A Search for Dark Matter in the Sun with AMANDA and IceCube

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(1)ACTA UNIVERSITATIS UPSALIENSIS Uppsala Dissertations from the Faculty of Science and Technology 97.

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(3) Olle Engdegård. A Search for Dark Matter in the Sun with AMANDA and IceCube.

(4) Dissertation presented at Uppsala University to be publicly examined in Polhemssalen, Ångström Laboratory, Uppsala, Thursday, December 15, 2011 at 13:15 for the degree of Doctor of Philosophy. The examination will be conducted in English. Abstract Engdegård, O. 2011. A Search for Dark Matter in the Sun with AMANDA and IceCube. Acta Universitatis Upsaliensis. Uppsala Dissertations from the Faculty of Science and Technology 97. 118 pp. Uppsala. A search for weakly interacting massive particles (WIMPs) annihilating in the Sun was performed with the IceCube and AMANDA neutrino telescopes, using data from 2008 corresponding to 149 days of livetime. Assuming that particles in the dark matter halo scatter and accumulate in the centre of the Sun, Majorana WIMPs may pair-wise annihilate and give rise to a neutrino signal detectable in an experiment at Earth. No excess of muon-neutrinos from the Sun was observed, and limits on the νμ-flux were set for masses between 50 GeV and 5 TeV considering WIMPs annihilating into b⎯b and W+W-. Separate limits were also calculated for the case of the lightest Kaluza-Klein particle. The flux limits were converted to limits on the spin-dependent and spin-independent WIMP-proton cross sections, σSD and σSI. The search was combined using a joint likelihood method with AMANDA and IceCube data from 2001–2007, yielding the 90% CL upper limits Φμ < 103 km-2y-1 for a WIMP mass of 1000 GeV and σSD < 1.28×10-4 pb for 250 GeV, both for the W+W- spectrum. Keywords: Dark matter, WIMP, neutralino, MSSM, Kaluza-Klein, IceCube, AMANDA, neutrino telescope Olle Engdegård, Department of Physics and Astronomy, High Energy Physics, 516, Uppsala University, SE-751 20 Uppsala, Sweden.. © Olle Engdegård 2011 ISSN 1104-2516 ISBN 978-91-554-8218-3 urn:nbn:se:uu:diva-160833 (http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-160833).

(5) Contents. Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 The author’s contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Units and conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Dark matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Observational evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Candidates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Direct detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Indirect detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 IceCube and AMANDA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Neutrino detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 IceCube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 AMANDA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Processing and filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 The ice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Signal and background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Simulation overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 The atmospheric background . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Other background sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 The IceCube simulation chain . . . . . . . . . . . . . . . . . . . . . . . . . 5 An AMANDA trigger study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Triggers in 2007 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Reconstruction techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Maximum likelihood . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 First guess methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 The low-energy likelihood landscape . . . . . . . . . . . . . . . . . . . . 7 Preparing the IC40 data analysis . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Experimental data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Simulation datasets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Event selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1 The AMANDA and IceCube streams . . . . . . . . . . . . . . . . . . . . 8.2 Hit selections and reconstructed tracks . . . . . . . . . . . . . . . . . . .. 7 9 9 10 11 11 13 16 17 21 21 24 28 30 32 35 35 36 38 39 41 43 43 44 45 47 47 49 50 51 53 53 54 59 60 60.

(6) 8.3 Data cleaning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4 First Cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.5 Second Cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.6 A multivariate SVM cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.7 The final sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Search for a Solar excess . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1 Signal content in data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2 Muon flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3 Cross-sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.4 Stream selections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.6 Systematic uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Joint analysis of 2001–2008 data . . . . . . . . . . . . . . . . . . . . . . . . . 10.1 Combined likelihood . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2 Preparing additional data samples . . . . . . . . . . . . . . . . . . . . . . 10.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Populärvetenskapligt sammandrag . . . . . . . . . . . . . . . . . . . . . . . A Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B SVM variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B.1 AMANDA stream . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B.2 IceCube stream . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 60 62 62 64 68 73 73 77 78 78 79 80 87 87 88 89 90 95 98 99 101 105 105 107 109 111.

(7) Abbreviations. AMANDA AMS ANIS ANTARES. Antarctic Muon And Neutrino Detector Array. Alpha Magnetic Spectrometer. All Neutrino Interaction Simulation. Astronomy with a Neutrino Telescope and Abyss environmental RESearch project. ATWD Analog transient waveform digitizer. CAPRICE Cosmic AntiParticle Ring Imaging Cherenkov Experiment. CDMS Cryogenic Dark Matter Search. CL Confidence level. CMB Cosmic microwave background. COG Centre of gravity, calculated from the hits treating the integrated charge in each DOM as a mass. CORSIKA Cosmic ray simulations for Kascade. COUPP Chicagoland Observatory for Underground Particle Physics. CRESST Cryogenic Rare Event Search with Superconducting Thermometers. DAMA Dark matter experiment. DAQ Data Acquisition System. DM Dark matter. DOM Digital optical module. EDELWEISS Expérience pour DEtecter Les Wimps En Site Souterrain. FADC Fast analog to digital converter. HEAT High Energy Antimatter Telescope. IBFVRM Iterative Brute Force Variable Removal Method. IC IceCube. IC40 The 40-string configuration of IceCube that was taking data from April 2008 to April 2009. ICL IceCube Laboratory. JAMS Just another muon search, a reconstruction algorithm in AMANDA . 7.

(8) KIMS LC LEP LHC LKP LLH LSP MAPO MC MMC MOND MSSM MWE OM PAMELA PDF PE PICASSO PMT SPE. SUSY SVM SWAMP TFT. TMVA TWR ULEE WIMP WMAP 8. Korea Invisible Mass Search. Local coincidence. Large Electron-Positron collider. Large Hadron Collider. Lightest Kaluza-Klein particle. Log-likelihood, usually meaning a fitting method. Lightest supersymmetric particle. The building housing the AMANDA DAQ, named after Martin A. Pomerantz. Monte Carlo, simulation on a stochastic event-by-event basis. Muon Monte Carlo, software for propagating charged leptons through matter. Modified Newtonian Dynamics. Minimally supersymmetric standard model. Metres water equivalent. Optical module. Payload for Antimatter Matter Exploration and Light-nuclei Astrophysics. Probability density function. Photoelectron. Project In Canada to Search for Super-Symmetric Objects. Photomultiplier tube. Single photo electron, used to denote when a PMT registers one single photon or when a track reconstruction is done using only the first hit in each DOM. Supersymmetry. Support Vector Machine, a machine learning method used here for classification of signal and background. Swedish amplifier. The TFT Board is an internal committee that supervises detector triggers, filtering and transmission of data from the South Pole. Toolkit for multivariate data analysis with ROOT. Transient waveform recorder, the new DAQ for AMANDA, installed in 2007. Ultra low energy event trigger. Weakly interacting massive particle. Wilkinson Microwave Anisotropy Probe..

(9) 1. Introduction. As the title of this thesis indicates, this is mainly a presentation of a search for Solar dark matter with AMANDA and IceCube. The nature of the dark matter is still unknown, but it is thought to be about five times more abundant in the Universe that the ordinary kind. Popular current theories suggest that dark matter particles could accumulate in the centre of the Sun, pairwise annihilate and produce neutrinos that could be detected in the AMANDA and IceCube neutrino telescopes at the South Pole. The outline of the thesis is as follows: A brief introduction to dark matter is given in Chapter 2, ending with a general description of how it could be detected in our experiments. In Chapter 3 the hardware and software of these detectors are described in detail, starting with the principles of neutrino detection. In Chapter 4 we discuss what the signal and background look like in this analysis and how they are simulated. A study made on the trigger system of AMANDA is presented in Chapter 5. Chapter 6 is devoted to explaining the various track reconstruction methods that we use. The full analysis, searching for an excess of neutrinos from the Sun with data from 2008, is laid out in Chapters 7–9. Finally, we combine this result with data from 2001–2007 in Chapter 10 and make some concluding remarks in Chapter 11.. 1.1. The author’s contribution. During the time of my PhD studies at Uppsala University I have worked together with many skilled people in the IceCube Collaboration. Apart from developing the analysis presented here, using combined AMANDA and IceCube data from 2008, I have also made the first joint analysis where data samples from several dark matter analyses are combined in a likelihood method that can be used with future data, enhancing the total sensitivity. The emphasis of my work has been on exploring how to make use of low-energy muons. I have in particular studied reconstruction methods at low energies and optimised a new low-threshold trigger for AMANDA that was implemented just before the start of data acquisition in 2008. I also designed an online data filter for 2009, optimised for low-energy up-going muons, and have been an active member of IceCube’s software development community. In 2007 and 2008 I performed and supervised acceptance testing of IceCube DOM s in Uppsala, starting with two weeks training at DESY, Zeuthen. I also 9.

