7 channels and soft channels to b ¯ b and c ¯ c . For the iDM lighter than 100 GeV, comparing with FIG. 3 and 4 based on the Super-K 90% C.L. exclusion limit, we can see that the IceCube plus DeepCore also has capability to test or further constrain the iDM model with soft annihilation channels to b ¯ b and c ¯ c . the cross section is 10 5 times higher than the iSI DM case, we reach a similar conclusion that the limits are quite constraining on hard channels, are lessened in softer channels like c ¯ c and b ¯ b and are quite loose in the light quark channels. In order to see how the inelastic property of DM nucleus scattering changes the limits, we also calculate the Super-K limits on σ$_{n}$ · Br$_{i}$ to different annihila- tion channels for eDM. In the SI case, making the scattering inelastic changes the results at most an order of magnitude for reasonable δ . In the SD case, however, the limit is loosened by 3 orders of magnitude when hydrogen no longer contributes to the dark matter capture in the Sun. IV. NEUTRINO CONSTRAINT FROM TERRESTRIAL INELASTIC DARK MATTER ANNIHILATIONS 4 For the $_{b}$¯b and W $^{+}$W − channels, the constraints are available for DM heavier than 250 GeV and 500 GeV respectively. For the constraints to iDM, one can see the Ref. [15]. The escape velocity of the Earth v ≃ 10 km/s is very small compared to the escape velocity of the Sun ≃ 10 3 km/s and the velocity dispersion of local DM u ∼ ¯ v ≃ 270 km/s, so the right hand side of the where we use a similar notation as Ref. [16] χ ′ χ ′ 2 − > u 2 v 2 (22) χ ≡ m$_{χ}$ m$_{N}$ , s ≡ √ 1 − 2 δ/ ( µw $^{2}$) , (23) χ ′ − ≡ χ − s 2 , χ ′ ≡ χ ( 1 + s 2 ) + 1 − s 2 4 . (24) and But it is worth remarking, additional IceCube 6 special strings named DeepCore, are powerful to improve the capability of the detector and reduce the detection threshold down to 10 GeV [31, 32]. In the FIG. 6, we show the total number of events at the IceCube plus DeepCore. Here we use the effec- tive neutrino detection area of IceCube plus Deep- Core given by Ref. [32] to calculate the event rate at the detector. The number of background events from atmospheric neutrinos within a 3 ◦ window is estimated ∼ 50 in the energy range E ∼ (10 , 200) GeV. For heavy iDM m$_{χ}$ > 100 GeV, the IceCube plus DeepCore is very powerful to test most of the iDM annihilation channels, which include all hard Now we turn to Eq. (4) and (13) and see the first reason of suppression explicitly. We can rewrite Eq. (13) as Unlike the Sun, the main constituents of the Earth are heavy nuclei, such as O, Al, Si, Mg, Fe and Ni. Since the abundances of Fe and Al are 31.9% and 1.59% respectively, we expect that the abundance of such heavy elements helps the capture process. Nevertheless, probing neutrino signals from terrestrial iDM annihilations is more difficult than probing them from solar iDM annihi- lations. There are two main reasons for this. First, as a gravitational system, the Earth is far smaller than the Sun with a rather small escape velocity, so it is more difficult to trap DM in the center of the Earth. In the iDM scenario, the situation be- comes even worse due to the kinetic suppression induced by inelastic capture condition. Second, it is well known that terrestrial DM capture and an- nihilation processes can not reach equilibrium in the ordinary DM scenario, so the annihilation rate of DM trapped in the Earth is even smaller than half of the capture rate. The on-going large volume neutrino telescopes, such as IceCube and KM3NET, are more powerful to probe high energy neutrinos. IceCube located between depth of 1.45 km and 2.45 km in the south pole will have an effective detecting area of 1 km $^{2}$. In 2007, IceCube consisted of 22 strings has pro- vided a more stringent upper limit to muon flux from the Sun [30]. The main shortcoming of Ice- Cube 22-strings is its high energy threshold. So the experimental results are only useful to constrain the heavy DM $^{4}$. The complete detector consisted of 80 strings might reduce the energy threshold to 50 GeV. We need to notice that the effective de- tecting area of IceCube decreases rapidly in the low energy region. In addition, the angular resolution becomes worse in such energy region. So the capa- bility of IceCube to search for light DM is weaker than that for heavy DM.