Based on numerous observations from cosmology and astronomy, dark matter (DM) is believed to constitute over ∼80% of all matter in the universe [1][2][3][4]. The quest to establish the particle nature of DM is also tied to observations in high energy astrophysics, including observations in neutrinos. The search for neutrinos produced by annihilations or decays of DM is one major aspect of indirect detection of DM from astrophysical objects. The Sun is particularly well suited for such searches as it has been gravitationally capturing candidates for DM particles such as weakly interacting massive particles (WIMPs) from the surrounding halo for its entire lifetime of 4.5 billion years [5][6][7][8][9]. These particles accumulate in the Sun, where they annihilate into standard model (SM) particles as their density builds up. This process provides a route to studying WIMP interactions with nucleons since there is time for equilibrium to be established between captures and annihilations [10][11][12][13][14].
Given the high matter density of the Sun, the only SM particles that can escape the Sun with relatively little attenuation are neutrinos [15][16][17][18][19][20][21]. (Secluded DM models where DM annihilation proceeds via a long-lived mediator which can decay outside the Sun into SM particles, also allow for the production of gamma rays in addition to neutrinos correlated with the direction of the Sun [21][22][23][24][25][26][27][28][29][30][31][32]). Several experiments including Super-Kamiokande [33], IceCube [34,35] and ANTARES [36,37] have looked for neutrino signatures of DM annihilation in the Sun. These searches are especially useful for probing spin-dependent DM-proton scattering cross sections, and have already outperformed direct detection experiments by more than an order of magnitude in terms of sensitivity. IceCube's previously published searches using three years of data already result in the world's best constraints on the spindependent scattering cross section for DM mass in the range Oð100Þ GeV to 10 TeV.
Due to IceCube's optimal sensitivity to TeV-PeV neutrinos, the detector's probing of DM parameter space below 50 GeV has been limited up until now, while a large parameter space for GeV WIMPs remains unconstrained [38]. This work for the first time extends IceCube's reach to 5 GeV DM masses for some of the studied annihilation channels. The paper is structured as follows. Section II describes the IceCube detector and the process of data selection used in this analysis. Section III presents the analysis, including the details of the signal and background estimation methods used. The results are discussed in Sec. IV. Section V presents our conclusions and places the results in context.
The IceCube Neutrino Observatory-located at the South Pole-consists of an array of 5160 photodetectors on 86 strings embedded within 1 km 3 of the Antarctic ice. Each photodetector unit-known as a digital optical module (DOM)-is a downward facing photomultiplier tube (PMT) with associated electronics enclosed within a glass vessel [39]. The typical horizontal spacing between the strings is 125 m with 60 DOMs per string. The exception are the 8 strings in the bottom-center of the array known as DeepCore, which has a geometry optimized to lower the energy threshold of IceCube [40]. A higher density of high-quantum efficiency DOMs, coupled with the outer array acting as a veto region to reject atmospheric muons makes DeepCore particularly suitable for detecting neutrinos as low as ∼5 GeV in energy. A detailed description of the instrumentation and signal reconstruction can be found in Refs. [41,42].
We use IceCube and DeepCore data collected between January 1st, 2011 and January 1st, 2018 with a total livetime of 6.75 years. The event selection and reconstruction used in this analysis follows the same methods as those used in Ref. [43]. The IceCube DOMs surrounding the DeepCore volume are used to veto atmospheric muons. This is achieved by rejecting events in which photons in a certain time-window are observed outside before they are detected in DeepCore. The photoelectrons detected within the DeepCore volume are fitted using a multidimensional likelihood to estimate the energy and direction of a neutrino event. Each event is classified as either "tracklike" or "cascadelike", depending on whether the fit is better described by a ν μ charged-current (CC) interaction, or a hadronic shower with no muon resulting from neutral current interactions as well as ν τ =ν e CC interactions. An eleven variable boosted decision tree (BDT) is used to further reject atmospheric muons.
