestiveofacore-collapseSN(althoughthereareafew examplesofcircumstellarmaterialaroundspectroscopicallyconfirmed typeIaSNe).Sincethe1990s,however,evidenceaccumulatedinfavor ofatypeIaSN.AnalysesofX-rayspectrawithExosat,ASCA,XMMNewtonand,morerecently,ChandraindicateanoverabundanceofFe andSiintheejectaandrelativelylittleoxygenemission.Suchacompositionisinconsistentwithacore-collapseSN,andisinsteadtypicalof atypeIaSN.Furthermore,noneutronstarhasbeendetectednearits center,eitherinradioorinX-rays.InX-rays,thelimitonthefluxfrom ahypotheticalcentralcompactobjectshowsthat,ifitwerepresent, itsintrinsicX-rayluminositywouldbemorethan100timessmaller thanthatofthecompactremnantofatypicalcore-collapseSNsuchas CasA.InfraredstudieswithSpitzerpointagaintowardtheconclusion thatthiswasatypeIaSN,althoughwithsignificantcircumstellarmaterial.Recenthydrodynamicalsimulationsshowthatthemorphology oftheremnantanditsexpansioncharacteristicscanbereproducedby amodelofatypeIaSNoriginatingfromawhitedwarfthataccreted massbywindaccretionfromanasymptoticgiantbranchstarwithmass (4 5)M .
ThepopulationofGalacticSNremnants
AnotherinterestingGalacticSNremnantisCasA,whichisobservedas abrightsourceinradioandX-rays.Atvisiblewavelengthsthisremnant displaysaringofexpandingknots.Fromtheirexpansionvelocity,and assumingnodeceleration,onecanestimatethatthisSNexplodedaround AD1671.Itsdistancefromusisestimatedat3.4+0.3 0.1 kpc.Itisquite puzzlingthatforsucharecentandrelativelynearbySNthereisno historicalrecord.
GalacticSNeofcourseoccuratamuchhigherratethanSNevisible tothenakedeye,giventhat,formostlinesofsightclosetotheGalactic plane,obscurationbydustlimitsourviewinvisiblelighttoafewkpc. Asof2017,thecatalogofGalacticSNremnantslists381objects.7 The 7Seehttp://www.physics.umanitoba. ca/snr/SNRcat,whichisregularly updated. remnantageisoftenuncertainorundetermined,but O(20 30)are estimatedtobelessthan2000yrold.AswewillseeinSection10.2.1, typicalestimatesfortherateofSNexplosionsinourgalaxyareoforder 2SNepercentury.Accordingtothisestimate,thereshouldbeabout 40remnantsyoungerthan2000yr(raisingtoabout60ifwetake3 SNepercenturyasanestimateoftherate).Thisisnotinconsistent withthenumberofknownyoungremnants,althoughitsuggeststhat moreyoungremnantshavestilltobediscovered.Comparingwiththe
8Needlesstosay,bythiswemeanthat thesignalfromtheSNreachedEarth around1900.Theactualexplosiontook placeabout25,000yrsago,giventhe timetakenbylighttoreachusfromthe Galacticcenter.Thesameappliestoall theotherSNexplosiondatesmentioned above.
7SNeinTable10.1forwhichconvincinghistoricalrecordsexist,wecan estimatethatabout10 20%ofthegalacticSNeexplodinginthelast 2000yearshavebeenrecordedinwriting.
AmongtheknownGalacticSNremnants,therecordfortheyoungest iscurrentlyheldbyG001.9+00.3.ThisremnantislocatedinthedirectionoftheGalacticcenter,atadistancefromthecenterofabout300pc inprojection.Fromitsexpansionrate,assumingnodeceleration,the explosiondateisestimatedastheyear1855 ± 11.Sincesomedecelerationmusthaveoccurred,thisisactuallyanupperboundonitsage,and theexplosiondatewasmostlikelyaround1900.8 Theremnantwasfirst
observedbyVLA(VeryLargeArray)radioobservations,andinX-rays byChandra.
10.2PropertiesofSupernovae
9Or,theotherwayaround,Shapley in1919usedthisSNasanargument againsttheislanduniversehypothesis (i.e.theexistenceofothergalaxies, separatedfromoursbyhugedistances), arguingthatSN1885AinAndromeda wouldhave M = 16,whichwas“out ofthequestion”.Thetypicalabsolutemagnitudeofmostnovaeisaround 8 8.
10
ModernresearchonSNebeganin1885whenHartwigdiscoveredthe firstextragalacticSN,intheAndromedagalaxy.Itwasfirstinterpreted asanova.However,whenin1919Lundmarkestimatedthedistanceto Andromeda,itbecameclearthatHartwig’s“nova”hadactuallybeen O(103)timesbrighterthanaclassicalnova.9 However,itwasonlywith
thepioneeringpaperbyBaadeandZwickyin1933thatthenotionofSNe wasputforwardandafirstcleardistinctionwasmadebetweennovae andsupernovae.In1933,justoneyearafterChadwick’sdiscoveryofthe neutron,BaadeandZwickyputforwardtheideaofaneutronstar10 and
Actually,evenbeforethediscoveryof theneutron,in1931,neutronstarswere somewhatanticipatedbyLevLandau, whowroteaboutstarswhere“atomic nucleicomeinclosecontact,forming onegiganticnucleus”. furtherspeculatedthatSNeareanend-stateofstellarevolution,with thesourceofenergybeingprovidedbythegravitationalenergyreleased bythecollapseoftheprogenitorstartoaneutronstar.11
11“Withallreserveweadvancethe viewthatsupernovaerepresentthe transitionfromordinarystarsintoneutronstars,whichintheirfinalstages consistofcloselypackedneutrons”, W.BaadeandF.Zwicky,Meetingof theAmericanPhysicalSociety,December1933,publishedin Phys.Rev. 45 (1934)138.
