4 structure [24]. We also assume the DM infinity velocity distribution is a Maxwell-Boltzmann dis- tribution which depends on parameters v$_{⊙}$ and v$_{0}$ . As discussed in Ref. [15], if these two parame- ters vary in the region of 200 km/s < v$_{⊙}$, v$_{0}$ < 300 km/s, the capture rate will be changed by a factor less than two. One should also notice that, if the velocity distribution deviates from an ordi- nary Maxwell-Boltzmann distribution, the result will also be changed. In our discussions, for sim- plicity, we assume the solar chemical composition does not change in the Sun. The capture rate is sensitive to the abundance of heavy nuclei and in- creasing the number density of heavy nuclei in the center of the Sun will increase the overall capture rate by a few [15]. There are also uncertainties aris- ing from the nuclear form factor. For the SI scat- tering, the Helm form factor we used in the calcu- lation is less accurate at large momentum transfers and might be improved by using some more precise form factors [25]. For the SD scattering, the nu- clear structure functions in Ref. [21] are only con- sidered for direct DM search on the Earth, so the q$_{max}$ used in the finite momentum transfer approx- imation may not be large enough for DM-nucleus scattering in the Sun if our DM is heavy. III. LIMITS FROM THE NEUTRINO TELESCOPES FIG. 1: Capture rate of 50 GeV spin-independent iDM with DM-nucleon cross section of σ SI n ∼ 10 − $^{4}$pb as a function of the mass splitting δ due to different species of nuclei in the Sun. We choose ρ$_{χ}$ = 0 . 3 GeV cm − $^{3}$, v$_{⊙}$ = 220 km/s and v 0 = 220 km/s in the Maxwell- Boltzmann distribution. GLYPH<s32> FIG. 2: Capture rate of 50 GeV spin-dependent iDM with σ SD n ∼ 10 pb as a function of the mass splitting δ due to different species of nuclei in the Sun. 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The capture rate is always sensitive to the abundance of heavy nuclei. Finally, we give some short comments on the possible uncertainty in the calculation for solar DM capture rate. The input astrophysics parameters are the local DM mass density ρ$_{χ}$ , velocity of the Sun v$_{⊙}$ , average local circular velocity v$_{0}$ , and so- lar elemental abundances ϵ$_{i}$ . The capture rate is proportional to ρ$_{χ}$ and the results will increase if a larger local DM mass density is available [23] or the solar system is passing through DM sub- The different DM annihilation channels give dif- ferent initial neutrino spectra [26]. If the DM anni- hilates to e $^{+}$e − or µ $^{+}$µ $^{−}$, they will not contribute to neutrino signals. This is because for muons, they always lose most of their energy before de- caying in the center of the Sun. For annihilation channel to τ $^{+}$τ $^{−}$, the neutrinos are induced by τ leptonic decays τ → µνν , eνν , and hadronic de- cays such as τ πν , Kν , ππν et al. For the heavy final annihilation states W $^{+}$W $^{−}$, ZZ , t ¯ t , they produce neutrinos via cascade decays and the neutrino spectra for such channels are hard. For quark channels, the hadronization process pro- duces mesons and baryons, and then induces neu- trinos via hadron decays. The neutrino spectra for such channels are soft. Notice that the light mesons easily lose their energy before decays, so Γ$_{A}$ = C$_{⊙}$/ 2 (17)