Low energy IceCube data and a possible Dark Matter related excess

0.27 MB·

by  Marco Chianese

Low energy IceCube data and a possible Dark Matter related excess
M.Chianesea,b,G.Mielea,b,S.Morisia,b,E.Vitaglianob,c
aINFN,SezionediNapoli,ComplessoUniv.MonteS.Angelo,I-80126Napoli,Italy
bDipartimentodiFisicaEttorePancini,Universita`diNapoliFedericoII,ComplessoUniv.MonteS.Angelo,I-80126Napoli,Italy
cMax-Planck-Institutfu¨rPhysik(Werner-Heisenberg-Institut),Fo¨hringerRing6,80805Mu¨nchen,Germany
Abstract
In this Letter we focus our attention on the IceCube events in the energy range between 60 and 100 TeV, which show an order
2-sigmaexcesswithrespecttoapower-lawwithspectralindex2. Weanalyzethepossibleoriginofsuchanexcessbycomparing
6
thedistributionofthearrivaldirectionsofIceCubeeventswiththeangulardistributionsofsimplydistributedastrophysicalgalac-
1tic/extragalacticsources,aswellaswiththeexpectedfluxcomingfromDMinteractions(decayandannihilation)fordifferentDM
0
2profiles. The statistical analysis performed seems to disfavor the correlation with the galactic plane, whereas rules out the DM
annihilationscenarioonlyincaseofsmallclumpinesseffect. Thesmallstatisticstillnowcollecteddoesnotallowtoscrutinizethe
r
acases of astrophysical isotropic distribution and DM decay scenarios. For this reason we perform a forecast analysis in order to
MstresstheroleoffutureNeutrinoTelescopes.

3Keywords: IceCube,NeutrinoTelescopes,NeutrinoPhysics,DarkMatter
2

]1. Introduction primary ratio measurements [4, 7]. On the other hand, galac-
h
p ticastrophysicalneutrinos,whicharenotaffectedbymagnetic
- TheobservationofastrophysicalneutrinosmadebytheIce- fields,haveaflux∝ E−γ,withγ≈2.
pCube experiment (IC) [1] has been an important step in the Even considering νextragalactic sources to be significant (a
e
hfield of Neutrino Astronomy, whose impact on both Particle- reasonablehypothesisgiventhehighgalacticlatitudesofsome
[andAstro-Physicshasstilltobeunveiled. Recently[2]theIC events) it is not easy to justify a steep flux [8]. Models with
Collaboration has delivered in a preliminary work the results pγ interactions produce peakedspectra [9], so one couldhave
3
vof four years data. In Figure 1 (upper panel) we report the a steep flux depending on the position of the peak. However,
4so-called excess in the number of events as a function of the in this case one expects a peak in the spectra in the region
3neutrino energy, which is the number of events detected in IC of several PeV like for Active Galactic Nuclei [10]. Another
9onceonehassubtractedthebackground(atmosphericconven- kindof pγ source, GammaRayBurst, providesafluxwithan
2tionalandpromptneutrinosplusmuons[2]),andanastrophys- upper limit (given by searches for correlation with observed
.0icalcomponentcharacterizedbya Eν−γ power-law, withγ = 2 GRB) more than one order of magnitude below the observed
1being considered as benchmark prediction [1, 2, 3]. The plot flux [11]. Moreover, hard and smooth spectra are expected in
0
seemstosuggestthepresenceofanexcessofeventsintheen- pp scenarios [12], like for extragalactic Supernova Remnants
6
1ergyrange60-100TeVthathassometension,order2σ,with [13]. Moregenerally,theoreticalmodelsofaccelerationmech-
:thesimpleEν−2contribution. AscanbeseenfromRef.[2],such anismforhadronicmatterproduceafluxthatshouldbeatmost
v
an excess partially disappears if one considers a steeper astro- assoftasE−2.2[14]1.