(10) brought this experience twice to the South Pole, where I was responsible for closing down the testing the first time and for setting things up the second time. At the South Pole I helped out with the deployment of IceCube strings and the preparation of IceTop tanks. I have participated in ten collaboration meetings, the International CosmicRay Conference in Beijing 2011 (ICRC 2011) and the Swedish Particle Days, presenting results or ongoing work and having good discussions with colleagues. The contribution to ICRC 2011 [1] is attached at the end of this thesis, and a more detailed paper is in preparation [2]. Finally, I am happy to have been involved in various outreach projects, giving a number of lectures about IceCube, dark matter and the South Pole to Swedish school pupils.. 1.2. Units and conventions. Particle masses are measured in electronvolts (eV) throughout this thesis, setting c D 1. Cross sections have the unit cm2 or picobarn (with 1 pb D 1036 cm2 ). In the context of WIMP annihilations, the hard channel denotes the branch N W C W  (or  C   ) and the soft channel denotes the branch b b.. 10.

(11) 2. Dark matter. According to the standard model of cosmology, the visible density of matter is actually only a small fraction of the total matter density of the Universe. The rest is dark, i.e., not visible on any electromagnetic wavelength. The presence of the dark matter has instead mostly been inferred from gravitational effects. Its exact properties are currently unknown.. 2.1. Observational evidence. Rotation curves of galaxies Evidence for dark matter can be found on several scales [3]. The study of rotation curves of individual spiral galaxies is arguably the most convincing, with one example shown in Figure 2.1. The tangential velocity of hydrogen gas at distance r from the galactic centre is expected from Newtonian dynamics to be r GM.r/ ; (2.1) v.r/ D r where the total mass out to r is. Z. M.r/ D 4. r. .r 0 /r 02 dr 0. (2.2). 0. and .r 0 / is the mass density profile. If all mass was contained in the visible disk, we would expect to see v / r 1=2 for larger radii. The fact that the observed velocity in Figure 2.1 is constant far outside the disk radius (about 5 kpc) implies that M.r/ / r, consistent with a large halo of unseen matter.. Weak lensing Another way of identifying a discrepancy between visible and gravitational mass is through weak gravitational lensing. This can be used on a galactic scale with the lensing of distant galaxies by foreground structures [5], or on the scale of galaxy clusters [6]. The visible matter of the cluster 1E0657-558 (the Bullet cluster) was mapped in X-ray by the Chandra satellite and compared to the gravitational potential contours [7]. Shown in Figure 2.2, this revealed a striking separation of dark and visible matter. Since this object is actually two 11.

(12) Figure 2.1: Rotation curve for the dwarf spiral galaxy NGC-6503, showing the predicted contributions of gas, disk and dark matter halo. Figure taken from Ref. [4].. Figure 2.2: The galaxy cluster merger 1E0657-558 (the Bullet cluster). The visible matter, in color, is imaged in X-ray by Chandra. The green contours are weak lensing reconstructions of the gravitation potential. Figure taken from Ref. [7].. merging galaxy clusters, the separation can be explained by the collision and interaction of hot gas in each cluster, slowing this part down, while the dark matter interacts weakly or not at all and passes through unhindered (except for the gravitational tug).. Cosmology The methods above can help us to estimate the amount of dark matter in individual astrophysical objects, but not the total content in the Universe. In a flat universe, the total average energy density equals the critical density, c D 12. 3H 2 ; 8GN. (2.3).

(13) where H is the Hubble parameter and GN is Newton’s gravitational constant. If the abundance of any substance i is expressed as the density i , then we can define the quantity i as i i D : (2.4) c P If the total density tot D i i is equal to 1, then i is the fraction of the Universe’s energy accounted for by substance i . The currently most precise values of the cosmological parameters are derived from the WMAP satellite experiment, measuring anisotropies in the cosmic microwave background. When data from the final seven-year exposure of WMAP is fitted together with other recent cosmological observations, we get the following values for the baryon, dark matter, dark energy and total density [8]: b 0.0456˙0.0016. DM 0.227˙0.014. ƒ 0.728C0:015 0:016. tot 1.0023C0:0056 0:0054 .. (2.5). We seem to be living in a universe with about 5% baryons, 23% dark matter and 73% dark energy.. A dark matter halo model For a general dark matter halo Navarro, Frenk and White suggested [9] the density profile s ; (2.6) .r/ D .r=rs /.1 C r=rs /2 where s and rs are constants for the particular astrophysical object. It has been successful in approximating the profile of structures spanning a mass range of 20 orders of magnitude [10] and in particular the main features of the Milky Way halo [11]. It does not, however, properly describe the inner region within r  0:1 kpc [12]. More important for the direct detection of dark matter in the lab or indirectly from the Sun, is the local density DM . A canonical value is DM  0:3 GeV/cm3 [13].. 2.2. Candidates. Many solutions have been proposed to the dark matter problem, most involving the extension of the standard model with new particles. Suggestions to keep the standard model intact but instead change the laws of gravity, so called Modified Newtonian Dynamics (MOND), have successfully explained a selection of all observations but struggle with accommodating other results such as the Bullet cluster mentioned above. Likewise, non-radiating baryonic objects 13.

(14) like brown dwarfs, neutron stars and black holes probably make up only a small fraction of the non-luminous mass [14]. Particle candidates need to interact gravitationally but very weakly (or not at all) through the electromagnetic force. Since it is assumed that the dark matter was produced together with the baryons in the primordial Big Bang soup, it should be stable, i.e, have a lifetime of at least the age of the Universe. Any such dark matter particle, let us denote it , will be continuously created and N annihilated in the early hot universe through reactions of the type N $ ``, for some particle `. As the Universe expands and cools down to temperatures below m , no more  particles will be produced. The annihilations will continue until the annihilation rate falls below the expansion rate and the relic abundance will be fixed at this point of freeze out. The relic density can be approximately [13] expressed as  h2 . 3  1027 cm3 s1 ; hA vi. (2.7). H (km/s)/Mpc and where h is the scaled Hubble parameter defined as h D 100 hA vi is the thermally averaged annihilation cross section multiplied by the relative velocity. It so happens that if we assume  to be a weak scale particle, with a mass and interaction strength close to the W boson, then  becomes similar to the observed value of DM and this particle could thus explain most of the dark matter. This is the motivation for a Weakly Interacting Massive Particle (WIMP), the subject of study in this thesis. We will focus on the lightest neutralino from Supersymmetry, but Kaluza-Klein dark matter will also be mentioned.. Supersymmetry Supersymmetry [15] (SUSY) is a symmetry between fermions and bosons that postulates the existence of a supersymmetric partner for every SM particle; a fermion for every boson and a boson for every fermion. Each SM particle would differ only in spin from its supersymmetric partner and thus have the same mass. Since no SUSY particles have been seen so far, supersymmetry would be a broken symmetry up to the energy scale of recent experiments. We will mostly be concerned with the minimal supersymmetric extension to the standard model (MSSM), the model with minimal total field content. The full set of particles in MSSM is shown in Table 2.1. Particle names in SUSY follow the general logic that bosons get an s- prefix and fermions get an -ino suffix. From this table we see that MSSM requires two charged and three neutral Higgs bosons. Their superpartners mix with the electroweak gauge bosons to create two charged and four neutral mass eigenstates. We define the MSSM to include a new symmetry, with the corresponding conserved quantity R-parity. Defined as R D .1/3.BL/C2S , with the 14.

