Differential limit on the extremely-high-energy cosmic neutrino flux in the presence of astrophysical background from nine years of IceCube data

We report a quasidifferential upper limit on the extremely-high-energy (EHE) neutrino flux above $5\times {10}^6\mathrm{GeV}$ based on an analysis of nine years of IceCube data. The astrophysical neutrino flux measured by IceCube extends to PeV energies, and it is a background flux when searching for an independent signal flux at higher energies, such as the cosmogenic neutrino signal. We have developed a new method to place robust limits on the EHE neutrino flux in the presence of an astrophysical background, whose spectrum has yet to be understood with high precision at PeV energies. A distinct event with a deposited energy above $10^6\mathrm{GeV}$ was found in the new two-year sample, in addition to the one event previously found in the seven-year EHE neutrino search. These two events represent a neutrino flux that is incompatible with predictions for a cosmogenic neutrino flux and are considered to be an astrophysical background in the current study. The obtained limit is the most stringent to date in the energy range between $5\times {10}^6$ and $2\times {10}^{10}\mathrm{GeV}$. This result constrains neutrino models predicting a three-flavor neutrino flux of $E_{\nu }^2{\varphi }_{{\nu }_e+{\nu }_{\mu }+{\nu }_{\tau }}\simeq 2\times {10}^{-8}\mathrm{GeV}/{\mathrm{cm}}^2\sec \mathrm{sr}$ at $10^9\mathrm{GeV}$. A significant part of the parameter space for EHE neutrino production scenarios assuming a proton-dominated composition of ultra-high-energy cosmic rays is disfavored independently of uncertain models of the extragalactic background light which previous IceCube constraints partially relied on.

Figure 1

Event count distributions before the track quality cut of the sample, including all three flavors of neutrinos as a function of NPE and ${\chi }_{\text{track}}^2/\mathrm{d}.\mathrm{o}.\mathrm{f}.$ The colors indicate the expected number of events seen by the IceCube EHE neutrino analysis in the nine-year exposure. The solid line in each panel indicates the track quality selection criteria, where events above the lines are retained. Simulations of a cosmogenic (GZK) neutrino model [24] are shown in the left panel, and the background simulations of atmospheric muons, conventional atmospheric neutrinos, and prompt atmospheric neutrinos are shown in the right panel.

Figure 2

Event count distributions before the muon bundle cut, including all three flavors of neutrinos as a function of NPE and $\cos ({\theta }_{\mathrm{LF}})$. The colors indicate the expected number of events seen by the IceCube EHE neutrino analysis in the nine-year exposure. The solid line in each panel indicates the muon bundle selection criteria, where events above the lines are retained. The major sources of remaining background are rare high-energy atmospheric neutrinos and muons originating in UHECRs. Again, cosmogenic (GZK) neutrinos are shown in the left panel, while background simulations are shown in the right panel.

Figure 3

Event distributions as functions of the energy proxy and cosine of the reconstructed zenith angle for simulations of the (left panel) cosmogenic (GZK) model [24] and (right panel) astrophysical neutrino model with a $E_{\nu }^{-2}$ spectrum with an intensity of $E_{\nu }^2{\varphi }_{{\nu }_e+{\nu }_{\mu }+{\nu }_{\tau }}={10}^{-8}\mathrm{GeV}/{\mathrm{cm}}^2\sec \mathrm{sr}$. The colors indicate the expected number of events seen by the IceCube EHE neutrino analysis based on the data collected over nine years. Rare misreconstructed events are distributed in the unphysical region of the energy-direction parameter space and included in the figure. Events classified in the non-track-like category are plotted in the bins of $\cos (\text{zenith})=-1.1$.

Figure 4

Event distributions as functions of the energy proxy and cosine of the reconstructed zenith angle for the flux ${\varphi }_{\mathrm{diff}}={\kappa }_E{E}_{\nu }^{-1}$, spanning a one-decade energy interval centered at $E_{\nu }^c$. The event distributions include the contributions from all three neutrino flavors. Events classified as non-track-like are plotted in the bins of $\cos (\text{zenith})=-1.1$. From left to right, the distributions for ${\log }_{10}(E_{\nu }^c/\mathrm{GeV})=7.6$, 8.0, and 9.0 are shown. Note that this energy proxy was designed to work across all event topologies for the EHE analysis. Better energy estimates are obtained by dedicated energy reconstructions optimized for a specific event topology. For display purposes, the normalization ${\kappa }_E$ has been set here so the energy flux $E_{\nu }^2{\varphi }_{\mathrm{diff}}=1.0\times {10}^{-8}\mathrm{GeV}/{\mathrm{cm}}^2\sec \mathrm{sr}$ at an energy of $E_{\nu }^c$.

Figure 5

Distribution of the negative log-likelihood ($-\log L_{\mathrm{diff}}$) for the hypothesis of $E_{\nu }^{-1}$ flux ranging over an energy interval of one decade, centered at $E_{\nu }^c$, on the ${\lambda }_{\mathrm{diff}}\text{−}{\lambda }_{\alpha }$ plane. Here ${\lambda }_{\mathrm{diff}}$ denotes the multiplier to the one-decade box-type spectrum ${\varphi }_{\mathrm{diff}}$ and ${\lambda }_{\alpha }$ is the multiplier to the power-law nuisance spectrum ${\varphi }_{\alpha }$ representing the astrophysical background. The star indicates the minimum on the $-\log L_{\mathrm{diff}}$ plane. From left to right, the distributions for ${\log }_{10}(E_{\nu }^c/\mathrm{GeV})=7.6$, 8.0, and 9.0 are shown. These results are calculated using the nine-year set of IceCube data containing two PeV-energy events described in Sec. 5. The power-law index of astrophysical flux, $\alpha$, is set to 2 in these examples.

Figure 6

All-flavor differential 90% C.L. upper limit based on the nine-year sample of IceCube data (solid line). Cosmogenic neutrino model predictions (assuming primary protons) by Kotera et al. [8] and Ahlers et al. [24], and an astrophysical neutrino model by Murase et al. [30] are shown for comparison. Differential limits for one-energy-decade $E_{\nu }^{-1}$ flux by other experiments are also shown for Auger (2015) [4], (ICRC2017) [10], and ANITA [31] with appropriate normalization by considering the energy bin width and neutrino flavor. The previous IceCube limit from the analysis of seven years of data [5] with the similar likelihood ratio framework but without a nuisance astrophysical background flux parameter is also shown for reference (dashed line).