## Introduction

The IceCube Collaboration revisited six previous studies investigating the nature of the astrophysical neutrino flux in a combined maximum-likelihood analysis that used up to three observables—energy, zenith angle and event topology—to derive improved constraints on the energy spectrum and the composition of neutrino flavors (νe , νμ , ντ) of the astrophysical neutrino flux.

This combined study showed that the energy spectrum of the astrophysical neutrino flux is well described by a power law with a best-fit spectral index of -2.50 ± 0.09, for energies between 25 TeV and 2.8 PeV. A continuous power-law spectrum with an index of -2, which is a popular benchmark model, was excluded with a significance of 3.8 sigma.

+ Info: “A combined maximum-likelihood analysis of the high-energy astrophysical neutrino flux measured with IceCube,” IceCube Collaboration: M. G. Aartsen et al., *The Astrophysical Journal* 809:98 (2015), DOI: 10.1088/0004-637X/809/1/98

See paper on the IOP site or arXiv.

## Data release

Suggested citation for this dataset:

IceCube Collaboration (2016): A combined maximum-likelihood analysis of the astrophysical neutrino flux. IceCube Neutrino Observatory. Dataset. DOI:10.21234/B4WC7T

Click here to download (.zip, 1.5MB)

Included in the download are the following files:

**energy_bins.txt**– This file contains the edges of the energy bins, in GeV, that were defined to determine the differential astrophysical neutrino spectrum (see Figure 6 in the paper). There are nine bins, equally spaced by the logarithm of the energy, between 10^{4}GeV and 10^{7}GeV.**bestfit.txt**– This file contains the best-fit values for the normalization (E^{2}* flux) of the astrophysical neutrino flux, in 10^{-8}GeV s^{-1}sr^{-1}cm^{-2}, for each of the nine energy bins (see Table 6 in the paper). Note that this is the all-flavor normalization, i.e. the sum of the flux of electron, muon, and tau neutrinos, assuming that the individual fluxes for each neutrino flavor are equal at Earth due to neutrino oscillations.**scan_*.txt**– These files contain profile likelihood scans for the normalization (E^{2}* flux ) of the astrophysical neutrino flux, in 10^{-8}GeV s^{-1}sr^{-1}cm^{-2}, for each of the nine energy bins. The first column specifies the normalization, the second column the corresponding negative log-likelihood value (-2* ln L). Note that the all-flavor normalization is specified, i.e. the sum of the flux of electron, muon, and tau neutrinos, assuming that the individual fluxes for each neutrino flavor are equal at Earth due to neutrino oscillations.**scan_*.pdf**– These plots display the profile likelihood scans for the normalization (E^{2}* flux) of the astrophysical neutrino flux. They can be reproduced using the scan_norm_astro*.txt data files.**covariance.txt**– This file contains the values of the covariance matrix, i.e., for the normalizations of the astrophysical neutrino flux in the nine energy bins specified above, in units of (10^{-8}GeV s^{-1}sr^{-1}cm^{-2})^{2}. The matrix was estimated by the minimizer algorithm (Minuit). Approximate error bars for the best-fit normalizations can be obtained by calculating the square root of the diagonal entries of this matrix.**covariance.pdf**– This plot shows the correlation matrix, i.e., normalized covariance matrix, for the normalizations of the astrophysical neutrino flux in the nine energy bins defined above. This plot can be reproduced using the covariance.txt file.

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