Searching for eV-scale sterile neutrinos with eight years of atmospheric neutrinos at the IceCube neutrino telescope

We report in detail on searches for eV-scale sterile neutrinos, in the context of a 3+1 model, using eight years of data from the IceCube neutrino telescope. By analyzing the reconstructed energies and zenith angles of 305,735 atmospheric $ u_mu$ and $bar{ u}_mu$ events we construct confidence intervals in two analysis spaces: $sin^2 (2theta_{24})$ vs. $Delta m^2_{41}$ under the conservative assumption $theta_{34}=0$; and $sin^2(2theta_{24})$ vs. $sin^2 (2theta_{34})$ given sufficiently large $Delta m^2_{41}$ that fast oscillation features are unresolvable. Detailed discussions of the event selection, systematic uncertainties, and fitting procedures are presented. No strong evidence for sterile neutrinos is found, and the best-fit likelihood is consistent with the no sterile neutrino hypothesis with a p-value of 8% in the first analysis space and 19% in the second.