12 Seehttp://graspa.oapd.inaf.it/ asnc.htmlforanon-lineversion.
Inthefollowingyearssystematicsearches,performedparticularlyby ZwickyatPalomarMountain,ledtothediscoveryof54SNeupto1956, and82morefrom1956to1963.Inrecentyears,largelystimulatedby theimportanceoftypeIaSNefordeterminingtheexpansionrateof theUniverse,intensivesearcheshavedramaticallyincreasedthenumber ofdetectedSNe.BrowsingtheAsiagoSupernovaCatalog12 onefinds
thatintheperiod1980–1989wereobserved O(200)SNe,intheperiod 1990–1999werefoundover900SNe,andintheperiod2000–2009were observed O(3500)SNe,obviouslyallofthemextragalactic.Asof2017 thetotalnumberofSNeinthecatalogisabout9000,andisincreasingat arateofabouttwoSNeperday.Thislargesample,combinedwiththe improvedqualityoftheobservations,hasallowedremarkableprogress inourunderstandingofthepropertiesofSNe.Futurelargesynoptic surveysareexpectedtodetectpossibly O(105)SNeperyear,atredshifts z ∼ 0 5 1.
Muchprogresshasalsobeenmadeinrecentyearsinidentifyingthe progenitorstarsoflocalSNexplosions,bycomparisonswitharchival datafromHSTorground-basedtelescopes.Currently O(20)progenitors havebeenidentified.Todrawstatisticalconclusionsfromthissample, mostoftheinformationcomesfromprogenitorsatadistancebelow
28Mpc,althoughobjectsoutsidethisdistance,suchasthemassive progenitorofSN2005glat60Mpc,havealsobeenidentified.
SNethatismoredirectfromanobservationalpointofviewisbased ratheronthespectrumofthelightemittedatmaximumluminosity.
NowadaysweunderstandthattherearetwobasicallydifferentmechanismsbehindSNexplosions:eitherthecorecollapseofastar,powered bytheenergyreleasedinthegravitationalcollapse(justasproposedby BaadeandZwicky)orthethermonuclearexplosionofawhitedwarfin abinarysystemthataccretesmassfromacompanion,goingbeyondits Chandrasekharlimit.13 However,aswenowdiscuss,aclassificationof 13Aswewilllaterdiscuss,anotherpossibilitythathasbeenproposedinthe literatureisa“double-degenerate”scenario,inwhichthethermonuclearexplosionresultsfromthemergeroftwo whitedwarfs.
10.2.1SNclassification
Thefirstdistinction,proposedbyR.Minkowskiin1941,wasbetween typeIandtypeIISNe.TypeIaredefinedbythefactthattheirspectrumnearmaximumluminositydoesnotshowevidentHlines,while typeIIneartheirpeakluminosityhaveprominenthydrogenlines.Subsequently,inthelate1980sitwasrealizedthattypeISNedidnot constituteahomogeneousclass,andthatitwasnecessarytodistinguishbetweentwofundamentallydifferentclasses,whichweredenoted astypeIaandtypeIb.TypeIaSNearedefinedastypeISNethat, intheirspectrumtakennearmaximumluminosity,showadeepabsorptiontrough,typicallyaround6000–6150 ˚ A,producedbyblue-shiftingof twoSiIIlineswithrest-framewavelengths λ =6347and6371 ˚ A(often collectivelydenotedas λ6355).ThesignificanceoftheseSilines,aswell aslinesofotherintermediate-masselementssuchasCa,Mg,SandO thatarepresentinthespectrumoftypeIaSNeatmaximumlight,is thatthepartoftheejectathatisexposedshortlyaftertheexplosion hasundergonethermonuclearprocessing,leadingtotheproductionof intermediate-masselements.Thisthermonuclearprocessinghas,however,beenincomplete,sinceSi,O,etc.havenotbeenburntfurtherto eventuallyproduceelementsoftheirongroup.
Themeanvelocitiesoftheejecta,obtainedfromtheblueshiftofthe spectrallines,areoforder5000km/s,withpeakvelocitiesaslargeas 20,000km/s c/15.ThetypicalspectrumofatypeIaSNisshown intheuppercurveoftheleftpanelinFig.10.2.ItshowsstrongSiII absorptionatabout6150 ˚ A,whileHlinesareabsent.Atlatetimes,say aftermorethan4months,thetypicalspectrumofatypeIaSNchanges, andratherthanbeingdominatedbylinesofintermediate-masselements, itisnowdominatedbyablendofdozensofFeemissionlines,mixedwith someColines.Thisisaconsequenceofthefactthat,withtime,the initiallyverydenseejectabecomemoreandmoretransparentbecause oftheirexpansionor,inotherwords,thephotosphere(i.e.thesurface fromwherethephotonscanstarttofreestreamtowardus)recedes, exposingtheproductsofthermonuclearburningintheinnercore.
