重离子碰撞的相对论流体力学二核物质的压缩与夸克胶子等离子体的相变Relativistichydrod

NUCLEARPHYSICSAELSEVIERNuclearPhysicsA595(1995)383-408Relativistichydrodynamicsforheavy-ioncollisions.II.Compressionofnuclearmatterandthephasetransitiontothequark-gluonplasma*DirkH.Rischkea'l,Yarl~Pt~rsfinb,JoachimA.MaruhnhaPhysicsDepartment,PupinPhysicsLaboratories,ColumbiaUniversity,538W120thStreet,NewYork,NY10027,USAblnstitutfiirTheoretischePhysikderJ.W.Goethe-Universitiit,Robert-Mayer-Str.10,D-60054Frankfurt/M.GermanyReceived21April1995;revisedI1July1995AbstractWeinvestigatethecompressionofnuclearmatterinrelativistichydrodynamics.Nuclearmatterisdescribedbyao--w-typemodelforthehadronmatterphaseandbytheMITbagmodelforthequark-gluonplasma,withafirstorderphasetransitionbetweenbothphases.Inthepresenceofphasetransitions,hydrodynamicalsolutionschangequalitatively,forinstance,one-dimensionalstationarycompressionisnolongeraccomplishedbyasingleshockbutviaasequenceofshockandcompressionalsimplewaves.Weconstructtheanalyticalsolutiontotheslab-on-slabcollisionproblemoverarangeofincidentvelocities.Theperformanceofnumericalalgorithmstosolverelativistichydrodynamicsistheninvestigatedforthisparticulartestcase.Consequencesfortheearlycompressionalstageinheavy-ioncollisionsarepointedout.1.IntroductionToinvestigateheavy-ioncollisiondynamicsinrealistic,i.e.(3+1)-dimensional,situa-tionsbymeansofhydrodynamicsrequiresnumericalschemestosolvethehydrodynami-calequationsofmotion.Priortostudyingquestionsofphysicalinterest,however,one*ThisworkwassupportedbytheDirector,OfficeofEnergyResearch,DivisionofNuclearPhysicsoftheOfficeofHighEnergyandNuclearPhysicsoftheUSDepartmentofEnergyunderContractNo.DE-FG-02-93ER-40764.JPartiallysupportedbytheAlexanderyonHumboldt-StiftungundertheFeodor-Lynenprogram.0375-9474/95/$09.50(~)1995ElsevierScienceB.V.AllrightsreservedSSDI0375-9474(95)00356-8384D.H.RischkeetaL/NuclearPhysicsA595(1995)383-408hastocheckwhethertheseschemesreproduceanalyticalsolutions,asfarassuchexistatall.Inapreviouspaper[t]wehavepresentedtwoalgorithmsforidealrelativistichydrodynamics,theSHASTA,aflux-correctedtransportalgorithm[2]andtherelativis-ticHLLE,aGodunov-typealgorithm[3].Wehaveinvestigatedtheirperformancefortheexpansionofmatterintothevacuum,wheretheyareconfrontedwithtwoproblemsgenericforsimulationsofheavy-ioncollisions.Thesearethepresenceofvacuumitselfandthequalitativechangeinthetypeofthehydrodynamicalexpansionsolutionifphasetransitionsoccurintheequationofstate(EoS).AswasexplainedindetailinRefs.[1,4],matterthatundergoesafirstorderphasetransitionmayexhibitthermodynamicallyanomalousbehaviourinacertainrangeofindependentthermodynamicvariables,signalledbyachangeofsignofthequantity~r202P2c~1--cs~--~+,(l)e+pwherec2=__ap/ael¢isthevelocityofsound,e,p,ando-aretheenergydensity,pressureandspecificentropy,respectively.Forthermodynamicallynormal(TN)matter,2;0,forso-calledthermodynamicallyanomalous(TA)matter2;0[1,4].AswasshowninRefs.[1,4,5],fortheone-dimensionalexpansionofTNmatterasimplerarefactionwaveisthestablehydrodynamicalsolution,whileforTAmattersuchawaveisunstablewithrespecttoformationofararefactionshockwave.Moreover,aninitialdiscontinuityisboundtodecayintoasimplewaveinTNmatter,butcannotdosoifmatterisTA(orevenif2;onlyvanishesinsteadofbecomingnegative).Thus,rarefactiondiscontinuitiesformthestablehydrodynamicalsolutionintheexpansionofTAmatter.Ontheotherhand,forthecompressionofTAmatteracompressionalsimplewaveformsthestablehydrodynamicsolution,butitisunstableinTNmatterwithrespecttoformationofacompressionalshockwave.Analogously,acompressionalshockdis-continuityisboundtodecayintoacompressionalsimplewaveinTAmatter,whileitcannotdosoinTNmatter.Thus,compressionshocksarestableinthecompressionofTNmatter.AsoutlinedinRef.[1],inrealisticcasestheEoShasbothTNandTAregions.Consequently,thehydrodynamicalsolutionfortheone-dimensionalexpansionismorecomplicated,involvingasequenceofsimplewaves,regionsofconstantflowanddis-continuities.ItwasshowninRef.[4]thatthesameholdsforthecompression.Thecorrespondinghydrodynamicalsolutionwasexplicitlyconstructedinthecaseofaone-dimensionalslab-on-slabcollision.(ForTNmatterthistestproblemandthecorre-spondingperformanceoftheSHASTAandrelativisticHLLEalgorithmswasstudiedinRef.[3].)ThenuclearmatterequationsofstateusedinRef.[4]featuredafirstorderphasetransitionbetweenthequark-gluonplasma(QGP),describedbytheMITbagmodel,andhadronicmatter,describedbyphenomenologicalequationsofstate[6,7].InthisworkwefirstconstructanuclearmatterEoSsimilartothatofRef.[4].WealsousetheMITbagEoS[8]fortheQGPphase,butforthehadronicphase,weemployaversionoftheo--oJmodel[9](plusmassivethermalpions)whichfeaturesD.H.Rischkeetal./NuclearPhysicsA595(1995)383-408385morerealisticvaluesforthegroundstateincompressibilityandtheeffectivenucleonmassthantheoriginalversionproposedbyWalecka[6].ForthisEoS,weconstructanalyticallythehydrodynamicalcompressionsolutionasdescribedinRef.[4].WithatabulatedversionoftheEoS,wethentesttheabilityofthenumericalalgorithmstoreproducethissolution.Thisisnotonlyanecessarystepwhichshouldbetakenpriortoapplyingthesealgorithmstomorerealisticsimulati