III. RESULTS FROM ICECUBE-22 The number of signal events, N$_{s}$, from simpzilla anni- hilations in the Sun predicted in a neutrino telescope of effective area A$_{eff}$ during an exposure time T, is given by where dN$_{ν}$/dE is the muon neutrino flux at the detector, N$_{t}$ is the number of tops per annihilation, BR$_{W}$ is the branching ratio of W decaying into neutrinos (0.326) and Γ$_{A}$ is the annihilation rate in the center of the Sun. The effective area is a measure of the efficiency of the detec- tor and includes the neutrino-nucleon interaction prob- ability, the energy loss of the produced muon from the interaction point to the detector and the detector trigger and analysis efficiency. In order to compare our expected signal with IceCube- 22 observations, we use the neutrino effective area of IceCube-22 published in [18], and shown in Figure 4. In 104.3 days of live time IceCube-22 has detected 13 events from the direction of the Sun, while the expected number of atmospheric neutrinos is 18.5 [18]. The expected sig- nal strength for the given live time is shown in Figure 5. We have assumed a 15% uncertainty in the expectation of the atmospheric neutrino flux at the relevant energies (E$_{ν}$ ≥ 50 GeV) in order to calculate the 90% CL upper limit on a possible signal, µ 90 s , following the prescription in [21]. We obtain µ 90 s = 3.1. A scan in the (m$_{X}$, σ$_{XN}$ ) pa- rameter space, selecting models that predict less events than µ 90 s leads to the 90% CL exclusion region shown in Figure 6 (read cross–hatched area). The results disfavour a large region of the parameter space, and we discuss their significance in section V. The sensitivity of the completed IceCube detector can be estimated from the expected number of background events (due to atmospheric neutrinos) and the detector effective area. An estimation of the expected effective area of IceCube-86 at trigger level has been given in [16]. Previous analyses of IceCube and AMANDA show that the effective area is reduced between a factor of 5 to 10 between trigger level and the final analysis level, due to the cuts that are applied to clean the data sets and se- lect high quality tracks. We have taken a conservative approach here and we have reduced the trigger effective area given in [16] by a factor between 15 for low energies down to 5 at the higher energies, and used that as our estimate of where the effective area of IceCube-86 at a final analysis level might be. The curve used is shown as the upper curve in Figure 4. We have calculated the number of atmospheric neu- We have used recently published results from the 22-string IceCube detector on WIMP dark matter searches [17, 18] to extend the search to strongly inter- acting dark matter candidates in the mass range ∼ 10 4 ≲ m$_{X}$ ≲ 10 15 GeV. The fact that the IceCube results are compatible with the expected atmospheric neutrino back- ground allows us to set restrictive limits on the mass ver- sus nucleon cross section parameter space. A note on the complementarity of direct and indirect trino events in IceCube using the measured atmospheric neutrino flux by AMANDA [22]. We parametrized the curve in Figure 10 in [22] as dN atm ν /dEdΩ = A E − γ GeV − 1 cm − 2 s − 1 sr − $^{1}$, with A=0.11407 and γ = 3.142. The expected number of atmospheric neutrino events in IceCube-86 from the direction of the Sun in a exposure time T is then given by N$_{ν}$ = T · ∫ dN atm ν /dEd Ω A$_{eff}$ dE d Ω, where the angular integration is performed over the 0.5 ◦ that the Sun subtends in the sky. We have assumed no contamina- tion of misreconstructed atmospheric muons in the final sample, and therefore we use only the 3.4 atmospheric neutrino events from the direction of the Sun predicted by the integral above in 365 days live time. As in the previous section, we have used a 15% uncertainty on the overall normalization of the atmospheric neutrino flux, as also indicated by the AMANDA measurement, and calculated the sensitivity including this uncertainty. The 90% CL exclusion region from IceCube-86 is shown in Figure 6 as the black line. It agrees well with the predic- tions made in [14]. 1 10 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 11 10 12 10 13 10 14 10 15 M  (GeV) Expected number of events in 104.3 days IC22 =10$^{-28}$ cm 2 =10$^{-26}$ cm 2 =10$^{-24}$ cm 2 =10$^{-22}$ cm 2 =10$^{-20}$ cm 2 4 N$_{s}$ ( m$_{X}$, σ$_{XN}$ ) = $^{N$_{t}$}$·$^{BR$_{W}$}$· Γ$_{A}$( m$_{X}$, σ$_{XN}$ $^{)}$· $^{T}$· ∫ dN$_{ν}$ dE A$_{eff}$ dE (5) FIG. 5: Expected number of events in the IceCube-22 detec- tor, in 104.3 days of lifetime. The rate is determined by our simulations and is shown for five different values of the cross section as labeled. V. CONCLUSIONS IV. SENSITIVITY OF THE COMPLETED ICECUBE-86 DETECTOR