Multi-year search for dark matter annihilations in the Sun with theAMANDA-II and IceCube detectors

Abstract

A search for an excess of muon-neutrinos from dark matter annihilations in
the Sun has been performed with the AMANDA-II neutrino telescope using data
collected in 812 days of livetime between 2001 and 2006 and 149 days of
livetime collected with the AMANDA-II and the 40-string configuration of
IceCube during 2008 and early 2009. No excess over the expected atmospheric
neutrino background has been observed. We combine these results with the
previously published IceCube limits obtained with data taken during 2007 to
obtain a total livetime of 1065 days. We provide an upper limit at 90%
confidence level on the annihilation rate of captured neutralinos in the Sun,
as well as the corresponding muon flux limit at the Earth, both as functions of
the neutralino mass in the range 50 GeV-5000 GeV. We also derive a limit on the
neutralino-proton spin-dependent and spin-independent cross section. The limits
presented here improve the previous results obtained by the collaboration
between a factor of two and five, as well as extending the neutralino masses
probed down to 50 GeV. The spin-dependent cross section limits are the most
stringent so far for neutralino masses above 200 GeV, and well below direct
search results in the mass range from 50 GeV to 5 TeV.

Full text

Page 1

Multi–year search for dark matter annihilations in the Sun with the AMANDA–II
and IceCube detectors
R. Abbasi,29Y. Abdou,23T. Abu-Zayyad,34M. Ackermann,42J. Adams,16J. A. Aguilar,22M. Ahlers,29
D. Altmann,1K. Andeen,29J. Auffenberg,29X. Bai,32, ∗M. Baker,29S. W. Barwick,25R. Bay,7J. L. Bazo Alba,42
K. Beattie,8J. J. Beatty,18,19S. Bechet,13J. K. Becker,10K.-H. Becker,41M. Bell,39M. L. Benabderrahmane,42
S. BenZvi,29J. Berdermann,42P. Berghaus,32D. Berley,17E. Bernardini,42D. Bertrand,13D. Z. Besson,27
D. Bindig,41M. Bissok,1E. Blaufuss,17J. Blumenthal,1D. J. Boersma,1C. Bohm,35D. Bose,14S. B¨ oser,11
O. Botner,40L. Brayeur,14A. M. Brown,16S. Buitink,14K. S. Caballero-Mora,39M. Carson,23M. Casier,14
D. Chirkin,29B. Christy,17F. Clevermann,20S. Cohen,26C. Colnard,24D. F. Cowen,39,38A. H. Cruz Silva,42
M. V. D’Agostino,7M. Danninger,35J. Daughhetee,5J. C. Davis,18C. De Clercq,14T. Degner,11F. Descamps,23
P. Desiati,29G. de Vries-Uiterweerd,23T. DeYoung,39J. C. D´ ıaz-V´ elez,29M. Dierckxsens,13J. Dreyer,10
J. P. Dumm,29M. Dunkman,39J. Eisch,29R. W. Ellsworth,17O. Engdeg˚ ard,40S. Euler,1P. A. Evenson,32
O. Fadiran,29A. R. Fazely,6A. Fedynitch,10J. Feintzeig,29T. Feusels,23K. Filimonov,7C. Finley,35
T. Fischer-Wasels,41S. Flis,35A. Franckowiak,11R. Franke,42T. K. Gaisser,32J. Gallagher,28L. Gerhardt,8,7
L. Gladstone,29T. Gl¨ usenkamp,42A. Goldschmidt,8J. A. Goodman,17D. G´ ora,42D. Grant,21T. Griesel,30
A. Groß,24S. Grullon,29M. Gurtner,41C. Ha,8,7A. Haj Ismail,23A. Hallgren,40F. Halzen,29K. Han,42
K. Hanson,13D. Heereman,13D. Heinen,1K. Helbing,41R. Hellauer,17S. Hickford,16G. C. Hill,2
K. D. Hoffman,17B. Hoffmann,1A. Homeier,11K. Hoshina,29W. Huelsnitz,17, †J.-P. H¨ ulß,1P. O. Hulth,35
K. Hultqvist,35S. Hussain,32A. Ishihara,15E. Jacobi,42J. Jacobsen,29G. S. Japaridze,4H. Johansson,35
A. Kappes,9T. Karg,41A. Karle,29J. Kiryluk,36F. Kislat,42S. R. Klein,8,7J.-H. K¨ ohne,20G. Kohnen,31
H. Kolanoski,9L. K¨ opke,30S. Kopper,41D. J. Koskinen,39M. Kowalski,11T. Kowarik,30M. Krasberg,29G. Kroll,30
J. Kunnen,14N. Kurahashi,29T. Kuwabara,32M. Labare,14K. Laihem,1H. Landsman,29M. J. Larson,39
R. Lauer,42J. L¨ unemann,30J. Madsen,34A. Marotta,13R. Maruyama,29K. Mase,15H. S. Matis,8
K. Meagher,17M. Merck,29P. M´ esz´ aros,38,39T. Meures,13S. Miarecki,8,7E. Middell,42N. Milke,20
J. Miller,40T. Montaruli,22, ‡R. Morse,29S. M. Movit,38R. Nahnhauer,42J. W. Nam,25U. Naumann,41
S. C. Nowicki,21D. R. Nygren,8S. Odrowski,24A. Olivas,17M. Olivo,10A. O’Murchadha,29S. Panknin,11
L. Paul,1C. P´ erez de los Heros,40A. Piegsa,30D. Pieloth,20J. Posselt,41P. B. Price,7G. T. Przybylski,8
K. Rawlins,3P. Redl,17E. Resconi,24, §W. Rhode,20M. Ribordy,26M. Richman,17A. Rizzo,14J. P. Rodrigues,29
F. Rothmaier,30C. Rott,18T. Ruhe,20D. Rutledge,39B. Ruzybayev,32D. Ryckbosch,23H.-G. Sander,30
M. Santander,29S. Sarkar,33K. Schatto,30T. Schmidt,17S. Sch¨ oneberg,10A. Sch¨ onwald,42A. Schukraft,1
L. Schulte,11A. Schultes,41O. Schulz,24, §M. Schunck,1D. Seckel,32B. Semburg,41S. H. Seo,35Y. Sestayo,24
S. Seunarine,12A. Silvestri,25G. M. Spiczak,34C. Spiering,42M. Stamatikos,18, ¶T. Stanev,32T. Stezelberger,8
R. G. Stokstad,8A. St¨ oßl,42E. A. Strahler,14R. Str¨ om,40M. St¨ uer,11G. W. Sullivan,17H. Taavola,40I. Taboada,5
A. Tamburro,32S. Ter-Antonyan,6S. Tilav,32P. A. Toale,37S. Toscano,29D. Tosi,42N. van Eijndhoven,14
A. Van Overloop,23J. van Santen,29M. Vehring,1M. Voge,11C. Walck,35T. Waldenmaier,9M. Wallraff,1
M. Walter,42R. Wasserman,39Ch. Weaver,29C. Wendt,29S. Westerhoff,29N. Whitehorn,29K. Wiebe,30
C. H. Wiebusch,1D. R. Williams,37R. Wischnewski,42H. Wissing,17M. Wolf,35T. R. Wood,21K. Woschnagg,7
C. Xu,32D. L. Xu,37X. W. Xu,6J. P. Yanez,42G. Yodh,25S. Yoshida,15P. Zarzhitsky,37and M. Zoll35
(IceCube Collaboration)
1III. Physikalisches Institut, RWTH Aachen University, D-52056 Aachen, Germany
2School of Chemistry & Physics, University of Adelaide, Adelaide SA, 5005 Australia
3Dept. of Physics and Astronomy, University of Alaska Anchorage,
3211 Providence Dr., Anchorage, AK 99508, USA
4CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA
5School of Physics and Center for Relativistic Astrophysics,
Georgia Institute of Technology, Atlanta, GA 30332, USA
6Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA
7Dept. of Physics, University of California, Berkeley, CA 94720, USA
8Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
9Institut f¨ ur Physik, Humboldt-Universit¨ at zu Berlin, D-12489 Berlin, Germany
10Fakult¨ at f¨ ur Physik & Astronomie, Ruhr-Universit¨ at Bochum, D-44780 Bochum, Germany
11Physikalisches Institut, Universit¨ at Bonn, Nussallee 12, D-53115 Bonn, Germany
12Dept. of Physics, University of the West Indies,
Cave Hill Campus, Bridgetown BB11000, Barbados
13Universit´ e Libre de Bruxelles, Science Faculty CP230, B-1050 Brussels, Belgium
arXiv:1112.1840v2 [astro-ph.HE] 12 Dec 2011