Xiphysical component with power-law Eν−2.58, even though such Indepenνdently of the detailed theoretical model, we have,
ranexponentforaneutrinofluxcanbehardlyexplained. most importantly, observational constraints coming from mul-
a
In general, the cosmic ray spectrum is characterized by a timessengerapproacheslike[16],whichcombineICdatawith
power-law[4],whichisusuallyunderstoodintermsofacceler- Fermiγ-raymeasurements,andgivestrongboundstoahadronu-
ationfromshockfronts,theso-calledFermimechanism[4,5]. clearorigin(whileleaveroomforhidden pγ sources[17]). In
Anastrophysicalneutrinofluxisexpectedtobeproduceddur- fact, a spectrumas softasthe oneobtained fittingIC dataim-
ing the hadronic matter acceleration and interaction with radi- plies, when assuming sources transparent to radiation with re-
ation (pγ) or with gas (pp). Thus its dependence on energy specttotwo-photonannihilation,anexpectedγ-rayfluxbigger
shouldbe,atthesource,mostlyrelatedtothedifferentialspec- than the measured one [16, 17]. The previous considerations
trum of charged cosmic rays and to the pions production ef- supporttheassumptionofanastrophysicalE−2power-lawused
ν
ficiency. If needed, one should take into account propagation toobtaintheexcessreportedinFigure1.
effects so that, for example, the galactic cosmic ray spectrum
at the Earth becomes ∝ E−(γ+δ) (γ+δ ≈ 2.7) up to the ankle
1Thisistruewhenconsideringtheminimalunbrokenpowerlawscenario;
at 1 ∼ 10 PeV [6]. The quantity δ depends on galactic mag- consideringdifferentvaluesforδ[15]orincludingabreakintheneutrinospec-
netic fields and is evaluated through cosmic rays secondary to trumcanleadtoasteepflux,whichishoweverconstrainedbydata(seebelow).
PreprintsubmittedtoElsevier March24,2016
icalsources,respectively;
ii)inducedbyDarkMatterviadecayorannihilation,hencere-
latedtothefirstorsecondpoweroftheparticularDarkMatter
(DM)densityprofileadopted.
Moreover,eventhoughthesmallnumberofeventsalreadyde-
tected does not allow to exclude all DM scenarios, one can
perform a forecast analysis in order to determine the required
statistics.
InordertocomparetheICobservationswithpossibleDM
predictionsweconsiderbothdecayingandstableDarkMatter
cases. Inthefirstcase,60−100TeVneutrinosdetectedatIce-
Cube would be originated directly from the decay of the DM
particles,whileforastableDMparticleneutrinosareonlypro-
ducedviaannihilation. Inbothcasestheresultingneutrinoflux
wouldbecomposedbybothagalacticandanextragalacticDM
component.Differentapproachesproposedinliterature[18,20,
21,22,23,24,25,26,27,28,29,30,31,32,33,34]havestud-
iedthepossiblepresenceofDMhintsinthePeVrange,namely
for the most energetic IC events. Here we take an alternative
point of view, assuming that PeV events have bottom-up ori-
ginandconsideringforlowerenergydataapossibletop-down
originduetoDMparticleswithmassscaleO(100)TeV.Inde-
pendentlyofthemassscaleandoftheDMcouplings,neutrinos
originatedfromDMwouldhaveanangulardistributionthatis
more peaked around the Galactic Center where a higher DM
density is expected. This is true in particular when assuming
an annihilating DM, because of the squared enhancement fac-
tor. Of course, this effect is dependent on the assumed DM
Figure1: TheupperpanelshowstheexcessinthenumberofIceCubeneu-
galactichaloprofiles;forexample,onecouldtaketheNavarro-
trinoeventswithrespecttothesumofthebackground(atmosphericneutrinos
andmuons)andanastrophysicalcomponentdescribedbyaE−2power-law,as Frenk-White profile (NFW) [35] or different distributions like
ν
functionoftheneutrinoenergy.Inthelowerpanel,wereportthesameexcessin the Isothermal profile (Isoth.), which implies a more isotropic
thewholeneutrinoflux(summedonallflavors)oncethattheaverageeffective
flux.
areaoftheparticularenergybinand1347daysofdatatakinghavebeentaken
intoaccount.
