CantheexcessintheFeXXVILyγ linefromtheGalacticCenterprovideevidencefor17keVsterile neutrinos? D. A. Prokhorov∗ KoreaAstronomyandSpaceScienceInstitute,Hwaam-dong,Yuseong-gu,Daejeon,305-348,RepublicofKorea Joseph Silk Astrophysics,DepartmentofPhysics,UniversityofOxford,KebleRoadOx13RH,Oxford,UnitedKingdomand Institut d’Astrophysique de Paris, 98bis Blvd Arago, Paris 75014, France The standard model of particle physics assumes that neutrinos are massless, although adding non-zeros is requiredbytheexperimentallyestablishedphenomenonofneutrinooscillationsrequiresneutrinostohavenon- 0 zeromass.Sterileneutrinos(orright-handedneutrinos)areagoodwarmdarkmattercandidate.Wefindthatthe 1 excessoftheintensityinthe8.7keVline(attheenergyoftheFeXXVILyγline)inthespectrumoftheGalactic 0 center observed by the Suzaku X-ray mission cannot be explained by standard ionization and recombination 2 processes. Wesuggestthattheoriginofthisexcessisviadecaysofsterileneutrinoswithamassof17.4keV n andestimatethevalueofthemixingangle.Theestimatedvalueofthemixinganglesin2(2θ)=(4.1±2.2)×10−12 a liesintheallowedregionofthemixingangleofdarkmattersterileneutrinowithamassof17-18keV. J 1 I. INTRODUCTION strengths and find that there is an unexpected excess in the ] 8.7keVlinefromtheGalacticcenterintheSuzakudata. We E H Several astrophysical observations, suchastheindications demonstratethatthisexcesscannotbeexplainedbymeansof ofcentralcoresinlow-massgalaxies,thelownumberofsatel- standardionizationandrecombinationprocesses. Wepropose . h lites observed around the Milky Way, and the near constant an explanation of the excess in the 8.7 keV line in terms of p cores of the least luminous satellites, have revived interest 17.4keVneutrinodecays. - in sterile neutrinos as a warm dark matter candidate. Elec- o r troweak singlet right-handed (sterile) neutrinos with masses t II. THEEXCESSINTHE8.7KEVLINEFROMTHE s inthefewkeVrangenaturallyariseinmanyextensionsofthe a Standard Model and could be produced in the early universe GALACTICCENTERANDITSORIGIN [ through the Dodelson-Widrow mechanism involving (non- 1 resonant)oscillationswithactiveneutrinospecies[1].Theex- X-rayemissionfromtheGalacticcenterhasbeenobserved v perimentallyestablishedphenomenonofneutrinooscillations for almost 30 years. A component of the diffuse emission 5 requires neutrinos to have non-zero mass, and sterile neutri- is thermal and is produced by a high temperature plasma in 1 nos(orright-handedneutrinos)areanaturalwarmdarkmatter the inner 20 parsecs of the Galactic Center (∼ 8 keV). The 2 candidate. most pronounced features in the emission lines are Fe I Kα 0 Direct constraints on masses and mixing angles are ob- at 6.4 keV, and the K-shell lines 6.7 and 6.9 keV from the . 1 tainedbothfromtheLymanalphaforestpowerspectrumand helium-like (FeXXV Kα) and hydrogen-like (FeXXVI Lyα) 0 X-ray observations of the radiative decay channel, the latter ions of iron, respectively. An analysis of the ratio of the 6.7 0 providing a photon with energy E=m c2/2, where m is the keV to 6.9 keV lines is an interesting test of plasma com- 1 s s sterile neutrino mass. Most recently, X-ray observations of ponents (see, e.g. [5], [6]). For the first time, the FeXXVI : v the local dwarf Wilman 1 have shown marginal evidence for Lyγat8.7keVwasdetectedbytheSuzakuX-raymission[4]. Xi a 5 keV sterile