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2
14Vrije Universiteit Brussel, Dienst ELEM, B-1050 Brussels, Belgium
15Dept. of Physics, Chiba University, Chiba 263-8522, Japan
16Dept. of Physics and Astronomy, University of Canterbury, Private Bag 4800, Christchurch, New Zealand
17Dept. of Physics, University of Maryland, College Park, MD 20742, USA
18Dept. of Physics and Center for Cosmology and Astro-Particle Physics,
Ohio State University, Columbus, OH 43210, USA
19Dept. of Astronomy, Ohio State University, Columbus, OH 43210, USA
20Dept. of Physics, TU Dortmund University, D-44221 Dortmund, Germany
21Dept. of Physics, University of Alberta, Edmonton, Alberta, Canada T6G 2G7
22D´ epartement de physique nucl´ eaire et corpusculaire,
Universit´ e de Gen` eve, CH-1211 Gen` eve, Switzerland
23Dept. of Physics and Astronomy, University of Gent, B-9000 Gent, Belgium
24Max-Planck-Institut f¨ ur Kernphysik, D-69177 Heidelberg, Germany
25Dept. of Physics and Astronomy, University of California, Irvine, CA 92697, USA
26Laboratory for High Energy Physics,´Ecole Polytechnique F´ ed´ erale, CH-1015 Lausanne, Switzerland
27Dept. of Physics and Astronomy, University of Kansas, Lawrence, KS 66045, USA
28Dept. of Astronomy, University of Wisconsin, Madison, WI 53706, USA
29Dept. of Physics, University of Wisconsin, Madison, WI 53706, USA
30Institute of Physics, University of Mainz, Staudinger Weg 7, D-55099 Mainz, Germany
31Universit´ e de Mons, 7000 Mons, Belgium
32Bartol Research Institute and Department of Physics and Astronomy,
University of Delaware, Newark, DE 19716, USA
33Dept. of Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, UK
34Dept. of Physics, University of Wisconsin, River Falls, WI 54022, USA
35Oskar Klein Centre and Dept. of Physics, Stockholm University, SE-10691 Stockholm, Sweden
36Department of Physics and Astronomy, Stony Brook University, Stony Brook, NY 11794-3800, USA
37Dept. of Physics and Astronomy, University of Alabama, Tuscaloosa, AL 35487, USA
38Dept. of Astronomy and Astrophysics, Pennsylvania State University, University Park, PA 16802, USA
39Dept. of Physics, Pennsylvania State University, University Park, PA 16802, USA
40Dept. of Physics and Astronomy, Uppsala University, Box 516, S-75120 Uppsala, Sweden
41Dept. of Physics, University of Wuppertal, D-42119 Wuppertal, Germany
42DESY, D-15735 Zeuthen, Germany
(Dated: December 13, 2011)
A search for an excess of muon–neutrinos from dark matter annihilations in the Sun has been
performed with the AMANDA–II neutrino telescope using data collected in 812 days of livetime
between 2001 and 2006 and 149 days of livetime collected with the AMANDA–II and the 40–string
configuration of IceCube during 2008 and early 2009. No excess over the expected atmospheric
neutrino background has been observed. We combine these results with the previously published
IceCube limits obtained with data taken during 2007 to obtain a total livetime of 1065 days. We
provide an upper limit at 90% confidence level on the annihilation rate of captured neutralinos in the
Sun, as well as the corresponding muon flux limit at the Earth, both as functions of the neutralino
mass in the range 50 GeV–5000 GeV. We also derive a limit on the neutralino–proton spin–dependent
and spin–independent cross section. The limits presented here improve the previous results obtained
by the collaboration between a factor of two and five, as well as extending the neutralino masses
probed down to 50 GeV. The spin–dependent cross section limits are the most stringent so far
for neutralino masses above 200 GeV, and well below direct search results in the mass range from
50 GeV to 5 TeV.
PACS numbers: 95.35.+d, 95.30.Cq, 11.30.Pb
I.INTRODUCTION
There is an impressive corpus of astrophysical and cos-
mological observations that indicate that a yet unknown
∗Physics Department, South Dakota School of Mines and Tech-
nology, Rapid City, SD 57701, USA
†Los Alamos National Laboratory, Los Alamos, NM 87545, USA
‡also Sezione INFN, Dipartimento di Fisica, I-70126, Bari, Italy
§now at T.U. Munich, D-85748 Garching, Germany
¶NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
form of non–luminous matter constitutes about 23% of
the content of the universe. This matter can not be bary-
onic though, as the abundance of baryons in any form
is strongly constrained by the inferred primordially syn-
thesized abundances of deuterium and helium, as well
as the observed small-scale anisotropy in the cosmic mi-
crowave background (see, e.g., the review in Ref. [1]).
However, the observational limits on non–baryonic dark
matter in the form of relic stable particles from the Big
Bang are not so strong and, indeed, a wealth of mod-
els exist that propose candidates with interaction cross

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sections, masses and relic densities which are compati-
ble with observations. Generically, any particle physics
model that provides a stable weakly–interacting massive
particle (WIMP) is of interest from the point of view of
the dark matter problem. One class of models that are
extensively studied for their interest in particle physics
are supersymmetric extensions of the Standard Model.
Several flavours of supersymmetry are currently under
scrutiny at the LHC, and both ATLAS and CMS have
already probed parts of the parameter space of specific
benchmark models [2, 3].
the Minimal Supersymmetric extension to the Standard
Model (MSSM), which provides a WIMP candidate in
the lightest neutralino, ? χ0
and Higgs bosons. Assuming R–parity conservation, the
neutralino is stable and a good dark matter candidate.
Accelerator searches and relic density constraints from
WMAP data allow a lower limit to be set on the mass of
the MSSM neutralino [4]. Typical lower limits for m? χ0
values chosen for tanβ, the ratio of the vacuum expecta-
tion values of the two neutral Higgses. Theoretical argu-
ments based on the requirement of unitarity set an upper
limit on m? χ0
be exploited to build realistic models which provide relic
neutralino densities of cosmological interest to address
the dark matter problem.
In this paper we focus on
1, a linear combination of the su-
persymmetric partners of the electroweak neutral gauge–
1
from such studies lie around 20 GeV, depending on the
1of 340 TeV [5]. Within these limits, the al-
lowed parameter space of minimal supersymmetry can
Relic neutralinos in the galactic halo can lose energy
through scatterings while traversing celestial bodies, like
the Sun, and become gravitationally bound into orbits in-
side. The build-up of the accreted particles is limited by
annihilations, which ultimately create high–energy neu-
trinos [6]. In this paper we present two independent
searches for a neutrino flux from the annihilations of neu-
tralinos captured in the center of the Sun, performed with
the AMANDA–II and IceCube neutrino telescopes. The
overwhelming majority of triggers in AMANDA–II and
IceCube, O(1010/year), are due to atmospheric muons
reaching the depth of the array. The analyses are there-
fore based on the search for up–going muon tracks from
the direction of the Sun when it is below the horizon, and
have been optimized in order to maximize the sensitivity
to the predicted signal from MSSM neutralinos. The re-
sults can, however, be interpreted generically in terms of
any other dark matter candidate which would produce a
similar neutrino spectrum at the detector. The first anal-
ysis (Analysis A) uses the data taken with AMANDA–
II during 812 days of livetime in stand–alone operation
between March 2001 and October 2006. In 2007 the de-
tector was switched to a new data acquisition system
(DAQ) which included full waveform recording, and this
allowed us to integrate the detector as a subsystem of Ice-
Cube. Analysis B uses 149 days of livetime collected be-
tween April 2008 and April 2009 (when AMANDA–II was
decommissioned) using the new AMANDA–II DAQ and
data from both detectors, AMANDA–II and IceCube.
600400 2000 200400 600
X (m)
600
400
200
0
200
400
600
Y (m)
FIG. 1. Surface location of the IceCube 40–string configura-
tion (filled squares) and AMANDA–II (filled circles)
We have previously published a search for dark matter
accumulated in the Sun using data taken in 2007 with
the 22–string configuration of IceCube [7]. In Section VI
we combine these three independent analyses (Analysis
A, Analysis B and the results from Ref. [7]) which cover
the period 2001–2008, presenting competitive limits on
the muon flux from neutralino annihilations in the Sun
and limits on the spin–dependent and spin–independent
neutralino–proton cross section.
II.THE AMANDA–II AND ICECUBE
DETECTORS
The AMANDA–II detector consisted of an array of 677
optical modules (OM) deployed on 19 vertical strings at
depths between 1500 m and 2000 m in the South Pole
ice cap. The optical modules consisted of a 20 cm diam-
eter photomultiplier tube housed in a glass pressure ves-
sel connected through a cable to the surface electronics,
where the photomultiplier pulses were amplified, time–
stamped and fed into the trigger logic. The inner ten
strings used electrical analog signal transmission, while
the outer nine strings used optical fiber transmission.
The strings were arranged in three approximately con-
centric circles of 60 m, 120 m and 200 m diameter respec-
tively. The vertical separation of the optical modules in
strings one to four was 20 m, and 10 m in strings five
to nineteen. Several calibration devices (a 337 nm N2
laser and three DC halogen lamps, one broadband and
two with filters for 350 and 380 nm) were deployed at
several locations in the array. Additionally, a YAG laser
calibration system was set up on the surface, able to send
light pulses through optical fibers to a diffuser located at
each optical module.
The original AMANDA–II data acquisition system
could only measure the maximum amplitude of the pho-

