Results from the search for dark matter in the Milky Way with 9 years of data of the ANTARES neutrino telescope

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Results from the search for dark matter in the Milky

Way with 9 years of data of the ANTARES neutrino

telescope

A. Albert, M. André, M. Anghinolfi, G. Anton, M. Ardid, J. -J. Aubert, T.

Avgitas, B. Baret, J. Barrios-Martí, S. Basa, et al.

To cite this version:

A. Albert, M. André, M. Anghinolfi, G. Anton, M. Ardid, et al.. Results from the search for dark

matter in the Milky Way with 9 years of data of the ANTARES neutrino telescope. Physical Review B:

Condensed Matter and Materials Physics (1998-2015), American Physical Society, 2017, 769,

pp.249-254. �10.1016/j.physletb.2017.03.063�. �in2p3-01433541�

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Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Results

from

the

search

for

dark

matter

in

the

Milky

Way

with

9 years

of

data

of

the

ANTARES

neutrino

telescope

A. Albert

a

,

M. André

b

,

M. Anghinolﬁ

c

,

G. Anton

d

,

M. Ardid

e

,

J.-J. Aubert

f

,

T. Avgitas

g

,

B. Baret

g

,

J. Barrios-Martí

h

,

S. Basa

i

,

V. Bertin

f

,

S. Biagi

j

,

R. Bormuth

k

,

l

,

S. Bourret

g

,

M.C. Bouwhuis

k

,

R. Bruijn

k

,

m

,

J. Brunner

f

,

J. Busto

f

,

A. Capone

n

,

o

,

L. Caramete

p

,

J. Carr

f

,

S. Celli

n

,

o

,

q

,

T. Chiarusi

r

,

M. Circella

s

,

J.A.B. Coelho

g

,

A. Coleiro

g

,

R. Coniglione

j

,

H. Costantini

f

,

P. Coyle

f

,

A. Creusot

g

,

A. Deschamps

t

,

G. De Bonis

n

,

o

,

C. Distefano

j

,

I. Di Palma

n

,

o

,

C. Donzaud

g

,

u

,

D. Dornic

f

,

D. Drouhin

a

,

T. Eberl

d

,

I. El Bojaddaini

v

,

D. Elsässer

w

,

A. Enzenhöfer

f

,

I. Felis

e

,

L.A. Fusco

r

,

x

,

S. Galatà

g

,

P. Gay

y

,

g

,

S. Geißelsöder

d

,

K. Geyer

d

,

V. Giordano

z

,

A. Gleixner

d

,

H. Glotin

aa

,

ab

,

ac

,

T. Grégoire

g

,

R. Gracia Ruiz

g

,

K. Graf

d

,

S. Hallmann

d

,

H. van Haren

ad

,

A.J. Heijboer

k

,

Y. Hello

t

,

J.J. Hernández-Rey

h

,

J. Hößl

d

,

J. Hofestädt

d

,

C. Hugon

c

,

ae

,

G. Illuminati

n

,

o

,

h

,

C.W. James

d

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M. de Jong

k

,

l

,

M. Jongen

k

,

M. Kadler

w

,

O. Kalekin

d

,

U. Katz

d

,

D. Kießling

d

,

A. Kouchner

g

,

ac

,

M. Kreter

w

,

I. Kreykenbohm

af

,

V. Kulikovskiy

f

,

ag

,

C. Lachaud

g

,

R. Lahmann

d

,

D. Lefèvre

ah

,

ai

,

E. Leonora

z

,

aj

,

M. Lotze

h

,

S. Loucatos

ak

,

g

,

M. Marcelin

i

,

A. Margiotta

r

,

x

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A. Marinelli

al

,

am

,

J.A. Martínez-Mora

e

,

A. Mathieu

f

,

R. Mele

an

,

aq

,

K. Melis

k

,

m

,

T. Michael

k

,

P. Migliozzi

an

,

A. Moussa

v

,

C. Mueller

w

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E. Nezri

i

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G.E. P˘av˘ala ¸s

p

,

C. Pellegrino

r

,

x

,

C. Perrina

n

,

o

,

P. Piattelli

j

,

V. Popa

p

,

T. Pradier

ao

,

L. Quinn

f

,

C. Racca

a

,

G. Riccobene

j

,

K. Roensch

d

,

A. Sánchez-Losa

s

,

M. Saldaña

e

,

I. Salvadori

f

,

D.F.E. Samtleben

k

,

l

,

M. Sanguineti

c

,

ae

,

P. Sapienza

j

,

J. Schnabel

d

,

F. Schüssler

ak

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T. Seitz

d

,

C. Sieger

d

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M. Spurio