neutrino [2]. The inferred mixing angle lies The observed line intensities by Suzaku are listed in Table 2 inanarrowrangeforwhichneutrinooscillationscanproduce of [4]. For convenience, we list below the most important r a allofthedarkmatterandforwhichsterileneutrinoemission lines(forouranalysis)takenfromthepaperby[4]. Themea- fromcoolingneutronstarscanexplainpulsarkicks. sured intensities of the lines of the hydrogen-like iron ions Infactifsterileneutrinosprovideasignificantfraction(al- are: ILyα =1.66−+00..1019×10−4ph/(cm2s),ILyβ =2.29−+11..3315×10−5 though not necessarily all, see [3],) of the dark matter, the ph/(cm2s),andILyγ =1.77−+00..5662×10−5ph/(cm2s). Theerrors GalacticCenterprovidesanevenmoreattractiveenvironment areat90%confidencelevel[4]. to search for radiative decay signals. If the sterile neutrino The measured ratio of the FeXXVI Lyβ to FeXXVI Lyα massisindeedaround17keV,weexpectaX-raylinenear8.5 iron lines equals ≈ 0.138 ± 0.059 and is in agreement with keV.ThediffuseX-rayemissionfromtheGalacticCenterus- the theoretical value of ≈ 0.14 in the gas temperature range ingtheX-rayimagingspectrometeronSuzakuwasanalyzed between5and15keV(seelinelist[7];forareview,see[8]). by[4],whodetectthe8.7keVlinecorrespondingtheFeXXVI WenotethatthemeasuredintensityoftheFeXXVILyγ = Lyγ. Wehavereanalysedthedataonhydrogen-likeironline 1.77+0.62 × 10−5 ph/(cm2 s) iron line has an significant ex- −0.56 cess above the value derived from the theoretical model [7] andthemeasuredintensityI oftheFeXXVILyαironline. Lyα The ratio of the the FeXXVI Lyγ to FeXXVI Lyα iron lines ∗[email protected] equaled 0.038 in the gas temperature range between 5 and 2 15 keV is from the theoretical model (see, [7]). Therefore Decays of sterile neutrinos in the dark matter halo of the theexpectedvalueoftheintensityintheFeXXVILyγlineis Milky Way are a promising way to explain the excess in the 0.038×I = 6.3+0.4×10−6 ph/(cm2 s)andismuchsmaller 8.7keVline. Theamountdarkmatterwithinthefieldofview Lyα −0.4 thanthemeasuredintensitybySuzaku. Therefore,theexcess oftheSuzakuobservation(seeFig. 1of[4])isonlyaminute oftheintensityinthe8.7keVlineequals≈(1.1±0.6)×10−5 fractionofthetotalmassofthedarkmatterhalooftheMilky ph/(cm2 s). Way. We consider the model of the Milky Way dark halo Todemonstratethatthisexcesscannotbeexplainedbyion- presented in [9] and used to derive constraints on the sterile izationandrecombinationprocesses,wecalculatetheratioof neutrino parameters by [10]. The Milky Way halo density is the fully stripped (FeXXVII) ionic fraction to the hydrogen- describedbytheNavarro-Frenk-White(NFW)profile likeironionicfractionusingtheratiooftheintensitiesofthe M 1 FeXXVILyγtoLyαlinesasafunctionoftemperatureT. ρ (r)= vir , (3) Theratiorγα oftheFeXXVILyγtoFeXXVILyαironline NFW 4παr(rs+r)2 intensitiesisgivenby where the dark matter halo parameters of preferred models Eγ(T)NFeXXVI+Rγ(T)NFeXXVII obtained in [9] correspond to Mvir = 1012M⊙, rs = 21.5 kpc rγα = E (T)N +R (T)N (1) and numerical constant α ≃ 1.64 (see [10]). A mass within α FeXXVI α FeXXVII thefieldofviewof M ≃ 2.5×106M isderivedfromthis fov ⊙ where E and E are the impact excitation rate coefficients, model. γ α and R and R are the rate coefficients for the contribution ThedecayfluxintoasolidangleΩ(withinthefieldofview) γ α from recombination to the Lyγ and Lyα spectral lines, re- isgivenby(see,e. g. [11]) spectively. Excitationandrecombinationratecoefficientsare takenfrom[8]. F = ρNFW(~r) Γc2d3~r, (4) FromEq.