Sterile Neutrino Searches at the IceCube Neutrino Observatory

The IceCube Neutrino Observatory is capable of performing a unique search for sterile neutrinos through the exploitation of a matter enhanced resonant neutrino oscillation phenomena. As atmospheric muon neutrinos pass the dense material within the Earth, neutral current elastic forward scattering is predicted to induce a transition into a sterile state. This thesis presents two 3+1 sterile neutrino analyses by searching for spectral differences in the reconstructed energy and zenith direction of muon neutrino events, indicative of a transition into a sterile state. The first search probes the parameter space $\Delta$m$^2_{41}$ and sin$^2$(2$\theta_{24}$) with relevant sensitivity to the global best fit region for a 3+1 sterile neutrino hypothesis. The second search performs a scan through sin$^2$(2$\theta_{24}$) and sin$^2$(2$\theta_{34}$) in the oscillation averaged out region of high-$\Delta$m$^2_{41}$ ($\Delta$m$^2_{41}$ $\gtrsim$ 10eV$^2$). The analyses are performed using an improved event selection, which was found to extract 305,891 well reconstructed muon neutrino events with a sample purity above 99.9\%, from eight years of IceCube data. Novel simulation techniques, along with updated calibration, and a re-assessment of the systematic uncertainties are also discussed. The first analysis finds a best fit sterile hypothesis point at $\Delta$m$^2_{41}$ = 4.47eV$^2$ and sin$^2$($\theta_{24})$ =0.10, consistent with the no-sterile hypothesis at the 8\% confidence level. The second analysis finds a best fit sterile hypothesis at sin$^2$($\theta_{34})$ = 0.40, sin$^2$($\theta_{24})$ = 0.006, consistent with the null hypothesis at the 19\% confidence level. % and provides a significant improvement in the worlds measurements using muon neutrino disappearance.