r

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x

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Th. Stolarczyk

ak

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M. Taiuti

c

,

ae

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Y. Tayalati

ap

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A. Trovato

j

,

M. Tselengidou

d

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D. Turpin

f

,

C. Tönnis

h

,

∗

,

B. Vallage

ak

,

g

,

C. Vallée

f

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V. Van Elewyck

g

,

ac

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D. Vivolo

an

,

aq

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A. Vizzoca

n

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o

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S. Wagner

d

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J. Wilms

af

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J.D. Zornoza

h

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J. Zúñiga

h

a_GRPHE,_Université_de_Haute_Alsace,_Institut_{universitaire}_de_technologie_de_Colmar,₃₄_rue_du_{Grillenbreit,}_BP_50568,₆₈₀₀₈_Colmar,_France b_Technical_University_of_Catalonia,_Laboratory_of_Applied_{Bioacoustics,}_Rambla_Exposició,₀₈₈₀₀_Vilanova_i_la_Geltrú,_Barcelona,_Spain c_INFN_–_Sezione_di_Genova,_Via_Dodecaneso_33,₁₆₁₄₆_Genova,_Italy

d_{Friedrich-Alexander-Universität}_{Erlangen-Nürnberg,}_Erlangen_Centre_for_{Astroparticle}_Physics,_{Erwin-Rommel-Str.}_1,₉₁₀₅₈_Erlangen,_Germany e_Institut_{d’Investigació}_per_a_la_Gestió_Integrada_de_les_Zones_Costaneres_(IGIC),_Universitat_Politècnica_de_València,_C/_Paranimf_1,₄₆₇₃₀_Gandia,_Spain f_{Aix-Marseille}_Université,_CNRS/IN2P3,_CPPM_UMR_7346,₁₃₂₈₈_Marseille,_France

g_APC,_Université_Paris_Diderot,_CNRS/IN2P3,_CEA/IRFU,_Observatoire_de_Paris,_Sorbonne_Paris_Cité,₇₅₂₀₅_Paris,_France

h_IFIC_–_Instituto_de_Física_Corpuscular_(CSIC_–_Universitat_de_València),_c/_Catedrático_José_Beltrán,_2,_E-46980_Paterna,_Valencia,_Spain

i_LAM_–_Laboratoire_{d’Astrophysique}_de_Marseille,_Pôle_de_l’Étoile_Site_de_{Château-Gombert,}_rue_Frédéric_Joliot-Curie_38,₁₃₃₈₈_Marseille_Cedex_13,_France j_INFN_–_Laboratori_Nazionali_del_Sud_(LNS),_Via_S._Soﬁa_62,₉₅₁₂₃_Catania,_Italy

k_Nikhef,_Science_Park,_Amsterdam,_The_Netherlands

l_{Huygens-Kamerlingh}_Onnes_{Laboratorium,}_Universiteit_Leiden,_The_Netherlands

m_Universiteit_van_Amsterdam,_Instituut_voor_Hoge-Energie_Fysica,_Science_Park_105,₁₀₉₈_XG_Amsterdam,_The_Netherlands n_INFN_–_Sezione_di_Roma,_P.le_Aldo_Moro_2,₀₀₁₈₅_Roma,_Italy

o_Dipartimento_di_Fisica_{dell’Università}_La_Sapienza,_P.le_Aldo_Moro_2,₀₀₁₈₅_Roma,_Italy p_Institute_for_Space_Science,_RO-077125_Bucharest,_M˘agurele,_Romania

q_Gran_Sasso_Science_Institute,_Viale_Francesco_Crispi_7,₀₀₁₆₇_L’Aquila,_Italy r_INFN_–_Sezione_di_Bologna,_Viale_Berti-Pichat_6/2,₄₀₁₂₇_Bologna,_Italy s_INFN_–_Sezione_di_Bari,_Via_E._Orabona_4,₇₀₁₂₆_Bari,_Italy

t_Géoazur,_UCA,_CNRS,_IRD,_Observatoire_de_la_Côte_d’Azur,_Sophia_Antipolis,_France u_Univ._Paris-Sud,₉₁₄₀₅_Orsay_Cedex,_France

v_University_Mohammed_I,_Laboratory_of_Physics_of_Matter_and_Radiations,_{B.P. 717,}_Oujda_6000,_Morocco

w_Institut_für_Theoretische_Physik_und_Astrophysik,_Universität_Würzburg,_Emil-Fischer_Str._31,₉₇₀₇₄_Würzburg,_Germany x_Dipartimento_di_Fisica_e_Astronomia_{dell’Università,}_Viale_Berti_Pichat_6/2,₄₀₁₂₇_Bologna,_Italy

y_Laboratoire_de_Physique_{Corpusculaire,}_Clermont_{Univertsité,}_Université_Blaise_Pascal,_CNRS/IN2P3,_BP_10448,_F-63000_{Clermont-Ferrand,}_France

