A lower bound on the mass of Dark Matter particles

arXiv:0808.3902v1[hep-ph]28Aug2008AlowerboundonthemassofDarkMatterparticlesAlexeyBoyarskya,b,OlegRuchayskiyc,andDmytroIakubovskyibaETHZ,Z¨urich,CH-8093,SwitzerlandbBogolyubovInstituteforTheoreticalPhysics,Kiev03780,Ukrainec´EcolePolytechniqueF´ed´eraledeLausanne,InstituteofTheoreticalPhysics,FSB/ITP/LPPC,BSP726,CH-1015,Lausanne,SwitzerlandWediscusstheboundsonthemassofDarkMatter(DM)particles,comingfromtheanalysisofDMphase-spacedistributionindwarfspheroidalgalaxies(dSph’s).Afterreviewingexistingapproaches,wechoosetwomethodstoderivesuchabound.ThefirstmethoddependsontheinformationaboutthecurrentphasespacedistributionofDMparticlesonly,whilethesecondoneusesboththeinitialandfinaldistributions.WediscusstherecentdataondSph’saswellasastronomicaluncertaintiesinrelevantparameters.Asanapplication,wepresentlowerboundsonthemassofDMparticles,comingfromvariousdSph’s,usingbothmethods.Themodel-independentboundholdsforanytypeoffermionicDM.Stronger,model-dependentboundsarequotedforseveralDMmodels(thermalrelics,non-resonantlyandresonantlyproducedsterileneutrinos,etc.).ThelatterboundsrelyontheassumptionthatbaryonicfeedbackcannotsignificantlyincreasethemaximumofadistributionfunctionofDMparticles.CombiningtheseresultswiththeX-rayboundsofDMdecaylines,weconcludethatthescenariowhenDMismadeofsterileneutrinosproducedvianon-resonantoscillationswiththeactiveneutrinos,isdisfavored.TheresultsofthisworkallowtoreachthisconclusionwithoutrelyingontheLyman-alphaanalysis.ThemodelofDMsterileneutrinosresonantlyproducedinthepresenceofleptonasymmetryremainsviable.WithinminimalneutrinoextensionoftheStandardModel(theνMSM)bothmassandthemixingangleoftheDMsterileneutrinoareboundedfromaboveandbelow,whichsuggestsapossibilityforitsexperimentalsearch.I.INTRODUCTIONThenatureofDarkMatterisoneofthemostintriguingquestionsofparticleastrophysics.ItsresolutionwouldhaveaprofoundimpactonthedevelopmentofparticlephysicsbeyonditsStandardModel.Althoughthepossibilityofhavingmassivecompacthaloobjects(MACHOs)asadominantformofDMisstillunderdebates(seerecentdiscussionin[1]andreferencestherein),itiswidelybelievedthatDarkMatterismadeofnon-baryonicparticles.However,theStandardModelofelementaryparticlesdoesnotcontainaviableDarkMatterparticlecandidate–massive,neutralandlong-livedparticle.Activeneutrinos,whicharebothneutralandstable,formstructuresinatop-downfashion[2,3,4,5,6],andthuscannotproduceobservedamountoftheearly-typegalaxies[seee.g.7,8].Therefore,theDMparticlehypothesisimpliestheextensionoftheStandardModel(SM).TheDMparticlecandidatesmayhaveverydifferentmasses(forreviewsofDMcandidatesseee.g.[9,10,11,12]):massivegravitonswiththemass∼10−19eV[13],axionswiththemass∼10−6eV[14],sterileneutrinoshavingmassinthekeVrange[15],sypersymmetric(SUSY)particles(gravitinos[16],neutralinos[17],axinos[18]withtheirmassesrangingfromeVtohundredsGeV),WIMPZILLAswiththemass∼1013GeV[19,20],andmanyothers.Thus,themassofDMparticlesbecomesanimportantcharacteristicswhichmayhelptodistinguishbetweenvariousDMcandidatesand,moreimportantly,mayhelptodifferentiateamongdifferentmodelsbeyondtheSM.Itwassuggestedin[21]thatquitearobustandmodel-independentlowerboundonthemassofDMparticlescanbeobtainedbyconsideringphasespacedensityevolutionofcompactastrophysicalobjects,mostnotablydwarfspheroidalsatellites(dSph’s)oftheMilkyWays.Theideawasdevelopedfurtherinanumberofworks(seee.g.[22,23,24,25,26,27,28])AnotherwaytodistinguishbetweenvariousDMmodelsandparticularlytoputaboundontheDMmass,istheanalysisoftheLyman-α(Ly-α)forestdata[29,30,31].1Thismethodessentiallyconstrainsthepossibleshapeofpowerspectrumofdensityfluctuationsatcomovingscales∼Mpc.AssumingaDMmodel,i.eaparticularprimordialvelocitydistributionofDMparticles,onecanobtainarelationbetweentheDMparticlemassinthismodelandtheshapeofthepowerspectrum,probedbyLy-α.Althoughverypromising,theLy-αmethodisverycomplicatedandindirect.Firstofall,undertheassumptionthatthedistributionoftheneutralhydrogentracesthatoftheDM,onecanreconstructpowerspectrumofdensity1Absorptionfeaturebytheneutralhydrogenatλ=1216˚Aatdifferentredshiftsinthedistantquasarspectra.2fluctuationsatredshiftsz∼2−5fromthestatisticsofLyman-αabsorptionlines.OnecanthenperformafitoftheLyman-αdata(oftentogetherwiththemeasurementsofanisotropyoftemperatureofcosmicmicrowavebackgroundandthedataoflarge-scalestructuresurveys),toextracttheinformationaboutcosmologicalmodels.ThisisusuallydonebyusingtheMonte-CarloMarkovchaintechnique[32].Atredshifts,probedbyLy-α,theevolutionofstructureentersalready(mildly)non-linearstage.Therefore,toproperlyrelatemeasuredpowerspectrumwiththeparametersofagivencosmologicalmodelonewouldhavetoperformprohibitivelylargenumberofhydrodynamicnumericalsimulations.Therefore,varioussimplifyingapproximationshavetoberealized[30,33,34,35,36,37,38,39].Apartfromthesecomputationaldifficulties,thephysics,enteringtheLy-αanalysisiscomplicated,andnotyetfullyunderstood(seee.g.[40,41,42,43,44]).Moreover,theDMparticlescansignificantlyinfluencethebackgroundphysics,furthercomplicatingtheLy-αanalysis[45,46].Thesystematicuncertainties,associatedwith