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tomultiplier pulses and only eight hits could be buffered
at a time. From 2003, each channel was connected to
a Transient Waveform Recorder (TWR), a flash ADC
that samples at 100 MHz with 12 bit resolution, being
able to collect the full photomultiplier waveform in each
channel [8]. The TWR system was run in parallel with
the original DAQ until 2007, when the original DAQ was
switched off. From this point, until its decommissioning
in May 2009, AMANDA–II was run only with the TWR
DAQ system.
The construction of the IceCube detector began in
2005 and 40 strings surrounding the AMANDA–II array
had been deployed by 2008. With its denser string con-
figuration, AMANDA–II played the role of a low–energy
subdetector of IceCube, and both detectors where run
in an ’OR’ configuration until AMANDA–II was decom-
missioned. Figure 1 shows the surface location of the
AMANDA–II and IceCube strings during the 2008 data
taking period. The IceCube strings consist of 60 Digital
Optical Modules (DOMs) separated vertically by 17 m.
The inter–string separation is 125 m. Contrary to the
AMANDA–II optical modules, the IceCube DOMs dig-
itize the photomultiplier signals in–situ. They are also
self–calibrating units, frequently exchanging timing cal-
ibration signals with the surface electronics. A descrip-
tion of the IceCube DOM and the DAQ can be found in
Refs. [9, 10].
Both IceCube and AMANDA–II used triggers that se-
lected events based on the number of hit optical modules
in a certain time window (at least 24 modules hit within
2.5 µs in AMANDA–II, and at least 8 modules hit within
5 µs in IceCube). Additionally, a trigger tailored for low
energy events required N hit modules in a given time
window out of M consecutive modules in the same string
(N/M condition). This trigger was set to 6/9 in strings
one to four and 7/11 in strings five to nineteen for most
of the AMANDA–II livetime, with a time window of 2.5
µs. The condition was 5/7 in all IceCube strings, with a
time window of 1.5 µs.
Muons from charged–current neutrino interactions
near the array are detected by the Cherenkov light they
produce when traversing the ice. The hit times along
with the known detector geometry and the optical prop-
erties of the ice allow the reconstruction of the tracks
passing through the detector. A detailed description of
the reconstruction techniques used in AMANDA and Ice-
Cube is given in Ref. [11]
III. SIGNAL AND BACKGROUND
SIMULATIONS
The simulation of the neutralino–induced neutrino sig-
nal was performed using the WimpSim program [12] for a
sample of neutralino masses (50, 100, 250, 500, 1000,
3000 and 5000 GeV). Two extreme annihilation chan-
nels were considered in each case, a soft neutrino chan-
nel, ? χ0
1? χ0
1→ b¯b and a hard neutrino channel, ? χ0
1? χ0
1→
W+W−, (? χ0
this mass is therefore below the W production thresh-
old). This choice covers the range of neutrino energies
that would be detectable with AMANDA–II/IceCube for
typical MSSM models. Note, however, that neutrinos
with energies above about a few hundred GeV will inter-
act in the Sun, and do not escape; only the lower energy
neutrinos from the decays of the products of such interac-
tions will get out of the dense solar interior. This cutoff,
rather than the WIMP mass, sets the neutrino spectrum
for WIMP masses above 1 TeV. The simulated angular
range was restricted to zenith angles between 90◦(hori-
zontal) and 113◦, with the generated number of events as
a function of angle weighted by the time the Sun spends
at each declination. WimpSim propagates the neutrinos
taking into account energy losses and oscillations in their
way out of the Sun as well as vacuum oscillations to the
Earth, giving the expected neutrino flux at the location
of the detector for each neutralino mass simulated. The
neutrino–nucleon interactions in the ice around the de-
tector producing the detectable muon flux were simulated
with nusigma [12] using the CTEQ6 [13] parametrization
of the nucleon structure functions.
1? χ0
1→ τ+τ−was chosen for 50 GeV neu-
tralinos, since they are assumed to annihilate at rest and
The backgroundforthedark matter searches
arises from up–going atmospheric neutrinos and mis–
reconstructed downward–going atmospheric muons. We
have simulated the atmospheric neutrino flux according
to Ref. [14], using the ANIS program [15], with energies
between 10 GeV and 325 TeV and zenith angles between
80◦and 180◦(vertically up–going). The simulation in-
cludes neutrino propagation through the Earth, taking
into account the Earth density profile [16], neutrino ab-
sorption and neutral current scattering. The simulation
of atmospheric muons was based on the CORSIKA air
shower generator [17] using the South Pole atmosphere
parameters and the H¨ orandel parametrization of the cos-
mic ray composition [18]. We have simulated 1011in-
teractions, distributed uniformly with zenith angles be-
tween 0◦and 90◦, and with primary energies, Ep, be-
tween 600 GeV and 1011GeV. We note that the back-
ground simulations were not used in the evaluation of
the actual background remaining at final cut level in the
analyses presented below, but off–source data was used
to that end. Background simulations were used as a con-
sistency check at the different steps of the analyses.
Muons were propagated from the production point
to the detector taking into account energy losses by
bremsstrahlung, pair production, photo–nuclear interac-
tions and δ–ray production as implemented in the code
MMC [19]. The Cherenkov light produced by the muon
tracks and secondaries was propagated to the optical
modules taking into account photon scattering and ab-
sorption according to the measured optical properties of
the ice at the detector [20], as well as the measured dust
layer structure of the ice at the South Pole [21]. The
Photonics [22] program was used to this end.

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5
m? χ0
1(GeV) channel
¯Ψ(deg)
Veff (m3)µ90
s
ΓA(s−1)Φµ (km−2y−1)σSD
χp (cm2)σSI
χp(cm2)
50τ+τ−
b¯b
W+W−
b¯b
W+W−
b¯b
W+W−
b¯b
W+W−
b¯b
W+W−
b¯b
W+W−
b¯b
6.8
13.1
4.6
6.8
3.5
4.4
3.2
3.9
3.0
3.6
3.0
3.4
3.0
3.4
2.4×104
3.6×103
2.7×105
3.0×104
2.1×106
1.2×105
4.1×106
6.2×105
5.3×106
1.1×105
5.7×106
1.7×106
5.4×106
1.9×106
16.4
31.7
16.5
21.9
15.2
1.2×1024
4.5×1026
1.1×1023
1.0×1025
6.9×1021
5.6×1023
2.6×1021
5.5×1022
1.2×1021
2.7×1022
2.3×1021
9.6×1021
1.9×1022
8.0×1021
2.8×104
4.7×105
3.9×103
3.2×104
1.0×103
6.5×103
6.9×102
1.4×103
3.6×103
1.2×103
5.1×102
6.9×102
4.3×102
6.5×102
2.66×10−39
7.70×10−37
8.67×10−40
7.27×10−38
3.24×10−40
2.12×10−38
4.85×10−40
9.81×10−39
8.82×10−40
1.86×10−38
1.53×10−38
6.16×10−38
4.38×10−38
1.43×10−37
1.02×10−41
2.94×10−39
1.94×10−42
1.62×10−40
4.05×10−43
2.65×10−41
4.47×10−43
9.05×10−42
6.81×10−43
1.44×10−41
1.05×10−41
4.21×10−41
2.92×10−41
9.55×10−41
100
250
[2.3,22.5]
13.5
11.4
7.4
14.2
11.2
10.7
9.5
10.3
500
1000
3000
5000
TABLE I. ANALYSIS A: For each neutralino mass and annihilation channel the table shows: The median of the space–angle
distribution,¯Ψ, the effective volume, Veff, the 90% CL upper limit on the expected signal, µ90
limits on the annihilation rate at the center of the Sun, ΓA, on the muon flux at the Earth, Φµ, and on the spin–dependent
and spin–independent neutralino–proton cross sections, σSD
s , and the corresponding 90% CL
χp and σSI
χp. The limits include systematic uncertainties.
IV. DATA ANALYSIS
Below we describe the two analyses performed with
AMANDA–II data in stand–alone mode and with
AMANDA–II run in coincidence with the 40–string con-
figuration of IceCube. In both cases the cuts were opti-
mized on data when the Sun was above the horizon, so
the data analysis was kept blind to the actual direction
of the Sun.
A. ANALYSIS A
(AMANDA–only analysis)
The data set used in this analysis corresponds to a to-
tal of 812 days of effective livetime, and comprises a total
of 7.25×109events collected when the Sun is below the
horizon between the beginning of March 2001 and the end
of October 2006. Data from periods where the detector
showed unstable behaviour or periods where test or cali-
bration runs were performed, were removed from the final
data sample. The remaining events were cleaned of hits
induced by electronic cross–talk, dark noise or unstable
modules, and the data set was retriggered to make sure
that the required amount of physical hits participated in
building the trigger. The events were first reconstructed
with two fast first–guess track finding algorithms, Di-
rectWalk [11] and JAMS [23]. These reconstructions are
aimed at identifying muon tracks and give a rough first
estimate of their direction, using it as a first angular cut
in order to reduce the data sample, still dominated by
down–going atmospheric muons at this level. Events with
zenith angles smaller than 70◦as reconstructed by the
DirectWalk or the JAMS reconstructions were rejected
at this stage. Two maximum likelihood reconstructions
were applied to the remaining events. One uses Direct-
Walk and JAMS as seeds, performing an iterative maxi-
mization of the probability of observing the actual event
geometry (hit times and positions) with respect to a given
track direction. In reality, the negative of the logarithm
of the likelihood is minimized in order to find the best–fit
zenith and azimuth. In order to exploit the fact that most
of the events that trigger the detector are down–going
atmospheric muons, an iterative Bayesian reconstruction
incorporating the known atmospheric muon zenith angle
distribution as prior, was also performed. A comparison
between the likelihoods of the standard and the Bayesian
reconstructions can then be used to evaluate the likeli-
hood that an event is down–going or up–going.
The reconstructed events were then processed through
a series of more stringent angular cuts on the direction of
the tracks as obtained with the likelihood fits (zenith an-
gle > 80◦), to reduce the atmospheric muon background
and retain as much of a potential signal as possible. At
this level, only a fraction of 3×10−3of the data and the
simulated atmospheric muon background survive, while
69% of the simulated atmospheric neutrino background
was kept. Between 36% and 78% of the neutralino signal
survived these cuts, depending on the neutralino mass
and annihilation channel.
The final event selection step was performed using a
boosted decision tree (BDT) classifier [24]. We have se-
lected 21 variables that showed good separation power
and a correlation below 65% between any pair. The vari-
ables used for the classification scheme can be grouped in
two major classes: variables related to the hit topology of
the event and variables related to the quality of the track
reconstruction. Among the first class there are variables
like the number of hit optical modules, the number of