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(20) . Table 2.1: Particles and fields in the standard model, with their superpartners in MSSM . Table adapted from Ref. [16].. baryon number B, lepton number L and spin S , this gives all SM particles R D C1 and all SUSY particles R D 1. It also implies that the lightest MSSM particle must be stable. This lightest supersymmetric particle is in many MSSM scenarios the neutralino Q 0 1 . This neutralino, a Majorana particle only interacting through the weak force, turns out to be a perfect dark matter WIMP. From now on we will use the notation   Q 01 . It should be noted that supersymmetry primarily tries to solve problems in theoretical particle physics, like stopping the Higgs mass from diverging and unifying the three running coupling constants. It is interesting that it produces a very good solution to the astrophysical problem of dark matter — as a byproduct. Searches for missing energy in the LEP accelerator have set a lower limit [17] on the neutralino mass, m > 47 GeV, assuming gaugino mass unification.. Kaluza-Klein Theories of Universal Extra Dimensions (UED) add one or more compact dimension to the four observed space-time dimensions. Each standard model particle free to propagate through the UED is associated to an infinite tower of excited Kaluza-Klein states. If momentum conservation is assumed in the extra dimension, we get a new symmetry called KK-parity. Conservation of this parity implies that the lightest Kaluza-Klein particle (LKP) is stable and thus a possible dark matter candidate [18]. In many models the LKP is the first excitation of the B-field, often called the Kaluza-Klein photon [19]. 15.

(21) Figure 2.3: The event rate modulation seen by DAMA. Figure taken from Ref. [23].. 2.3. Direct detection. There are several techniques for directly measuring halo WIMPs scattering elastically on target nuclei. The nuclear recoil, with an energy of ~10 keV, can be detected using phonons, scintillation light, ionisation or a combination of these. Two general strategies stand out: In the first there is an attempt to identify individual signal events — a few tens of events per kg and year is expected — requiring a low-background environment, often cryogenic, and a careful event selection guided by signal and background models. Among many examples, this is the approach of the XENON [20] experiment (scintillation and ionisation in a liquid and gaseous xenon target), the CDMS [21] experiment (phonons and ionisation in a semiconductor target) and the CRESST experiment [22] (phonons and scintillation in a CaWO4 crystal target). The second analysis strategy is to search for an annual modulation in the event rate. Since the dark matter flux at the Earth results from the Solar system travelling through the halo, the Earth’s motion around the Sun causes the apparent flux to shift slightly with a period of one year. A modulation of this kind, shown in Figure 2.3, has been seen by DAMA (the DAMA/NaI and DAMA / LIBRA experiments) [23] with a significance of 8.9 , using NaI(Tl) crystal scintillators over 13 annual cycles. Indications of a modulation have also been seen recently in the CoGeNT experiment [24], although only at 2.8 , with data spanning 458 days. These modulation results are not compatible in standard dark matter scenarios with the null results from XENON [20] and CDMS [21]. Nonetheless, the DAMA collaboration has not been able to find any systematic effect that could cause the observed modulation. Only results from other experiments with different systematics could begin to settle this matter. Adding to the puzzle, CRESST rejects the background hypothesis at a confidence level of 4.7, a recent claim that is not compatible in any obvious way with the other experiments. Figure 2.4 shows current upper limits on the WIMP-nucleon cross section, together with the favoured regions by DAMA and CoGeNT. It should be noted that it is possible in principle to make all the results discussed here compatible; see Ref. [25] for one example. 16.

(22) Figure 2.4: WIMP-nucleon cross-section, with upper limits from CDMS [21], EDEL WEISS [26], XENON [20] and an earlier run of CRESST [27]. Shown are also favoured regions from DAMA [28], CoGeNT [24] and CRESST [22]. For the positive CRESST results, M1 marks the point of the most significant fit and M2 marks a point of slightly less significance. Figure taken from Ref. [22].. 2.4. Indirect detection. Dark matter WIMPs undergoing pair-wise annihilation outside the detector can give rise to annihilation products detectable in an experiment on (or near) the Earth. Typical sources are the galactic centre, the dark matter halo, neighbouring dwarf galaxies and gravitational wells such as the Earth and the Sun. Evidence of dark matter annihilations in these locations would be a flux of cosmic rays, photons or neutrinos that is incompatible with background expectations. This means that many experiments have been able to test dark matter hypotheses. Even though all such searches have so far yielded null or inconclusive results, the last few years have seen several intriguing observations, of which one of recent interest is the measurement of the fraction of positrons in the total e  C e C flux above ~5 GeV. This quantity is shown in Figure 2.5 for various recent experiments. It was indicated to be larger than expected in data from experiments like HEAT [29], CAPRICE [30] and AMS [31] and later confirmed with high statistics in PAMELA [32]. This anti-matter excess has been interpreted by some as the product of dark matter annihilations, but several less exotic explanations [33] involving new models of cosmic-ray sources and propagation have also been put forth. Even more recently, Fermi [34] has confirmed and extended the positron-fraction excess up to 200 GeV.. Neutrinos from the Sun Dark matter WIMPs in the galactic halo can become gravitationally trapped by dense objects like the Earth and the Sun, by scattering repeatedly on nucle17.

(23) e+/(e+ + e-). 10-1. PAMELA AESOP 2006 AMS-01 CAPRICE 1994 HEAT 2000 HEAT 1994/95. 10-2. MASS 1989 MT 1987 TS 1993. 1. 10. 102. Energy/GeV. Figure 2.5: Positron fraction as measured by various experiments. The left panel includes the prediction from secondary production from cosmic-ray nuclei interacting with the interstellar gas. Left figure taken from Ref. [34]. Right figure taken from Ref. [33] (adapted from Ref. [32]).. ons over cosmological timescales, losing momentum in each scattering event. The capture rate of a dark matter particle  in the Sun can approximately be expressed [35, 36] as    DM 270 km=s 3 20 1 Cˇ 3:4  10 s 0:3 GeV=cm3 vN DM ! (2.8)  H H He  100 GeV 2 SD C SI C 0:07SI  ; 106 pb m where DM is the local halo density, vN DM is its velocity dispersion and m is the WIMP mass. Most capture events occur on hydrogen nuclei, in a spindependent and spin-independent fashion, with a small contribution from helium and heavier elements. In the conventional halo model used here, DM D 0:3 GeV/cm3 and vN DM D 270 km/s. The balance between capture, annihilation and thermal evaporation in the Sun is given by the time evolution of the number of WIMPs N , dN D Cˇ  CA N 2  CE N: dt. (2.9). The annihilation rate is here A D 12 CA N 2 . The evaporation rate CE is negligible [37] for WIMP masses above ~5 GeV. Solving Equation 2.9 for N , the annihilation rate can then be written p  1 A .t / D Cˇ tanh2 t Cˇ CA : (2.10) 2 18.