TypeIbSNe,incontrast,aredefinedastypeISNewhosespectrum nearmaximumbrightnessdoesnotshowtheSiIIabsorptionlinethat definestypeIaSNe.Infact,itisusefultodistinguishfurtherbetween
Fig.10.2 Leftpanel:SpectraofbasicSNtypesnearmaximumluminosity.TypeII aredefinedbyaclearsignatureofHα.TypeIaisdefinedbyalackofHlinesand astrongSiIIabsorptionatabout6150 ˚ A.TypeIb/clackbothHandSilines,but typeIbhasHelines,whicharenotpresentintypeIc.Tenmonthslater(rightpanel) SNIashowstrongemissionsof[FeII]and[FeIII],SNIb/caredominatedby[CaII] and[OI].ThesesamelinesplusstrongHα emissionaretypicalofSNIIatlatetimes. FromCappellaroandTuratto(2001).
typeIbandtypeIcSNe.NeithertypeshowsHorSilinesnearmaximum luminosity.However,nearmaximumluminosity,typeIbSNeshowHe lines,whiletypeIcSNehaveneitherHnorHelines.Atlatetime,the spectraoftypeIbandtypeIcbecomeverysimilar,indicatingthatthe distinctionamongIbandIc(sometimescollectivelydenotedasIbc)is lessfundamentalthanthedistinctionbetweentypeIaandtypeIbc. small no yes no yes no Hlines? SiIIlines? Helines?
IaIbIIL IIb IIP plateau? yes noyes corecollapse thermonuclear explosion Ic envelope large
Fig.10.3 Adecisiontreeforthe classificationofSNe,basedonspectralfeaturesnearmaximumlight and,fortypeIISNe,onthetemporalevolutionofthelightcurve.
TypeIISNearedefinedbythefactthattheyshowprominentHlines inthespectrumtakennearmaximumluminosity.Theyarefurtherdividedintotwoclasses,dependingnotonfurtherspectralfeatures,but ratheronthedeclinewithtimeoftheirlightcurves.Thosethat,after reachingmaximumluminosity,showaplateauofalmostconstantluminosityforabout2–3monthsarecalledII-P,whilethosethatshowa declineapproximatelylinearinmagnitude(andexponentialinluminosity,recallingthatthemagnitudeisobtainedfromthelogarithmofthe luminosity;seetheComplementSection10.6)arecalledII-L.AcomparisonbetweenthespectraoftypeIa,IbandIISNe,bothatmaximum luminosity(leftpanel)andafter10months(rightpanel),isshownin Fig.10.2.AdecisiontreebasedonthesecriteriaisshowninFig.10.3. TheseparationintotypeIandtypeII,however,doesnotreallyreflect theunderlyingexplosionmechanisms.Rather,typeIaSNarebelieved
tooriginatefromthethermonuclearexplosionofacarbon–oxygenwhite dwarf(WD)inabinarysystem.Inthesimplestandcommonlyaccepted scenario,calledsingle-degenerate,awhitedwarf(WD)accretesmatter fromacompanionsuchasaredgiant(orevenamainsequencestarfor asufficientlyclosebinarysystem)untilitsmassgoesbeyondtheChandrasekharlimit MCh 1.39M .Thenthestarundergoesadisruptive thermonuclearexplosion,andisdispersedintheexternalspaceinthe formofagaseousnebula.Nocompactremnantisformedintheprocess. Analternativescenario,calleddouble-degenerate,ratherinvolvesthecoalescenceoftwoWDs,whichagainresultsinathermonuclearexplosion, andnocompactremnant.
Incontrast,typesIb,Ic,IILandIIPallcorrespondtocorecollapse SNe,i.e.tothegravitationalcollapseoftheinnerpartofthestar.When astarhasexhaustedthenuclearfuelinitscore,itisnolongerableto balanceitsself-gravitybythepressuregeneratedbythethermonuclear reactions,andacomplicateddynamicsbegins.Aswewilldiscussin detailinSection10.3,thiscanleadtoaSNexplosion,withejectionof theexternallayersofthestars,whilethecorecollapsestoaNSoraBH.
Thedifferencebetweenthevarioustypesofcorecollapsecanbetraced tothemassandsizeoftheprogenitorstar,andtothesizeandcompositionofitsenvelope.Intheearlyphaseoftheexplosiontheejecta areverydenseandopaquetoelectromagneticradiation.Thisimplies thatthelightemittedinthisearlystage,includingthespectrumnear maximumluminosity,onlyprobestheoutermostlayersandistherefore mostlysensitivetothesizeandcompositionoftheenvelope.
ThemassoftheHenvelopeofastarcanvary,dependingonmany factors.Forinstance,starscanlosetheirenvelopethroughstrongstellarwinds,asintheWolf–Rayetstars.14 Furthermore,whenastarisa 14Wolf–Rayet(WR)starsoriginate fromluminousOBstarswithstrong andbroademissionlinesandanatmospheremademostlyofHe,while Hisdeficientortotallyabsent.It isbelievedthattheyareverymassive evolvedstars,whoseHlayerhasbeen blownawaybystrongstellarwinds, producedbyradiationpressure.Asa result,WRstarsarecontinuallyejectinggasathighspeed,withline-of-sight velocitiesthatcanbeover2000km/s. TheresultingDopplerbroadeningisresponsiblefortheobservedbroadnessof theiremissionlines.Thesewindsare alsoresponsibleforasurfacecompositionthatshowsthepresenceofproductsofthenuclearburningintheinner regions.
