Neutrinos: The Key to Ultrahigh Energy Cosmic Rays

Observations of ultrahigh energy cosmic rays (UHECR) do not uniquely determine both the injection spectrum and the evolution model for UHECR sources—primarily because interactions during propagation obscure the early Universe from direct observation. Detection of neutrinos produced in those same interactions, coupled with UHECR results, would provide a full description of UHECR source properties.

Figure 1

(a) A fit of UHECR spectrum with flat extragalactic injection spectrum. Upper and lower edges of shaded area are for $m=4$ and $3$. Galactic contribution is (dotted line) with $\gamma =2.6$. (b) Fitting with steep injection spectrum ($\gamma =1.7$).

Figure 2

Neutrino production in three simplified models for the source spectrum and evolution of UHECR. To enhance the contrast between different models, the source luminosity is extended out to $1+z_{\max }=10$.

Figure 3

Neutrino production for the UHECR models shown in Fig. 1. The injection spectrum is cut off at $E_c=3\times {10}^{21}\mathrm{GeV}$, and the source evolution is that described in Ref. 20. Model results depend mildly on the cosmological model, ${\Omega }_{\Lambda }=0.0$ or 0.7.