(1)theratioofthefullystripped(FeXXVII)ionic s Z 4π(~r −~r)2 2 Ω 0 fractiontothehydrogen-likeironionicfractionis where|~r |=8.5kpcisthedistancetotheGalacticcenter. The 0 N E (T)−r E (T) decayrateΓisgivenby(e.g. [11]andreferencestherein) FeXXVII = γ γα α (2) N r R (T)−R (T) FeXXVI γα α γ m 5 Γ=1.38×10−22sin2(2θ) s s−1. (5) Notethatwedonotusetheassumptionofcollisionalioniza- (cid:18)1keV(cid:19) tionequilibrium. Toestimatethevalueofthemixingangle,weusetheinferred For the best fit value of the intensity ratio of the Lyγ to valueofm =17.4keVandthevalueoftheenergyfluxexcess. Lyαironlines(1.77×10−5/(1.66×10−4) ≈ 0.107)foundby s Then,fromEqs.(4),(5)thevalueofthemixingangleisgiven [4],wefindthattheratioofthefullystripped(FeXXVII)ion by fractiontothehydrogen-likeironionfractionliesintherange (−40,−20) when the electron temperature is in the range (5 sin2(2θ)=(4.1±2.2)×10−12. (6) keV,15keV).Sincetheratioofthefullystripped(FeXXVII) tohydrogen-like(FeXXVI)ionfractionsshouldnotbenega- Using Eq. (5) we derive the following constraint on the tive,weconcludethattheexcesscannotbeexplainedbyion- decayrate: ization and recombination processes. A more physically ac- ceptable explanation of the excess is that of sterile neutrino Γ=(9.0±4.8)×10−28s−1. (7) decays,undertheassumptionthatsterileneutrinosconstitute a significant fraction of dark matter. In the next section, we Note that the derived values of the mixing angle of calculatethemixingangleusingourinferredvalueofthein- sin2(2θ)=(4.1±2.2)×10−12anddecayrateofΓ=(9.0±4.8)× tensityexcessinthe8.7keVline. 10−28s−1lieintheallowedregionforadarkmattersterileneu- trinowithamassof17-18keV(see[12]). Suchaneutrinois capable of accounting for a substantial fraction, if not all, of III. RADIATIVEDECAYSOFSTERILENEUTRINOS thedarkmatter. Anadditionalcontributionofcomparablestrengthcomesin Thesterileneutrinopossessesaradiativedecaychannelde- apoint-likesourceifacuspofdarkmatterdevelopsaroundthe caying to an active neutrino and a photon with energy E = centar black hole. The dark matter cusp mass is constrained m c2/2. Sincetheexcessinthe8.7keVlinecorrespondstoa observationallybystellarorbitmeasurementsandistakento s sterileneutrinomassof17.4keV,inthissectionweestimate be3×106M⊙withinthecentral0.001pc. Thisiscomparable themixinganglesin2(2θ)anddecayrateforsuchasterileneu- to the mass of the central black hole. Such a cusp is natu- trino. rallyproducedviaadiabaticcontractionofdarkmatteraround Using the excess in the 8.7 keV line intensity equal to the black hole within its sphere of influence, about 3 pc for I ≈ (1.1 ± 0.6) × 10−5ph/(cm2s) and the definition of theMilkyWayblackhole[13],[14]. Typicallyaboutasmuch excess theenergyflux F = I ×E,wefindthatthevalueofthe massiscapturedinthespikeasisinthecentralblackholeand s excess energy flux excess in the 8.7 keV line equals (9.6 ± 5.2) × with a density profile of ρ ∝ r−9/4 or even steeper. Dynami- 10−5keV/(cm2s). calhistoriesofmergingcomplicatethispicture. Inparticular, 3 binaryblackholemergers, hadtheyoccurred, woulddestroy thetotalmassofthedarkhalo≃ 1012M ,howeveritsuffices ⊙ suchaspike(see[15],[16],[17]). ≃2.5×106M toproduceasignificantflux(1.1±0.6)×10−5 ⊙ However an alternative and more conservative