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Constraints on the equation of state of ultra-dense matter from observations of neutron sta

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arXiv:astro-ph/0110336v1 15 Oct 2001**TITLE**ASPConferenceSeries,Vol.**VOLUME**,**PUBLICATIONYEAR****EDITORS**

Constraintsontheequationofstateofultra-densematterfromobservationsofneutronstars

M.H.vanKerkwijkAstronomicalInstitute,UtrechtUniversity,P.O.Box80000,3508TAUtrecht,TheNetherlands

Abstract.Idiscussconstraintsontheequationofstateofmatteratsupra-nucleardensitiesthatcanbederivedfromobservationsofneutronstars.IfocusonrecentworkonVelaX-1,whichmaywellbesubstantiallymoremassivethanthecanonical1.4M⊙,andontheprospectsofferedbythe‘isolated’or‘thermally-emitting’neutronstars.

1.Theequationofstateforultra-densematterTounderstandthecorecollapseofmassivestars,thesupernovaphenomenon,andtheexistenceandpropertiesofneutronstars,requiresknowledgeoftheequationofstate(EOS)formatteratsupra-nucleardensity.TheEOSisdeter-minedbythebehaviourofelementaryparticlesatcloseproximitytoeachotherandhenceisoffundamentalphysicalinterest.Itismodeledusingquantum-chromodynamicscalculations,butthesearenotdevelopedwellenoughtodeter-minethedensitiesatwhich,e.g.,mesoncondensationandthetransitionbetweenthehadronandquark-gluonphasesoccur.Atdensitiesslightlyhigherthannu-clearandathightemperatures,themodelpredictionscanbecomparedwiththeresultsofheavy-nucleicollisionexperiments.Forhigherdensitiesandlowtem-peratures,however,thisisnotpossible;themodelscanbecomparedonlywithneutron-starparameters.RecentreviewsofourknowledgeoftheEOS,andtheuseofneutronstarsforconstrainingit,aregivenbyHeiselberg&Pandharipande(2000),Lattimer&Prakash(2000,2001),andBalberg&Shapiro(2000).ThedifferentmodelsfortheEOSpredicthighlydifferentmass-radiusre-lations,andadirectconstraintontheEOSwouldbesetbyasimultaneousmeasurementoftheradiusandmassofaneutronstar.Thishasnotyetbeenpossible,andobservationaltestshavebeenlimitedtopredictionsforextrema,suchasthemaximumpossiblemassandtheminimumpossiblespinororbitalperiod.Forinstance,forEOSwithaphasetransitionathighdensities,suchasKaoncondensation(BrownandBethe1994),onlyneutronstarswithmass<1.5M⊙couldexist(forlargermasses,ablackholewouldbeformed).Sofar,susceptibilitytosystematicerrorsandmodelinguncertaintieshavebefuddledmostattemptstoconstraintheEOSobservationally(e.g.,radiusde-terminationsfromX-raybursts,Lewinetal.1993;innermoststableorbitfromkHzQPOs,VanderKlis2000).Theonlyaccuratemeasurementsarethefastestspinperiodandsomeprecisemasses.Theformer,1.5ms,excludesthestiffestEOS(PSRB1937+214;Backeretal.1982);thelatterIdiscussbelow.

12M.H.vanKerkwijk2.NeutronstarmassesMostmassdeterminationshavecomefromradiotimingstudiesofpulsars;seeThorsett&Chakrabarty1999foranexcellentreview.Themostaccurateonesareforpulsarsthatareineccentric,short-periodorbitswithotherneutronstars,suchastheHulse-TaylorpulsarPSRB1913+16,inwhichseveralnon-Keplerianeffectsontheorbitcanbeobserved:theadvanceofperiastron,thecombinedeffectofvariationsinthesecond-orderDopplershiftandgravitationalredshift,theshapeandamplitudeoftheShapirodelaycurveshownbythepulsearrivaltimesasthepulsarpassesbehinditscompanion,andthedecayoftheorbitduetotheemissionofgravitationalwaves.Thorsett&Chakrabartyfoundthatforallradio-pulsarbinaries,themasseswereconsistentwithbeinginasurprisinglynarrowrange,whichcanbeapproximatedwithaGaussiandistributionwithastandarddeviationofonly0.04M⊙.Themeanofthedistributionis1.35M⊙,closetothe“canonical”valueof1.4M⊙.Neutron-starmassescanalsobedeterminedforsomebinariescontaininganaccretingX-raypulsar,fromtheamplitudesoftheX-raypulsedelayandopticalradial-velocitycurvesincombinationwithconstraintsontheinclination(thelatterusuallyfromthedurationoftheX-rayeclipse,ifpresent).Thismethodhasbeenappliedtoabouthalfadozensystems(Joss&Rappaport1984;Nagase1989;VanKerkwijk,VanParadijs,&Zuiderwijk1995b).Themassesaregenerallynotveryprecise,butareconsistentwith∼1.4M⊙inallbutonecase.TheoneexceptionistheX-raypulsarVelaX-1,whichisina9-dayorbitwiththeB0.5IbsupergiantHD77581.Forthissystem,aratherhighermassofaround1.8M⊙hasconsistentlybeenfoundeversincethefirstdetailedstudyinthelateseventies(VanParadijsetal.1977;VanKerkwijketal.1995a).Aproblemwiththissystem,however,isthatthemeasuredradial-velocityorbit,onwhichthemassdeterminationrelies,showsstrongdeviationsfromapureKe-plerianradial-velocitycurve.Thesedeviationsarecorrelatedwithinonenight,butnotfromonenighttoanother.Apossiblecausecouldbethatthevaryingtidalforceexertedbytheneutronstarinitseccentricorbitexciteshigh-orderpulsationmodesintheopticalstarwhichinterfereconstructivelyforshorttimeintervals.Wehaveobtainedabout150newspectra,takeninasmanynights,oftheopticalcounterpart,aBsupergiant,inordertoimprovethemassdetermination(Barzivetal.2001).Thesecovermorethan20orbits,andmakeitpossibletoaverageoutthevelocityexcursions.Unfortunately,however,wefoundthattheaveragevelocitycurveshowssystematiceffectswithorbitalphase(seeFig.1),whichdominateourfinaluncertainty.Whileourbestestimatestillgivesahighmass,of1.86M⊙,the2σuncertaintyof0.33M⊙doesnotallowustoexcludesoftequationsofstateconclusively.Whilewecannotdrawafirmconclusion,itisworthwonderinghowVelaX-1couldbetheonlyneutronstarwithamasssodifferentfromallothers.Barzivetal.(2001)discussthisinsomedetailandwarnedagainsttakingthenarrowmassrangearound1.4M⊙asevidenceforanuppermasslimitsetbytheEOS.Afterall,forallEOS,neutronstarssubstantiallylessmassivethan1.4M⊙canexist,yetnoneareknown.Coulditbethatthenarrowrangeinmasssimplyreflectstheformationmechanism,i.e.,thephysicsofsupernovaexplosionsand

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