2. Theanalysis
Inordertoinferaboutthephysicaloriginoftheexcesswe
Starting from the excess in the number of events one can
compare the angular distribution of the observed events in the
obtain the corresponding quantity for the whole neutrino flux
energybin60-100TeV(inthefollowingwediscusstheproce-
(summedonallflavors)oncetheeffectiveareaofthedetectoris
dure to take into account the presence of the background and
takenintoaccount[1].InFigure1(lowerpanel)wereportsuch
of the experimental errors) with the angular distributions of
afluxasafunctionoftheneutrinoenergy.Asalreadydiscussed
astrophysical galactic sources (galactic plane) and extragalac-
inRef.[18],weassumeforsimplicitytheequalitybetweenthe
tic ones (isotropic distribution), as well as with the expected
deposited and neutrino energy due to low statistics at our dis-
fluxcomingfromDMinteractions(decayandannihilation). In
posal. At the energy scale O(100) TeV, this is not strictly true
this approach the astrophysical E−2 power-law contribution is
forneutralcurrentinteractions[19]. Whenasignificantstatis-
regarded just as an additional term to the background events
tics is collected, the average ratio between the two energies,
counting for atmospheric neutrinos and muons. For this rea-
whichisoftheorderof(97%σCC+23%σNC)/(σCC+σNC)∼
sonhereafterwedenoteasbackgroundthesumofatmospheric
75%,couldbeapplied.
neutrinos,muonsandneutrinoscomingfromtheastrophysical
InthisLetterweassumethattheaboveexcess,mainlycon-
E−2 power-law. Moreover, due to the small number of events
centratedintheenergyrange60-100TeV,hasagenuinephys-
collected till now in the energy bin under study, in this analy-
icalorigin. Underthisansatz,itisworthpursuing,forthisen-
sis we take the simplicity assumption to consider just one ad-
ergybin,astudyinordertounveilthenatureofsuchanexcess.
ditional component to neutrino background at a time (alterna-
Weperformouranalysisassumingasnullhypothesisoneofthe
tive scenarios i) or ii) of previous section) to explain the ex-
followingalternativesforthesourceoftheICdata:
cess. This allows us to be more predictive even though more
i)astrophysical,whichcanbeinvestigatedbystudying,infirst
involved scenarios can be proposed where the excess in neu-
approximation, the correlation with the galactic plane or with
trino flux can be explained in terms of several components of
anisotropicdistributionforgalacticorextragalacticastrophys-
differentorigin. Otheranalyseshavealreadybeenpresentedin
2
literature with different assumptions [29, 36]. In particular, in Galactichalo,andofanExtraGalacticterm
Ref. [29]ithasbeenstudiedthepossibilitythatthewholeneu-
dJ dJG dJEG
trinospectrumhasaDMorigin,whileRef. [36]analyzedonly = + (3)
thehighenergyneutrinospectrum(E >150TeV)considering dΩdE dΩdE dΩdE
ν
also mixed components to the neutrino flux. Differently from where
pgruelvarioeuffiscaineanlcyyseosf[t2h9e,I3C6d],etwecetoarlsfoortaakllenienutotriancocofluanvtortshe[4a4n]-. dJG = f (E) (cid:90) ∞ρ [r(s,cosθ)]ds, (4)
InFigure2itisreportedthenormalizedICeffectivearea,aver- dΩdE 4πMτ 0 h
agedintheenergyrangeconsidered(60−100TeV),asfunction dJEG = ΩDMρc (cid:90) ∞ dz f (cid:0)E(cid:48)(cid:1)(cid:12)(cid:12)(cid:12) . (5)
ofsinδ,whereδisthedeclinationintheequatorialcoordinates dΩdE 4πMτ H(z) E(cid:48)=E(1+z)
0
system. Intheregionsinδ>0(NorthPole)theeffectiveareais
InthepreviousexpressionsMandτstandformassandlifetime
mainlyaffectedbytheEarthabsorptionforallneutrinoflavors,
ofDMparticles2,whereasρ (r)istheDMgalactichaloprofile,
whereasforsinδ<0(SouthPole)onlythemuoneffectivearea √ h
beingr(s,cosθ) = s2+R2−2sRcosθwithR (cid:39) 8.5kpc(the
isslightlydependentonthedeclination.
