Clustering properties of a sterile neutrino dark m

arXiv:0807.0646v1[astro-ph]3Jul2008Clusteringpropertiesofasterileneutrinodarkmattercandidate.D.Boyanovsky∗DepartmentofPhysicsandAstronomy,UniversityofPittsburgh,Pittsburgh,Pennsylvania15260,USA.(Dated:July3,2008)Theclusteringpropertiesofsterileneutrinosarestudiedwithinasimpleextensionoftheminimalstandardmodel,wheretheseneutrinosareproducedviathedecayofagaugesingletscalar.Thedistributionfunctionafterdecouplingisstronglyoutofequilibriumandfeaturesanenhancementatsmallcomovingmomentum∝1/√p.DarkmatterabundanceandphasespacedensityconstraintsfromdwarfspheroidalgalaxiesconstrainthemassinthekeVrangeconsistentwithaYukawacouplingtoagaugesingletwithmassandvacuumexpectationvalueintherange∼100GeVandadecouplingtemperatureofthisorder.Thedarkmattertransferfunctionandpowerspectrumareobtainedfromthesolutionofthenon-relativisticBoltzmann-Vlasovequationinthematterdominatedera.Thesmallmomentumenhancementofthenon-equilibriumdistributionfunctionleadstolongrangememoryofgravitationalclusteringandasubstantialenhancementofthepowerspectrumatsmallscalesascomparedtoathermalrelicorsterileneutrinoproducedvianon-resonantmixingwithactiveneutrinos.Thescaleofsuppressionofthepowerspectrumforasterileneutrinowithm∼keVproducedbyscalardecaythatdecouplesat∼100GeVisλ∼488kpc.AtlargescalesT(k)∼1−Ck2/k2fs(teq)+···withC∼O(1).Atsmallscales65kpc.λ.500kpccorrectionstothefluiddescriptionandmemoryofgravitationalclusteringbecomeimportant,andwefindT(k)≃1.902e−k/kfs(teq),wherekfs(teq)∼0.013/kpcisthefreestreamingwavevectoratmatter-radiationequality.TheenhancementofpoweratsmallscalesmayprovideapossiblerelieftothetensionbetweentheconstraintsfromX-rayandLyman-αforestdata.I.INTRODUCTIONIntheconcordanceΛCDMstandardcosmologicalmodeldarkmatter(DM)iscomposedofprimordialparticleswhicharecoldandcollisionless[1].Inthiscolddarkmatter(CDM)scenariostructureformationproceedsinahierarchical“bottomup”approach:smallscalesbecomenon-linearandcollapsefirstandtheirmergerandaccretionleadstostructureonlargerscales.CDMparticlesfeaturenegligiblesmallvelocitydispersionleadingtoapowerspectrumthatfavorssmallscales.Inthishierarchicalscenario,denseclumpsthatsurvivethemergerprocessformsatellitegalaxies.Largescalesimulationsseeminglyyieldanoverpredictionofsatellitegalaxies[2]byalmostanorderofmagnitudelargerthanthenumberofsatellitesthathavebeenobservedinMilky-Waysizedgalaxies[2,3,4,5,6].SimulationswithintheΛCDMparadigmalsoyieldadensityprofileinvirialized(DM)halosthatincreasesmonotonicallytowardsthecenter[2,7,8,9,10]andfeaturesacusp,suchastheNavarro-Frenk-White(NFW)profile[7]ormoregeneralcentraldensityprofilesρ(r)∼r−βwith1≤β.1.5[4,7,10].Thesedensityprofilesaccuratelydescribeclustersofgalaxiesbutthereisanaccumulatingbodyofobservationalevidence[11,12,13,14,15,16,18,19]thatseemtoindicatethatthecentralregionsof(DM)-dominateddwarfspheroidalsatellite(dSphs)galaxiesfeaturesmoothcoresinsteadofcuspsaspredictedby(CDM).Morerecently[19]a“galaxysize”problemhasbeenreported,wherelargescalesimulationsatz=3yieldgalaxiesthataretoosmall,thisproblemhasbeenarguedtoberelatedtothatofthemissingdwarfgalaxies.Warmdarkmatter(WDM)particleswereinvoked[20,21,22]aspossiblesolutionstothesediscrepanciesbothintheoverabundanceofsatellitegalaxiesandasamechanismtosmoothoutthecuspeddensityprofilespredictedby(CDM)simulationsintothecoredprofilesthatfittheobservationsin(dShps).(WDM)particlesfeaturearangeofvelocitydispersioninbetweenthe(CDM)andhotdarkmatter(HDM)leadingtofreestreamingscalesthatsmoothoutsmallscalefeaturesandcouldbeconsistentwithcoreradiiofthe(dSphs).Ifthefreestreamingscaleoftheseparticlesissmallerthanthescaleofgalaxyclusters,theirlargescalestructurepropertiesareindistinguishablefrom(CDM)butmayaffectthesmallscalepowerspectrum[23]soastoprovideanexplanationofthesmootherinnerprofilesof(dSphs),fewersatellitesandthesizeofgalaxiesatz=3[19].Sterileneutrinoswithmasses∼keVmaybesuitable(WDM)candidates[24,26,27,28,29,30].Themainpropertythatisrelevantforstructureformationofanydarkmattercandidateisitsdistributionfunctionafterdecoupling[31,32],whichdependsontheproductionmechanismandthe(quantum)kineticsofitsevolutionfromproductionto∗Electronicaddress:[e-mail]smsofsterileneutrinoproduction[24,25,26,27,33],andmixingbetweensterileandactiveneutrinoscanbeoneofthem[24,25,26].ThereisconsiderabletensionbetweentheX-ray[34]andLyman-αforest[35,36]dataifsterileneutrinosareproducedviatheDodelson-Widrow(DW)[24]non-resonantmixingmechanism,leadingtothesuggestion[37]thatthesecannotbethedominant(DM)component.ConstraintsfromtheLyman-αforestspectraareparticularlyimportantbecauseofitssensitivitytothesuppressionofthepowerspectrumbyfree-streaminginthelinearregime[35,36].ThemostrecentconstraintsfromtheLyman-αforest[36]improveuponpreviousones,butrelyontheDodelson-Widrow[24]modelforthedistributionfunctionofsterileneutrinos,leavingopenthepossibilityofevadingthesetightconstraintswithnon-equilibriumdistributionfunctionsfromotherproductionmechanisms.Thegravitationalclusteringpropertiesofcollisionless(DM)inthelinearregimearedescribedbythepo