The two main differences in the event reconstruction with respect to that in [43] are at the final data reduction level and are discussed here. One, we no longer require that the stopping vertex of the reconstructed muon be contained within DeepCore. Two, the boosted decision tree (BDT) cut is loosened to allow additional particles in the data sample. The purpose of the aforementioned relaxed cuts is to enhance the overall number of neutrinos in the data at the cost of an increase of 13% background contamination with respect to that given in [43]. The final sample includes 192,212 events. This is also the first time that an IceCube analysis utilizes both "tracklike" and "cascadelike" events to search for dark matter. At the low energies considered in this work, tracks and cascades show negligible differences in their angular resolutions. The median angular resolution of events in this sample at 10 GeV is ∼35°and improves to ≤ 5°above 200 GeV.
We use an unbinned likelihood ratio method to search for neutrinos correlated with the direction of the Sun. The one-dimensional likelihood function is given by,
where n s is the number of signal neutrino events, N is the total number of data events, Ψ i is the angular distance between the reconstructed direction of the ith event and the direction of the Sun, SðΨ i Þ is the signal probability distribution function (PDF) for the ith data event, and BðΨ i Þ is the background PDF for the ith data event. Given the similar angular resolutions of tracks and cascades in this sample, the likelihood does not depend on eventtopology and tracks and cascades are treated identically. We also calculate a test statistic (TS), given by twice the logarithm of the ratio of the best-fit likelihood to the null (background-only) hypothesis,
where ns is the best fit value of the number of signal events. The modeling of the signal PDF from simulation and the background PDF from randomized data are described below.
A. Signal and background probabilities
We consider only DM masses higher than 5 GeV for which evaporation from the Sun is negligibly small [44,45]. Ignoring self-interactions, the number of DM particles in the Sun N χ ðtÞ is given by,
where Γ cap is the WIMP capture rate, and the second term expresses the annihilation rate in terms of a factor K ann , that accounts for the DM number density and the velocity-averaged annihilation cross section [46]. Once equilibrium has been reached between WIMP capture and annihilation rate, the capture rate and annihilation rate Γ ann are related by,
The factor of two accounts for the fact that every annihilation event involves two DM particles. The capture rate itself is a function of DM-proton cross section (σ SD spin-dependent and σ SI spin-independent). On the observable side, the neutrino/anti-neutrino flux at Earth from DM annihilation in the Sun dϕ ν =dt is given by,
where D is the Earth-Sun distance and dN ν =dE is the spectral energy distribution of the final-state neutrinos and anti-neutrinos produced as a result of DM annihilation. This means that using the measured flux of neutrinos and the assumed DM annihilation spectra, we can constrain the annihilation rate under equilibrium [Eqs. ( 4) and ( 5)], and therefore, the DM-proton cross section. We consider DM annihilation via three different channels: b b, ττ and νν. The annihilation spectra are modeled using WIMPSIM [31,47], while the neutrino interactions in the detector are simulated using GENIE [48]. At any given energy, we can weight the simulations by a desired flux model to calculate the total signal or background weights. The signal weight at a given energy is computed using the all-flavor neutrino spectrum from WIMPSIM for a given DM mass and channel, whereas the background weights are obtained from the atmospheric neutrino spectrum [49]. The signal PDF generation is a two-step process. First, for each annihilation channel and WIMP mass we determine an optimal range in reconstructed neutrino energy that maximizes the ratio of the summed signal weights and the square root of the background weights. Table I lists the optimal reconstructed neutrino energy ranges for each mass and annihilation channel. In the second step, we obtain the signal PDF by weighting the angular separation between the simulated neutrino and the reconstructed neutrino by the WIMPSIM flux at the given reconstructed neutrino energy. This procedure effectively assigns a higher weight to the neutrinos in the optimized energy range and a directional correlation with the Sun. Figure 1 (left panel) illustrates the signal and background PDFs as a function of the angular separation from the Sun.