Page 6

6
non–scattered, or ’direct’, hits1, the number of strings
with hits within a 50 m radius cylinder around the track,
and the number of strings with direct hits in the same
cylinder, the center of gravity (c.o.g.) of the spatial po-
sition hits, the distance of the c.o.g. to the geometrical
center of the detector, the length of the direct hits pro-
jected onto the direction of the track, the smoothness of
the distribution of direct hits along the track and vari-
ables related to the probability of detecting a photon in
the hit modules given the reconstructed track hypoth-
esis. Among the variables related to the reconstruction
quality, we have used the angle of the standard maximum
likelihood reconstruction, the difference of log–likelihoods
between the standard reconstruction and the Bayesian re-
construction and a measure of the angular resolution of
the first–guess reconstructions.
In order to exploit the differences in the final muon en-
ergy spectra at the detector produced by the annihilation
of neutralinos of different mass, we trained BDTs sepa-
rately for each neutralino mass and annihilation channel,
using the same 21 variables in each case.
training samples consisted of 50% of each of the simu-
lated signal samples. Data when the Sun is above the
horizon were used as the background sample. The BDT
classifies the given data as background or signal accord-
ing to a continuous parameter that takes values between
1 (signal–like) and –1 (background–like). A cut on the
BDT output was chosen for each model as to maximize
the discovery potential. Details of the data analysis and
a complete list of the variables used can be found in
Ref. [25].
After the BDT cut the data sample is reduced by a fac-
tor between 1×10−7and 3×10−7with respect to trigger
level, depending on the signal model used for the opti-
mization, and its purity is closer to the irreducible atmo-
spheric neutrino background. We note however that the
approach taken in this and the analysis described in Sec-
tion IVB does not require to reach a pure atmospheric
neutrino sample, since we use the shape of the normal-
ized space angular distributions with respect to the Sun
of both signal and background to build our hypothesis
testing. Details are given in Section V below.
The signal
1. Systematic uncertainties
The effect of different systematic uncertainties on the
signal expectation was evaluated by varying the relevant
parameters in the Monte Carlo and processing this new
sample through the same analysis chain as the nominal
sample. Systematic uncertainties affect the sensitivity of
the detector to a given signal, a quantity that is char-
acterized by the effective volume. The effective volume
1Hits with a time stamp that corresponds to the time that light
takes to travel directly from the track hypothesis to the optical
module.
is defined as Veff = (nfinal/ngen) × Vgen and calculated
by generating a given number of signal events ngen in
a geometrical volume Vgen around the detector. nfinal
is the remaining number of events after the analysis cuts
have been applied to the generated event sample. The ef-
fective volume depends on neutrino energy, but in what
follows we will show the integrated volume over the neu-
trino spectrum produced by a given neutralino mass. The
relative uncertainty in the effective volume is then given
by,
∆Veff
Veff
=Vsys− Veff
Veff
(1)
where Veff is the effective volume of the baseline analy-
sis and Vsysthe effective volume calculated with a given
assumption for systematic effects. Since we are not rely-
ing on atmospheric muon and neutrino Monte Carlo to
estimate the background, we evaluate the effect of sys-
tematics only on the signal expectation.
Systematic uncertainties can be classified in different
categories. There are systematics induced from the un-
certainties in quantities used in the signal Monte Carlo;
neutrino cross sections, oscillation parameters or muon
energy losses. The uncertainties in the oscillation pa-
rameters used to calculate the expected neutrino flux
at the detector were taken from Ref. [26] and lead to
an uncertainty of less than ±3%. Further, uncertain-
ties from the neutrino–nucleon cross section calculation
within WimpSim and the simulation of muon energy loss in
the ice have been estimated to be ±7% [12] and ±1% [19]
respectively.
An additional source of systematics is the implemen-
tation of the optical properties of the ice in the detector
response simulation, as well as the in–situ optical module
sensitivity. The AMANDA–II calibration light sources
were used to measure photon arrival time distributions as
a function of the relative emitter–receiver distance. Such
measurements allow us, in principle, to extract an effec-
tive scattering length and absorption length that charac-
terize the deep ice where the detector is located. How-
ever, the ice at the South Pole presents a layered struc-
ture, with slightly different optical properties due to the
presence of different concentrations of dust at different
depths [27]. Moreover the process of melting the ice to
deploy the strings and the subsequent refreeze of the wa-
ter column changes the local optical properties of the
ice in the drill hole. The inverse problem of extracting
the ice properties from the measured photon arrival time
information is then a quite difficult one, and different im-
proved implementations have been applied in AMANDA
with time. We have used the two most recent ice models
as an estimation of the uncertainties introduced by the
different implementations of the ice properties as a func-
tion of depth. The relative uncertainty induced in the
detector effective volume by this effect ranges between
3% and 30%, depending on neutrino energy.
The uncertainty on the total sensitivity of the deployed
optical modules (glass plus PMT) also contributes to