memberofaclosebinarysystem,theinteractionwiththecompanion canhaveimportanteffectsonitsenvelope;thetwostarscanundergoa phaseofacommonenvelopeevolution,ormaterialcanbetransferred fromastartotheotherthroughRoche-lobeoverflow.Itisgenerally acceptedthattypeIISNederivefromtheexplosionofstarswithmass intherange10 30 M .InatypicalSNoftypeII-Ptheprogenitorisa redsupergiantwhoseHenvelopehasalargemass,oforder5 10 M . TheenergyoftheexplosioncompletelyionizestheHenvelope.Thegas thenentersastageofprolongedrecombination,whichmaintainsanapproximatelyconstanttemperature,typicallybetween5000and8000K, andthephotonsemittedduringrecombinationproducetheplateauof typeII-PSNe.Thedurationofthisplateaudependsonthemassofthe Henvelope.Asthephotosphererecedes,thedominantmechanismfor photonemissionbecomesthedecayofvariousradioactivenucleinewly synthesizedintheexplosion,whichatfirstcanextendtheplateaufor abrieftime.Then,theSNentersinthephasewhereitsluminosityis powereduniquelybyradioactivedecays.Sinceradioactivedecaysfollow anexponentiallaw N (t)= N0e t/τ (where N (t)isthenumberofnuclei attime t,and τ isrelatedtothehalf-life τ1/2 by τ1/2 = τ ln2),thecorrespondingluminosity L decreasesexponentially,withaslopedetermined
15HardX-raysand γ-rayswerealso directlydetectedfromthetypeII SN1987AintheLargeMagellanic Cloud.The 56NidecaychainalsopowersthelightcurveoftypeIaSNe.For thetypeIaSN2014J,whichisatadistanceofjust3.3Mpc,ithasbeenpossibletodetectwiththeINTEGRAL satellitethetwomain γ-raylinesdue tothe 56Codecay;seeChurazov etal. (2014)andDiehl etal. (2015).
bythehalf-lifeofthedominantprocess.Thusinthisstagelog L,and hencethenegativeoftheapparentmagnitude,decreaseslinearly.
TypeII-LsupernovaeareduetothecorecollapseofstarswithanH envelopeofabout1 2 M .Inthiscase,becauseofthesmallerenvelope mass,thevelocityofexpansionoftheH-richenvelopeislarger,andthe SNentersdirectlyintothephasedominatedbyradioactivedecays,with littleornoplateau,andalineardecreaseofthemagnitude.Intermediate casesexistbetweentypicaltypeII-PandtypicaltypeII-Lsupernovae, dependingonthesizeoftheHenvelope.
Inthephasepoweredbyradioactivedecaysanimportantroleisplayed by 56Ni,whichisthemainproductofburningatnuclearstatisticalequilibriumintheconditionsoftemperatureanddensitytypicallypresent inSNe.Inparticular, 56Niproduces 56Cothroughelectroncapture
withahalflifeof6.1days,emittingphotonswithenergiesof750,812and 158keV.Themainsourceofluminositylaterbecomestheradioactive decayof 56Coto 56Fe,whichgoesmostlythroughelectroncapture(81%)
and,toalesserextent(19%),through
Theprocesshasahalf-lifeof77.7daysandthephotonsfromelectron captureareemittedatenergiesof1.238MeVand847keV.These γrayphotonsaredown-scatteredandthermalizedintheejectauntilthey emergeasopticalornear-infraredphotons.15 Thesubsequentimportant
radioactivedecayisthatofadifferentisotopeofcobalt, 57Co,whichis initiallylessabundantbuthasalongerlifetime, τ1/2 271days.
Ingeneral,becauseoftheveryhighexpansionvelocityoftheejecta, thelinesoftypeIISNeshowsignificantDopplerbroadening.However, approximately10–15%oftypeIISNeshow,ontopofthebroadlines, somenarrowlines,andarethenclassifiedastypeIIn,where“n”stands fornarrow.TheyareinterpretedastypeIISNewithsignificantcircumstellarmaterial,whichismostlikelyduetoepisodesofstrongmass lossesbeforetheSNexplosion.Whentheejectahitsthiscircumstellar material,someofitskineticenergyisconvertedtoradiation,andproduceslineswhosebroadeningratherreflectsthemuchsmallervelocity ofthecircumstellarmaterial.
ThecloserelationbetweentypeIbandtypeIISNeisclearlyseenby comparingtheleftandrightpanelsofFig.10.2.Ontheleftpanel,which showsthespectranearmaximumluminosity,thespectraoftypeIband typeIISNelookverydifferent.However,afterabout10months,we seethatthespectraoftypeIbSNearesimilartothoseoftypeII, withstronglinesfromneutraloxygenandsingly-ionizedcalcium.In contrast,thespectrumofatypeIaSNremainsverydifferent,andafter 10monthsisratherdominatedbyironlines.Themeaningofthese patternscanbeunderstoodbyobservingthatthelightemittednear maximumluminosityonlycarriesinformationsabouttheexternallayers
ofthestars,giventhattheopticaldepthoftheejectaatthattimeis high.After10monthsweareinsteadreceivinglightfree-streamingfrom deeperregionsoftheejecta,andwefindthattypeIbandtypeIISNe nowlookverysimilar.Thenaturalinterpretationofthesefactsisthat typeIbSNearetheresultofthecorecollapseofstarsthathavelosttheir Henvelope,becauseofstellarwindsorinteractionwithacompanion. ThisexplainsthelackofHlines,whichinsteaddominatethespectrumat maximumluminosityintypeIISNe,andthesimilarityofthespectraat latertimes.Thisinterpretationisfurthersupportedbytheexistenceof casesintermediatebetweentypeIbandtypeII;themissinglinkwasfirst providedbySN1993J,whosespectrumevolvedfromthatofatypeIIto typeIbinjustafewweeks.Thisisinterpretedastheresultofthecore collapseofastarwhoseHenvelopehadarathersmallmass,ofabout 0.2 M .Thereareotherexamplesofthistype,soSNethatquickly evolvefromtypeIItotypeIbaresometimesclassifiedasmembersofa newclass,calledtypeIIb.InFig.10.3werepresentthisclasswithan arrowconnectingtypeII-LwithtypeIb.
