Measurement of the atmospheric neutrino energy spectrum from 100 GeV to 400 TeV with IceCube

A measurement of the atmospheric muon neutrino energy spectrum from 100 GeV to 400 TeV was performed using a data sample of about 18 000 up-going atmospheric muon neutrino events in IceCube. Boosted decision trees were used for event selection to reject misreconstructed atmospheric muons and obtain a sample of up-going muon neutrino events. Background contamination in the final event sample is less than 1%. This is the first measurement of atmospheric neutrinos up to 400 TeV, and is fundamental to understanding the impact of this neutrino background on astrophysical neutrino observations with IceCube. The measured spectrum is consistent with predictions for the atmospheric ${\nu }_{\mu }+{\overline{\nu }}_{\mu }$ flux.

Figure 1

The predicted flux of atmospheric muon neutrinos. The solid line is the conventional ${\nu }_{\mu }+{\overline{\nu }}_{\mu }$ flux [3], averaged over the zenith range 90° to 180°. The long-dashed line is the prompt ${\nu }_{\mu }+{\overline{\nu }}_{\mu }$ flux [9], also averaged over the zenith range 90° to 180°. The dot-dashed curve is the sum of the conventional and prompt models. The flux predictions from [3] were extended to higher energies as discussed in Sec. 3c. For reasons discussed in Sec. 5b, the zenith region from 90° to 97° was not used in the analysis. The zenith-averaged conventional flux, for the range 97° to 180°, is shown in the figure as the short-dashed line. The prediction for the zenith-averaged prompt flux is not affected by this change in angular region.

Figure 2

IceCube Neutrino Observatory and its component arrays.

Figure 3

Overhead view of IceCube 40 string configuration.

Figure 4

Digital Optical Module.

Figure 5

Effective live time of the simulation used to train the unfolding algorithm, as a function of neutrino energy.

Figure 6

Distribution of the PLogL variable (from the MPE fit), for neutrino simulation, muon background simulation, and for data. A cut at a value of 8 based on the PLogL from a 32-iteration SPE fit has already been applied to reduce the amount of data requiring higher level processing. PLogL was then recalculated based on the result of the MPE fit.

Figure 7

Distribution of the difference between LineFit zenith angle and MPE fit zenith angle, for neutrino simulation, muon background simulation, and for data.

Figure 8

Distribution of the Bayesian likelihood ratio, for neutrino simulation, muon background simulation, and for data.

Figure 9

Zenith angles from the SPE fits for the two subevents created by the geometric split. Neutrino simulation (left) and data (right). Box size is proportional to the event density.

Figure 10

Output of the BDTs for data, as well as neutrino and muon background simulation weighted to the same live time (359 days). The vertical solid lines mark the chosen cut value of 0.73 for each BDT.

Figure 11

Effective area for up-going muon neutrinos as a function of neutrino energy, for various zenith regions.

Figure 12

Effective areas as a function of energy for each BDT. BDT 1 (long-dashed line) performs better than BDT 2 at low energies, while BDT 2 (short-dashed line) performs better than BDT 1 at higher energies. Events are required to pass only one of the BDTs, and the net effective area is the solid line. In contrast to Fig. 11, this plot reflects the zenith-averaged effective area for the region 97° to 180°. This corresponds to the zenith region used for the analysis.

Figure 13

Distributions of the $dE/dX$ observable, for data and for simulation. The additional cut at zenith angle of 97° has been applied. Error bars for data are statistical only.

Figure 14

Correlation between neutrino energy and the reconstructed muon $dE/dX$ observable, from simulation weighted to the atmospheric neutrino spectrum of [3, 9].

Figure 15

Estimated neutrino energy resolution, from simulation.

Figure 16

Unfolding of known, toy spectrum. The solid line is the assumed spectrum used for regularization, the sum of the conventional and prompt atmospheric neutrino flux models from Refs. [3, 9]. The dashed line is the arbitrary, toy spectrum used for generating the toy data. The unfolded result is shown without error bars.

Figure 17

Results of the atmospheric neutrino energy spectrum unfolding. The unfolded spectrum is shown in black; vertical lines are the estimated uncertainties. The gray line is the spectrum that provided the expected shape for the regularization, and includes the conventional atmospheric neutrino flux according to Honda et al. [3] and the prompt flux according to Enberg et al. [9]. This is the zenith-averaged ${\nu }_{\mu }+{\overline{\nu }}_{\mu }$ flux for the region 97°–180°.

Figure 18

Possible variability in the true neutrino flux consistent with DOM sensitivity and ice property uncertainties. The solid line is the predicted atmospheric neutrino flux ([3, 9]). The dashed lines are the maximum and minimum of the possible range of variability consistent with DOM sensitivity and ice model uncertainties. As mentioned in the text, work is ongoing to reduce this range of uncertainty.

Figure 19

Cosine(${\theta }_Z$) distributions for data and for simulation, using zenith angle from the MPE fit. Simulation has been normalized to the data. Error bars for data are statistical only.

Figure 20

Comparison of unfolded energy spectra for different zenith ranges. Separate unfoldings were performed for the zenith range 97°–124° (black) and the zenith range 124°–180° (gray). The unfolded results for each region (horizontal lines) and the predicted spectrum corresponding to each region (curves) are shown. Uncertainties for these results are not shown.

Figure 21

Statistical and regularization-induced uncertainties in the unfolded result. The errors in each bin are given as the percent of the true flux.

Figure 22

Sources of uncertainty in the unfolded energy spectrum. The solid lines are the systematic uncertainties due to DOM sensitivity and ice property uncertainties; the short-dashed lines are the uncertainties implied by zenith-dependent inconsistencies in data/simulation comparisons; and the long-dashed lines are the statistical and regularization uncertainties from toy MC studies. Not shown is the uniform 4% uncertainty due to miscellaneous normalization errors assumed to be independent of energy.

Figure 23

Comparison with previous measurements of the atmospheric neutrino energy spectrum; the Fréjus result [43], upper and lower bands from SuperK [44], an AMANDA forward folding analysis [45], and an AMANDA unfolding analysis [39]. All measurements include the sum of neutrinos and antineutrinos. The AMANDA unfolding analysis was a measurement of the zenith-averaged flux from 100° to 180°. The present analysis (IC40 unfolding), which extends the measurement up to 400 TeV, is a measurement of the zenith-averaged flux from 97° to 180°. Vertical error bars include systematic as well as statistical uncertainty.

Figure 24

Comparison of various prompt flux models to the unfolded result. The models shown are the sum of the Honda flux [3], plus one of Sarcevic [9], Naumov [11], or Martin [10]. Vertical error bars include systematic as well as statistical uncertainty.