Sun-Galactic Center distance) and cosθ ≡ cosbcosl. More-
over we take Ω = 0.2685, ρ = 5.5 × 10−6GeVcm−3 and
(cid:112) DM c
H(z) = H0 ΩΛ+Ωm(1+z)3 withh ≡ H0/100kms−1Mpc−1,
ΩΛ = 0.6825 and Ωm = 0.3175 [39]. The quantity f (E) ≡
dN/dE is the neutrino energy spectrum produced by the de-
cayofaDMparticle,whoseexpressiondependsonthespecific
model considered. Since the excess is localized in the energy
range 60 - 100 TeV, it is reasonable to assume that the neu-
trinoenergyspectrumisalmostpeakedinthesamerange. This
meanstoassumeanegligibleneutrinoenergyspectrumforen-
ergy larger than 100 TeV. Note that a not vanishing neutrino
energy spectrum for energy smaller that 60 TeV does not pro-
vide any contribution neither to the galactic component nor to
theextragalacticonefortheenergybinconsidered. Therefore,
independentlyoftheshapeoftheenergydistribution f (E),the
redshift integral in Eq. (5) has an upper limit that is at most
Figure2: NormalizedIceCubeeffectiveareaasfunctionofthedeclinationδ, equaltozmax =100TeV/60TeV−1. Thisisdeterminedbythe
onceithasbeenaveragedintheenergyrange60−100TeV. relation E(cid:48) = E(1+z)whentheconditions E(cid:48) ≤ 100TeVand
60TeV ≤ E ≤ 100TeVareapplied. Therefore, byintegrating
Eq.(5)inthe60-100TeVrangeoneobtains
Inordertosimplifythedescription,inthefollowingweob-
taintheexpectedneutrinoangulardistributionsfortheanalyzed dJEG (cid:39) ΩDMρc (cid:90) zmax dz
caseswithoutexplicitlyconsideringtheICeffectivearea,which dΩ 4πMτ 0 (1+z)H(z)
willbeinsteadconsideredfortherealanalysis. ×(cid:40)(cid:90) EM f(E)dE+(cid:2)f(E )E − f(E )E (cid:3)z(cid:41), (6)
In case of astrophysical scenarios, namely galactic plane M M m m
Em
andisotropicdistribution,theexpectedangulardistributionsin
where E = 60 TeV and E = 100 TeV. There exist two
thearrivaldirectionsare m M
interestinglimits:
Θ(sinb+sinb )−Θ(sinb−sinb )
pgal(sinb,l) = gal gal , (1) i)theneutrinoenergyspectrumisfullycontainedintheenergy
4πsinb
gal binconsidered,then f (E )(cid:39) f (E )(cid:39)0;
m M
1
piso(sinb,l) = . (2) ii) the neutrino energy spectrum is wider than the energy bin,
4π
hence the energy distribution f (E) can be considered almost
Notethatthegalacticplaneangulardistributiondependsonthe flatwithinit,namely f (E )(cid:39) f (E ).
m M
Galacticlatitudebonly(lbeingtheGalacticlongitude),where Thisimpliesthattheangulardistributiontakestheform
b represents the angular size of the Galactic disk. It is rea-
gal (cid:90) ∞
sonabletoassumethatthegalacticneutrinoangulardistribution pdec(cosθ)∝ ρ [r(s,cosθ)]ds+Ω ρ β , (7)
h DM c α
hasthesamecharacteristicsofthegalacticgamma-rayone[37].