(24) p For timescales t  1= Cˇ CA the capture and annihilation rates are in equilibrium, so 1 (2.11) A D Cˇ : 2 This is true for many WIMP models with the present age of the Sun, t  5  109 years. Since the annihilations occur well within the Sun, mostly within 1% of the Solar radius [38], no produced particles other than neutrinos will be able to escape to the surface and beyond. Even though the  N annihilation channel is suppressed in the MSSM, detectable muon-neutrinos can be produced indirectly [39] through the channels N t tN;  C   ; W C W  ; Z 0 Z 0 ;  !c c; N b b; Z 0 H10 ; Z 0 H20 ; H10 H30 ; H20 H30 and H ˙ W  :. (2.12). The actual annihilation branching ratios are dependent on the model, in particular on the bino, wino and higgsino content of the neutralino. Large water Cherenkov detectors like Super-Kamiokande, ANTARES, AMANDA and IceCube can search for an excess of neutrinos from the Sun in the GeV to TeV range, which could signify the presence of dark matter WIMPs. To pin down the dark matter properties, enough events must be collected to construct an energy spectrum; the upper cutoff would mark the WIMP mass and the shape could be compared to predictions from different sets of annihilation branching ratios.. The relation to direct detection Using IceCube data we can set limits on the WIMP-proton cross section and compare it with results from direct-detection experiments. IceCube is in general more sensitive to SD than direct-detection experiments but less sensitive to SI , and this complementary effect is very helpful in exploring the full WIMP parameter space. As seen in Figure 2.6, IceCube has already excluded MSSM models inaccessible by XENON, and vice versa.. 19.

(25) σSI (cm2 ). 10-41 10-42 10-43 10-44 10-45 10-46 10-47 10-48 10-49 MSSM models around 100 GeV XENON100 2011 10-50 IC/AMANDA 2001-2008 10-51 -48 -47 -46 -45 -44 -43 -42 -41 -40 -39 -38 10 10 10 10 10 10 10 10 10 10 10 σSD (cm2 ) Figure 2.6: The spin-dependent and spin-independent WIMP-nucleon cross section. Shown are MSSM models for a WIMP mass around 100 GeV, together with the limit on SI from XENON [20] and the limit on SD , assuming the W C W  annihilation channel, from AMANDA and IceCube (this work).. 20.

(26) 3. IceCube and AMANDA. IceCube and AMANDA are high-energy neutrino telescopes, hidden deep in the Antarctic glacier near the geographical South Pole. They are Cherenkov detectors using ice as an optical medium. We will often in this thesis consider IceCube and AMANDA to be two parts of one single detector, and simply call it “IceCube” or “the detector”. 3.1. Neutrino detection. Before diving into the detector details, let us first have a brief look at how neutrinos are detected. As a neutrino ` of flavour ` traverses matter — in our case ice or the rock below — it can interact weakly with a nucleon N through the charged current ` .N ` / C N ! ` .`C / C X;. (3.1). ` .N ` / C N ! ` .N ` / C X;. (3.2). or the neutral current. where ` is a charged lepton and X is a hadronic component. For the energies concerned here, the energy transfer will always be large enough to dissociate the nucleon into a hadronic shower. Our main interest lies in charged current interactions where the incoming particle is a  or N  . Events in which no muon is created are generally called cascade events and will be of less interest to us, since their particle directions are very difficult to reconstruct. This also applies to muon events where most of the initial energy has been given to X. Both ` and the particles in X will in general travel at a speed very close to c, faster than the local speed of light cice D nc , where n is the refractive index of the ice. As a charged particle moves through a dielectric medium, it will cause polarisation and subsequently depolarisation of the medium. For particle speeds v < cice the changes to the electromagnetic fields will cancel as seen from a distance, but for v > cice they will interfere constructively and propagate in a cone as Cherenkov radiation [41]. The optical part of the Cherenkov spectrum can be measured by photomultiplier tubes. The principle. 21.

(27) Figure 3.1: Cherenkov radiation from a charged particle travelling to the right at ˇc > cice . Figure adapted from Ref. [40].. is illustrated in Figure 3.1, which also shows the angle of emission c , given by 1 cos c D ; (3.3) ˇn where ˇ D v=c. The direction of the emitted photons will not be exactly perpendicular to the shock front, since they move with the group speed [42, 17] and are governed by the group refractive index ng D n  . dn : d. (3.4). It has been shown [43] that the errors introduced in calibration, simulation and reconstruction by simply using a constant n D 1:32 are not more than ~1% in our detector. This implies that c  41ı when ˇ D 1.. Propagation of charged leptons in ice Leptons lose energy while traversing matter through several effects. Ionisation of nearby atoms involves small energies over a large number of interactions and is often considered a continuous process. Radiative losses through bremsstrahlung, pair production and photonuclear interactions are much more stochastic, especially at high energies. In this context, the energy released as Cherenkov radiation is very small. Muon energy losses are shown in Figure 3.2 for a wide range of energies, although the main focus in this thesis lies within 10–1000 GeV. 22.

(28)   . .   &$"%!.   &! '(%" . .  !" .      .  

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(30)   . . Figure 3.2: Simulated muon energy losses in ice. Figure adapted from Ref. [44].. The total average energy loss per unit of length can be written [17] as . dE D a.E/ C b.E/E; dx. (3.5). where a.E/ is the ionisation energy loss and b.E/ is the slope of the total radiative loss. If these slowly varying functions are approximated as constant, at a D 0:26 GeV mwe1 (metres water equivalent) and b D 0:36  103 mwe1 [44], the average range for a muon with initial energy E0 becomes   E0 1 x0  ln 1 C : (3.6) b Ecrit Here Ecrit is the critical energy, defined as the point where the losses due to ionisation and radiative processes are equal. This gives muons in ice a range of about 360 m at 100 GeV and 2.4 km at 1 TeV. The probability of the muon decaying before losing most of its energy is negligible at these relativistic energies; the muon lifetime is 2.2

(31) s, which, with time dilation, implies an average range in vacuum of 66 km for a 10 GeV muon. Whereas muons travel in a nearly straight line, electrons, being much lighter, are heavily scattered and typically do not reach more than a few metres. They mostly lose energy through bremsstrahlung, creating electromagnetic cascades. Since the Cherenkov light from these cascade events is emitted from a small region, there will not be a single coherent light 23.

(32) cone and reconstructing the particle direction is much more difficult than for muons. Tau leptons, with a lifetime of only 2:9  1013 seconds, produce similar cascade events when decaying directly to electrons or hadrons — at least below ~1 PeV. Cascade events are in general much harder to extract from the background, so this WIMP search will focus exclusively on muon tracks.. 3.2. IceCube. Centred about 1 km from the geographical South Pole, IceCube has today a total of 5160 Digital Optical Modules (DOMs) buried at depths between 1450 and 2450 m in the Antarctic glacier. These are distributed on 86 vertical strings, a configuration that was completed in December 2010. Six of these strings belong to the DeepCore, a central subarray with smaller inter-string and inter-DOM distances. Deployed in early 2010, DeepCore is designed for high sensitivity at low energies. The distance between the standard strings is about 125 m, with about 17 m between DOMs on the same string. In all, IceCube covers an horizontal area of about 1 km2 . Near the top of each standard string are two surface tanks of frozen water with two DOMs in each tank. Together these tanks constitute the IceTop array, a detector for cosmic-ray air showers. All strings and IceTop tanks are connected to the IceCube lab, a building on the surface that serves as a centre for the DAQ and online data processing. Figure 3.8 is a schematic view of the subdetectors. The specific configuration in 2008, with 40 strings deployed (IC40), is shown in Figure 3.3. Using hot water under high pressure, a water column of about 50 cm diameter is melted, into which the string cable is lowered together with the 60 attached DOMs. The water is not fully frozen again until a few weeks later.. Coordinate system The coordinate system used throughout this thesis has the origin in the middle of the IceCube array, so that the surface lies at z D 1948 m. The z-axis points upward. The y-axis points towards Greenwich at 0ı longitude and the x-axis lies 90ı from the y-axis in the negative direction to create a standard right-handed system. Angles are defined in a spherical coordinate system: The zenith angle, 2 Œ0;  , is 0 at the positive z-axis, and the azimuth angle,  2 Œ0; 2/, is 0 at the positive x-axis and runs counter-clockwise as seen from above. In the context of particle tracks, these angles always define the direction from which the particle originates, so a straight down-going particle would have a zenith angle of D 0.. 24.