TypeIcSNealsofitwellinthisscheme.Againtheirspectrumatlate timeisthesameasthatoftypeIbandtypeII,showingthattheyare core-collapseSNe.ThelackofbothHandHelinescanbeunderstoodon recallingthatamassivestar,duringitslifetime,goesthroughdifferent stagesofnuclearburning,whichresultsinaonion-likestructure.In particular,themostexternallayersofthestarconsistofaHenvelope, ontopofaHeenvelope.TypeIceventsarethennaturallyinterpreted asthecorecollapseofstarsthathavelostboththeirHandtheirHe envelopes.16
TypeIb,IcandIISNarethencollectivelydenotedascore-collapse SNe,andcanbethoughtasasequenceIc–Ib–IIb–IIL–IIP,fromsmaller tolargerHandHeenvelopes.TypeIc,IbandIIbSNearealsocollectivelycalled“stripped-envelopeSNe”.AninterestingsubclassoftypeIc SNe,denotedtypeIc-BL(for“broad-line”)consistsoftypeIcSNewith unusuallybroadabsorptionlines,andphotosphericvelocitiesinexcess of20,000km/s.
Thedifferencebetweencore-collapseandtypeIaSNeisfurtherhighlightedbythefactthatcore-collapseSNehaveonlybeenobservedin spiralgalaxies,nearsitesofrecentstarformation.Thisagainindicates thattheirprogenitorsaremassiveshort-livedstars.TypeIaSNe,in contrast,havebeenobservedbothinspiralandinellipticalgalaxies. Thelattershowlittleornosignofrecentstarformation,showingthat typeIaSNearenotrelatedtomassivestars,sincethesehaveashort life-time.Rather,theirprogenitorsmustbelow-massstars.
10.2.2Luminosities
LuminosityofTypeIaSNe
ThethermonuclearexplosionoftypeIaSNetakesplacewhenthemass oftheWDgoesbeyondafixedthreshold,givenbytheChandrasekhar mass.Asaresult,theirintrinsicluminosity,toafirstapproximation,is
16LikelytypeIchavesomeHeliumtoo intheirouterlayer,butthisheliumproducesnolineduetothelackoffavorablephysicalconditions,seeDessart, Hillier,LiandWoosley(2012).
uniform.TypeIaSNerisetomaximumluminosityinaperiodofabout 20days,reachingapeakvalueoftheabsolutebluemagnitude MB,peak whoseaverageoverseveraltypeIaeventsisgivenby17 17WequotethevaluefromP.Astier et al. [TheSNLSCollaboration](2006). Thedependenceon h0 comesfromthe factthat,foragivenflux F,theluminosityis L =4πFd2 L,where dL(z) istheluminositydistance.ForSNe atcosmologicaldistances dL ∝ h 1 0 , so L∝ h 2 0 .Then,from M = (5/2)log10 L+const. (seeeq.(10.155) intheComplementSection10.6)we get M = M (h0,ref )+5log10 h0/h0,ref , where h0,ref isthereferencevaluechosenforthereducedHubbleconstant h0
18Theexactnumericalvaluesofthecoefficientsinthisrelationdependonthe sampleoftypeIaSNeused.Herewe haveusedthenumbersfromtheoriginalpaperbyPhillips(1993),obtained howeverwithasamplethatisquitelimitedcomparedwithmorerecentones.
Usingeqs.(10.156)and(10.161)intheComplementSection10.6,for thetypicalpeakluminosityinthebluebandofatypeIaSNweget
ThishugeluminosityallowsustoseetypeIaSNeatcosmologicaldistances.Then,thefactthattheirintrinsicpeakluminosityis,toafirst approximation,quiteuniform,makestypeIaSNepotentialstandard candlesforcosmologicalpurposes.Actually,theobservedspreadinpeak magnitudesoftypeIaSNebyitselfwouldstillbetoolargeforthemtobe usedasaccuratestandardcandlesincosmology.However,theresidual differencesintheintrinsicluminositiesoftypeIaSNecanbecorrected thankstoempiricalrelationsbetweenthepeakluminosityandtheshape ofthelightcurve,withfasterdecliningSNebeingfainter.Theoriginal correlation,knownasthePhillipsrelation(orthePskovskii–Phillipsrelation),isexpressedintermsof∆m15(B),thedeclineratein B-band magnitudeafter15days,andhastheform18
(MB )peak = 21 727+2 698∆m15(
19ThediscoveryoftheacceleratedexpansionusingtypeIaSNehasbeen awardedwiththe2011NobelPrize inPhysicstoSaulPerlmutter,Brian SchmidtandAdamRiess.