0
UsingtheFermi-LATtemplate[38],thequantityb hasbeen
gal with
varied in the range [2◦,4◦]. We assume for simplicity that the (cid:90) zmax dz
astrophysical sources are uniformly distributed in the Galactic βα = (1+z)αH(z), (8)
0
disk. Indeed, it is worth observing that, however, such an ap-
whereα = 1and0inthefirstandsecondcaserespectively,so
proximationdoesnotdramaticallychangethequalitativeresult
ofouranalysis,whichismainlyaffectedbythelowstatisticsat providing β1 = 0.43/H0 and β0 = 0.56/H0. In the following,
ourdisposal.
IncaseofdecayingDMscenario, theexpecteddifferential 2Theseparametersdefineanoverallconstantthatresultsirrelevantinthe
neutrinofluxresultstobeasumofthecontributionduetothe presentanalysis.
3
tobemoreconservativeweconsideronlythecasecorrespond- In particular, this expression is very sensitive to the difference
ing to a larger extragalactic contribution (α = 0), since in this betweenthefunctionsEDFandCDFatthetwoendpoints,sug-
casetheisotropiccosmologicalcontributionresultstobemore gestingthattheAnderson-Darlingtestisasuitabletestforour
competitive with the Galactic term. It is worth observing that analysis(notethattheGalacticCenterisincorrespondenceof
including explicitly the IC effective area in Eq. (6) does not cosθ=1).
change this result, and the case with α = 0 still represents the Totakeintoaccounttheatmosphericbackground,wecon-
mostconservativescenario. siderallpossibledifferentchoicesof5backgroundeventsamong
Similarly,oneobtainsthefollowingangulardistributionincase 12,namely12!/(5!7!) = 792combinations. Moreover,wein-
ofannihilatingDMscenario clude in our analysis the angular uncertainty affecting the re-
(cid:90) ∞ constructionofthearrivaldirectionforICevents,whichforthe
pann(cosθ)∝ ρ2[r(s,cosθ)]ds+(Ω ρ )2∆2β , (9) shower-liketopologyisverylarge,namelyoftheorderof15◦.
h DM c 0 α
0 Inparticular,wetreattheuncertaintiesondeclinationandright
where∆2istheclumpinessfactor[40](seealsoRef.[41]). The ascensionasmaximumerrors,andpropagatethemonthequan-
quantity0∆2rangesfrom104to108[42]dependingonthemodel tity cosθ. Note that for galactic plane scenario the variable to
0 beconsideredistheGalacticlatitudeb.
considered. In our analysis we consider three particular cases
where∆2 isequalto104,106 and108 correspondingtoanex- Toconsiderinourstatisticalteststheaboveangularuncer-
0 tainty,foreachchoiceof5backgroundevents,weconsider100
tragalactic contribution that is sub-dominant, comparable and
possibleextractionsofthe7remainingeventsfromtheirmax-
dominant with respect to the galactic one, respectively. How-
ever,recentstudieslike[43]statethatthecumplinessfactor∆2 imum error intervals using a uniform probability. In this way,
0 forthe100differentchoicesofobservedeventswecomputethe
canbeaslargeasfewtimes106,consideringunphysicallarger
corresponding TS values, which once compared with the null
valuesforsuchaquantity.