(33) IC40 and AMANDA in 2008. 600 400. Y (m). 200 0 200 400 600. 600. 400. 200. 0. X (m). 200. 400. 600. Figure 3.3: IceCube depicted from above, in its 40-string configuration (squares) together with AMANDA (circles). The dots show the full 86-string IceCube detector, finished in 2010. The outer strings of IC40 are defined by the filled squares. All others strings, including AMANDA, will be called inner strings.. The Digital Optical Module The Digital Optical Module (DOM), pictured in Figure 3.4, is the fundamental piece of hardware for detection as well as data acquisition in IceCube [45]. It is used in IceCube, IceTop and DeepCore. The glass sphere, able to withstand a pressure of 70 MPa [46], houses a downward-facing photomultiplier tube1 (PMT) with 10 dynodes and a diameter of 25 cm, a high voltage generator, a mainboard for digital and analog signal processing and an LED flasher board. The PMT is optically coupled to the glass sphere by a gel and has a spectral range of 300-650 nm, but the gel and the glass together set a lower cutoff at 350 nm. Before the water column refreezes after drilling and deployment, the DOM is supported by a 5 cm thick cable (shown to the right in Figure 3.4) that also carries power and communication. The DOM mainboard contains an FPGA and a CPU, where the FPGA in general performs time-critical operations and acts as an interface between the CPU and the DOM hardware [45]. Digitisation of PMT pulses is performed on the DOM mainboard with two separate systems. The Analog Transient Waveform Digitizer (ATWD) has three channels for waveform capture at different amplifications — 16x, 2x and 0.25x — in order to cover a large dynamic range of the PMT, and one additional DOM-internal channel for calibration and monitoring. The digitiser 1. Hamamatsu R7081-02.. 25.

(34) Figure 3.4: The Digital Optical Module (DOM). To the right the nected to, and supported by, a string cable.. DOM. is shown con-. collects 128 samples over 422 ns. To reduce deadtime, the DOM can alternate between two identical and independent ATWD chips. For very bright events the ATWD capture window might be too small, so a second digitising system, the fast analog to digital converter (FADC), stores 256 samples over 6.4

(35) s. The FADC was not used in the work presented here. Digitisation in IC40 will only occur if a local coincidence (LC) condition is fulfilled. When a PMT pulse exceeds the discriminator threshold at 0.25 photoelectrons we have a hit, and an LC pulse is sent to the nearest DOM neighbours above and below on dedicated twisted-pair copper wires. This signal is also relayed to the next-to-nearest DOM. By requiring a hit in at least one neighbouring or next-to-nearest DOM within ˙1

(36) s before pulses are digitised and the surface DAQ is notified, noise and bandwidth demands are heavily reduced. Only hits that fulfil this LC criterion in IC40 participate in the trigger and are sent to the surface. A few DOMs with broken LC systems are exempted from this rule by being read out in the case of a trigger but not contributing to the trigger. In later configurations of IceCube, starting with IC59 in 2009, single hits are also sent to the surface but with much less information; only the amplitude of the peak FADC bin and its two neighbouring bins, together with a timestamp. These hits are dominated by noise and a sophisticated hit-cleaning algorithm must be applied at a later stage to extract useful information. Only a few percent of the total PMT rate correspond to hits that are matched by an LC signal [45]. 26.

(37) 80 70. String number. 60 50. 40 30 200. 10. 20. 30. DOM number. 40. 50. 60. Figure 3.5: DOMs in IC40. The filled circles mark DOMs that are inactive or excluded from the data analysis in this thesis.. The dark noise rate of the PMT in a DOM deployed in the ice, at temperatures between -40ı C and -10ı C, is about 650 Hz. This is thought to be mostly due to decays of radioactive isotopes contaminating the glass pressure sphere [47]. For calibration purposes, both for geometry and timing, the DOM flasher board is equipped with 12 LEDs peaking around 410 nm, directed outwards at different angles. Also used in studies of ice properties, these can be flashed in arbitrary combinations with a repetition rate up to 610 Hz [47]. Of the 2400 DOMs in IC40, 52 were either inactive or explicitly excluded from data analysis for various reasons. A full view of the bad DOMs is shown in Figure 3.5.. IceCube triggers and DAQ Since the DOMs deliver digital signals to the surface, the IceCube DAQ [45] is completely software-based. Each string is connected to a Domhub, a rackmounted Linux computer in the IceCube lab. The Domhub controls the transfer of power, software, firmware, calibration and data between the surface and the DOM. It fetches continuously timing from a master clock, based on a GPS receiver, and calibrates the DOMs once per second.. 27.

(38) 1000 1200. Depth (m). 1400 1600 1800. 2000 2200 2400 0. 5. 10 AMANDA string number. 15. 20. Figure 3.6: The depth distribution of the AMANDA strings. For comparison, an IceCube string is shown at position 0.. The Domhub passes the LC-tagged DOM hits to a central trigger system, where the following triggers were active in 2008:  Multiplicity 8 (M8). At least 8 hit DOMs in total, within 5

(39) s.  String trigger. This condition requires that at least 5 DOMs are hit within a sequence of 7 DOMs on the same string (often written 5-out-of-7), in a window of 1.5

(40) s.  Trigger for ultra low energy events (ULEE). A 3-out-of-4 string trigger on the 4 innermost strings, with a veto in the topmost 38 DOMs on each string. These strings are selected so to be surrounded by double string layers.. 3.3. AMANDA. The construction of the Antarctic Muon And Neutrino Detector Array (AMANDA) was completed in 2000. The primary goal was to build a highly capable experiment for discovering astrophysical sources of high-energy neutrinos [48], but it would also serve as a proof-of-concept for IceCube. As shown in Figures 3.3 and 3.6, it has 19 strings deployed at depths of 1500–2000 m, with a horizontal diameter of 200 m. This array, traditionally called AMANDA - II, was operational until April 2009 when it was permanently decommissioned. Being a prototype project, several different technologies and configurations were tested. The cables range from co-axial in the four innermost strings (1– 4) to twisted-pair in strings 5–19, with the addition of optical fibres in 11–19. The optical modules (OMs) do not in general contain much more than a 2028.

(41) 20. String number. 15. 10 5. 00. 5. 10. 15. 20. 25. OM number. 30. 35. 40. 45. Figure 3.7: Optical modules in AMANDA. The filled circles mark OMs that are inactive or excluded from the data analysis in this thesis.. cm PMT2 with 14 dynodes. The anode signal is here passed directly to the surface electronics, widening the PMT pulse from about 15 ns to 30–500 ns, depending on the cable type [40]. The dark noise in the OMs on strings 1–4 is about 500 Hz, similar to the IceCube DOMs, but about 1500 Hz on strings 5–19 which are using a different glass sphere with a higher content of 40 K. In total, AMANDA comprises 677 optical modules, of which 163 were either inactive or explicitly excluded from this analysis. This selection of bad OMs, shown in Figure 3.7, includes the entire string 17 which never reached its intended depth due to problems during deployment.. AMANDA triggers and DAQ The AMANDA DAQ [49, 50, 51, 52] was housed in the MAPO building, a few hundred metres from the IceCube lab. Pulses from the electrical channels are amplified here with the so called Swedish Amplifiers (SWAMPs) [50], and pulses from the optical fibres are converted to electrical pulses in the Optical Read-out Boards (ORBs). These signals are passed into the Digital Multiplicity Adder (DMADD) [53], a hardware trigger, applying individual discriminator thresholds for each channel.. 2. Hamamatsu R5912-2.. 29.