http://dx.doi.org/10.1016/j.physletb.2017.03.063

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250 A. Albert et al. / Physics Letters B 769 (2017) 249–254

z_INFN_–_Sezione_di_Catania,_Viale_Andrea_Doria_6,₉₅₁₂₅_Catania,_Italy

aa_LSIS,_Aix_Marseille_Université,_CNRS,_ENSAM,_LSIS_UMR_7296,₁₃₃₉₇_Marseille,_France ab_Université_de_Toulon,_CNRS,_LSIS_UMR_7296,₈₃₉₅₇_La_Garde,_France

ac_Institut_{Universitaire}_de_France,₇₅₀₀₅_Paris,_France

ad_Royal_Netherlands_Institute_for_Sea_Research_(NIOZ),_Landsdiep_4,₁₇₉₇_SZ_’t_Horntje_(Texel),_The_Netherlands ae_Dipartimento_di_Fisica_{dell’Università,}_Via_Dodecaneso_33,₁₆₁₄₆_Genova,_Italy

af_Dr._{Remeis-Sternwarte}_and_ECAP,_Universität_{Erlangen-Nürnberg,}_{Sternwartstr.}_7,₉₆₀₄₉_Bamberg,_Germany ag_Moscow_State_University,_Skobeltsyn_Institute_of_Nuclear_Physics,_Leninskie_gory,₁₁₉₉₉₁_Moscow,_Russia ah_{Mediterranean}_Institute_of_Oceanography_(MIO),_{Aix-Marseille}_University,_13288,_Marseille_Cedex_9,_France ai_Université_du_Sud_Toulon-Var,_{CNRS-INSU/IRD}_UM_110,_83957,_La_Garde_Cedex,_France

aj_Dipartimento_di_Fisica_ed_Astronomia_{dell’Università,}_Viale_Andrea_Doria_6,₉₅₁₂₅_Catania,_Italy

ak_Direction_des_Sciences_de_la_Matière,_Institut_de_recherche_sur_les_lois_{fondamentales}_de_l’Univers,_Service_de_Physique_des_Particules,_CEA_Saclay,

91191 Gif-sur-YvetteCedex,France

al_INFN_–_Sezione_di_Pisa,_Largo_B._Pontecorvo_3,₅₆₁₂₇_Pisa,_Italy

am_Dipartimento_di_Fisica_{dell’Università,}_Largo_B._Pontecorvo_3,₅₆₁₂₇_Pisa,_Italy an_INFN_–_Sezione_di_Napoli,_Via_Cintia,₈₀₁₂₆_Napoli,_Italy

ao_Université_de_Strasbourg,_CNRS,_IPHC_UMR_7178,_F-67000_Strasbourg,_France

ap_University_Mohammed_V_in_Rabat,_Faculty_of_Sciences,₄_av._Ibn_Battouta,_B.P._1014,_R.P.₁₀₀₀₀_Rabat,_Morocco aq_Dipartimento_di_Fisica_{dell’Università}_Federico_II_di_Napoli,_Via_Cintia,_80126,_Napoli,_Italy

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Articlehistory:

Received15December2016

Receivedinrevisedform7February2017 Accepted28March2017

Availableonline31March2017 Editor:S.Dodelson Keywords: Darkmatter WIMP Indirectdetection Neutrinotelescope GalacticCentre ANTARES

Using data recorded withthe ANTARES telescope from 2007to 2015, a new searchfor dark matter annihilation intheMilky Wayhasbeenperformed.Three halomodels andﬁveannihilation channels, WIMP+WIMP→bb¯,W+W−,

τ

+

τ

−,

μ

+

μ

−and

ν

¯,withWIMPmassesrangingfrom50 GeV_c2 to100

TeV c2,

were considered. No excess over the expected background was found, and limits on the thermally averagedannihilationcross-sectionwereset.

1. Introduction

Awidevarietyofobservationssupplyevidencefortheexistence ofdarkmatter(DM)[1,2].Itsnature,however,isso-farunknown, andattempts to elucidate it have given rise to a lively and var-ied research programme in physics. A common hypothesis is to considerdarkmatter tobe madeofnew,unknown particles.The assumptionthattheseparticlesareathermalrelicoftheBigBang leads to the conclusion that they are weakly interactingmassive particles(WIMPs).

Differentapproachesareusedtosearchfortheseparticles: pro-duction at particle accelerators [3], direct detection of the recoil fromcollisions with nuclei[4]or indirectdetection by means of thesecondaryparticlesthattheyproducewhentheydecayor an-nihilate [5]. Mostof theparticles that havebeen putforward as WIMPs candidates annihilate in pairs and subsequently produce standardmodelparticles,includingneutrinos.Neutrinotelescopes mayplayaparamountrole inthesearchforWIMPsvia their an-nihilationproducts,becauseoftheirparticularlycleansignalsand lowexpectedbackgrounds.

