Searches for sterile neutrinos with IceCube DeepCore

We show that study of the atmospheric neutrinos in the 10–100 GeV energy range by DeepCore sub-array of the IceCube Neutrino Observatory can substantially constrain the mixing of sterile neutrinos of mass $\sim 1$ eV with active neutrinos. In the scheme with one sterile neutrino we calculate ${\nu }_{\mu }-$ and ${\bar{\nu }}_{\mu }-$ oscillation probabilities as well as zenith angle distributions of ${\nu }_{\mu }^{CC}$ events in different energy intervals in DeepCore. The distributions depend on the mass hierarchy of active neutrinos. Therefore, in principle, the hierarchy can be identified, if ${\nu }_s$ exists. After a few years of exposure the DeepCore data will allow to exclude the mixing $\mathrm{\mid }{U}_{\mu 4}{\mathrm{\mid }}^2\ge 0.02$ indicated by the LSND/MiniBooNE results. Combination of the DeepCore and high energy IceCube data will further improve sensitivity to ${\nu }_s$ mixing parameters.