Atmospheric and astrophysical neutrinos above 1 TeV interacting in IceCube

The IceCube Neutrino Observatory was designed primarily to search for high-energy (TeV-PeV) neutrinos produced in distant astrophysical objects. A search for $\gtrsim 100\mathrm{TeV}$ neutrinos interacting inside the instrumented volume has recently provided evidence for an isotropic flux of such neutrinos. At lower energies, IceCube collects large numbers of neutrinos from the weak decays of mesons in cosmic-ray air showers. Here we present the results of a search for neutrino interactions inside IceCube’s instrumented volume between 1 TeV and 1 PeV in 641 days of data taken from 2010–2012, lowering the energy threshold for neutrinos from the southern sky below 10 TeV for the first time, far below the threshold of the previous high-energy analysis. Astrophysical neutrinos remain the dominant component in the southern sky down to a deposited energy of 10 TeV. From these data we derive new constraints on the diffuse astrophysical neutrino spectrum, ${\mathrm{\Phi }}_{\nu }=2.06_{-0.3}^{+0.4}\times 10^{-18}{(E_{\nu }/10^5\mathrm{GeV})}^{-2.46\pm 0.12}{\mathrm{GeV}}^{-1}{\mathrm{cm}}^{-2}{\mathrm{sr}}^{-1}{\mathrm{s}}^{-1}$ for $25\mathrm{TeV}<E_{\nu }<1.4\mathrm{PeV}$, as well as the strongest upper limit yet on the flux of neutrinos from charmed-meson decay in the atmosphere, 1.52 times the benchmark theoretical prediction used in previous IceCube results at 90% confidence.

Figure 1

Fluxes of vertically down-going muons and neutrinos detectable in IceCube. The upper line shows the flux of penetrating, single atmospheric muons at the depth of IceCube, while the remaining lines show neutrino fluxes multiplied by the probability that a neutrino of the given energy would interact in 1 km of glacial ice. The dotted lines show the total interacting flux of atmospheric neutrinos of all flavors [19, 28], while the corresponding solid lines show the interacting flux that arrives at the depth of IceCube without accompanying muons above 1 TeV [57]. Accompanying muons suppress the effective ${\nu }_{\mu }$ flux from $\pi$ and $K$ decay below the level of the effective ${\nu }_e$ flux from $K$ decay at 50 TeV, producing a kink in the spectrum. The $E^{-2}$ astrophysical neutrino flux, shown here with the normalization of [7], always arrives without accompanying muons.

Figure 2

Distribution of photon counts per event after each stage of the event selection. The total number of collected photons is on average proportional to the total deposited energy; for example, $10^3$ photons correspond to roughly 10 TeV deposited energy. The stepped lines show the prediction from Monte Carlo simulation of penetrating atmospheric muons (blue) atmospheric neutrinos (red), while the points show experimental data. Left: Preselected events transmitted from the South Pole (Sec. 2a). Center: Removed events with veto hits (Sec. 2b). Right: Fiducial volume scaled with photon count (Sec. 2c).

Figure 3

An illustration of the incoming-muon veto procedure described in Sec. 2b. Each panel shows a snapshot in time with the current position of the muon marked by the blue arrowhead and the position of the reconstructed vertex marked by a green star. Panel (a) shows a penetrating muon before its largest energy loss. The dashed grey lines mark the positions at which photons induced by a muon would be detected with minimal and maximal delay. The photon that falls inside this window is counted towards the veto total, while the random noise photon that falls outside the window is not. Panel (b) shows a penetrating muon after its largest energy loss. The dashed circle marks the positions where photons propagating from the vertex at the speed of light in ice would be detected with minimal delay. Here the photon is not counted towards the veto since it is detected at a time compatible with propagation from the reconstructed vertex. Panel (c) shows how the veto procedure is inverted to detect a neutrino-induced muon. Photons induced at the cascade vertex spread outwards at the speed of light in ice, while the muon moves at the speed of light in vacuum. Eventually the muon out-runs the light front from the cascade, and photons collected in the track detection window can be used to positively identify an out-going muon in the event.

Figure 4

Fraction of preselected penetrating muon background events (Sec. 2a) that pass the veto conditions (Sec. 2b), derived from Monte Carlo (MC) simulation. The outer-layer veto reduces the rate of the highest-energy muons by $10^4$, but degrades rapidly at lower energies. The incoming-track veto scales in a similar way with respect to energy, but is more sensitive because it considers isolated photon detections. In contrast to the outer-layer veto, its efficiency also improves with increasing distance $d$ from the detector border of the reconstructed vertex.

Figure 5

Fiducial volume scaling function evaluated at four different photon counts. Top: Overhead view, showing the positions of the IceCube strings and the boundaries of the fiducial volume for events with a given total photon count. Bottom: Side view, showing the modules along strings.