Page 7

7
101
102
103
104
105
106
MC neutrino energy [GeV]
10-9
10-8
10-7
10-6
10-5
10-4
Rate [Hz]
MC energy of atmospheric νµ
Only AMANDA triggered
Only IC triggered
IC and AMANDA triggered
FIG. 2. Monte Carlo neutrino energy distribution at final
level of Analysis B, of the events triggering only AMANDA–
II (full line), only IceCube (dashed line) or both detectors
(dotted line).
the uncertainty in the effective volume. Two additional
Monte Carlo samples with the light collection efficiency
of each module globally shifted by ±10% with respect
to the baseline simulation were produced and the events
passed through the complete the analysis chain. The ef-
fect on the effective volume lies between 20% and 40%.
The overall systematic uncertainties in the detector ef-
fective volume lie between 20% and about 50% depend-
ing on the neutralino mass model being tested.
total uncertainty in Veff has been calculated under the
assumption that all uncertainties are uncorrelated, i.e.,
∆V/V =
i
The
??
i(∆V/V )2
B.ANALYSIS B
(AMANDA–IceCube combined analysis)
The data set used in this analysis comprises a total
of 1.7×1010events collected between the middle of April
and end of September 2008, plus the period March 20
– April 1 2009. Only runs where both AMANDA–II
and IceCube were active were used, which corresponds
to a total livetime of 149 days when the Sun was be-
low the horizon. The surface geometry of AMANDA–
II/IceCube–40 used in the analysis is shown in Fig-
ure 1. The denser AMANDA–II array plays the role of
a low energy detector, as can be seen in Figure 2 which
shows the energy distribution of neutrinos triggering the
AMANDA–II array and the IceCube array, at final cut
level. We have therefore simplified the analysis with re-
spect to the approach taken in analysis A, and optimized
the cuts for two energy regions, low neutrino energies and
high neutrino energies. We used 100 GeV neutralinos an-
nihilating into b¯b as a benchmark for the low–energy op-
timization, and 1000 GeV neutralinos annihilating into
W+W−for the high–energy optimization.
mization that was finally used on each WIMP model was
decided at the end of the analysis, based on which one
achieved the best sensitivity for the given model.
The opti-
1.Data analysis
Data analysis proceeded on slightly different lines for
the low–energy and high–energy streams. Events that
had hits in the AMANDA–II detector were reconstructed
with the JAMS first–guess reconstruction and then with
an iterative likelihood fit. For events with hits only in the
IceCube strings, a simple line–fit [11] proved to work well
and it was used as the first–guess. A series of straight
cuts on event quality and track direction were performed
in order to reduce the amount of data while keeping as
much of the signal as possible, before using a multivari-
ate classifier for the final separation. The cut variables
used at this stage were slightly different between the low–
energy and the high–energy streams, reflecting the differ-
ent geometry and size of the AMANDA–II and IceCube
detectors, as well as the fact that we want to use Ice-
Cube as a veto for the low–energy stream. Events classi-
fied as belonging to the low–energy stream were required
to have an AMANDA–II trigger, a reconstructed zenith
angle larger than 90◦, at least 25% of direct hits (with
a minimum of four direct hits), a distance between the
first and last direct hit of at least 25 m, and less than five
hits in any of the IceCube strings. Events in the high–
energy stream were also required to have a reconstructed
zenith angle larger than 90◦and smaller than 120◦, a
reduced log–likelihood smaller than 6.5, a difference be-
tween the angles of the likelihood reconstruction and the
first–guess fit smaller than 40◦, at least 3 direct hits, at
least 2 strings with direct hits and a distance between
the first and last direct hit of at least 141 m. These cuts
reduced the data and atmospheric muon simulation by a
factor of about 2000 in each case, while just reducing the
low–energy and high–energy signal streams by a factor
of 9 and 2.4, respectively.
After these straight cuts, a support vector machine
(SVM) [28] was used for the final classification of the
events. We trained two SVMs independently, one for the
low–energy sample and another one for the high–energy
sample. The signal training samples consisted of 50% of
the simulated signal samples considered in each stream.
Data when the Sun is above the horizon were used as the
background sample. The choice of variables to use in the
SVM was done iteratively: from an original group of 35
variables, the SVM was trained on all variables but one
at a time. A variable for which the SVM performance
did not worsen when removed, was discarded. A set of
12 variables were identified by this method as useful for
signal and background discrimination in the low–energy
stream, and ten for the high–energy stream. As in Anal-
ysis A, the variables are related to the event topology
and the quality of the track reconstruction. Three of the

Page 8

8
FIG. 3. Figure of merit of the model discovery potential (upper panels) and sensitivity (lower panels) as a function of SVM
output of Analysis B. The left plots correspond to the low–energy analysis optimization and the right plots to the high–energy
optimization.
variables were common to both streams: the zenith differ-
ence between the reconstructed track and the position of
the Sun, the angular difference between the reconstructed
track and a line joining the centers of gravity of the first
and the last (in time) quartiles of the hits, and the hor-
izontal distance from the detector center to the center
of gravity of the hits. Among the other variables used
in a particular stream are the number of hit strings, the
angular resolution of the track fit and the smoothness of
the distribution of direct hits projected along the track
direction. Details of the data analysis and the complete
list of the variables used can be found in Ref. [29]. The
SVM classifies the given data as background or signal ac-
cording to a continuous parameter, Q, that takes values
between 0 (signal–like) and 1 (background–like). A cut
value of Q = 0.1 was used for both data sets, and it is jus-
tified in Section V below. A fraction of 2.2×10−3of the
data in the low–energy analysis and 4.1×10−3of the data
in the high–energy analysis remain after this cut, while
24% and 39% of the signal are retained, respectively. No
further cuts were applied after the SVM classification.
2. Systematic uncertainties
The uncertainties in analysis B were evaluated as in
the previous analysis, by varying the optical module sen-
sitivity and the ice model in the Monte Carlo and evalu-
ating the effect on the effective volume after all analysis
steps. The values for the uncertainties pertaining to theo-
retical inputs (neutrino–nucleon cross section, oscillation
parameters and muon propagation in ice) were taken as
for analysis A.
With the deployment of IceCube, the ice properties at
deeper depths than the AMANDA location needed to be
evaluated, and a new ice model was developed that cov-
ered the whole IceCube volume and a better description
of the layered structure of the ice. Two approaches were
taken in updating the AMANDA ice properties model-
ing: extrapolating the AMANDA model based on new ice
core data and using IceCube flasher data. The difference
in the effective volume induced by these two approaches
was taken as an estimation of the uncertainty in the anal-
ysis due to the ice optical properties. This uncertainty
ranges from 2% to 4%, depending on the analysis stream,
while the DOM sensitivity uncertainty lies between 12%
and 24%. The uncertainties were added in quadrature to
obtain the total uncertainty of each of the two streams
of the analysis.
V. RESULTS
The BDT classifiers of Analysis A were trained to
maximize the model discovery potential (MDP) as de-
fined in Ref. [30], which measures the possible contri-
bution of a signal when a given number of background
events, nB, are expected. Reference [30] gives an analyt-
ical parametrization for the sensitivity of the experiment
for a chosen discovery level at a given confidence level,
kMDP=
?S
a2
8+9b2
13+ a√nB+b
2
?b2+ 4a√nB+ 4nB
(2)
where ?s represents the signal efficiency. This figure of
merit was chosen to represent the strength of the signal
flux needed for a 5σ significance discovery (a=5) at 90%
confidence level (b=1.28).
The SVMs in Analysis B were trained to optimize the
sensitivity (the median upper limit of the number of sig-
nal events at 90% confidence level, ¯ µ90
tector effective volume, Veff) to the signal, although such
optimization was found to be equivalent to maximizing
the discovery potential. This is illustrated in Figure 3,
where lower panels show the sensitivity, while the upper
s divided by the de-

Page 9

9
m? χ0
1(GeV)
50
channel
τ+τ−
b¯b
W+W−
b¯b
W+W−
b¯b
W+W−
b¯b
W+W−
b¯b
W+W−
b¯b
W+W−
b¯b
¯Ψ(deg)
8.0
13.1
5.3
9.0
2.8
4.7
2.4
3.4
2.2
2.7
2.2
2.6
2.2
2.4
Veff (m3)
7.40×104
5.49×103
4.33×105
4.81×104
9.33×106
3.35×105
2.26×107
1.50×106
3.23×107
3.88×106
3.12×107
8.00×106
3.05×107
9.24×106
µ90
s
10.8
19.0
7.8
11.7
6.2
7.4
5.3
6.6
5.1
5.9
5.2
5.6
5.2
5.7
ΓA(s−1)
8.11×1023
1.73×1026
1.19×1023
7.06×1024
2.99×1021
3.24×1023
9.23×1020
4.98×1022
6.78×1020
1.39×1022
1.01×1021
5.18×1021
1.19×1021
4.32×1021
Φµ (km−2y−1)
1.95×104
1.81×105
4.27×103
2.30×104
4.38×102
3.76×103
2.40×102
1.24×103
2.04×102
6.05×102
2.16×102
3.70×102
2.14×102
3.48×102
σSD
1.86×10−39
3.97×10−37
9.60×10−40
5.70×10−38
1.41×10−40
1.53×10−38
1.70×10−40
9.15×10−39
4.95×10−40
1.01×10−38
6.56×10−39
3.37×10−38
2.17×10−38
7.81×10−38
χp (cm2)σSI
7.55×10−42
1.61×10−39
2.41×10−42
1.36×10−40
1.95×10−43
2.10×10−41
1.73×10−43
9.05×10−42
4.22×10−43
8.67×10−42
4.97×10−42
2.56×10−41
1.60×10−41
5.78×10−41
χp(cm2)
100
250
500
1000
3000
5000
TABLE II. ANALYSIS B: For each neutralino mass and annihilation channel the table shows: The median of the space–angle
distribution,¯Ψ, the effective volume, Veff, the 90% CL upper limit on the expected signal, µ90
limits on the annihilation rate at the center of the Sun, ΓA, on the muon flux at the Earth, Φµ, and on the spin–dependent
and spin–independent neutralino–proton cross sections, σSD
s , and the corresponding 90% CL
χp and σSI
χp. The limits include systematic uncertainties.
panels show the figure of merit of the discovery poten-
tial, both as a function of the cut on the SVM output Q.
The left plot corresponds to the low–energy optimization
and the right plot to the high–energy optimization. The
figure shows that the chosen cut on the SVM (Q = 0.1),
based on the sensitivity plots, lies very close to the max-
imum of the discovery potential curves.
We use the shape of the space angle distribution of
the final data samples with respect to the Sun to build
a confidence interval for µs, the number of signal events
compatible with the observed data distribution at a given
confidence level, that we will choose to be 90%. The plots
in Figure 4 show an example of the angular distribution
of the remaining data after all cuts, compared with the
angular distribution of the expected background obtained
from time–scrambled data from the same declination of
the Sun. Angles shown are space angles with respect to
the Sun position, and the different plots correspond to
Analysis A and Analysis B as indicated in the caption.
A probability density function for the space angle ψ
can be constructed as follows,
f(ψ|µs) =
µs
nobsfS(ψ) +
?
1 −
µs
nobs
?
fB(ψ) (3)
representing the probability of observing a given angle ψ
when µssignal events are present among the total num-
ber of observed events nobs. The functions fS(ψ) and
fB(ψ) are the angular probability density functions of
signal and background respectively, obtained by fitting
and normalizing the corresponding angular distributions.
The likelihood of the presence of µssignal events in an
experiment that observed exactly nobsevents, can then
be expressed as follows
L(µs) =
nobs
?
i=1
f(ψi|µs), (4)
To define confidence intervals based on Eq. (3) we use
the likelihood–ratio test statistic R(µs) = L(µs)/L(? µs)
the result of best fit to the observed ensemble of space
angles.For each µs, L(µs) ≤ L(? µs) and R(µs) ≤ 1.
lnR(µs) ≥lnR90(µs) for 90% of the cases. A confidence
interval [µlow, µup] at 90% confidence level can then be
calculated as [µlow, µup]={µ | lnR(µs) ≥lnR90(µs)}.
In the absence of a signal, µupis the 90% confidence
level limit on the number of signal events, µ90
limit can be directly transformed into a limit on the vol-
umetric rate of neutrino interactions in the detector due
to a signal flux, Γν→µ, since we would expect a num-
ber µs= Γν→µVeff·tliveof neutrinos in the livetime tlive.
Therefore
as proposed by Feldman and Cousins [31], where ? µs is
Through a series of pseudo experiments with varying val-
ues of µ, a critical value R90(µs) can be found such as
s.This
Γν→µ≤ Γ90
ν→µ=
µ90
s
Veff· tlive
(5)
This volumetric interaction rate is directly propor-
tional to the neutralino annihilation rate in the Sun, ΓA,
through
Γν→µ=ΓAρN
4πD2
?
?∞
0
dEνσνN
?Eµ≥ Ethr
Posc(µ,i)
µ
| Eν
?dNK
?
i
?
i
?
K
BK
dEν
?
(6)
where D?is the distance to the Sun, σνN the neutrino–
nucleon cross section (above a given muon energy thresh-
old, Ethr
µ, taken as 10 GeV), ρNthe nucleon number den-
sity of the detector medium, Posc(µ,i) the probability
that a produced neutrino of flavour i oscillates to flavour
µ before reaching the detector (including the probability

