Sterile neutrinos as subdominant warm dark matter

arXiv:0707.1495v2[astro-ph]20Sep2007SterileneutrinosassubdominantwarmdarkmatterA.Palazzo1,2,D.Cumberbatch1,A.Slosar1,andJ.Silk11Astrophysics,DenysWilkinsonBuilding,KebleRoad,OX13RH,Oxford,UnitedKingdom2SezioneINFNdiBari,ViaAmendola173,70126,Bari,ItalyAbstractInlightofrecentfindingswhichseemtodisfavorascenariowith(warm)darkmatterentirelyconstitutedofsterileneutrinosproducedviatheDodelson-Widrow(DW)mechanism,weinvesti-gatetheconstraintsattainableforthismechanismbyrelaxingtheusualhypothesisthattherelicneutrinoabundancemustnecessarilyaccountforallofthedarkmatter.WefirststudyhowtoreinterpretthelimitsattainablefromX-raynon-detectionandLyman-αforestmeasurementsinthecasethatsterileneutrinosconstituteonlyafractionfsofthetotalamountofdarkmatter.Then,assumingthatsterileneutrinosaregeneratedintheearlyuniversesolelythroughtheDWmechanism,weshowhowtheX-rayandLyman-αresultsjointlyconstrainthemass-mixingpa-rametersgoverningtheirproduction.Furthermore,weshowhowthesamedataallowustosetarobustupperlimitfs∼0.7atthe2σlevel,rejectingthecaseofdominantdarkmatter(fs=1)atthe∼3σlevel.PACSnumbers:95.35.+d,14.60.Pq,14.60.St1I.INTRODUCTIONRecentastrophysicalobservations,suchastheindicationsofcentralcoresinlow-massgalaxies[1,2,3,4,5,6,7,8,9],andthelownumberofsatellitesobservedinMilkyWay-sizedgalaxies[10,11,12],indicatetwopossibleshortcomingsofthe[Λ]CDMparadigm(see[13,14])andhaveboostedtheinterestinawarmdarkmatter(WDM)scenariowhichmayalleviatethesepossiblesmallscaleproblems[15,16].Electroweaksingletrighthanded(“sterile”)neutrinosνswithmassinthekeVrangeappeartobeappealingcandidatessincetheynaturallyariseinmanyextensions[17,18,19,20,21,22]oftheStandardModelandtheycouldbeproducedintheearlyuniversethroughtheDodelson-Widrow(DW)mechanism[23]involving(non-resonant)oscillationswiththeactivespecies.Directconstraintsonmassandmixingangleofthesterileneutrino1canbeobtainedbyexploitingX-rayobservations[26,27,28,29].Indeed,sterileneutrinospossesaradiativedecaychannel[30,31],whichgivesrisetophotonspotentiallydetectableinastrophysicalX-rayandγ-raysources.LimitsofsuchkindhavebeenderivedexploitingdiffusecosmicX-raybackground[27,32],MilkyWay“blanksky”observations[33,34,35,36],X-rayspectraofnearbygalaxies[35,37]orclustersofgalaxies[38,39,40],andgamma-raylineemissionsearchesinthegalacticcenterregion[41].Indirectconstraintsontheneutrinomasscanbeachievedbytheobservationsofcosmologicalstructureformationonverysmallscales,whereWDMtypicallysuppressestheclusteringprocess.Inthiscontext,Lyman-αforestmeasurements(henceforthLy-α)constitutethemostsuitableprobe[42],beingsensitivetracersoftheprimordialdensityfluctuationsonthesmallestscales.AssumingthatsterileneutrinosareproducedsolelythroughtheDWmechanismandrequiringthattheymustaccountforallthedarkmatterdensityΩs=Ωdm,therecentX-rayanalyses[32,33,34,35,36,37,38,39,40]determineupperlimitsontheirmasswhichlieintherange(3-8keV).Ontheotherhand,underthesamehypotheses,thelatestLy-αanalyses[43,44]ofthehighredshiftfluxpowerspectra,measuredbytheSDSSsurvey[45],furnishlowerboundsintherange(10-13keV),incleartensionwiththeX-rayupperlimits.2Whiletheseresultsimplythatsterileneutrinoscannotaccountfortheentireamountofdarkmatterintheuniverse,3thepossibilityexiststhattheDWmechanismcouldhavepro-ducedonlyafractionfs=Ωs/Ωdmofitstotalcontent.Thisdoesnotpreventsterileneutrinosfromplayinganimportantroleinothercontexts,suchaspulsarkicks[52,53,54,55,56],supernovaexplosions[57,58],andreionizationoftheuniverse[59,60,61,62,63,64,65].Indeed,ithasbeenalreadyrecognized[49]thatasterileneutrinoexplanationofthepulsarkickscanbereconciledwiththeexistingX-rayconstraintsassumingthe(lowestpossible)relicabundanceprovidedbytheDWproductionmechanism.Furthermore,thesuppressionofsmallscalestructuresinducedbyWDM,whilereducingproblemsatlowredshifts,de-laystheonsetofreionization[59,60],possiblytoanextentdifficulttoreconcilewiththeWMAP3findings[66].WhethertheX-raysemittedbysterileneutrinoscaneffectivelydi-minishthisinconsistencyisstillanopenquestion[62,64,65],andasubdominant(fs1)1NoticethattheLSND[24]andMiniBooNE[25]experimentsarenotsensitivetotheextremelysmallmixinganglesinvolvedintheDWmechanism.2Similarlowerbounds(∼10keV)havebeendeterminedbyQSOgravitationallensingobservations[46].3Thisconclusioncanbeevadedinvokingalternativeproductionmechanisms(notconsideredinthiswork),suchasresonantoscillations[47],generationoperativeduring[48]orpriorto[49]oscillationsorlowreheatingtemperatures[50,51].2relicabundancewouldprobablyreducethetensionalsointhiscontext.Therefore,itseemsinterestingtoinvestigateinasystematicwaytheconstraintsattain-ableonthemass-mixingparameterswhichregulatetheDWproductionmechanismrelaxingtheusualassumptionof“dominant”darkmatter(Ωs=Ωdm).Withthispurposeinmind,wefirstaddresstheissueofreinterpretingtheX-rayandLy-αconstraintsinthepresenceofaνssubdominantrelicabundance(ΩsΩdm)whichisfixedapriori,i.e.independentlyoftheoscillationparameters.Then,wetreatthegeneralcaseinwhichtherelicabundancedependsonmass-mixingparametersaspredictedbytheDWmechanism.Wedeterminetherangeofsuchparameterst