In this paper the results from the search for dark matter in the Milky Way using data recorded with the ANTARES neutrino telescopefrom2007to2015, withatotal livetimeof2102days arepresented.Onlyneutrinosdetectedviamuonsproducedinside oraround thedetectorare considered.Here andinthe following “neutrino”means

ν

μ

+ ¯

ν

μ,unlessstatedotherwise.

InSection 2 itis presentedhow theneutrino ﬂuxcan be de-rivedfromtheannihilationofDMparticles.The detectorandthe

*

Correspondingauthor.

E-mailaddress:ctoennis@iﬁc.uv.es(C. Tönnis).

reconstruction methodare described inSection 3,while thenew analysismethodologyisexplainedinSection4.Theresultsare pre-sentedinSection5.

Comparedtoworkpreviously published [6],aconsiderably in-creaseddatasampleisusedandamaximumlikelihoodmethodor “unbinnedmethod”isapplied.Inaddition,morerecentparameters fortheDMhalointheMilkyWayareused.

2. Darkmatterphenomenology

In thistypeof indirectsearch twoimportantingredients have to be considered: the amount and spatial distribution of dark matter inthesource underconsideration,andtheenergyspectra of the standard model particles produced by WIMP annihilation. Thesetwofeaturesaretoalargeextentindependentofeachother. Theyarerelevantformodellingtheexpectedsignalandenterinto theanalysisatdifferentstages.

The signal spectra used forthe analysis presented herewere calculated using the code described in [7]. Spectra were ob-tainedforﬁveannihilationchannelsand17WIMPmassesbetween 50 GeV_c2 and100

TeV

c2 .Thesespectratake intoaccount theeffectof

neutrinooscillations.Inthefollowing,theresultsforeach annihi-lationchannelaregivenassuminga100%branchingratio.Theﬁve annihilationchannelsare:

WIMP

+

WIMP

→

bb

¯

,

W+W−

,

τ

+

τ

−

,

μ

+

μ

−

,

ν

μ

ν

¯

μ

.

(1) Ofthesechannels,thebb-channel

¯

producesthesoftestneutrino spectra,whilstthe

ν

μ

ν

¯

μ-channelproducesthehardestspectra. Al-though the

ν

μ

ν

¯

μ-channelissuppressedinmanymodels, suchas those with theWIMP being thelightest neutralino of

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supersym-Table 1

TableofdarkmatterhaloparametersfortheMilkyWayastaken from[10]and

[11].ρlocalisthelocaldensityandrsisthescalingradius.

Parameter NFW Burkert McMillan

rs[kpc] 16.1+17₋₇.8.0 9.26+5 .6 −4.2 17.6±7.5 ρlocal[GeV/cm3] 0.471₋₀+0..048061 0.487+0 .075 −0.088 0.390±0.034

Fig. 1. TheintegratedJ-Factor, Jint,foracone-shapedregioncentredonthe

GalacticCentrewithanopeningangle.Forthehalomodelstheparametersfrom

Table 1areused.ThecalculationsaredoneusingthecodeCLUMPY[13].

metricmodels,itisincludedinthisstudyinordertobeasmodel independentaspossible.

Thesecond ingredient,i.e.theamountanddistributionofdark matter in the source, is described by the so-called J-Factor. The J-Factor, J

(ψ)

,istheintegral ofthedarkmatter densitysquared,

ρ

2

DM, over a line of sight at an angular separation

ψ

from the

centreofthesource.Therelativesignalstrengthatanangular sep-aration

ψ

tothesourceisdescribedbytheexpression J

(ψ)

d

(ψ)

. TheJ-Factorcanbeintegratedoveranobservationwindow

: Jint

()

=

ρ

_DM2

·

dl

·

d

.

(2)

Jint relates the thermally averaged annihilation cross-section

σ

v

totheneutrinoﬂux νμ+¯νμ viathefollowingequation:

d

νμ+¯νμ dE_ν_μ_{+ ¯}_ν_μ

=

σ

v

8

π

M2_WIMP

·

dNνμ+¯νμ dE_ν_μ_+¯_ν_μ

·

Jint

(),

(3)

whereNνμ+¯νμ isthe average numberof neutrinosin theenergy

bindEνμ+¯νμ per WIMP annihilation, v is theWIMP velocity and

MWIMPistheWIMPmass.