Figure 6

Atmospheric neutrino flux models used in this analysis. The dotted lines in each panel show the neutrino fluxes at Earth’s surface as a function of true zenith angle at 1, 10, and 100 TeV. The conventional fluxes are taken from [19] and the prompt flux from [28]; both were corrected to account for the cosmic-ray flux of [77]. The solid lines show the fluxes of ${\nu }_{\mu }$ and ${\nu }_e$ that can be observed as isolated neutrino interactions in IceCube. The observable fluxes are suppressed in the northern sky ($\cos \theta \le 0.2$, to the left of the vertical dashed line) by absorption in the Earth, especially in its much denser core ($\cos \theta <-0.8$) [65], and in the southern sky ($\cos \theta >0.2$, to the right of the line) by self-veto by accompanying muons [57]. Astrophysical neutrinos are absorbed in the Earth as well, but are never accompanied by muons.

Figure 7

Average deposited-energy spectra expected from the various sources of neutrinos in this analysis from the southern and northern skies. The conventional atmospheric component corresponds to the calculation of [19], with corrections for the knee of the cosmic-ray spectrum and the fraction vetoed by accompanying muons, while the prompt component corresponds to the calculation of [28] with similar corrections, but with the normalization taken from the previously published upper limit of 3.8 [53]. The astrophysical component corresponds to Eq. (1) with ${\mathrm{\Phi }}_0=10^{-18}{\mathrm{GeV}}^{-1}{\mathrm{cm}}^{-2}{\mathrm{sr}}^{-1}{\mathrm{s}}^{-1}$ and $\gamma =2$.

Figure 8

Deposited-energy spectra from the northern and southern skies (points) with the best-fit combination of atmospheric and astrophysical contributions from Table 1. Below 3 TeV, the events observed from the northern sky are adequately explained by conventional atmospheric neutrinos. In the same energy range in the southern sky, penetrating atmospheric muons account for the remaining events. Above 10 TeV, an extra component is required to account for the observed high-energy events, especially those in the southern sky. Since atmospheric neutrinos of any kind are often vetoed by accompanying muons, the excess is best explained by astrophysical neutrinos. We interpret the excess over the best-fit sum around 30 TeV as a statistical fluctuation.

Figure 9

Zenith angle distribution of events depositing more than 1, 25, and 100 TeV (points) with the best-fit combination of atmospheric and astrophysical contributions from Table 1, using the same color scheme as in Fig. 8. At the lowest energies the sample is concentrated at the horizon, as expected from conventional atmospheric neutrinos. The astrophysical component contributes significantly to the sample above 25 TeV, and the bulk of the sample is down-going. By 100 TeV only the astrophysical component remains, and the up-going flux is suppressed by absorption in the Earth.

Figure 10

Verification of atmospheric neutrino veto with low-energy data. The points show events depositing less than 3 TeV, while the stacked histograms show the expected contributions from conventional atmospheric neutrinos, penetrating muons, and the negligible contribution of astrophysical neutrinos, using the color scheme of Fig. 8. These match the observed data much better than the dotted line, which shows the number of events that would be collected if atmospheric neutrinos were never vetoed by accompanying muons.

Figure 11

Profile likelihood scans showing the correlation between the astrophysical power-law index and the normalizations of the astrophysical (top panel) and prompt atmospheric components (bottom panel). The astrophysical normalization is the flux per neutrino flavor in units of ${\mathrm{\Phi }}_0/{10}^{-18}\mathrm{G}\mathrm{e}{\mathrm{V}}^{-1}{\mathrm{c}\mathrm{m}}^{-2}{\mathrm{s}\mathrm{r}}^{-1}{\text{\hspace{0.17em} s\hspace{0.17em}}}^{-1}$, while the prompt normalization is given in units of the prediction of [28]. The colors show the test statistic (3), obtained by fixing the parameters shown on the axes and varying all others to obtain the conditional best fit. The x shows the best-fit point as in Table 1 and the contours show confidence regions in the ${\chi }^2$ approximation [81] with 2 degrees of freedom. The thin dotted line shows the conditional best fit for each value of $\gamma$.

Figure 12

Unfolding the non-atmospheric excess as piecewise-constant per-flavor fluxes $E^2\mathrm{\Phi }$. The horizontal error bars show the range of primary neutrino energies that contribute to each bin, while the vertical error bars show the range of $E^2\mathrm{\Phi }$ that change the $-2\mathrm{\Delta }\ln L$ test statistic by less than 1. The black points show the fit to the data sample presented here; the light grey data points are from the 3-year data sample of [7], shifted slightly to the right for better visibility. Above the highest observed energy, the error bars provide upper limits on the flux; these are less constraining than the upper limits of [83] above 10 PeV. The thin lines show models for the diffuse astrophysical neutrino background: the Waxman-Bahcall (WB) upper bound from the total luminosity of EeV cosmic rays [60] (blue, dashed), the starburst galaxy model of [46] (green, dot-dashed), and the active galactic nucleus (AGN) core emission model of [40] (purple, dotted).