Dark matter distribution in the universe and ultra

arXiv:astro-ph/0010050v12Oct2000Darkmatterdistributionintheuniverseandultra-highenergycosmicraysPasqualeBlasi∗∗NASA/FermilabAstrophysicsCenterAbstract.Twoofthegreatestmysteriesofmodernphysicsaretheoriginofthedarkmatterintheuniverseandthenatureofthehighestenergyparticlesinthecosmicrayspectrum.Wediscussherepossibledirectandindirectconnectionsbetweenthesetwoproblems,withparticularattentiontotwocases:inthefirstwestudythelocalclusteringofpossiblesourcesofultra-highenergycosmicrays(UHECRs)drivenbythelocaldarkmatteroverdensity.InthesecondcasewestudythepossibilitythatUHECRsaredirectlygeneratedbythedecayofweaklyunstablesuperheavydarkmatter.INTRODUCTIONMostofouruniverseismadeofadarkelusivecomponent,whosenatureisstillunknown.Thismysteriouscomponentdominatesthegravitationalinteractionsinourworldanddeterminesthedistributionofvisiblematter,thatweassociatewithgalaxies,clustersandsuperclustersofgalaxiesandtheirluminousconstituents.Weknowfromthemeasureofthevaluesofcosmologicalparameters,thatmostofthedarkmattermustbeofnonbaryonicnature.Thisimportantfindingstimulatedtheblossomingofnumerousproposalsofnewparticles,inthecontextoftheoriesofGrandUnificationorextensionsoftheStandardModel.Someofthepossibilitiesthathavebeenproposedinvoketheexistenceofsuperheavyparticles,withmasscomparablewiththemassoftheinflaton.Theseparticlesmightbealmoststableandcontributethewholeofcolddarkmatterneededtoexplaincosmologicalandastrophysicalobservations.Independentofthenatureofdarkmatter,astrophysicalobservationsofthevisibleuniverseallowustoknowhowdarkmatterisdistributedinspace:primordialfluctuationsinthedensityfieldresulttodayinastructureddistributionofthedarkandvisiblecomponentsintheuniverse.Galaxiesarepartofthisclustering,butsimilarlocaloverdensitiescanbeseenonlargerscales,uptoafewtensMpc,wheretheuniversestartsbeingwelldescribedbyahomogeneousdensityfield.Anapparentlyunrelatedmysteryofmodernphysicsistheexistenceofparticleswithenergyinexcessof1020eVinthecosmicradiation,theso-calledultrahighenergycosmicrays(UHECRs).Theseparticlesarethoughttobeofextragalac-ticorigin,bacausethegalacticmagneticfieldisunabletoconfineparticleswithsuchenergy.AspointedoutinthepioneeringpapersbyGreisen[1]andZatsepinandKuzmin[2],ifthesourcesaredistributedhomogeneouslyintheuniverse,theprocessofphotopionproductionoffthephotonsofthecosmicmicrowaveback-ground(CMB)shouldcauseastrongsuppressioninthespectrumofUHECRsabove∼5×1019eV,whatisnowknownastheGreisen-Zatsepin-Kuzmin(GZK)cutoff.Neverthelesswedodetectparticleswithenergymuchinexcessofthiscut-offenergy,andwehavebeenunabletoidentifyanystraightforwardastrophysicalsourceinthedirectionofarrivaloftheseevents.Canthetwomysteries,ofdarkmatterandUHECRsberelated?Wediscussheretwopossibleconnections:insections2and3weexploretheconsequencesthatalocalclusteringofthesources,drivenbythecorrespondingdarkmatterclustering,haveontheobservedfluxesofUHECRs,incomparisonwiththecaseofhomogeneousdistribution.TheinitialpredictionbyGreisenandZatsepinandKuzmin,wasinfactderivedintheassump-tionofsourcesequallydistributedinspace.ItwaslatershownbyBerezinskyandGrigorieva[3]thatalocaloverdensitybyafactor∼10over∼20MpcwouldmaketheproblemoftheexistenceofUHECRslesssevere.Thelocaldensityofsourcescannowbeextractedfromlargecatalogs,sothatarealisticdeterminationofthedensityfieldcanfinallybeusedinthecalculationofthefluxesofUHECRs.WeuseherethePSCzandCfAcatalogsforthepurposeofcalculatingthedensityfield.ThefluxesofUHECRsarecalculatednumericallybymontecarlosimulations.Insection4weconsideradirectconnectionbetweendarkmatterandUHECRs,inthecasethatdarkmatteriscomposedofsuperheavyquasi-stableparticles.Particlesfulfillingtheserequirementshavebeenrecentlydiscussedin[4–7][seealsoJ.Ellis(theseproceedings)].WewillreviewherethecurrentsituationandstresssomeconsequencesofthismodelontheobservablelargescaleandsmallscaleanisotropiesinthearrivaldirectionsofUHECRs.MEASURINGTHEGALAXYDENSITYFIELDInordertodeterminetheeffectsoftheinhomogeneityofthesourcedistributiononthecosmicrayspectrum,weneedtomeasurethegalaxydensityfield,andinparticularitsdependenceonredshift.Ingeneral,itmaywellbethatthesourcesofUHECRsareofsometypenotdirectlyrelatedtootherknownobjectslikegalax-ies,butweassumeherethatthesourcesofUHECRshaveadensityfieldthatisproportionaltothatofordinarygalaxies.Wefollowtheapproachpresentedin[8].Thegalaxydensityfieldisusuallymeasuredbyselectinggalaxiesfromanimagingskysurveyandtakingtheirredshifts.Almostinvariably,thegalaxiesareselectedtobebrighterthansomelimitingfluxfliminsomeband,expressedasan“apparentmagnitude”mlim=−2.5log10(flim/f0),wheref0isanarbitraryzero-point.Forall(orforsomerandomsubsample)ofthegalaxiesbrighterthanthis,theirspectraaretakenandtheirredshiftszaredetermined.However,wecannotsimplyusetherawdistributionofredshiftsfromsuchaflux-limitedsurvey,regardlessofthewaythegalaxieswereselected.Herewedescribetheproperwaytoderivedensityfieldsfromgalaxyredshiftsurveys.Welimitourselvestomeasuringthedensityinredshiftspace,ignoringtheeffectsofdeviationsfromtheHubblelawduetogalaxypeculiarvelocities.Thesubjectofgalaxydensityfields