Cosmic PeV neutrinos and the sources of ultrahigh energy protons

The IceCube experiment recently detected the first flux of high-energy neutrinos in excess of atmospheric backgrounds. We examine whether these neutrinos originate from within the same extragalactic sources as ultrahigh energy cosmic rays. Starting from rather general assumptions about spectra and flavors, we find that producing a neutrino flux at the requisite level through pion photoproduction leads to a flux of protons well below the cosmic-ray data at $\sim 10^{18}\mathrm{eV}$, where the composition is light, unless pions/muons cool before decaying. This suggests a dominant class of accelerator that allows for cosmic rays to escape without significant neutrino yields.

Figure 1

Total $\nu +\overline{\nu }$ fluxes of our four fiducial models. Normalizations are fixed to yield three $\gtrsim 1\mathrm{PeV}$ events in IceCube for model 1 or ten $\gtrsim 100\mathrm{TeV}$ events for models 2, 3, and 4, following the methods in the text. To rescale for the flux of any $\nu$ or $\overline{\nu }$ flavor $i$ multiply by the corresponding postoscillation $N_i$ divided by $N_{\nu +\overline{\nu }}$ for each model in Table 1. The IceCube data (circles) assume a 1:1:1 flavor ratio and $\nu =\overline{\nu }$ [11].

Figure 2

Effective solid angle $\mathrm{\Delta }{\mathrm{\Omega }}_{\text{eff}}$ for ${\nu }_e$, ${\nu }_{\mu }$, and ${\nu }_{\tau }$ (“$\nu$”); ${\overline{\nu }}_{\mu }$ and ${\overline{\nu }}_{\tau }$ (“$\overline{\nu }$”); and ${\overline{\nu }}_e$ as a function of $E_{\nu }$. The upper set of lines average over the full sky, while the bottom set shows the contribution only from angles below the horizon.

Figure 3

Neutrino event spectra for models 1 and 2 versus the electromagnetic-equivalent $E_{\text{em}}$ for showers (left panels) and $E_{\text{em}}^{\mu }$ for contained-vertex muons (right panels). Shower components (as labeled) include ${\nu }_e$, ${\overline{\nu }}_e$, ${\nu }_{\tau }$, and ${\overline{\nu }}_{\tau }$ charged current (CC); all flavor (${\nu }_X$, ${\overline{\nu }}_X$) neutral current (NC); and ${\overline{\nu }}_{e}e$ Glashow resonance channels yielding $e$ and hadrons (included in ${\overline{\nu }}_e$ line) and $\tau$. Muon components include ${\nu }_{\mu }$ and ${\overline{\nu }}_{\mu }$ CC, ${\nu }_{\tau }$ and ${\overline{\nu }}_{\tau }$ CC decaying to muons, and ${\overline{\nu }}_{e}e$ channels yielding a $\mu$ or $\tau$. The total neutrino fluxes are shown in Fig. 1, normalized to three total $>\mathrm{PeV}$ events in IceCube for model 1 and ten $>100\mathrm{TeV}$ events for model 2. Note that the curves would decrease somewhat below $\sim 10^5\mathrm{GeV}$ if energy dependence in $V_{\text{eff}}$ [10] was incorporated rather than $V_{\text{eff}}=0.4{\mathrm{km}}^{-3}$.

Figure 4

Neutrino event spectra for models 3 and 4 versus the electromagnetic-equivalent $E_{\text{em}}$ for showers (left panels) and $E_{\text{em}}^{\mu }$ for contained-vertex muons (right panels). Shower components (as labeled) are the same as in Fig. 3. The total neutrino fluxes from both models are also shown in Fig. 1, normalized to ten total $>100\mathrm{TeV}$ events.

Figure 5

Ratio of neutrino shower to contained-vertex muon events versus deposited energy for models 1, 2, 3, and 4.

Figure 6

The ultrahigh energy cosmic-ray spectrum. Shown are the proton fluxes associated with neutrino models 1 (dashed) and 2 (solid). Normalizations are obtained from IceCube neutrino data (as described in the text) with 50% uncertainty bands. These are compared to KASCADE-Grande [40], HiRes-II [16], Auger [18], and Telescope Array [19] data.

Figure 7

Proton fluxes associated with neutrino models 3 (dashed) and 4 (solid), in the same fashion as described in Fig. 6 and compared to the same UHECR data. Boosting the flux of model 4 by a factor of 5 results in the dotted curve.