Inouranalysis,weconsidertwodifferentDMgalactichalo hypothesisTSdistribution,providearangeofp-values. Sucha
rangeisfinallyaveragedonthe792differentbackgroundcom-
profiles[41]: theNavarro-Frenk-Whitedistribution
binations. InTable1wereportsuchanaveragerangeforeach
ρNFW (cid:39) ρh , (10) test. As we can see from Table 1, the IC data indicate that a
h r/r (1+r/r )2
c c
Scenario KS AD
wherer (cid:39)20kpcandρ =0.33GeVcm−3,andtheIsothermal
c h Gal.plane 0.007-0.008 notdefined
distribution Astrophysics
ρ Iso.dist. 0.20-0.55 0.17-0.54
ρIsoth (cid:39) h , (11)
h 1+(r/rc)2 NFW 0.06-0.16 0.03-0.14
DMdecay
wherer (cid:39)4.38kpcandρ =1.39GeVcm−3. Isoth. 0.08-0.22 0.05-0.19
c h
Since in each case the distributions depend on one angle DMannih. NFW (0.3−0.9)×10−4 (0.3−3.8)×10−4
only,wecanperformaone-dimensionalstatisticaltest. Inpar- ∆2=104 Isoth. (0.9−2.8)×10−3 (1.0−5.0)×10−3
0
ticular,weusetwodifferentnon-parametricstatisticaltests:the DMannih. NFW 0.02-0.05 0.02-0.07
Kolmogorov-Smirnovtest(KS)[45]andtheAnderson-Darling ∆2=106 Isoth. 0.10-0.28 0.08-0.29
0
test (AD) [46]. These statistical tests make a comparison be- DMannih. NFW 0.19-0.54 0.17-0.53
tween the cumulative distribution function (CDF) of the null ∆2=108 Isoth. 0.20-0.55 0.17-0.54
0
hypothesis distribution function and the empirical cumulative
Table1:Backgroundaveragerangeofp-valuesforallthescenarios,usingthe
distributionfunction(EDF),givenby
Kolmogorov-SmirnovandtheAnderson-Darlingtests.
1(cid:88)n
EDF(cosθ)= Θ(cosθ−cosθ) , (12)
n i
i=1 correlation with the galactic plane is disfavored. Note that in
thiscase,theAnderson-Darlingtestisnotwelldefinedsinceits
where n is the number of observed events cosθ. Note that,
i CDFisvanishingwithintheregionb<b (seeEq. (14)). Itis
incaseofgalacticplaneangulardistribution,thevariablecosθ gal
worthobservingthatvaryingtheangularsizeb intherange
hastobechangedintosinb. IntheKolmogorov-Smirnovtest, gal
[2◦,4◦]doesnotsignificantlychangethep-valuerangereported
the Test Statistics (TS) is the maximum distance between the
intheTable.Moreover,theDMannihilationscenarioisalready
previoustwocumulativedistributionfunctionsanditisdefined
excludedfromICdataforbothDMhalodensityprofilesincase
as
ofasmallclumpinessfactor(∆2 =104). Ontheotherhand,for
TS ≡sup |EDF(cosθ)−CDF(cosθ)| , (13) 0
KS θ alargerclumpinessfactor(∆2 =108)wegetaresultsimiliarto
0
whereasintheAnderson-DarlingtesttheTestStatisticsisgiven the one of the astrophysical isotropic distribution. This is due
by tothefactthatinthiscasetheannihilatingDMangulardistri-
bution is almost isotropic. It is worth observing that due to a
1(cid:88)n
TS ≡ −n− (2i−1)[ln(CDF(cosθ)) certain lack of events from the Galactic Center, the NFW DM
AD n i
i=1 profile that is more peaked in this central region results to be
+ln(1−CDF(cosθn+1−i)] . (14) moreintensionwiththeobservationsthantheIsothermalpro-
4
file. This results in smaller p-values for NFW with respect to
IsothermalasshownintheTable,suchdifferenceisexacerbated
forannihilatingDMscenario.
3. Forecast
Itisofinteresttoaskaboutthestatisticsrequired(number
ofevents)inordertodistinguish,atacertainconfidencelevel,a
DMinduceddistributionfromanisotropicone. Toanswerthis
question we perform a forecast analysis restricted to decaying
DMscenarioandannihilatingDMonewith∆2 = 106 thatare
0
not already excluded by present data. For a given number of
events,wegenerate105setsofdata(inthe60-100TeVenergy
range) according to the isotropic distribution, and perform the
twostatisticaltestsundernullhypothesisthatthedatasamples Figure4: ForecastanalysisincaseofannihilatingDMscenariowithclumpi-
comefromadecayingDMdistributionorfromanannihilating nessfactor∆20 =106forNFW(blue,lower)andIsothermal(red,upper)halo
densityprofiles. Thesolid(dashed)linesarerelatedtotheAnderson-Darling
DMone. Forsimplicityweassumethateachdatasampleisnot
(Kolmogorov-Smirnov)statisticaltest.
