We report constraints on the sources of ultrahigh-energy cosmic rays (UHECRs) above 10^{9}  GeV, based on an analysis of seven years of IceCube data. This analysis efficiently selects very high- energy neutrino-induced events which have deposited energies from 5×10^{5}  GeV to above 10^{11}  GeV. Two neutrino-induced events with an estimated deposited energy of (2.6±0.3)×10^{6}  GeV, the highest neutrino energy observed so far, and (7.7±2.0)×10^{5}  GeV were detected. The atmospheric background-only hypothesis of detecting these events is rejected at 3.6σ. The hypothesis that the observed events are of cosmogenic origin is also rejected at >99% CL because of the limited deposited energy and the nonobservation of events at higher energy, while their observation is consistent with an astrophysical origin. Our limits on cosmogenic neutrino fluxes disfavor the UHECR sources having a cosmological evolution stronger than the star formation rate, e.g., active galactic nuclei and γ-ray bursts, assuming proton-dominated UHECRs. Constraints on UHECR sources including mixed and heavy UHECR compositions are obtained for models of neutrino production within UHECR sources. Our limit disfavors a significant part of parameter space for active galactic nuclei and new-born pulsar models. These limits on the ultrahigh-energy neutrino flux models are the most stringent to date.

IceCube is a neutrino observatory deployed in the glacial ice at the geographic South Pole. The νμ energy unfolding described in this paper is based on data taken with IceCube in its 79-string configuration. A sample of muon neutrino charged-current interactions with a purity of 99.5% was selected by means of a multivariate classification process based on machine learning. The subsequent unfolding was performed using the software Truee. The resulting spectrum covers an E ν -range of more than four orders of magnitude from 125 GeV to 3.2 PeV. Compared to the Honda atmospheric neutrino flux model, the energy spectrum shows an excess of more than 1.9σ in four adjacent bins for neutrino energies Eν≥177.8TeV . The obtained spectrum is fully compatible with previous measurements of the atmospheric neutrino flux and recent IceCube measurements of a flux of high-energy astrophysical neutrinos.

We present the development and application of a generic analysis scheme for the measurement of neutrino spectra with the IceCube detector. This scheme is based on regularized unfolding, preceded by an event selection which uses a Minimum Redundancy Maximum Relevance algorithm to select the relevant variables and a random forest for the classification of events. The analysis has been developed using IceCube data from the 59-string configuration of the detector. 27,771 neutrino candidates were detected in 346 days of livetime. A rejection of 99.9999 % of the atmospheric muon background is achieved. The energy spectrum of the atmospheric neutrino flux is obtained using the TRUEE unfolding program. The unfolded spectrum of atmospheric muon neutrinos covers an energy range from 100 GeV to 1 PeV. Compared to the previous measurement using the detector in the 40-string configuration, the analysis presented here, extends the upper end of the atmospheric neutrino spectrum by more than a factor of two, reaching an energy region that has not been previously accessed by spectral measurements.