(42) A trigger pulse is generated if any of these two trigger conditions are met within 2.5

(43) s, using only hits in AMANDA OMs:  Multiplicity 18 (M18). At least 18 hit OMs in total.  M8 & String trigger. A coincidence between M8 in AMANDA and a string trigger. The string-trigger condition is 3-out-of-5 on strings 1–4 and 3-out-of-3 on strings 5–19. When a trigger signal is received, the OM pulses are digitally sampled in a 10.24

(44) s window by the Transient Waveform Recorder (TWR) [51]. Pulses exceeding an adjustable sampling threshold are saved. From this point, the event information is sent to the IceCube DAQ, forcing a readout of the IceCube array and the creation of a global event.. 3.4. Processing and filtering. IceCube data is continuously transferred to the northern hemisphere over a satellite link. The available bandwidth for IC40 was about 35 GB/day, not nearly enough to accommodate the full rate of all triggered events at about 1.5 kHz. A first data filtering step, sometimes called L1 filtering, reduces the rate by a factor of 20. In this processing a number of online filters, listed for IC40 in Table A.3 in the appendix, are applied to each event. The event is accepted if it fulfils the conditions of at least one online filter. An IceCube committee that oversees triggering, filters and transmission (the TFT board) handles proposals for new filters and makes certain that the total rate of collected events are kept within the available bandwidth. The data arriving via satellite to the computing facilities in the north is subjected to further processing, the L2 processing, where raw data is processed once again and more sophisticated track reconstructions are made. The general steps from raw data to the reconstructions used in this thesis is described in what follows.. Extraction of hits The PMT waveforms are first passed through a calibration program that, among other things, combines the three ATWD channels, accounts for individual DOM gains and subtracts waveform baselines. Calibrated waveforms are fed into an algorithm that extracts hits in a format suitable for the reconstruction code. A hit is thus defined as an integrated charge, a leading-edge time and the identity number of the DOM (or OM). Data from AMANDA is cleaned from spurious pulses caused by crosstalk in the string cables. This is done with heuristic methods based on knowledge about how the cables are physically routed and the shape of typical crosstalk pulses. 30.

(45) At this point, we perform further hit selection to prepare one hitmap for each of the three reconstructions used in this work. A hitmap is simply a set of hits. IceCube hits are first cleaned from known bad DOMs. This is followed by time-window cleaning, where we only accept hits in a 6

(46) s window, placed so as to maximise the number of hits within. The resulting hitmap will later, in Chapter 8, be referred to as the standard IceCube hitmap3 . AMANDA hits are present in about 25% of the data events at this level and most of these events also have at least one IceCube hit. After cleaning out bad OM s, AMANDA hits are merged with IceCube hits (if available) to make one combined set of hits. By applying different hit selections, two hitmaps with AMANDA hits are created from this set. To make the first, the standard AMANDA hitmap4 , time-window cleaning is performed with a 4

(47) s window, followed by a space-time cut that requires every hit to be within 150 m and 500 ns of another hit. The second hitmap, the auxiliary AMANDA hitmap5 , is created by instead applying local coincidence conditions on the hits, followed by time-window cleaning at 6

(48) s. The local coincidence system built into the IceCube DOMs ensures that the reported hits have a very high probability of being caused by Cherenkov light in the ice. In contrast, AMANDA hits have a high noise content and therefore need more software-based cleaning.. Reconstructions Each of the three hitmaps created above will be the base for a track reconstruction. The angular resolutions of these tracks, defined as the median angular deviation from the Sun, are shown for one signal case in Table 3.1 at an early analysis level (L3) and after the final event selection. It should be noted that a more detailed account of the reconstruction methods mentioned here is given in Chapter 6. The standard IceCube track6 is a log-likelihood (LLH) fit from 32 iterations, seeded by a Linefit track (a first guess algorithm). The standard AMANDA track7 is also a 32-iteration LLH fit, but seeded by a JAMS track (another first guess algorithm). The auxiliary AMANDA track8 is a one-iteration LLH fit, seeded by a Linefit track, with an additional error-estimating fit applied (called the Paraboloid fit). The number of iterations in the fit is a trade-off between fit quality and processing time.. 3. Internally called MuonTWCleanPulseSeries. Internally called JAMSCleanIsolatedPulses. 5 Internally called CoincifyCombinedTWPulses. 6 Internally called SPEFit32. 7 Internally called JamsSPEFit32. 8 Internally called CombinedSPEFitParaboloid. 4. 31.

(49) IceCube standard AMANDA standard AMANDA auxiliary. Success rate L3 94% 87% 85%. Resolution L3 Final ı 6.6 2.2ı 35ı 8.3ı 40ı 10ı. Table 3.1: Success rate and angular resolution for reconstructions used in the analysis of IC40 data, evaluated on simulations of WIMPs with mass 1000 GeV annihilating in the Sun through the channel W C W . 3.5. The ice. The ice of the Antarctic glacier is the largest component of the IceCube detector and understanding this medium is still an ongoing effort. The age of the ice is depth dependent, with varying densities of dust impurities reflecting changing atmospheric conditions. The oldest ice, just above the bedrock at a depth of 2820 m, is believed to have formed about 165,000 years ago [54]. The transparency of the ice depends on how photons are scattered and absorbed. The total travelled distance where the photon survival probability has been reduced to 1=e defines the absorption length, a . The scattering length, s , is the average distance travelled before a photon is scattered. To account for the average scattering angle, described by hcos i and typically 0.94 in our case, we define the effective scattering length e as the distance travelled before the photon direction is randomised. For a large number of scattering events this can be written [55] as e D. s : 1  hcos i. (3.7). Of all known solids, available in large quantities, the South Pole ice is probably [55, 56] the most transparent medium for wavelengths between 200 and 400 nm. The transparency peaks close to 400 nm where the combination of the DOM glass, gel and PMT is most sensitive. The long average absorption length in IceCube, measured to be a  110 m, facilitates event energy estimations and the detection of faint light. In comparison, the effective scattering length is rather short at e  25 m. The dust concentration is highest in a depth band between 2000 and 2100 m, but the ice below this dust layer is the clearest of all depths. It is estimated [57] that this deep ice has a  190 m and e  50 m, which is exploited by the DeepCore subarray which mostly instruments this area.. 32.

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(56) 4. Signal and background. The aim of the work in this thesis is to search for a weak signal hidden in a background of atmospheric muons and neutrinos at least a billion times larger. It is therefore appropriate to describe in this chapter the physics giving rise to signal and background, and how they are treated in simulations. We will end with an account of how triggered events in general are created in the simulation software.. 4.1. Simulation overview. In experimental particle physics a massive effort is usually put into generating simulated data using Monte Carlo (MC) techniques. One typical reason is to test and to find the optimal design of a detector that is yet to be built. A second reason is to study and better understand the background in an experiment. A third reason is to see what a desired signal would look like. Since the signal is a very small part of the data before the final event selection, we use experimental data as background in the dark matter search presented here. This means that background MC is not necessary for modelling and understanding our background, but is merely used to confirm that the general simulation software is producing sensible results. If data and background MC agree at a reasonable level, we can be confident in the parts of the software that are also used in signal simulation. These parts, describing particle propagation in the ice and detector simulation, are described below in Section 4.5.. Weights Simulated events are in general given weights, for reasons related to computational efficiency. When simulating neutrinos we will force them all to interact with nuclei in the ice and let the weights reflect the actual probability for this to happen, given the relevant cross-sections. If the region of interest lies in the high-energy part of the power-law spectra describing the atmospheric background, a flatter distribution can be simulated with increased high-energy statistics, letting the weights account for the deviation from the physical distribution.. 35.

(57) 4.2. The atmospheric background. Almost all of our background consists of muons and neutrinos that are created when cosmic rays hit the upper layers of the atmosphere. When cosmic rays (protons here, but the effect of heavier nuclei is similar) interact with a nucleon N , a common reaction is pCN !.  ˙ .K ˙ / C X ,!