scenario is ph/(cm2 s)viadecaysofsterileneutrinos. cuspregeneration. Thiscannotoccurdirectlyinthedarkmat- Nearbylowsurfacebrightnessdwarfgalaxieshaveacentral ter because its relaxation time is extremely long. However, darkmatterdensityashighashρi ∼ 5M /pc3(200GeV/cm3) ⊙ thisisnotthecaseforthecentralstars,andonceacuspforms and are consistent with a common mass scale of ∼ 107M ⊙ inthestars,scatteringofdarkmatterparticlesoffofstarscan [22] and even a universal dark matter profile with a limiting redistributethedarkmatterinphasespaceonatimescaleof centraldarkmattersurfacedensityoflog(r ρ )=2.15±0.2,in 0 0 ordertherelativelyshortstar-starrelaxationtime[18],result- unitsoflog(M /pc2).[23]. Thecorrespondingdensityiswell ⊙ inginaρ∝r−3/2densitycuspinthecentralparsecofthedark withinthephasespaceconstraintsfor17keVsterileneutrinos. matter[19]. Oneexplanationofthecommonmassscaleisthatdarkmat- Sterile neutrinos would form such a dark matter cusp, al- ter haloes do not exist at lower masses. Warm dark matter thoughthespikedensityislimitedbyphasespaceconsidera- particleshavelargeenoughfreestreaminglengthstoeraseall tionsfornon-degenerateneutrinos(see,[20]). Usingtheval- densityfluctuationsthatmighthaveformedlowermasshalos uesofthevelocitydispersionfortheMilkyWayof100km/s ifthemassofthewarmdarkmatterparticleisapproximately [21]andasterileneutrinomassof17.4keV,wefindalimiton 5 keV for a minimum halo mass of 107M . In the present ⊙ thedensityρ < 1.4×109M /(pc3). Thiswouldguaranteea case,themassofsuchsterileneutrinosis2×8.7=17.4keV. cr ⊙ point-likesourceifthereisindeedacusp. Theminimumhalomassscaleisapproximately105M . Note ⊙ thattheactualdwarfmassescouldextendtolowervaluesthan evaluatedatthe300pcscaleby[22]. IV. CONCLUSIONS Weestimatedthemixingangleofsin2(2θ) = (4.1±2.2)× 10−12 from the excess in the intensity and the decay rate is Wehavefoundthatthereisanexcessintheintensityinthe found to be decay rate: Γ = (9.0 ± 4.8) × 10−28s−1. These 8.7 keV line observed from the Galactic center over the the- valueslieintheallowedregionofthemixingangleanddecay oretical value expected for the intensity in the FeXXVI Lyγ rateparameterspaceforadarkmattersterileneutrinowitha line.Thisintensityexcessequals(1.1±0.6)×10−5ph/(cm2s), massof17-18keV(see[12]). Sterileneutrinosinthisregion wheretheerrorsareatthe90%confidencelevel.Weshowthat of mass, decay rate and mixing angle parameter space can thisexcesscannotbeexplainedbymeansofstandardioniza- contributesignificantlytodarkmatter. Suchneutrinoswould tionandrecombinationprocesses, sincetheratioofthefully bevirtuallyindistinguishablefromcolddarkmatterexceptin stripped (FeXXVII) to FeXXVI ion fractions becomes (un- thelowestmassdwarfgalaxieswherecoreswouldbeformed. physically) negative in the temperature range of (5 keV, 15 Highresolutionx-rayobservationsshouldrevealapoint-like keV), when the observed ratio of FeXXVI Lyγ to FeXXVI line source of comparable strength to the Suzaku line excess Lyαironlinesisapplied. ifacuspispresentaroundthecentralblackhole. Wesuggestthataphysicallyacceptableexplanationofthe intensity excess in the 8.7 keV line is due to decays of ster- ile neutrinos that that are in a halo of dark matter around ACKNOWLEDGMENTS the Milky Way. The dark matter density profile we adopt is obtained by numerical simulations [9]. 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