## Introduction

The IceCube neutrino telescope at the South Pole has measured the atmospheric muon neutrino spectrum as a function of zenith angle and energy to search for the oscillation signatures of light sterile neutrinos. No evidence for anomalous *v*_{μ} or *v* –_{μ} disappearance is observed in either of two independently developed analyses, each using one year of atmospheric neutrino data.

The primary result of this search derives from the first year of data, taken during 2011, of the full 86-string IceCube configuration. This sample contains 20,145 reconstructed muons with energy between 400 GeV and 20 TeV, produced by the interactions of atmospheric neutrinos in the rock and ice below IceCube. Using this sample, the IceCube Collaboration has set limits on light sterile neutrinos in the mass range 0.1 eV^{2} < Δm^{2} < 10 eV^{2}, which extends to sin^{2}(2θ_{24}) ~ 0.02 at Δm^{2} = 3eV^{2}.

“Searches for Sterile Neutrinos with the IceCube Detector,” The IceCube Collaboration: M.G.Aartsen et al. *Physical Review Letters* 117, 071801 (2016). DOI: http://dx.doi.org/10.1103/PhysRevLett.117.071801

See paper on the PRL site or arXiv.

## Data release

Search for sterile neutrinos with one year of IceCube data.

Click here to download (.zip, 319MB)

Included in the download are the following files arranged in folders: *Note that the file descriptions listed below can also be found in a READ*

**/data:**

The observed_events.dat file contains the data event list. For each event two numbers are listed:

# ReconstructedMuonEnergy z_th

where ReconstructedMuonEnergy is the reconstructed muon energy in GeV and z_th is the reconstructed muon zenith angle given in radians.

**/monte_carlo:**

The NuFSGenMC_nominal.dat file contains the MC events reconstructed using the nominal detector configuration. The MC event properties listed are:

- PDGID
- ReconstructedMuonEnergy
- cos(th_reco)
- NeutrinoEnergy
- cos(th_true)
- mcweight
- neutrino_from_pion_flux
- neutrino_from_kaon_flux

where PDGID is the Particle Data Group identifier of incident neutrino, cos(th_true) is cosine of the true direction, cos(th_reco) is the cosine of the reconstructed direction, NeutrinoEnergy is the energy of the neutrino in GeV, ReconstructedMuonEnergy is the reconstructed muon energy in GeV, and mcweight is event MC weight given in units of GeV cm^{2} s sr. For convenience, we have also provided the pion and kaon neutrino flux for the Honda+Gaisser model, which is documented in Phys. Rev. D 89, 062007.

In order to obtain event distributions using this MC, one must fold it in with the neutrino flux at the IceCube Detector. This flux should be given in units of 1/(GeV cm^{2} s sr). The event weight is then given by

weight = mcweight * neutrino_flux,

where the neutrino_flux has to be evaluated in the true neutrino quantities.

If one wishes to use the provided nominal Honda+Gaisser model, then:

weight = mcweight * (neutrino_from_pion_flux + neutrino_from_kaon_flux)

**/atmospheric_flux:**

This folder contains the atmospheric flux calculations used in the analysis. The fluxes given in this file have been propagated through the Earth. We also provide the initial unpropagated fluxes. The seven atmospheric models used in this analysis are labeled as:

- Honda+Gaisser
- CombinedGHandHG_H3a_QGSJET-II-04
- CombinedGHandHG_H3a_SIBYLL2.3_rc1_pl
- PolyGonato_QGSJET-II-04
- PolyGonato_SIBYLL2.3_rc1_pl
- ZatsepinSokolskaya_pamela_QGSJET-II-04
- ZatsepinSokolskaya_pamela_SIBYLL2.3_rc1_pl

The first flux is documented in Phys. Rev. D 89, 062007, whereas the rest of the fluxes are reported in the following technote: http://dspace.mit.edu/handle/1721.1/98078

**/atmospheric_flux/differential:**

The differential fluxes are provided with the following structure:

- cos(th)
- NeutrinoEnergy
- nu_pion
- nubar_pion
- nu_kaon
- nubar_kaon

where cos(th) is the cosine of the zenith angle, the NeutrinoEnergy is the energy of the neutrino given in GeV, and the muon neutrino fluxes for the pion and kaon components are given in GeV^{-1} cm^{-2} s^{-1} sr^{-1}.