withsimilarlinearcorrelationsinthe V -and I-bands.Manyrefinements ofthisideahavebeendeveloped.Forinstance,thecorrelationbetween peakluminosityandtheshapeofthelightcurvecanbeexpressedeither usinga“stretchparameter”,definedintroducingastretchinthetime axisrelativetoastandardluminositytemplate(Perlmutter etal. 1997), orusingamulti-parameterfitinmultiplecolors(Riess etal. 1996), whichalsomakesuseofthefactthatfaintertype-IaSNeappearredder thanbrighterobjects.Withthesecorrectionsthedispersion MB canbe reducedtoabout∆MB 0 1and,asaresult,thedistancetotypeIa SNecanbededucedtoabout10%accuracy.Thishasallowedtheuse oftypeIaSNeatcosmologicaldistancesasaccurateprobesoftheexpansionoftheUniverse.Inthiswayitishasbeenshownthatinthe recentcosmologicalepochtheexpansionoftheUniverseisaccelerating, providingclearindicationinfavoroftheexistenceofadarkenergycomponent,thatdominatesthetotalenergybudgetoftheUniverseinthe recentcosmologicalepoch.19
Luminosityofcore-collapseSNe
Incontrast,theluminositiesoftypicalcore-collapseSNespanabroad rangeofabsolutepeakmagnitudes,fromabout 15to 20 5.Wesee, fromeq.(10.156)intheComplementSection10.6,thatadifferencein magnitude∆M 5correspondstoafactor100inluminosity.Exceptionally,core-collapseSNewithmagnitudeuptoabout M = 22have beenobserved.
Fig.10.4 Comparisonoftheabsolute R-bandlightcurveofvariousSNe.The curvelabeledSN1998dhisatypicalSNIa.AllothercurvesrepresentcorecollapseSNe,exceptpossiblythemostluminousSN2006gy,whichcouldbe apair-instabilitySN.FromSmith etal. (2007).
ContrarytotypeIaSNe,theredoesnotseemtobeacorrelation, suchasthePhillipsrelation,betweenthedeclinerateofthelightcurve andthepeakabsolutemagnitude.Fromsystematicstudiesof R-band photometry,20 takingintoaccountthehostgalaxyextinction,whichis 20SeetheComplementSection10.6for definitionsofthedifferentcolorbands. oftensignificant,onefindsthatthepopulationsoftypeIbandtypeIc SNearestatisticallyindistinguishable,withaveragevaluesofthepeak magnitudeintheredband
MR,peak = 18 2 ± 0 9 (10.6)
IndividualtypeIbandIcSNe,however,canhavefluctuationsinthe peakabsolutemagnitudeofapproximately ±2magnitudesaroundthese averagevalues.TypeIc-BLSNehaveasomewhathigherluminosity, withared-bandpeakmagnitude
MR,peak = 19.0 ± 1.1 , (10.7) andadistributionscatteredbyabout ±1magaroundthemean.
Figure10.4showstheR-bandluminositycurvesofvariousSNe,displayingatypicaltypeIaSN(SN1998dh)togetherwithavarietyof core-collapseSNe.WeseethetypicalplateauofatypeII-PSNinthe lightcurveofSN1999em,whileSN1987A,intheLargeMagellanic Cloud,thebestobservedsupernovaever,isconsideredanextremecase oftypeII-P,withasteadyincreaseinmagnitudelastingabout3months, andalowpeakmagnitude.AswewillseeinSection10.3.1,thelowluminosityofSN1987Aisduetothefactthat,atthetimeofexplosion,its
progenitorwasabluesupergiant,ratherthanaredsupergiant.Among theothercurvesinthefigure,SN1994WisatypeIInSNthatispoweredbyastronginteractionwithitscircumstellarmaterial.Particularly noteworthyistheuppercurve,whichreferstoSN2006gy,amostremarkableSNexplosion.ThistypeIInSNexplodedinSept.2006in thegalaxyNGC1260,atadistanceofabout73Mpc.Itreacheda peakvisualmagnitudeofabout 21.8,andstayedbrighterthan 21 forabout100days.Itwasalsocharacterizedbyaveryslowrise,reachingitsmaximumluminosityinabout70days,insteadofthe20daysof atypicalSN.Itstotalradiatedelectromagneticenergyisestimatedat ∼ 1051 erg,twoordersofmagnitudeslargerthantypicalcore-collapse SNe.Ayetmoreluminoussupernova,SN2005ap,hasbeenrecorded, abouttwiceasbrightasSN2006gyatpeakluminosity,althoughnot asenergeticoverall,sinceitslightcurvedeclinedinafewdays.Afew otherultra-luminousSNewithcomparableradiatedenergyhavebeen foundinrecentyears.Themechanismthatpowerstheseultra-luminous eventsisstilldebated.ApossibleexplanationisthatSN2006gyisa pair-instabilitySN,discussionofwhichwedefertopage33.
10.2.3Rates
ForthepurposesofdirectobservationwithGWdetectorsweareparticularlyinterestedintherateofSNeinourGalaxy(although‘thirdgeneration’GWinterferometerssuchastheEinsteinTelescopecould detectSNeatextragalacticdistances,andSNeatcosmologicaldistancesarealsopotentiallyinterestingsourcesofstochasticbackgrounds ofGWs).However,mostinformationonSNratescomesfromobservationsofSNeinothergalaxies.Totranslatetheinformationobtained fromothergalaxiesintopredictionsfortheSNrateinourGalaxy,the ratesmustbenormalizedtosomequantitycorrelatedtothestellarmass ofthegalaxy.ThemostcommonlyusedquantityistheB-bandluminosityofthegalaxyinquestion,whichisameasureofthestellarmass ofthegalaxy,atleastforgalaxiesofthesamemorphologicaltype.The classicalunitsistheSNu(SNunitinB-band),definedasthenumberof SNeventspercentury,per1010LB, ,where LB, isthesolarluminosity intheB-band.Whenonewishestoemphasizethatthenormalization hasbeenperformedtotheB-bandluminosity,thisunitisalsodenoted bySNuB.Anotherusefulnormalizationistothefar-infrared(FIR)band luminosity,andthecorrespondingunitisdenotedbySNuIR.ItsusefulnessisthattheFIRluminosityofagalaxyisgeneratedbydustheated bymassivestarsandisthereforeproportionaltothestarformationrate. TotransformfromSNutoratesinourGalaxyweneeditsB-bandluminosity,whichis
B,Gal 2 3 × 1010LB, , (10.8) sotherateofsupernovaexplosioninourGalaxy,expressedintermsof theSNuunit,isabout2.3SNu.RecentdeterminationoftheSNrates usingtheexistingdatabasesofextragalacticSNe,forthedifferenttypes ofSNeandfordifferentclassesofhostgalaxies,areshowninTable10.2.