Page 10

10
02
4
68 1012
14
ψ (°)
0
5
10
15
20
25
# events
Data
Expected bkg
02
4
68 1012
14
ψ (°)
0
5
10
15
20
25
# events
Data
Expected bkg
02
4
68 1012
14
ψ (°)
0
5
10
15
20
25
# events
Data
Expected bkg
02
4
68 10 12
14
ψ (°)
0
5
10
15
20
25
# events
Data
Expected bkg
FIG. 4. The space angular distribution with respect of the position of the Sun (first 15 degrees) of the remaining data events
in two analyses, after all cuts (dots). The histogram in all plots represents the expected background distribution obtained from
time–scrambled data in the same declination of the Sun, with the 1σ Poisson uncertainty shown as the shaded area. Upper
row: Analysis A: The left plot shows the case of optimizing the analysis for 100 GeV neutralinos and b¯b annihilation channel
as an example of a low–energy optimization. The right plot shows the case of 1000 GeV neutralinos and W+W−annihilation
channel as an example of a high–energy optimization. Lower row: Analysis B: The left plot shows the case of optimizing the
analysis for 100 GeV neutralinos and b¯b annihilation channel (the low–energy optimization). The right plot shows the case of
1000 GeV neutralinos and W+W−annihilation channel (the high–energy optimization)
that the neutrino escapes the dense solar interior), BKis
the branching ratio for annihilation into channel K, and
dNK
i/dEνthe number of neutrinos of flavour i produced
per annihilation and unit of energy from channel K. The
branching ratios to a given channel are the only unknown
quantities in the above equation. They depend on several
unknown SUSY parameters, i.e. the composition and the
mass of the neutralino. To be able to make concrete pre-
dictions and simplify the way the results are presented,
we have performed the analysis on two annihilation chan-
nels per simulated mass, W+W−(or τ+τ−if mχ< mW)
and b¯b, assuming 100% branching ratio to each channel
in turn. For a given mass, these channels produce the
hardest and softest neutrino energy spectra respectively
and are taken as representative of the range of possible
outcomes if nature chose the MSSM neutralino as dark
matter.
Equivalently to Eq. (6), we can relate the annihilation
rate and the muon flux at the detector, Φµ, above the
energy threshold Ethr
µ
as
ΦEµ≥Ethr
µ
=ΓAρN
4πD2
?
?
µ)
?∞
?
?
µis the differential neutrino cross
0
dEν
?Eν
Ethr
µ
dE
?
µX(E
?
µ)
dσν(Eν,E
dE
?
µ
i
Posc(µ,i)
?
K
BK
?dNK
i
dEν
?
(7)
where dσν(Eν,E
section for producing a muon with energy E
trino of energy Eν. The term X(E
of the muon produced with energy E
account energy losses between the production point and
the detector location. For each mass and annihilation
?
µ)/dE
?
µfrom a neu-
?
µ) denotes the range
?
µ, and takes into

Page 11

11
m? χ0
1(GeV)channelµ90
s
ΓA(s−1)Φµ (km−2y−1)σSD
χp (cm2)σSI
χp(cm2)
50τ+τ−
b¯b
W+W−
b¯b
W+W−
b¯b
W+W−
b¯b
W+W−
b¯b
W+W−
b¯b
W+W−
b¯b
20.1
25.5
19.4
23.7
15.4
27.1
10.9
12.7
6.8
14.0
9.3
9.9
8.7
9.4
6.83×1023
1.45×1032
8.75×1022
7.69×1029
2.73×1021
3.82×1023
7.13×1020
3.00×1022
3.43×1020
1.08×1022
6.34×1020
3.05×1021
7.11×1020
2.34×1021
1.64×104
1.13×105
3.15×103
1.83×104
3.99×102
4.42×103
1.86×102
7.50×102
1.03×102
4.69×102
1.36×102
2.17×102
1.27×102
1.89×102
1.57×10−39
2.47×10−37
7.07×10−40
4.53×10−38
1.28×10−40
1.80×10−38
1.31×10−40
5.54×10−39
2.50×10−40
7.86×10−39
4.13×10−39
1.98×10−38
1.28×10−38
4.25×10−38
6.26×10−42
1.00×10−39
1.67×10−42
1.07×10−40
1.74×10−43
2.39×10−41
1.32×10−43
5.46×10−42
2.12×10−43
6.56×10−42
3.10×10−42
1.49×10−41
9.36×10−42
3.09×10−41
100
250
500
1000
3000
5000
TABLE III. Results from the combination of Analysis A, Analysis B and the results of Ref. [7], covering 1065 days of livetime
between 2001 and early 2009. For each neutralino mass and annihilation channel the table shows: The 90% CL upper limit on
the expected signal, µ90
muon flux at the Earth, Φµ, and on the spin–dependent and spin–independent neutralino–proton cross sections, σSD
The limits include systematic uncertainties.
s , and the corresponding 90% CL limits on the annihilation rate at the center of the Sun, ΓA, on the
χp and σSI
χp.
channel considered, the integrals have been performed
with WimpSim, providing a relationship between the ex-
perimentally obtained limit on Γν→µand derived limits
on ΓAand Φµ.
If we assume equilibrium between the capture and
annihilation rates, the annihilation rate is proportional
to the neutralino–proton scattering cross section, which
drives the capture. Under the further assumption that
the capture rate is fully dominated either by the spin–
dependent (SD) or spin–independent (SI) scattering, we
can extract conservative limits on either the SD or the
SI neutralino–proton cross section from the limit on ΓA.
We have followed the method described in Ref. [32] in
order to extract limits on the SD and SI cross sections.
This conversion introduces an additional systematic un-
certainty in the calculation of the cross sections, due to
the element composition of the Sun, effect of planets on
the capture of halo WIMPs and nuclear form factors used
in the capture calculations. These effects influence the
SI and SD calculations differently, and are discussed in
Ref. [32]. The uncertainties introduced by the conversion
are small for the spin–dependent cross section, 2%, and
larger for the spin–independent cross section, 25%. We
have added these contributions in quadrature in order to
obtain the total systematic uncertainty on these quanti-
ties that we use in this work. We just note that recent
studies favour a somewhat higher value of the dark mat-
ter density, ρ0, closer to 0.4 GeV/cm3[33], than the stan-
dard value of 0.3 GeV/cm3assumed in our conversion.
Since variations in the dark matter density translate in-
versely into the calculated WIMP–proton cross section,
the conservative assumption on ρ0makes our limits con-
servative as well. A recent discussion on the effects of
uncertainties on the structure of the dark matter halo,
the dark matter velocity dispersion and the effect of the
gravitational influence of planets on the capture rate of
local dark matter has been presented in detail in Ref. [34].
The results on the quantities described above for each
neutralino mass and annihilation channel considered are
presented in Table I for Analysis A and in Table II for
Analysis B. The tables show the median of the space
angle distribution with respect to the Sun, the effective
volume for each analysis optimization, the 90% CL limits
on the expected signal, on the annihilation rate at the
center of the Sun, on the muon flux at the Earth, and
on the spin–dependent and spin–independent neutralino–
proton cross sections.
VI. COMBINATION OF RESULTS
Given that the data samples used in the analyses pre-
sented in this paper are independent, we can combine the
results in a statistically sound way. Since IceCube has al-
ready published an analysis using the same method on
another independent data set, the data collected with the
22–string detector in 2007, we can combine these three
analyses and cover a total livetime of 1065 days, stretch-
ing from March 2001 to April 2009. We use the combined
likelihood constructed from the likelihoods of the three
analyses,
L(µs) = L1(µsω1)L2(µsω2)L3(µsω3) =
nobs
1 ?
i=1
f1(ψi,1|µsω1)×
nobs
2 ?
i=1
f2(ψi,2|µsω2)×
nobs
3 ?
i=1
f3(ψi,3|µsω3)
(8)