(58) ˙ C  .N  / ,! e ˙ C e .N e / C N  . /,. (4.1). where X represents one or more hadrons. This neutrino flux, from pion or kaon decays, is called the conventional flux. If the reaction instead goes via short-lived charmed hadrons, the prompt process, the resulting energy spectrum will be flatter, since these short-lived particles decay before they have time to interact and lose much energy. Since the muons are relatively heavy and long-lived at 2.2

(59) s, a large fraction will reach the Earth’s surface and some may even penetrate a couple of kilometres of ice. Figure 4.1 shows to the left the abundance of various particles as the shower moves down through the atmosphere. Muons and neutrinos dominate at surface level and any hadrons, electrons or photons that are still present at this level will be completely gone deep down in the ice. Measurements of the

(60)  flux above 1 GeV are shown together with predictions based on a simplistic analytical model that is expected to be accurate only at high altitudes [17]. The flux of primary1 cosmic-ray particles is very close to isotropic, but since muons cannot penetrate more than a few kilometres of rock, the Earth blocks all muons from the northern hemisphere from reaching IceCube. The most effective way for removing the muon background is thus to only allow up-going events; in principle these will all be neutrinos if the reconstruction is reliable. The Earth is still transparent for neutrinos below 10 TeV. The right plot of Figure 4.1 shows the muon flux as function of depth below the surface. At around 20 km of water equivalent the flux becomes constant and only contains isotropic neutrinoinduced muons. Because of the tiny cross-section for neutrino-nucleon interactions, the background in the detector is still dominated by muons; only about one trigger in 106 is a neutrino event. The muon flux depends on atmospheric conditions and a seasonal variation of 10% in the trigger rate has been seen in IceCube [58].. 1. A primary will in this thesis denote any particle reaching our atmosphere. Technically, a cosmic-ray primary is created in an astrophysical source, yielding secondary particles in interactions with the inter-stellar medium.. 36.

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(67)  . . . . . . . .   

(68)   . Figure 4.1: Left: Particle fluxes from cosmic-ray showers above 1 GeV, derived from a simple analytical model, as function of altitude. The points show measurements of

(69)  . Right: The muon flux as function of depth below ground (or ice), with neutrinoinduced muons in the horizontal band. The centre of IceCube lies at about 1.8 km water equivalent. Both figures taken from Ref. [17], where more details can be found.. Simulating atmospheric muons Atmospheric muons are simulated by letting cosmic-ray primaries interact with the upper layers of the atmosphere. This is done with the MC event generator CORSIKA2 [59]. The cosmic ray spectrum and composition was taken from the polygonato model of Hörandel [60], which uses individual spectra and spectral breaks for each element from proton up to (in our case) iron. CORSIKA propagates particles down to the ice surface using a parametrised atmospheric model corresponding to a South Pole atmosphere in October 1997. The muon part of the shower is then brought through the ice down to the detector with the software MMC3 [44]. Muons belonging to independent showers can enter the detector within the same event readout window. These coincident events were simulated in separate samples. About 10% of the triggered events in IC40 are estimated to be double coincident events.. 2 3. COsmic Ray SImulations for KAscade Muon Monte Carlo.. 37.

(70) Figure 4.2: The atmospheric neutrino spectrum, between 332 GeV and 84 TeV, as measured by IC40 (black lined area). Also shown is the spectrum measured by AMANDA , an unfolding from IC40 data and the model of Honda et al. Figure taken from [64].. Simulating atmospheric neutrinos In the atmospheric neutrino simulation, the conventional flux model of Honda et al. [61] was used together with the prompt model of Enberg et al. [62]. Figure 4.2 shows a measurement [63] of the atmospheric neutrino spectrum between 100 GeV and 400 TeV, together with models. The prompt component is believed to become significant above ~100 TeV. Event samples are produced with the MC event generator ANIS4 [65] with an E 2 spectrum that was later reweighted to match the models above. ANIS creates each neutrino on a random spot on the surface of the Earth, at sealevel. It then propagates the particle through the Earth towards the detector and finally makes the neutrino interact in a specified volume, passing the charged leptons to MMC. ANIS does not include neutrino oscillations.. 4.3. Other background sources. Cosmic rays also interact with the atmosphere of the Sun and neutrinos from these interactions could be a potential background source for this analysis [66]. The number of expected events in our final sample was calculated based on estimations in Ref. [67] and was found to be much less than one. The Sun’s fusion processes are a steady source of electron-neutrinos, but their energies up to ~10 MeV are much too low to trigger our detector. This is also true for all nuclear processes on Earth. 4. All Neutrino Interaction Simulation.. 38.

(71) High-energy neutrinos from cosmic sources are also expected, but recent searches with IceCube conclude [68, 69, 64] that this flux is negligible compared to the atmospheric flux. The Sun will absorb cosmic-ray primaries and cast a certain cosmic-ray shadow upon us, reducing the muon flux in the ice slightly in this direction. A similar effect can be seen in the direction of the Moon [70], if explicitly searched for. With our low-energy event selection the effect is, however, negligible for this analysis. In a simple estimate, the reduction would be R. 2 ˇ ; ‰2. (4.2). where the angular radius of the Sun is ˇ  0:25ı and ‰ is the opening angle of the search cone. Using our best possible resolution in this analysis, a reasonable selection would be ‰ D 4ı and so R < 0:4%.. 4.4. Signal. Dark matter and Solar WIMPs were discussed in general terms in Chapter 2; it only remains now to detail the models that we simulate, and describe how they are simulated.. MSSM The branching ratios for the neutralino annihilations are heavily model dependent. It is possible, but very time-consuming, to scan parts of the parameter space — and such a scan is indeed used later in Chapter 11 where the result of the dark matter search is put into context — but when it comes to running a full-blown MC simulation it is not feasible to test more than a few different models. Since our detector is only sensitive to a particle’s energy and direction, we will look at the resulting neutrino spectra. The softest possible spectrum N and the hardest from  ! W C W  . comes from the channel  ! b b, These will in the remainder of this thesis be called simply the soft and the hard MSSM channel. If m < mW , the channel  !  C   will be used instead for the hard spectrum. Figure 4.3 shows the neutrino spectra from a selection of WIMP channels.. Kaluza-Klein We consider a model with 5-dimensions described by the mass m.1/  of the lightest Kaluza-Klein Particle (LKP), the first “photon” excitation of the B field , and the mass splitting q .1/ D .mq .1/  m .1/ /=m .1/ , where mq .1/ is. 39.

(72) 10. WIMP neutrino energies before trigger. -1. 50 soft 100 soft 500 soft. 10. 500 hard. -2. 500 KK. a.u.. 1000 hard. 10. 10. -3. -4. 10. 0. 10. 1. 10. 2. 10. 3. Energy (GeV). Figure 4.3: Simulated WIMP neutrino energies in the detector, before triggering. The labels indicate WIMP mass in GeV and annihilation mode.. the mass of the first quark excitation. We follow Ref. [71] in setting q .1/ D 0, which leads to a specific set of branching ratios [72], that defines our signal. The neutrino spectrum from LKP annihilations, for a given LKP mass, is very similar to the hard spectrum from neutralino annihilations in MSSM. This can be seen for the mass 500 GeV in Figure 4.3. For this reason, analysis methods will be developed for the MSSM channels and only applied to the LKP s in the end.. WIMP simulations The MC events were generated with WimpSim5 [73] together with DarkSUSY6 [74], with a neutrino energy threshold at 1 GeV. WimpSim uses Pythia7 [75] for generating annihilation products in the Sun, makes them interact and/or decay and collects the resulting neutrinos. These are propagated to the surface of the Sun and on to our detector, using the Nusigma8 package [73] for neutrino-nucleon interactions. Neutrino oscillations along the way are taken into account, with a standard set of oscillation parameters:. 12 33.2ı 5. 13 0.0ı. Version 2.07. Version 4.1.6-lite. 7 Version 6.400. 8 Version 1.14-pyr. 6. 40. 23 45.0ı. ıCP 0.0. m221 8.1105 eV2. m231 2.2103 eV2 .. (4.3).

(73) . . . . .    .   . . . 

(74)    . . . . .   . . . . . . . . . 

(75)    . .      . .   . . . . . . .  