L
Table10.2 ThelocalSNrates,pergalaxytype,inSNu.Asusual, h0 = H0/(100kms 1 Mpc 1).FromCappellaroandTuratto(2001).
GalaxySNtype typeIaIb/cIIAll
Weseethatcore-collapseSNearenotobservedinellipticalgalaxies, consistentlywiththefactthattheirprogenitorsaremassive,short-lived stars.Incontrast,therateoftypeIaSNeisconstant,withintheerror, fromellipticalgalaxiestolatespirals.TakingourGalaxytobetype Sb-Sbc(whichisaccountedforbyperforminganinterpolationofthe ratesonagridofgalaxytypes),usingeq.(10.8)andsetting h0 =0.70, onefindsthattheexpectedrates RG inourGalaxyare
RG(typeIb+Ic+II)=(1.7 ± 1.0)events/century , (10.9) and RG(typeIa)=(0 5 ± 0 2)events/century (10.10)
Thus,overallweget
RG(all)=(2.2 ± 1.2)events/century , (10.11)
i.e.approximatelybetweenoneandthreeGalacticSNepercentury. Thisratewouldimplythatthereshouldbeabout44 ± 24SNremnants inourGalaxyyoungerthan2000years,whichisconsistentwiththe O(20 30)thatarepresentlyknown;seethediscussiononpage9.
Fig.10.5
Probabilitiesforoneor moreSNeintheGalaxyoverdifferenttimespans,dependingonthe assumedSNrate.FromKistler, Yuksel,Ando,BeacomandSuzuki (2011).
SomewhathigherratesarepredictedusingthefivehistoricalSNeobservedinthelast1000yr,andgeneratingwithaMonteCarlosimulationanumberofSNeventsdistributedintheGalaxy,toseehowmany eventsarenecessaryinordertohavefiveeventswithapparentmagnitude mV < 0.UsingarealisticmodeloftheGalaxy,whichincludesthe thinandthickdisksaswellasthestellarhalo,plusarealisticdistributionofdusttocomputetheextinction,onefindsthatabout39events wouldbeneededtoproducethefivevisiblehistoricalSNeinthelast 1000yr,correspondingtoarate2121SeeTammann,LoefflerandSchroder (1994).
RG(all)=(3 9 ± 1 7)events/century (10.12)
Thisishigherthanthevaluegivenineq.(10.11),butconsistentwithin theerrors,especiallyinviewoftheuncertaintiesinthemodelization usedandofthelowstatisticsofhistoricalSNe.
Adirectestimateoftherateofcore-collapseSNeinourGalaxyisobtainedfromthe γ-raysproducedbytheradioactivedecayof 26Al.It canbeshownthatasubstantialfractionof 26AlisofGalacticorigin. Thepresent-dayequilibriummassin 26AlproducedbyongoingnucleosynthesisthroughouttheGalaxycanbeestimatedfromthis γ-rayflux, makingsomeassumptionsonitsthree-dimensionalspatialdistribution. Since 26Alismostlyproducedbymassivestars,fromthisonecaninfer thattherateofcore-collapseSNeintheGalaxyisequalto22 22SeeDiehl etal. (2006).
Fig.10.6 TheprobabilitydistributionforexplosionofaGalactic SNasafunctionofthedistance fromEarth,inkpc.FromAhlers, MertschandSarkar(2009).
AnupperboundontheGalacticSNratecanbeobtainedfromthe absenceofneutrinoburstsofGalacticoriginatneutrinodetectorssuch asBaksan,MontBlanc,IMBand(Super)-Kamiokande.Thedetection ofneutrinosfromSN1987AintheLargeMagellanicCloudshowsthat neutrinosfromaGalacticcore-collapseSNewouldbeclearlydetected. Theabsenceofanydetectionofneutrinoburstsinthelast30yearsputs anupperbound
Fig.10.7 Estimatesofthecorecollapsesupernovarateinthe nearbyuniverse,basedonthat expectedfrom22supernovaeobservedin1999–2008(bins),comparedwiththetheoreticalpredictionusingB-bandluminosity (dashedline).FromKistler,Yuksel, Ando,BeacomandSuzuki(2011).
RG(typeIb+Ic+II)=(1 9 ± 1 1)events/century , (10.14)
inexcellentagreementwitheq.(10.9).Givenarate,thecorresponding predictionfortheprobabilityofobservingatleastonegalacticevent duringagiventime-spanisgivenbythePoissondistributionforthat rate.TheseprobabilitiesareshowninFig.10.5fordifferentchoicesof therate,rangingfrom1eventpercenturyuptoa5percentury,and fordifferenttimespans.