affectedbythebackground.Toincludethebackgroundeffectin
theforecastanalysisonecansimplyincreaseour“predictions”
byafactorof∼12/7assuggestedbypresentdata. (cid:16) (cid:17)
Byvaryinginthesetof105 datasampleswegetadistribu- valueofclumpiness ∆2 =106 isshowninFigure4. Inpartic-
0
tionofp-valueforwhichitcanbedefinedthe p-valueat68% ular,wehaveobtainedthatinordertoexcludesuchascenario
ConfidenceLevel(C.L.).Thisvaluerepresentstheupperbound the required number of signal events is O(300). Such a huge
forp-valuesin68%ofcases. InFigure3wereportthe p-value statistics, even though cannot be reached in the present exper-
at68%C.L.asfunctionofthenumberofsignalevents(noback- imentalsetup, couldbeeventuallyreachedinfutureNeutrino
ground) in case of decaying DM scenario. As expected, the Telescopes[47,48].
4. Conclusionsandoutlook
In this Letter we have analyzed the 60 − 100 TeV bin of
IceCube data that seems to suggest the presence of a ∼ 2σ
excess once the sum of the background (atmospheric neutri-
nos and muons) and an astrophysical component described by
a E−2 power-law is subtracted. In order to get information on
ν
the possible origin of such an excess, we have compared the
distribution of the arrival directions of IceCube data with the
angulardistributionsofsimplydistributedastrophysicalgalac-
tic/extragalactic sources (galactic plane/isotropic distribution),
aswellaswiththeexpectedfluxcomingfromDMinteractions
(decayandannihilation)fordifferentDMprofiles. Thestatisti-
calanalysisperformedbymeansofKolmogorov-Smirnovand
Figure3: ForecastanalysisincaseofdecayingDMscenarioforNFW(blue, Anderson-Darlingtestsofhypothesisseemstodisfavorthecor-
lower)andIsothermal(red, upper)halodensityprofiles. Thesolid(dashed) relationwiththegalacticplane,whereasexcludestheannihilat-
lines are related to the Anderson-Darling (Kolmogorov-Smirnov) statistical
ingDMscenarioforbothNFWandIsothermaldensityprofiles
test.
in case of a small clumpiness factor (∆2 = 104). The small
0
number of events till now collected does not allow to distin-
Anderson-Darlingstatisticaltest(solidlines)ismoreappropri- guishbetweenthecaseofanisotropicdistribution(astrophys-
atethantheKolmogorov-Smirnovone(dashedlines). Indeed, icalextragalacticsourcesandannihilatingDMscenariowitha
thep-valuefallsdowntozeroveryrapidly. Assumingthatthe large clumpiness factor) and the remaining cases (DM decay
p-valuerequiredtoexcludeamodelisO(10−3),weseethatthe scenarios and DM annihilation ones with ∆2 = 106). In this
0
decayingDMscenariowillbecompletelyexcludedonlywhen concern we have performed a forecast analysis and we have
aO(200)numberofsignaleventsiscollectedintheenergybin foundthatO(200)(O(300))signaleventsarerequiredinorder
60-100TeV.ItisworthnoticingthattheNFWdensityprofile, to exclude the decaying DM scenario (annihilating DM sce-
since more spatially concentrated around the Galactic Center, nario with ∆2 = 106). If the lack of neutrino events towards
0
requiresasmallnumberofsignalevents,namelyO(100),tobe the Galactic Center is confirmed by future data, the NFW de-
excluded with respect to the Isothermal profile. The forecast cayingDMscenariowillbemoreeasilyexcluded.
analysisincaseofannihilatingDMscenariowithintermediate
5
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supportbytheInstitutoNazionalediFisicaNucleareI.S.TASP [hep-ph].
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