Constraints on Ultrahigh-Energy Cosmic-Ray Sources from a Search for Neutrinos above 10 PeV with IceCube

We report constraints on the sources of ultrahigh-energy cosmic rays (UHECRs) above $10^9\mathrm{GeV}$, based on an analysis of seven years of IceCube data. This analysis efficiently selects very high- energy neutrino-induced events which have deposited energies from $5\times 10^5\mathrm{GeV}$ to above $10^{11}\mathrm{GeV}$. Two neutrino-induced events with an estimated deposited energy of $(2.6\pm 0.3)\times 10^6\mathrm{GeV}$, the highest neutrino energy observed so far, and $(7.7\pm 2.0)\times 10^5\mathrm{GeV}$ were detected. The atmospheric background-only hypothesis of detecting these events is rejected at $3.6\sigma$. The hypothesis that the observed events are of cosmogenic origin is also rejected at $>99\%$ CL because of the limited deposited energy and the nonobservation of events at higher energy, while their observation is consistent with an astrophysical origin. Our limits on cosmogenic neutrino fluxes disfavor the UHECR sources having a cosmological evolution stronger than the star formation rate, e.g., active galactic nuclei and $\gamma$-ray bursts, assuming proton-dominated UHECRs. Constraints on UHECR sources including mixed and heavy UHECR compositions are obtained for models of neutrino production within UHECR sources. Our limit disfavors a significant part of parameter space for active galactic nuclei and new-born pulsar models. These limits on the ultrahigh-energy neutrino flux models are the most stringent to date.

Figure 1

Solid angle and time integrated exposure from April 2008 through May 2015 as a function of neutrino energy by flavor and flavor sum, including neutrino absorption effects in the Earth. The sharp peaked structure at $6.3\times 10^6\mathrm{GeV}$ for electron neutrinos is due to the Glashow resonance [44]. The Auger exposure [45] is included for reference.

Figure 2

Model-dependent 90% confidence-level limits (solid lines) for (upper panel) proton cosmogenic-neutrino predictions (dashed lines) from Ahlers [42] and Kotera [53] and (lower panel) astrophysical neutrino fluxes from AGN (BLR) models of Murase [56] and Padovani (long dashes: $Y_{\nu \gamma }=0.8$, short dashes: $Y_{\nu \gamma }=0.3$) [57], and the Fang pulsar model [59]. The range of limits indicates the central 90% energy region. Two lines of the Ahlers model represent different threshold energies of the extragalactic UHECR component. The deviation of the Kotera and Ahlers models below $10^8\mathrm{GeV}$ is due to different models of the extagalactic background light assumed for the calculation. The wide energy coverage of the current analysis (Fig. 1) allows a stringent model-dependent limit to be placed for both cosmogenic and astrophysical models.

Figure 3

Constraints on the UHECR source evolution model and all flavor $E^{-2}$ power-law flux model parameters. The colored areas represent the parameter space excluded by the current analysis. (Top) Cosmogenic flux parameters $m$ and $z_{\max }$ of the UHECR-source cosmological evolution function of the form ${\psi }_s(z)\propto (1+z{)}^m$, assuming proton-dominant UHECR primaries with only the CMB as the background photon field. A semi-analytic formulation [80], with the injected proton spectrum of $E^{-2.5}$ up to $6\times 10^{11}\mathrm{GeV}$, is used to estimate the neutrino flux. The boxes indicate approximate parameter regions for SFR [71] and FRII-A [72] and FRII-B [73], neglecting the minor far-redshift contributions. (Bottom) Upper limits on $E^{-2}$ power-law neutrino flux normalization ${\varphi }_0$ and spectral cutoff energy $E_{\nu }^{\text{cut}}$.

Figure 4

All-flavor-sum neutrino flux quasidifferential 90% C.L. upper limit on one energy decade $E^{-1}$ flux windows (solid line). The limits are derived using a log-likelihood ratio method. The median null observation limit (sensitivity) is also shown (dashed line). Cosmogenic-neutrino model predictions (assuming primary protons) are shown for comparison: Kotera et al. [53], Ahlers et al. [42], and an astrophysical neutrino model from Murase et al. [56]. Model-independent differential limits on one energy decade $E^{-1}$ flux from Auger [45] and ANITA-II [88] with appropriate normalization are also shown. A model-dependent upper limit on an unbroken $E^{-2}$ power-law flux from the current analysis ($E_{\nu }^2\varphi <9.2\times {10}^{-9}\mathrm{GeV}/{\mathrm{cm}}^2\mathrm{s}\mathrm{sr}$) is shown for reference (dotted line).