TheshapeoftheJ-Factorcruciallydependsonthehalomodel. Inthisanalysisthreemodelsareused:theNFW[8],theBurkert[9]

modelandthe “McMillan” [10] profile.The parameters for these models are taken from[11] and [10] and are shownin Table 1. The McMillan profileis a variantof the Zhaoprofile [12],which treats one of the shape parameters,

γ

, as a free parameter and thereforeisalsoreferred to asthe“

γ

free” model.The optimum valueof

γ

forthismodelis0

.

79

±

0

.

32.Theuncertaintiesonthe haloprofileparameters arenotusedinthisanalysis.InFig. 1the integratedJ-Factorsforthethreemodelsareshown.TheNFW pro-file givesa larger total amount of darkmatter that isalso more concentratedinthecoreofthesourcethanfortheBurkertprofile. Thisis dueto the fact that theNFW profileis a so-calledcuspy profileanddivergesatthecentreofthesource,incontrasttothe coredBurkertprofile.

3. Simulationandreconstruction

The ANTARES neutrino telescope [14] is installed at the bot-tomoftheMediterraneanSea,about40 kmfromToulonandabout 2475 mbelowtheseasurface.BeinglocatedintheNorthern hemi-sphere(42◦48N,6◦10E)allowstheANTARESdetectortodirectly observethe centreofthe MilkyWay,usingthe Earthasashield againstthebackgroundfromatmosphericmuons.

ANTARES consists of 12, 450-m long, detector lines that are anchoredtotheseabedandkeptverticalbybuoys.Eachline com-prises25storeyswiththree10-inch photomultipliers(PMTs)[15]

per storey. The PMTs are housed inside pressure-resistant glass spheres[16].

ThestoreysalsohousetheelectronicstocontrolthePMTs[17]

anda systemtomonitor thealignment ofthelines [18]. Forthe synchronisationofthe individual storeysasystemofoptical bea-cons[19],locatedatvariouspointsoftheapparatus,isused[20].

In this analysis two muon track reconstruction strategies are used:

Fit and QFit. In the QFit strategy [21] a

χ

2_-like _quality

parameter, Q,is minimised.Qiscalculatedfromthe squared dif-ferencebetweentheexpectedandmeasuredtimesofthedetected photons, takinginto account theeffect oflight absorption inthe water [21]. This strategy allows for the reconstruction of events withphotonhitsononlyoneline(single-lineevents).

Fit [22] maximises a likelihood ratio

in a multistep pro-cess.Thevalueof

oftheﬁnaliterationofthisprocessisusedas ameasureofthequalityofthereconstruction.Inaddition,the an-gularerrorestimate

β

isusedtodeﬁneacutemployedtoreduce thebackground.

The main background foranalyses using muon tracks are at-mosphericmuons.TakingadvantageoftheabsorptionoftheEarth that actsasan eﬃcient shieldagainst muons, mostof this back-ground can be rejected by accepting only upgoing-reconstructed muonsinthe analysis.Thanks to thedetector’slatitude,the cen-tre oftheMilkyWay iseﬃcientlyobserved,sinceit isbelowthe horizonmostofthetime.Tofurtherreduce thebackgroundof at-mospheric muonswrongly reconstructed asupgoing, cutson the parameters thatquantifythequality ofthereconstruction(Q,

), andontheestimateoftheangularerror(

β

)areused,asspeciﬁed in the next section. Atmospheric neutrinos are an additional but muchsmallerpartofthebackground.However,unlikeatmospheric muons,thisbackgroundisirreducible,althoughtheinformationof theenergyandcorrelationswiththesourcecanhelp to discrimi-nateitfromthesignal.

Inorder toevaluate thesensitivity ofthesearch, MonteCarlo simulations, using a detailed detector response for each data run, have been performed [23]. Concerning the background, at-mospheric neutrinos [24] andmuons [25] withenergies ranging from 10 GeV

c2 to 100 TeV

c2 have beensimulated withthe standard

ANTARES simulation chain [16,26,27]. From this simulation the detector resolutionand acceptance are calculated forall ﬁve an-nihilation channelsandforWIMP massesrangingfrom50 GeV_c2 to

100 TeV_c2 .

Inthispaper,datatakenfrom2007to2015, corresponding to 2102daysoflivetime,wasused.Theagreementbetweenthedata andthesimulationhasbeentestedextensivelyforboth reconstruc-tionstrategies.

4. Methodology

The maximum likelihood method is used to lookfor a signal of dark matter annihilation. The likelihood, which is a function of the number of signal events assumed to be present in the selected event sample, ns, is based on two probability

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252 A. Albert et al. / Physics Letters B 769 (2017) 249–254

thebackground events,respectively,asa function oftherelevant eventvariables. The likelihood isthen maximised by varying ns.