BesidetherateofGalacticSNe,anotherrelevantissue,particularlyfor GWastronomy,iswhatisthedistributionofdistancesfromtheEarth atwhichwecanexpectsuchevents.Thisquestioncanbeaddressed byperformingaMonteCarlocalculationwithalargenumberofsources drawnfromaprobabilitydistributionthatencodesourknowledgeofthe distributionofsupernovaremnantsintheGalaxy.Toobtainarealisticdistributionitisalsonecessarytotakeintoaccountthespiralarm structureoftheGalaxy.Theresult,showninFig.10.6,indicatesthat thedistributionofeventsasafunctionofdistancefromtheEarthis verybroad,anddistancesbetween,say,5and18kpccanbeconsidered astypical.
BothforGWastronomyandforneutrinoastronomyitisimportant toknowwhatdistancesadetectorshouldreach,inordertoexpectat leastoneeventperyear.Figure10.7showsthenumberofcore-collapse SNeactuallydetected,inthelocaluniverse,atdistancesupto10Mpc, duringtheperiod1999–2008,whilethedashedlinegivestheprediction obtainedfromtheratesinTable10.2,afterassigningtheappropriate blueluminosityandHubbletypetotheapproximately40majorgalaxies within10Mpc.Firstofalloneobservesthatthetheoreticalprediction islowerbyafactorofapproximately2–3,comparedwiththenumber ofobservedevents.Furthermore,thesampleofdetectedgalaxiesis likelyincomplete,becauseSNsurveysunder-samplesmallgalaxiesand
RG(typeIb+Ic+II) < 7 7events/century(90%c l ) (10.13)
theSouthernhemisphere,sotheactualnumberofSNeventsthatoccurredinthisperiodwithin10Mpccouldbeevenlarger.Apossible explanationforthisdiscrepancyisthattheB-bandluminosityisnotan accurateindicatorofthenumberofhigh-massstars,andhenceofthe core-collapseSNrate.Thisisduetothefactthatdifferentgalaxiescan havedifferentdustobscurationintheB-band,andthatB-bandlight receivescontributionfrombothhigh-massandlow-massstars.Inany case,usingtheactuallyobservedSNeshowninFig.10.7,weseethat thecore-collapseSNratereaches1eventperyearatadistanceofabout 6Mpc,whileat10Mpcwecanexpect2eventsperyear.Wealsoobserve thatallthe22SNeobservedinthisperiodwerecore-collapseSNe.This setsaboundontheratiooftypeIatocore-collapseeventsinthelocal universeoforder0.2(at90%c.l.).Thesameinformationisshown,in termsofthecumulativecore-collapseSNrateasafunctionofdistance, inFig.10.8.
Therateofcore-collapseSNeatevenlargerdistancesisshowninthe toppanelofFig.10.9(denotedthereby RCCSN).Ontheleftsideofthe figuretherateisplottedagainstthedistance(inMpc),whilebeyond z =0 1therateisshownagainsttheredshift.Sincemassivestarsare short-lived,therateofcore-collapseSNeshouldfollowthestarformation rate.Thecentralsolidlinegivesthepredictionobtainedusingafiducial cosmicstarformationhistory,withtheupperandlowerlinesgivingthe uncertaintyrangeofthetheoreticalmodel.Thebottompanelshowsthe ratiooftypeIatocore-collapseevents.Inthelocalregionwehavean upperbound(shownbythelinesat90%and99%c.l.),comingfrom thefactthatthe22SNeobservedinthelocalregionin1999–2008,and showninFig.10.7,wereallcore-collapseSNe.Atcosmologicaldistances thisratiotakesvaluesbetween0.2and0.4,consistentwiththevalues reportedinTable10.2.
10.3Thedynamicsofcorecollapse
10.3.1Pre-SNevolution
Theevolutionofamassivestarisgovernedbythecompetitionbetween thegravitationalcontractionunderitsowngravity,ontheonehand,and thepressureexertedbytheradiation,bythethermalgasand,inthe latestagesofitsevolution,bythepartiallydegenerateelectrongas,on theother.EnergyislostmainlytoradiationduringthecoreH-andHeburningphases,andtoneutrinoemissionafterwards,andthisenergyis providedbythethermonuclearreactionstakingplaceintheinnerparts ofthestar.Thesereactionsareverysensitivetothetemperaturein thecore.HightemperaturesarenecessarytoovercometheCoulomb repulsionofthepositivelychargednucleiandbringthemcloseenough. Atthatpointtheattractivepartoftheshort-rangestrongforcebetween nucleonscantakeoverandcreateaboundnuclearstate.Thehigher theelectricchargeofthenuclei,thehigheristheCoulombbarrierto beovercome.Whenaprotostellarcloudcollapsesunderitsownself-
Fig.10.8 Thecumulativerateof core-collapsesupernovaeinthe nearbyuniverse,basedonthatexpectedfrom22supernovaeobserved in1999–2008,comparedwiththe theoreticalpredictionusingB-band emissionfrom451galaxies(dashed), UVemissionfrom315galaxies(dotted),andthe589galaxiesofthe combinedcatalog(solid).Theverticalbandscorrespondstothereach ofdifferentpossibleneutrinodetectors.FromKistler,Haxtonand Y¨uksel(2013).
Fig.10.9 Evolutionofthecorecollapsesupernovarate(toppanel) andtheratioofTypeIatocorecollapseSNe(bottompanel).From Horiuchi,BeacomandDwek(2009).
