IceCube-86 IceCube-22 log$_{10}$(E /GeV) A eff (m 2 ) 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 1 10 2 10 3 10 -3 10 -2 10 -1 0 2000 4000 6000 8000 10000 E( ) (GeV) 1/N dN/dE (GeV -1 ) E  at center of the Sun E  at detector FIG. 4: Neutrino effective area of IceCube, both the 22-string detector and an estimation for the planned 86-string final con- figuration, as a function of neutrino energy. FIG. 3: Muon-neutrino energy distribution from top decays at the center of the Sun (dashed) and at the IceCube location (full line), after energy losses and oscillations have been taken into account. 3 The neutrino spectrum from simpzilla annihilations is modeled as producing a pair of quarks or gluons, which will fragment into high multiplicity hadronic jets. Long- lived light and charmed hadrons will lose energy through interactions in the dense solar interior before decaying, producing low energy neutrinos. On the other hand, due to its short lifetime, ∼ 10 − 25 s, the top quark will not have time to hadronize or lose energy through interac- tion in the medium before decaying into W b . The W then decays into lν$_{l}$ , with similar probability into each flavour l = e, µ, τ . Annihilations into top quarks is there- fore a promising channel to produce high energetic neu- trinos detectable by neutrino telescopes. Bottom quarks are also a potential source of high energy neutrinos [6]. However in this work we only consider neutrinos pro- duced from the top decay chain, which makes our results conservative. Note that although the initially available energy for each top is very high (the mass m$_{X}$ of the sim- pzilla), the available phase space is shared among many $^{produced particles (2.8}$×10 5 √ m$_{X/12}$ tops are produced per annihilation [6], where m$_{X/12}$ is the mass of the sim- pzilla in units of 10 12 GeV), so the average energy per produced particle is of O (TeV). The main consequence of this is that initial-state gluon radiation can be neglected, not playing an important role in further degrading the energy of the tops before they decay. This is illustrated in Figure 2, which shows the energy distribution of the tops at the production point (dashed line) and just be- fore decaying (full line), obtained with a full PYTHIA [19] simulation. Taking into account the above considerations, the en- ergy distribution of the neutrinos produced from top de- cays at the center of the Sun can be parametrized as The energy dependence of the neutrino flux at the de- tector (Earth) will be modified by neutrino energy losses in their way out of the Sun and by oscillations. In order to include these effects we use the publicly available Wimp- sim code [20], which we have modified so it takes the neu- trino spectrum from equation (4). We use as input the three flavours with their correct relative intensity from the top decay chain. Figure 3 shows the injection spec- trum of muon neutrinos at the Sun from simpzilla anni- hilations according to equation (4) (dashed line), and the resulting spectrum at the Earth (full line). The injection spectrum has been truncated at 10 TeV for display pur- poses. As mentioned earlier, the initial energy available in the annihilation is shared among an enormous amount of annihilation products and, furthermore, the energy of the resulting neutrinos is further reduced by energy losses in the Sun. The spectrum at the detector is therefore not very different from those of lighter dark matter can- didates, like MSSM neutralinos or Kaluza-Klein modes. This allows us to use IceCube-22 background determina- tion found in both WIMP and Kaluza-Klein dark matter analysis [17, 18]. Since IceCube is mainly sensitive to muon neutrinos through the detection of muon tracks, we only use the muon-neutrino flux at the detector for our calculations in what follows. where m$_{W}$ and m$_{t}$ are the W boson and top quark masses respectively, and we have omitted a constant normaliza- tion factor. dN dE$_{ν}$ ∝ E$_{ν}$ + m$_{W}$ √ ( E$_{ν}$ + m$_{t}$)[( E$_{ν}$ + m$_{t}$) 2 − m 2 $_{t}$][( E$_{ν}$ + m$_{W}$) 2 − m 2 $_{W}$] (4)