Thestatisticalsigniﬁcanceofthevalue obtainedisextractedfrom the distribution ofmaximum likelihoods produced by generating pseudo-experiments,i.e.samplesofeventswithknownamountsof backgroundandsignal.Thelikelihoodfunctionusedhastheform

L

(

ns

)

=

e−(ns+Nbg) Ntot

i=1

nsS

(ψ

i

,

Nhit,i

, β

i

)

+

NbgB

(ψ

i

,

Nhit,i

, β

i

)

,

(4) whereNbg istheexpectednumberofbackgroundevents,whichis

setequal to Ntot, thetotal numberof reconstructedevents. ns is

the variable that changes during the maximisation process. The twofunctionsSandBdepend on:

ψ

i,theangulardistanceofthe

i-thevent tothe centre ofthe MilkyWay; Nhit,i, thenumber of

hitsin the i-thevent;and

β

i, theangular errorestimate forthe

i-thevent. ThenumberofhitsNhit,i isaproxyforthemuon

en-ergy[28].

In order to take the source extension into account, in S the non-integratedJ-Factor,J

(ψ)

,isused,smearedoutwiththe point-spread function (PSF) assuming a 15% systematicuncertainty on the angular resolution, which is the dominant systematic error fromthedetectorinthisanalysis. Thiserrorisbasedon a2.5 ns uncertaintyinthetimingofdetectedphotonhitsinANTARES[29]. Bydoingthis, acombinationofthePSF andthe source morphol-ogyisobtainedthatisalsousedforgeneratingsignaleventsinthe pseudo-experiments.

Furtheruncertainties existduetothechoiceofthehalomodel andtheexpected neutrinosignal spectra.Theseuncertainties are studied by using different annihilation channels andhalo proﬁle functionsintheanalysis(seeFigs. 5 and6).

Aslightlymodiﬁedlikelihoodfunctionisdeﬁnedforsingle-line eventsreconstructedwiththeQFitstrategy:

L

(

ns

)

=

e−(ns+Nbg) Ntot

i=1

nsS

¯

(θ

i

, ¯

Nhit,i

,

Qi

)

+

NbgB

¯

(θ

i

, ¯

Nhit,i

,

Qi

)

,

(5) whereN

¯

hit,i isthenumberofhitsperstorey(insteadofthe

num-ber of hits per PMT) used for the reconstruction, and

θ

i is the

difference inzenithangle betweenthe i-theventandthe centre oftheMilkyWay.S and

¯

B are

¯

thecorrespondingprobability func-tionsdescribingthesignalandbackgrounddistributions.

The likelihood functions are then studied using pseudo– experiments, which are generated from the distribution of back-groundeventsfromtime-scrambleddataandthatofsignalevents from simulation. The signal events are generated by taking into account the angular resolution of the detector, the source mor-phology and the expected signal spectra. Ten thousand pseudo-experiments are simulated for each combinationof WIMP mass, annihilationchannelandreconstructionstrategy,andforeach con-sideredvalueofsignalevents,ns.Themaximumvalueconsidered

fornsis80fortheQFitstrategyand120(180)forthe

Fit

strat-egyusingtheNFW andMcMillan(Burkert)proﬁle.Themaximum valueswere chosenbecauseofdifferencesintheamountof back-groundinthesecases.Foreachpseudo-experimentateststatistic (TS)iscalculated: TS

=

log₁₀

L

(

nopt

)

L

(

0

)

,

(6)

wherenopt isthevalue ofns that maximisesthelikelihood

func-tion. Since for a ﬁxed signal strength the amount of detected

events mayvary, theTS distributions were combinedusing Pois-sonian weights producing new TS distributions. Sensitivities and limits are calculated following the approach suggested by Ney-man [30]. The 90% C.L. sensitivity in terms of detected neutrino events,

μ

¯

90%,iscalculatedastheaveragenumberofinserted

sig-nal events,whichleads toTS valuesthat arein 90%of thecases above themedianoftheTSdistributionforpurebackground.The 90%C.L.limitintermsofdetectedneutrinoevents,

μ

90%,is

calcu-lated byusing the TSvalue of theunblinded data insteadof the median of the backgroundif this TSvalue is above the median; otherwisethelimitissettothesensitivity.

The eventselection criteria, in particularthe deﬁnition ofthe cutsonQand

andthe selectionofthereconstructionstrategy, have beenoptimised with theModel Rejection Factormethod to obtainanunbiasedcutselectionforoptimalsensitivities[31].The cut parametershavebeentunedindividuallyforeachannihilation channelandseveralWIMPmassesinthemassrangeunder consid-eration,maintainingalwaysablindapproach,i.e.withnoaccessto theactualdata.

ItwasfoundthatformostcombinationsofWIMPmassand an-nihilation channelstheoptimumcutsare Q

<

0

.

7 and

>

−

5

.