**/atmospheric_flux/averaged:**

The second format is the bin-averaged neutrino flux, which we have averaged over true energy bins, cos(th) bins, and azimuth. This is given in order to more readily multiply with the detector response array.

The flux tensor has the following indices:

Phi_{cth,nu_e},

where cth is the cosine of the zenith angle and nu_e is the neutrino energy bin index.

The fluxes are given in HDF5 format and have the following data sets:

average_flux_nu_kaon | Dataset {21, 200} |

average_flux_nu_pion | Dataset {21, 200} |

average_flux_nubar_kaon | Dataset {21, 200} |

average_flux_nubar_pion | Dataset {21, 200} |

costh_reco_bin_edges | Dataset {22} |

e_true_bin_edges | Dataset {201} |

where the numbers in braces are the sizes along each dimension of the set. The units of the neutrino energy bin edges are given in GeV and the averaged fluxes are given in GeV^{-1} sr^{-1} cm^{-2} s^{-1}.

**/systematics_response_arrays:**

In order to assess systematic uncertainties due to detector effects, we also provide the response arrays for different non-nominal detector configurations.

The following list of systematic sets are provided:- DOM efficiency variants: 0.9, 0.95, 1.089, and 1.1979.

– SPICELEA ice model.

– SPICEMIE icevariant1 (+10% scattering) and icevariant2 (+10% absorption).

– SPICEMIE ice model with no hole ice.

For reference, we also provide the nominal response array:

– SPICEMIE ice model with 0.99 DOM efficiency.

Description of the SPICEMIE ice model can be found in the following paper NIM: A711:73,2013 (arXiv: 1301.5361).

These arrays, which have units of GeV cm^{2} s sr, have the following indexes:

T_{mu_e,cth,nu_e}

where mu_e is the index that represents the reconstructed muon energy bin, cth corresponds to the cos(th) bin, and nu_e corresponds to the true neutrino energy bin.

In order to estimate the total number of events in a given reconstructed-quantity bin, one has to perform the following multiplication:

N_{mu_e,cth} = T_{mu_e,cth,nu_e} * Phi{cth,nu_e} …(1)

where, on the right hand side, summation over the repeated nu_e index is assumed and Phi corresponds to the average neutrino flux in the bin with indices cth and nu_e.

In order to facilitate the multiplication given in equation (1), we also provide the average fluxes per bin that is in the same binning in atmospheric_flux/averaged/ directory for the models used in the analysis.

The arrays are given in HDF5 format and have the following data sets:

antineutrino_response_array | Dataset {10, 21, 200} |

neutrino_response_array | Dataset {10, 21, 200} |

costh_bin_edges | Dataset {22} |

proxy_energy_bin_edges | Dataset {11} |

true_energy_bin_edges | Dataset {201} |

where the numbers in braces are the sizes along each dimension of the set.

Finally, it is important to note that neutrino_response_array must be convolved with the corresponding average neutrino fluxes and the antineutrino_response_array with the corresponding average antineutrino fluxes. Then to compare to the data, one must add the resulting products.

**/examples:**

This directory contains script examples that illustrate how the data release can be used. The examples are given in two programming languages: Mathematica and Python.

**/examples/Mathematica:**

This directory contains a Mathematica notebook named IceCubeDataReleaseExample, which has the following sections:

– Looking at the data: explains how to draw reconstructed energy and cos(th) distributions.

– Using the nominal MC and comparing it with data: explains how to load and weight the nominal Monte Carlo to one of the provided atmospheric neutrino models.

– Using the detector response arrays: explains how to use the detector systematic response arrays in combination with the provided averaged neutrino fluxes.

**/examples/Python:**

This directory contains three Python scripts that draw the following distributions:

– 1D_energy_systematics.py: draws the reconstructed energy distribution both when using the nominal detector configuration and the seven provided flux variants, and when using the Honda+Gaisser provided model and the detector systematic variants.

– 1D_energy_zenith_distribution.py: draws the reconstructed energy and reconstructed zenith distribution for the nominal detector configuration using the full Monte Carlo and with the provided Honda+Gaisser model. Furthermore, for comparison, it overlays the data.

– 2D_energy_vs_zenith_systematics.py: draws distribution of events as a function of reconstructed cos(th) and reconstructed muon energy. Furthermore, for illustration, it also draws the effect of changing the DOM efficiency from its nominal value, 0.99, to 1.089.

For any questions about this data release, please write to data@icecube.wisc.edu.