The background PDFs are parametrized as a function of the angular separation from the Sun. For every event in the data, 30 azimuth angles are randomly sampled from a uniform distribution. These 30 angles are then combined with the Sun zenith angle to generate a random "fake" Sun position vector. The angle between the reconstructed neutrino direction and the randomized Sun direction is then used to fill the background PDF histogram. This process ensures that for any given position of the Sun, the background is estimated by randomizing the event directions with respect to the trajectory of the Sun (Fig. 1).
For all three annihilation channels, and DM masses between 5 GeV and 100 GeV (up to 500 GeV for crosschecks), we determine the best-fit number of signal event, n s that maximizes the likelihood in Eq. ( 1). We obtain no statistically significant deviation from the expected background for any of the masses and channels we scanned. Figure 1 (right panel) shows the observed distribution of events in a 200°by 180°region in Sun-centered coordinates. The highest TS obtained for any test was 0.11 for a mass of 300 GeV with DM annihilating to τ þ τ -. We note that such an underfluctuation of data across all tests we performed is not unlikely given that the tests are highly correlated. From background-only simulations, we expect all masses for a given channel to show a TS ¼ 0, 5% of the time.
The results presented in this work are sensitive to systematic uncertainties due to detector effects. The systematic uncertainties affect the overall event rate, as well as the angular and energy resolutions in the analysis. In order to study how these effects propagate into the signal PDFs and finally the upper limits on the DMproton scattering cross section, we repeat all the analysis steps on several simulated datasets. Each simulation was produced by varying the parameters of photon propagation at the detector, the DOM efficiency and the models of hole-ice (surrounding the strings) and the bulk ice (between the strings) up to AE10%. We then compare the sensitivity obtained in these simulations to that obtained from the baseline case. Table II describes the effect on the sensitivity for each WIMP mass for the two most notable systematics, for annihilation to b b (other channels show similar trends). At low masses (10 GeV), the most dominant systematic-DOM efficiency [39]-degrades the sensitivity up to 20%. At 100 GeV, the biggest impact is due to the modeling of bulk ice properties, such as the scattering and absorption of photons by ice [50,51]. The effect is below 8%.
We set 90% upper limits on n s and the annihilation rate Γ ann [s -1 ] of DM. The limits on annihilation rate are then converted to limits on the spin-dependent and spinindependent DM-proton cross sections following [52]. Tables III and IV summarize these results. Figure 2 shows the limits on the spin-dependent cross section as a function of DM mass. For each mass, we show the least constraining limits as obtained under the largest systematic variation for the respective mass (Table II). The differences between the limits for different channels depend on their spectral energy distributions relative to IceCube energy threshold. The differences between the limits for different masses are related to IceCube's varying angular resolution with energy. In particular, poorer angular resolution (∼35°) for neutrinos below ∼10 GeV, results in an increased number of background events in the search region, worsening the limits for lower masses and softer channels. For any given channel, IceCube limits on the spin-dependent WIMP-proton cross section presented in this paper are world-leading and are the strictest so far among indirect DM search experiments. IceCube is particularly sensitive to direct annihilation of DM into neutrinos and the constraints for this channel are stronger than those obtained via direct detection [53].
The predicted flux of solar atmospheric neutrinos is, in principle, a background for dark matter searches from the Sun [55][56][57]. However, as shown in Ref. [58], IceCube is not yet sensitive enough to detect the expected flux of neutrinos from cosmic ray interactions in the Sun. In fact, compared to the sensitivity required [56,57], the cross section limits reported in this work are still nearly two orders of magnitude higher.
We present a new analysis of low-energy neutrino data from the IceCube DeepCore detector to probe spindependent dark matter-proton scattering and dark matter annihilation rate in the Sun. Our limits are some of the strongest in the world for a range of dark matter masses between 5 GeV and 100 GeV. The work demonstrates that neutrino telescopes even with limited statistics and angular resolution at low-energies can still provide a powerful probe of new physics. The DM limits are also a powerful probe of the coupling constants of the nonrelativistic effective field theory of dark matternucleon interactions, including velocity-and momentumdependent interactions [59].