2, respectively. Once

μ

¯

90% (the 90% C.L. sensitivity on the average

numberofsignal eventsobtainedfromthelikelihoodfunction)is computed,thelimitsontheneutrinoﬂuxforagivenmassMWIMP

andannihilationchannelarecalculatedas

νμ+¯νμ,90%

=

¯

μ

90%

(

MWIMP

,

ch

)

i

A

i

(

MWIMP

,

ch

)

×

Tieff

,

(7)

where the index i denotes the periods with different detector conﬁgurations, ch the annihilation channel used andTi

eff the

to-tal corresponding livetime. In fact, throughout the considered 9 years, the number of available detector lines has changed from 5 to 12.The time spanover whichthe numberofavailable lines remains unchangedis deﬁnedas a particular detector conﬁgura-tion period.The effectiveareaaveraged overtheneutrinoenergy,

¯

A

i

eff

(

MWIMP

,

ch

)

,isdeﬁnedas:

A

i

=

ν,ν¯

⎛

⎜

⎝

MWIMP Ethν A i eff

(

Eν,ν¯

)

dNν,ν¯ dEν,ν¯

ch,MWIMP dEν,ν¯

MWIMP 0 dNνdEν

_ch_,_M WIMP dE_ν

+

dNν¯ dEν¯

ch,MWIMP dE_ν_¯

⎞

⎟

⎠ ,

(8) where Eth_ν is the energy threshold for neutrino detection in ANTARES (approximatively 10 GeV), MWIMP is the WIMP mass,

dNν,ν¯

/

dEν,ν is¯ the energyspectrum ofthe(anti-)neutrinosatthe detector’s location for annihilation channel ch (see Equation (1)) and WIMP mass MW I M P, and Aeff

(

Eν,ν¯

)

is the effective area of ANTARESasafunctionofthe(anti-)neutrinoenergy.

Duetotheirdifferentcross-sections,theeffectiveareasfor neu-trinos and anti-neutrinos are slightly different and therefore are considered separately. In addition, the fluxes of muon neutrinos andanti-neutrinosaredifferentandare convolutedwiththeir re-spectiveefficiencies.Theeffectiveareaforadetectorconfiguration periodisdefinedastheratiobetweentheneutrinoeventrateand the signalneutrinoflux fora certainneutrinoenergy. Itis calcu-latedfromsimulation.

5. Results

TheﬁnalresultsareobtainedbycomparingtheTSvalueofthe data,TSobs,totheTSdistributionspreviouslycalculatedunderthe

blindedprocedure.

In Fig. 2 a comparison between the unblinded data and the expected background is shown. No signiﬁcant excess above the

(6)

Fig. 2. ThenumberofeventsasafunctionofthedistancetotheGalacticCentre (crosses)incomparisontothebackgroundestimate(redline)forthe Fit recon-struction.Forthisplotaqualitycutof >−5.2 isused.(Forinterpretationofthe referencestocolourinthisﬁgurelegend,thereaderisreferredtothewebversion ofthisarticle.)

Fig. 3. 90%C.L.upperlimitsontheneutrinoﬂuxfromWIMPannihilationsinthe MilkyWayasafunctionoftheWIMPmassesforthedifferentchannelsconsidered. ForthisplottheNFWproﬁlewasused.

backgroundcanbeseen,whichisconsistentwiththefactthatall theTSobs valuesobtainedaresmallerthanthemediansofthe

cor-respondingbackgroundTSdistributions.Since allbackground-like resultsshouldequallyrejecttheconsidereddarkmattermodel, up-per limits have been set to the sensitivities calculated from the pseudo-experiments.

Theresultingupperlimitsintermsofneutrinoﬂuxare shown inFig. 3.ForeachannihilationchannelandWIMPmassrange,the reconstructionstrategy,QFitor

Fit,whichgivesthebest sensitiv-ityisused in theﬁnal result.

Fit isused forMWIMP

≥

260 GeV_c2

forthe

τ

+

τ

− and

μ

+

μ

− channels; forMWIMP

≥

750 GeV_c2 forthe

bb channel;

¯

for MWIMP

≥

150 GeV_c2 for W+W− andfor MWIMP

≥

100 GeV_c2 for the

ν

μ

ν

¯

μ channel. For the remaining values, i.e.at

lowWIMPmasses,theQFitresultsareused.

Fromthelimitsontheneutrinoﬂux,limitson

σ

v

canbe de-rived.The90%C.L.upperlimiton

σ

v

forthe

τ

+

τ

−channelasa functionoftheWIMPmassisshowninFig. 4,comparedwith lim-itsobtained byother indirectsearches.Mostof thedirect search experiments are not directly sensitive to

σ

v

. The limits for all annihilationchannelsfortheNFWhaloproﬁleareshowninFig. 5.