(76)   . Figure 4.4: Left: Muon energy versus neutrino energy. Right: Muon scattering angle versus muon energy. Shown is a 1000 GeV WIMP, hard channel, at the interaction vertex before detector triggers.. Here, 12 , 13 and 23 are the mixing angles, ıCP is the CP -violating phase and m221 and m231 are squared mass differences. Normal hierarchy was assumed in these simulations, so m231 > 0. In the detection volume, the neutrino is forced to interact either through a charged current or a neutral current, leaving a charged lepton and/or a hadron shower at a vertex close to the detector. Weights are stored for each event to account for the neutrino-ice interaction probability. This work will mostly be considering  events, where the outgoing muon shares the neutrino energy and momentum with a hadronic shower. The muon energies and scattering angles can be seen in Figure 4.4 for the hard channel of a 1000 GeV WIMP.. 4.5. The IceCube simulation chain. The IceCube simulation package IceSim9 consists of a chain of software modules which are applied in sequence to each MC event.. Physics simulation When a charged particle, from any of the MC event generators, has been placed in the ice near the detector, the particle (usually a muon) will be further propagated with the software MMC [44]. The number of calculated interactions needs to be minimised for computational efficiency, so the code approximates small energy losses as one continuous process. The emitted photons are not tracked individually. Instead, photon fluxes and photon arrival-time distributions, at points in a volume of ice, are read 9. Version V02-03-02RC.. 41.

(77) from large tables. These are constructed by the program Photonics [76] in detailed MC simulations, with a set of given sources of light and a model of the medium.. Detector simulation The number of expected photoelectrons at each PMT photocathode is calculated using the Photonics tables, along with the expected time distributions. Random hits, representing dark noise, are added, and the PMT response to individual photoelectrons is simulated. For hits in IceCube, the PMT pulse is fed into a module where the digitisation on the DOM mainboard is simulated, together with the local coincidence test. Finally, IceCube and AMANDA trigger conditions are applied and the triggered events are saved. These will be exposed to an almost identical copy of the online processing and filtering, described in Section 3.4.. 42.

(78) 5. An AMANDA trigger study. In 2007 IceCube was running with 22 strings and already much bigger than AMANDA , which was still planned to be taking data for three more years. At this point the epoch of using new AMANDA data for energies above a few TeV had passed, leaving that field to IceCube’s larger effective (and absolute) volume. The sensitivity to an E 2 point-source flux of  was shown to be twice as strong for IC22 with 0.75 years of data than for 3.8 years of AMANDA data [77]. But for lower energies — typically below 100 GeV, the focus region of this thesis — AMANDA’s shorter inter-string distance (40 m compared with 125 m in IceCube) and inter-OM distance (around 11 m compared with 17 m in IceCube) still made it the more capable detector. Since AMANDA had now become less valuable as a high-energy detector, it was argued that the AMANDA triggers should be optimised as much as possible for low energies, aiming for low-mass WIMPs. Thanks to the introduction of the TWR system in 2003, replacing the old muon-DAQ for good in 2007, the AMANDA DAQ could now be expected to handle an increased trigger rate and so began the study presented in this chapter. By modifying the string trigger in simulations, the expected yield from low-mass WIMPs was examined together with the impact of the optimisation on  events in general.. 5.1. Triggers in 2007. The final triggers in 2008 were listed in Section 3.3, but let us turn the clock back one year. During the data year of 2007, AMANDA had the following triggers:  Multiplicity 18 (M18). Accepting events with at least 18 hit OMs in total.  Multiplicity 13 (M13). Sends events with at least 13 hit OMs to the following two software triggers: – Fragment trigger. Accepts events with at least 20 fragments in total, a fragment being a time-localised PMT pulse. – Volume trigger. Accepting events with 4 pairs of OMs hit within a sphere of 60 m radius.  String trigger. Described in Section 3.2. In 2007 it was set to 6-out-of9 for strings 1–4 and 7-out-of-11 for strings 5–19, with the time window t D 2:5

(79) s. String trigger configurations like this will hence be identified as (6/9, 7/11). 43.

(80) 5.2. Simulation. In this simulation study a few different string trigger configurations were tested, and the performance was evaluated both for a 100 GeV WIMP signal with a soft spectrum, and for a generic sample of  events. Different settings were used for the inner (1–4) and outer (5–19) strings, because of differences in OM spacing and cable properties. The trigger efficiencies were compared with the baseline, i.e., the 2007 settings (6/9, 7/11) with t D 2:5

(81) s.. Muon neutrino simulation The  energies were fixed between 10 GeV and 10 TeV, and the zenith angles were fixed in the range 0–180ı while the azimuth angles were randomised. The trigger efficiency, defined simply as trig D. # Triggered events ; # Generated neutrinos. (5.1). is shown in Figure 5.1. The relative efficiency for a given configuration is now trig rel D baseline ; (5.2) trig presented in the lower part of Figure 5.1 for the case of (3/5, 3/3). The difference is most visible at the very lowest neutrino energies. Monte Carlo events with a very small amount of deposited light — these are typically energies below what AMANDA was designed for — are very time consuming to generate, and the statistics is therefore quite low in this sample. To get a picture of how much the string trigger contributes, compared with the other triggers (M18, Volume and Fragment), Figure 5.2 shows that for all energies the string-triggered fraction goes up markedly from the baseline to the scenario (3/5, 3/3) and for the lowest energies the new string trigger dominates alone.. WIMP signal simulation In the next part of the study, the signal channel of a 100 GeV WIMP with a soft spectrum was tested. The spectrum of this channel can be seen in Figure 7.3. To raise the proportion of physical triggers over noise triggers and still keep the trigger rate within the capacity of the DAQ, a multiplicity condition on the total number of hits in AMANDA was used in coincidence with the string trigger. Events now need to pass the string trigger and have at least M hits in total within the time window. Two possible time windows were tested, as a shorter window of 1

(82) s would give a lower rate of down-going muons. The efficiency improvement for different values of M is shown in Table 5.1 44.

(83) 6/9-7/11, Trigger efficiency. Zenith. . 10-1.   . 10-2.  . . 10-3.   . 10-4.  . . . . . .    . GeV. 3/5-3/3, Trigger efficiency relative 6/9-7/11.    . .    .  .

(84) . 

(85) . 3/5-3/3, Trigger efficiency relative 6/9-7/11         .  . .  . . . . . .    . 

(86).   . . . . . . . . 

(87) !. Figure 5.1: Top: Trigger efficiency trig for the baseline scenario as a function of  energy and zenith angle. Bottom: Relative efficiencies for the configuration (3/5, 3/3), as a function of zenith and energy to the left, and averaged over zenith to the right.. 5.3. Conclusion. After some discussions at the end of 2007 a formal proposal [78] was submitted to the IceCube TFT board. At this point it was still unknown how the AMANDA DAQ would respond to an increased trigger rate, or what the maximum technically possible rate could be. In December 2007 tests were performed live at the AMANDA counting house, MAPO, examining the impact on the rate and stability from modifications to the trigger. In the end, the TFT board approved a change of settings and in April 2008, just before the new IceCube data-year was to begin with IC40, AMANDA started running with the triggers described in Section 3.3.. 45.

(88) 180. Zenith. Zenith. 180 162. 162. 144. 144. 126. 126. 108. 108. 90. 90. 72. 72. 54. 54. 36. 36. 18. 18. 0. 0. 10. 21. 46. 100. 210. GeV. 460. 10. 21. 46. 100. 210. 460. GeV. Figure 5.2: Trigger type distribution in the baseline, (6/9, 7/11), to the left and for (3/5, 3/3) to the right. The trigger type is shown as pie charts, as a function of neutrino energy and incoming direction.. 3/5, 3/5, 3/5, 3/5, 4/7, 4/7,. 3/5 3/5 4/7 4/7 5/9 5/9. t (

(89) s) 2.5 1.0 2.5 1.0 2.5 1.0. M 0 0 0 0 0 0. rel 3.5 3.0 2.3 1.6 1.4 0.9. M 5 5 5 5 5 5. rel 3.3 3.0 2.1 1.6 1.4 0.9. M 11 11 11 11 11 11. rel 1.5 1.2 1.5 1.2 0.9 0.6. Table 5.1: Efficiency of string trigger configurations, rel , with respect to the baseline at (6/9, 7/11) with t D 2:5

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