Table Of ContentCantheexcessintheFeXXVILyγ 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]. The dark matter WearegratefultoKwang-ilSeonandVladimirDogielfor
mass from the Milky Way dark matter halo within the field valuablediscussions.
of view of the Suzaku observation is small compared with
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