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12
where µs is now weighted by the livetime tlive,i and ef-
fective volume Veff,iof each analysis through the weights
ωi, defined as
ωi =
Veff,itlive,i
?3
j=1Veff,jtlive,j
(9)
We have chosen to show conservative limits and there-
fore we have used in Eq. 9 the effective volumes of each
analysis reduced by its 1σ systematic uncertainty. A 90%
confidence limit for µsis then obtained using the same
procedure as for the single–analysis case explained in Sec-
tion V. The combined limit on Γν→µis now given by
Γν→µ=
µ90
s
?3
j=1Veff,jtlive,j
(10)
The calculation of the combined limits on the anni-
hilation rate and muon flux follows from Γν→µ as in
Eqs. (6) and (7). The results of this procedure are
shown in Table III and in Figures 5 and 6.
ures show the 90% CL limits on the muon flux, on the
spin–dependent and on the spin–independent neutralino–
proton cross sections, compared with current limits from
other experiments. The shaded area shows the allowed
parameter space of the 7–parameter MSSM, obtained by
a grid scan using DarkSusy [35].
only allowed models we have taken into account cur-
rent experimental limits on the neutralino mass from
LEP [1] and limits on the WIMP cross section from
the CDMS [36] and XENON [37] direct detection exper-
iments. We have allowed for a generous range of values
of the dark matter relic density Ωχh2around the favored
value of WMAP [38], accepting models in the scan which
predicted values of Ωχh2between 0.05 and 0.2.
An independent analysis using the point–source search
techniques described in Ref. [39] has been performed, us-
ing the Sun as another point source, and has been pre-
sented in Ref. [40]. The analysis used the cuts developed
for the point–source search without any further optimiza-
tion. The only difference being that the estimated energy
of the events was not included in the likelihood test in
order to avoid the bias to the E−2spectrum used in the
optimization of the point–source analysis. Since this data
set (2000–2006) practically overlaps with that of Analysis
A, we have not included the results of such an approach
in the combination presented above, but the results of
the point–source analysis provide a useful confirmation
of the robustness of the limits presented in this paper.
The fig-
In order to choose
VII.DISCUSSION
We have presented two independent analyses search-
ing for neutralino dark matter accumulated in the cen-
ter of the Sun using the AMANDA–II and the 40–string
IceCube detectors, covering different data taking peri-
ods. We have combined the obtained 90% confidence
101
102
103
104
WIMP mass (GeV)
102
103
104
105
106
Φµ(km−2y−1)
0.05<Ωχh2<0.20
MSSM muon flux limits
IC/AMANDA 2001-2008, b¯b
IC/AMANDA 2001-2008, W+W− (∗)
σSI<σlim
IC86 180 days sensitivity, W+W− (∗)
Super-K 2011, b¯b
Super-K 2011, W+W−
SI CDMS(2010)+XENON100(2011)
(∗)τ+τ−for mχ< mW
FIG. 5. 90% confidence level upper limits on the muon flux
from the Sun, Φµ, from neutralino annihilations as a function
of neutralino mass. The results from the analyses presented
in this paper are shown as the black dots joined with lines to
guide the eye (solid and dashed for the W+W−and the b¯b an-
nihilation channels respectively). The shaded area represents
the allowed MSSM parameter space taking into account cur-
rent accelerator, cosmological and direct dark matter search
constrains. The red curve shows the expected sensitivity of
the completed IceCube detector. Super–K results [42] are also
shown for comparison.
level limits on the muon flux and neutralino–proton spin–
dependent and spin–indepenent cross section with the
previously published limits from the 22–string IceCube
configuration, to obtain limits corresponding to a total
livetime of 1065 days. We compare these results to the
currently allowed MSSM–7 parameter space, obtained by
a grid scan using DarkSusy. The limits on the muon flux
are the most constraining so far for neutralino masses
mχ0 ? 100 GeV. Assuming that the neutralinos consti-
tute the bulk of dark matter in the Galaxy and that they
annihilate producing a hard neutrino spectrum at the
detector, the combined results of AMANDA–II and Ice-
Cube presented in this paper start to probe the allowed
7–parameter MSSM space.
MSSM is, by construction of these analyses, limited to
a model–by–model rejection/acceptance, but is not able
to say anything about the relative probability of certain
regions of the parameter space with respect to others,
neither identify a best–fit model given the results ob-
tained. This is the reason we have chosen to show the
allowed MSSM space as a uniform shaded area, since in-
dividual model density in the plot would not carry any
statistical meaning. Analyses that use experimental re-
sults to assign probabilities to the SUSY parameter space
are becoming common. A first evaluation of the possi-
bilities that IceCube presents in probing the constrained
MSSM, including individual model information, was done
in Ref. [41]. A more elaborate analyses in this direc-
tion, including event energy and direction information,
as well as constraints from direct dark matter search ex-
periments and accelerator results in a global fit to the
This comparison with the