Fig. 4. 90%C.L.limitsonthethermallyaveragedannihilationcross-section,σv,as afunctionoftheWIMPmassincomparisontothelimitsfromotherexperiments

[32–36].TheresultsfromIceCubeandANTARESwereobtainedwiththeNFW pro-ﬁle.

Fig. 5. 90%C.L.limitsonthethermallyaveragedannihilationcross-section,σv, asafunctionoftheWIMPmassforallannihilationchannelsusingtheNFWhalo proﬁle.

TheIceCube resultspresentedin Fig. 4(using tracksonly[32]

andusingcascadesaswell[33])refertothesamechannelandthe same halo model, therefore the difference between the limits is duetothedetectorperformance,positionandintegratedlivetime. The centreoftheMilkyWayisabove thehorizonoftheIceCube detectorandconsequently the neutrinocandidates correspond to downgoing events. To select neutrino candidates in the analyses of IceCube a veto for tracks starting outside the central part of the detectorhasto be used, whichreduces the acceptance.This, in addition to the better angularresolution of ANTARES andthe largerintegratedlivetimeinthisanalysis,explainsthedifference betweenthelimits.

For the analysis by H.E.S.S. a different set of halo parameter valuesis used,leading toa moreextended source.The resultsof FERMIandMAGICarebasedondwarfspheroidalgalaxiesanduse the bb annihilation

¯

channel. Results fromdirect detection exper-iments are not shownsince these experiments are typically not sensitiveto

σ

v

.

This result allows to partly constrain models where the ex-traterrestrial neutrinos observed by IceCube are partly explained in terms of annihilating dark matter candidates [37]. For WIMP masses above 100 GeV

(7)

unitar-254 A. Albert et al. / Physics Letters B 769 (2017) 249–254

Fig. 6. 90%C.L.limitsonthethermallyaveragedannihilationcross-section,σv,as afunctionoftheWIMPmassforthethreeconsideredhalomodelsfortheτ+τ−

channel.

ity [38] will become relevant, although there is an approach to overcometheselimitations[39].

Inorderto illustratethe largeeffect ofthechoice ofthehalo model and the proﬁle parameters, a comparison between upper limitsderived using the NFW, the Burkert andthe McMillan re-sults is shown in Fig. 6 for the

τ

+

τ

− channel. As can be seen, dependingontheWIMPmass,differencesofmorethanoneorder ofmagnitudeareobservedbetweenthedifferenthalomodels.

6. Conclusions

The results from a new search for dark matter annihilation in the Milky Way using data from the ANTARES neutrino tele-scope from 2007 to 2015 show no excess above the expected background. Limits at 90% C.L. have been set for the NFW, the McMillan and the Burkert proﬁle, ﬁve annihilation channels and WIMP massesranging from 50 GeV_c2 to 100

TeV

c2 . These limitsare

themoststringentforacertainregionoftheparameterspace.

Acknowledgements

The authors acknowledge the ﬁnancial support of the fund-ingagencies:CentreNationaldelaRechercheScientiﬁque(CNRS), Commissariat à l’énergie atomique et aux énergies alternatives (CEA),CommissionEuropéenne(FEDERfundandMarieCurie Pro-gram), Institut Universitaire de France (IUF), IdEx program and UnivEarthS Labexprogram atSorbonne ParisCité (ANR-10-LABX-0023 and ANR-11-IDEX-0005-02), Labex OCEVU (ANR-11-LABX-0060) and the A*MIDEX project (ANR-11-IDEX-0001-02), Région Île-de-France (DIM-ACAV), Région Alsace (contrat CPER), Région Provence-Alpes-Côte d’Azur, Département du Var and Ville de La Seyne-sur-Mer, France; Bundesministerium für Bildung und Forschung (BMBF), Germany; Istituto Nazionale di Fisica Nucle-are (INFN), Italy; Stichting voor Fundamenteel Onderzoek der Materie (FOM), Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), the Netherlands; Council of the President of

the Russian Federation for young scientists and leading scien-tific schools supporting grants, Russia; National Authority for Scientific Research (ANCS), Romania; Ministerio de Economía y Competitividad (MINECO): Plan Estatal de Investigación (refs. FPA2015-65150-C3-1-P, -2-P and -3-P, (MINECO/FEDER)), Severo Ochoa Centre of Excellence and MultiDark Consolider (MINECO), and Prometeo and Grisolía programs (Generalitat Valenciana), Spain; Ministryof Higher Education, Scientific Researchand Pro-fessional Training, Morocco. We also acknowledge the technical support ofIfremer, AIMandFoselevMarine fortheseaoperation andtheCC-IN2P3forthecomputingfacilities.

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