The Enigma of the Dark Matter

arXiv:hep-ph/0110122v19Oct2001IPPP/01/40DCPT/01/80FTUAM01/19IFT-UAM/CSIC-01-29October2001TheEnigmaoftheDarkMatterShaabanKhalil1,2andCarlosMu˜noz3,41IPPP,PhysicsDepartment,DurhamUniversity,DH13LE,Durham,U.K.2AinShamsUniversity,FacultyofScience,Cairo,11566,Egypt.3DepartamentodeF´ısicaTe´oricaC-XI,UniversidadAut´onomadeMadrid,Cantoblanco,28049Madrid,Spain.4InstitutodeF´ısicaTe´oricaC-XVI,UniversidadAut´onomadeMadrid,Cantoblanco,28049Madrid,Spain.AbstractOneofthegreatscientificenigmasstillunsolved,theexistenceofdarkmatter,isreviewed.SimplegravitationalargumentsimplythatmostofthemassintheUniverse,atleast90%,issome(unknown)non-luminousmatter.Someparticlecandidatesfordarkmatterarediscussedwithparticularemphasisontheneutralino,aparticlepredictedbythesupersymmetricextensionoftheStandardModelofparticlephysics.Experimentssearchingfortheserelicparticles,carriedoutbymanygroupsaroundtheworld,arealsodiscussed.Theseexperimentsarebecomingmoresensitiveeveryyearandinfactoneofthecollaborationsclaimsthatthefirstdirectevidencefordarkmatterhasalreadybeenobserved.1Whydoweneeddarkmatter?OneofthemostevasiveandfascinatingenigmasinphysicsistheproblemofthedarkmatterintheUniverse.Mostastronomers,cosmologistsandparticlephysicistsarecon-vincedthatatleast90%ofthemassoftheUniverseisduetosomenon-luminousmatter,thesocalled‘darkmatter’.However,althoughtheexistenceofdarkmatterwassuggested68yearsago,stillwedonotknowitscomposition.1In1933theastronomerFritzZwickyprovidedevidencethatthemassoftheluminousmatter(stars)intheComacluster,whichconsistsofabout1000galaxies,wasmuchsmallerthanitstotalmassimpliedbythemotionofclustermembergalaxies.But,onlyinthe1970’stheexistenceofdarkmatterbegantobeconsideredseriously.Itspresenceinspiralgalaxieswasthemostplausibleexplanationfortheanomalousrotationcurvesofthesegalaxies,aswewilldiscussindetailinthenextsubsection.Insummary,themeasuredrotationvelocityofisolatedstarsorgascloudsintheouterpartsofgalaxieswasnotasoneshouldexpectfromthegravitationalattractionduetotheluminousmatter.Thisleadastronomerstoassumethattherewasdarkmatterinandaroundgalaxies.Althoughthenatureofthisdarkmatterisstillunknown,itshypotheticalexistenceisnotsooddifwerememberthatthediscoveryofNeptunein1846byGallewasduetothesuggestionofLeVerrieronthebasisoftheirregularmotionofUranus.1.1DarkmatteringalaxiesTocomputetherotationvelocityofstarsorhydrogencloudslocatedfarawayfromgalacticcentresiseasy.OneonlyneedstoextrapolatetheNewton’slaw,whichworksoutstand-inglywellfornearbyastronomicalphenomena,togalacticdistances.Letusrecalle.g.thatforanaveragedistancerofaplanetfromthecenteroftheSun,Newton’slawim-pliesthatv2(r)/r=GM(r)/r2,wherev(r)istheaverageorbitalvelocityoftheplanet,G=6.67×10−11m3kg−1s−2istheNewton’sconstantandM(r)isthetotalmassinsidetheorbit.Thereforeoneobtainsv(r)=sGM(r)r.(1)Clearly,v(r)decreaseswithincreasingradiussinceM(r)isconstantandgivenbythesolarmassM⊙=1.989×1030kg.Thecredibilityofthisformulacanbededucedeasily.Forexample,themeandistancefortheEarthtotheSunis150×106kmimplyingv=30kms−1.ForNeptunewhosemeandistanceis30timesbiggerthevelocityis5.4kms−1.AsitiswellknownbothresultsforthevelocityoftheEarthandNeptunearecorrect.Inthecaseofagalaxy,ifitsmassdistributioncanbeapproximatedassphericalorellipsoidal,eq.(1)canalsobeusedasaestimate.Thusifthemassofthegalaxyisconcentratedinitsvisiblepart,onewouldexpectv(r)∼1/√rfordistancesfarbeyondthevisibleradius.Instead,astronomers,bymeansoftheDopplereffect,observethatthevelocityrisestowardsaconstantvalueabout100to200kms−1.ThusforlargedistancesM(r)/risgenericallyconstant.Hencethemassinteriortorincreaseslinearlywithr.AnexampleofthiscanbeseeninFig.1,wheretherotationcurveofM33,oneoftheabout45galaxieswhichformoursmallcluster,theLocalGroup,isshown.Forcomparison,theexpectedvelocityfromluminousdiskisalsoshown.Usingapproximation(1)andthevisiblemassofM33,4×1010M⊙,onecanroughlyreproducethiscurve.Thisphenomenonhasalreadybeenobservedforaboutathousandspiralgalaxies[2],andinparticularalsoforourgalaxy,theMilkyWay.Themostcommonexplanationfortheseflatrotationcurvesistoassumethatdiskgalaxiesareimmersedinextendeddarkmatterhalos.Whileatsmalldistancesthisdarkmatterisonlyasmallfractionofthe2Figure1:ObservedrotationcurveofthenearbydwarfspiralgalaxyM33,superimposedonitsopticalimage(fromref.[1]).galaxymassinsidethosedistances,itbecomesaverylargeamountatlargerdistances.Forinstancefor∗r=10kpcinFig.1,sincetheobservedvelocityisv≈120kms−1andtheexpectedvelocityduetotheluminousmatterisvlum≈40kms−1,oneobtainsusingapproximation(1)thefollowingratiobetweenthetotalmassandtheluminousmass,M≈9Mlum.Clearly,thistypeofanalysesimplythat90%ofthemassingalaxiesisdark.Cosmologistsusuallyexpressthepresent-daymassdensityaveragedovertheUniverse,ρ,inunitsoftheso-calledcriticaldensity,ρc≈10−29gcm−3,i.e.theydefineΩ=ρ/ρc.Wecanunderstandthecriticaldensitymuchlikethenotionofescapevelocity:ρ=ρc(Ω=1)correspondstothecancellationofkineticand(gravitational)potentialenergies.Ifρρc(Ω1)theUniverseexpandstoamaximum,andthencontractsleadingtoaninverseBigBang(closedUniverse).Ifρρc(Ω1)the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