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13
101
102
103
104
WIMP mass (GeV)
10-41
10-40
10-39
10-38
10-37
10-36
10-35
10-34
10-33
10-32
10-31
σSD
χp (cm2)
0.05<Ωχh2<0.20
MSSM SD cross-section limits
σSI<σlim
IC/AMANDA 2001-2008, b¯b
SI CDMS(2010)+XENON100(2011)
IC/AMANDA 2001-2008, W+W− (∗)
IC86 180 days sensitivity, W+W− (∗)
(∗)τ+τ−for mχ< mW
Super-K 2011, b¯b
Super-K 2011, W+W−
KIMS 2007
COUPP 2011
101
102
103
104
WIMP mass (GeV)
10-47
10-46
10-45
10-44
10-43
10-42
10-41
10-40
10-39
10-38
10-37
10-36
10-35
σSI
χp(cm2)
0.05<Ωχh2<0.20
MSSM SI cross-section limits
IC/AMANDA 2001-2008, b¯b
IC/AMANDA 2001-2008, W+W− (∗)
σSI<σlim
IC86 180 days sensitivity, W+W− (∗)
XENON100 2011
CDMS 2010
SI CDMS(2010)+XENON100(2011)
(∗)τ+τ−for mχ< mW
FIG. 6. Left: 90% confidence level upper limits on the spin–dependent neutralino–proton cross section, σSD
neutralino mass. The results from the analyses presented in this paper are shown as the black dots joined with lines to guide the
eye (solid and dashed for the W+W−and the b¯b annihilation channels respectively). The shaded area represents the allowed
MSSM parameter space taking into account current accelerator, cosmological and direct dark matter search constrains. The red
curve shows the expected sensitivity of the completed IceCube detector. Results from Super–K [42], KIMS [43] and COUPP [44]
are also shown for comparison. Right: 90% confidence level upper limits on the spin–independent neutralino–proton cross
section, σSI
dots joined with lines to guide the eye (solid and dashed for the W+W−and the b¯b annihilation channels respectively). The
shaded area represents the allowed MSSM parameter space taking into account current accelerator, cosmological and direct
dark matter search constrains. The red curve shows the expected sensitivity of the completed IceCube detector. Results from
CDMS [36] and Xenon [37] are also shown for comparison.
χp, as a function of
χp, as a function of neutralino mass. The results from the analyses presented in this paper are shown as the black
SUSY parameter space is being developed by the collab-
oration with data obtained with the 79–string detector.
Given that the Sun is essentially a proton target and
that the muon flux at the detector can be related to the
capture rate of neutralinos in the Sun, the IceCube lim-
its on the spin–dependent neutralino–proton cross section
are currently well below the reach of direct search exper-
iments, proving that neutrino telescopes are competitive
in this aspect. For the spin–independent limits, however,
direct dark matter search experiments can be competitive
due to the choice of target. Indeed, the latest results from
the XENON100 collaboration [37], using 100 days of live-
time, have already produced stronger spin independent
limits than those we present in this paper, as shown in
the right plot of figure 6. However there is some comple-
mentarity between direct and indirect searches for dark
matter given the astrophysical assumptions inherent to
the calculations. Both methods are sensitive to opposite
extremes of the velocity distribution of dark matter par-
ticles in the Galaxy (low–velocity particles are captured
more efficiently in the Sun, high–velocity particles leave
clearer signals in direct detection experiments), as well
as presenting different sensitivity to the structure of the
dark matter halo (a local void or clump can deplete or
enhance the possibilities for direct detection).
The data set used in Analysis B covered the time un-
til the decommissioning of the AMANDA–II detector
in 2009. The denser configuration of the AMANDA–II
strings was of key importance on increasing the sensitiv-
ity to low neutralino masses, while the sparsely spaced
IceCube strings alone would have yielded a worse result.
In order to supplant the role of AMANDA–II as a low–
energy array, the IceCube collaboration has deployed the
DeepCore array [45] in the clear South Pole ice, in the
middle of the IceCube layout. DeepCore lies about 500 m
deeper than AMANDA–II and its placement in the cen-
ter of IceCube means that three layers of IceCube strings
can be used as a veto to reject down–going atmospheric
muons. The deployment of DeepCore was finalized in
December 2010 and it is currently taking data embedded
in the IceCube data acquisition system. DeepCore is ex-
pected to lower the energy threshold of IceCube to the
O(10 GeV) region, and therefore be an important asset
in future dark matter searches with IceCube.
ACKNOWLEDGMENTS
We acknowledge the support from the following agencies:
U.S. National Science Foundation-Office of Polar Programs,
U.S. National Science Foundation-Physics Division, Univer-
sity of Wisconsin Alumni Research Foundation, the Grid
Laboratory Of Wisconsin (GLOW) grid infrastructure at the
University of Wisconsin - Madison, the Open Science Grid
(OSG) grid infrastructure; U.S. Department of Energy, and
National Energy Research Scientific Computing Center, the
Louisiana Optical Network Initiative (LONI) grid comput-
ing resources; National Science and Engineering Research
Council of Canada; Swedish Research Council, Swedish Po-
lar Research Secretariat, Swedish National Infrastructure for

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14
Computing (SNIC), and Knut and Alice Wallenberg Founda-
tion, Sweden; German Ministry for Education and Research
(BMBF), Deutsche Forschungsgemeinschaft (DFG), Research
Department of Plasmas with Complex Interactions (Bochum),
Germany; Fund for Scientific Research (FNRS-FWO), FWO
Odysseus programme, Flanders Institute to encourage scien-
tific and technological research in industry (IWT), Belgian
Federal Science Policy Office (Belspo); University of Oxford,
United Kingdom; Marsden Fund, New Zealand; Japan So-
ciety for Promotion of Science (JSPS); the Swiss National
Science Foundation (SNSF), Switzerland; J. P. Rodrigues ac-
knowledges support by the Capes Foundation, Ministry of
Education of Brazil.
[1] Particle Data Group, J. Phys. G 37, 075021 (2010).
http://pdg.lbl.gov/2011/reviews/
rpp2011-rev-dark-matter.pdf
[2] G. Aad et al., Phys. Rev. Lett. 106, 131802 (2011).
[3] S. Chatrchyan et al., Phys. Rev. Lett. 107, 221804
(2011).
[4] G. B´ elanger et al., JHEP03, 012 (2004).
[5] K. Griest and M. Kamionkowski, Phys. Rev. Lett. 64,
615 (1990).
[6] J. Silk, K. Olive and M. Srednicki, Phys. Rev. Lett. 55,
257 (1985); W. H. Press and D. N. Spergel, Astrophys. J.
296, 679 (1985); T. Gaisser, G. Steigman and S. Tilav,
Phys. Rev. D34, 2206 (1986).
[7] R. Abbasi et al., Phys. Rev. Lett. 102, 201302 (2009).
[8] W. Wagner et al., Proc. of the 28th Intl. Cosmic Ray
Conference, Tsukuba, Japan, 2003. HE2.3, 1365.
[9] R. Abbasi et al., Nucl. Instrum. Meth. A618, 139 (2010).
[10] R. Abbasi et al., Nucl. Instrum. Meth. A601, 294 (2009).
[11] J. Ahrens et al., Nucl. Instrum. Meth. A524, 169 (2004).
[12] M. Blennow, J. Edsj¨ o and T. Ohlsson, J. Cosm. and As-
tropart. Phys., JCAP01, 021 (2008).
Also http://www.physto.se/~edsjo/wimpsim.
[13] J. Pumplin et al., J. High Energy Phys. JHEP07, 012
(2002).
[14] P. Lipari, Astropart. Phys. 19, 193 (2003).
[15] A. Gazizov and M. Kowalski, Comput. Phys. Commun.
172, 203 (2005).
[16] A. M. Dziewonski and D. L. Anderson, Phys. Earth Plan.
Int. 25 297 (1981).
[17] D. Heck et al., FZKA report 6019, (1998).
http://www-ik.fzk.de/corsika.
[18] J. R. H¨ orandel, Astropart. Phys. 1, 195 (1993).
[19] D. Chirkin and W. Rhode, Proc. of the 27th Intl. Cos-
mic Ray Conference, Hamburg, Germany, 2001, HE2.02,
1017, and hep-ph/0407075.
[20] P. Askebjer et al., J. of Glaciology 41, 445, (1995).
[21] N. E. Bramall et al., Geophys. Res. Lett. 32, L21815,
(2005).
[22] J. Lundberg et al., Nucl. Inst. and Meth. A581, 619,
(2007).
[23] M. Ackermann, Ph. D. thesis, Humboldt Universit¨ at zu
Berlin, (2006),
http://edoc.hu-berlin.de/docviews/abstract.php?
id=27726
[24] B. P. Roe et al., Nucl. Inst. and Meth. A543, 577 (2005).
[25] A. Rizzo, PhD thesis, Brussels University Press, 2010.
ISBN 978 90 5487 844 5. http://w3.iihe.ac.be/
Publications/Thesis/thesis_alfio_rizzo_public_
defense.pdf
[26] M. Maltoni et al., New J. Phys. 6, 122 (2004).
[27] M. Ackermann et al., J. Geophys. Res., 111, D13203
(2006).
[28] C. J. C. Burges, Data Min. Knowl. Discov. 2, 121 (1998).
[29] O. Engdeg˚ ard, PhD thesis, Uppsala University, 2011.
ISBN: 978-91-554-8218-3.
[30] G.Punzi,Proc.ofStatistical
ticle Physics,Astrophysics and Cosmology,
STAT (2003) http://www.slac.stanford.edu/econf/
C030908/. Stanford,USA,
arXiv:physics/0308063.
[31] G. J. Feldman and R. D. Cousins, Phys. Rev. D57, 3873
(1998).
[32] G. Wikstr¨ om and J. Edsj¨ o, J. Cosm. and Astropart.
Phys., JCAP04, 009 (2009).
[33] R. Catena and P. Ullio, J. Cosm. and Astropart. Phys.,
JCAP08, 004 (2010).
[34] C. Rott, T. Tanaka and Y. Itow, J. Cosm. and Astropart.
Phys., JCAP09, 029 (2011).
[35] P. Gondolo et al., J. Cosm. and Astropart. Phys.,
JCAP07, 008 (2004).
[36] Z. Ahmed et al., Phys. Rev. D84, 011102 (2011).
[37] E. Aprile et al., Phys. Rev. Lett. 107, 131302 (2011).
[38] G. Hinshaw et al., Astrophys. J. Supplement Series, 180,
225 (2009).
[39] R. Abbasi et al., Phys. Rev. D79, 062001 (2009).
[40] J. Braun and D. Hubert, Proc. of the 31st Intl. Cosmic
Ray Conference, L’od´ z, Poland, 2009, arXiv:0906.1615.
[41] R. Trotta, R. Ruiz de Austri and C. P´ erez de los Heros,
J. Cosm. and Astropart. Phys., JCAP08, 034 (2009).
[42] T. Tanaka et al., Astrophys. J. 742, 78 (2011).
[43] H. S. Lee et al., Phys. Rev. Lett. 99, 091301 (2007).
[44] E. Behnke et al., Phys. Rev. Lett. 106, 021303 (2011).
[45] R. Abbasi et al., arXiv:1109.6096. Submitted to As-
tropart. Phys.
Problems inPar-
PHY-
September8-11, 2003.