High Energy Extraterrestrial Neutrino Fluxes and Their Detection

Abstract

Whereas $\gamma$-rays can be produced both by electromagnetic processes such as inverse Compton scattering of high energy electrons and by hadronic processes such as the production of neutral pions and their subsequent decays into $\gamma$-rays, high energy extraterrestrial neutrinos are unique messengers of hadronic acceleration processes because they can only be produced by the decay of charged pions or heavier mesons which can not be produced electromagnetically. For this reason, the observation of high energy extraterrestrial neutrinos plays a decisive role in the identification of the sources of charged hadronic cosmic rays. In the present chapter we describe both the detection methods for such neutrinos as well as scenarios for their production. We start by reviewing the neutrino interaction processes most relevant for neutrino detection, followed by a summary of the detection techniques and experiments. The second part discusses the production of neutrinos by interactions of the primary cosmic rays both within the sources and during propagation from the source to the observer, along with the resulting neutrino fluxes. Figure 9.1 summarizes the diffuse “grand unified” neutrino spectrum extending from the lowest energies dominated by the cosmological relic blackbody neutrino spectrum of temperature $\simeq$ $1.9\,$K to the highest energy neutrinos that are produced by interactions of primary cosmic rays either during propagation or within the sources. In the following we will restrict ourselves to the high energy range at a TeV and above. Relic neutrinos are discussed in the context of cosmology in Chap. 4 and as contributions to dark matter in Chap. 12 which also covers solar and terrestrial neutrinos.

Problems

9.1

Neutrino Absorption in the Earth

Use the neutrino-nucleon cross sections discussed in Sect. 9.1 and shown in Fig. 9.3 to estimate the energy above which neutrinos start to get absorbed when traversing a significant fraction of the Earth diameter.

9.2

A Rough Estimate of the Neutrino Spectrum of a Discrete Source of $\gamma$-Rays

Derive Eq. (9.14),

$$ \frac{dN_\nu }{dE_\nu }\simeq \frac{3}{13}\frac{L_\gamma }{E_{\mathrm{{max}},\nu }} \frac{1-\beta +\alpha }{E_\nu }\, \left( \frac{E_\nu }{E_{\mathrm{{max}},\nu }}\right) ^{-\beta +\alpha }\,, $$

for the differential neutrino spectrum of a discrete source optically thin against the reaction $p+\gamma \rightarrow N+\pi$ for protons which are accelerated to a power law spectrum $dN_p/dE\propto E^{-2-\beta }$ and interact with a target photon field with spectrum $n_\gamma (\varepsilon )=dN_\gamma /d\varepsilon \propto \varepsilon ^{-2-\alpha }$. Assume that the total neutrino luminosity $L_\nu$ is related to the total $\gamma$-ray luminosity $L_\gamma$ by $L_\nu \simeq \frac{3}{13}L_\gamma$ and the maximal neutrino energy is $E_{\mathrm{{max}},\nu }$. Hint: Assume that $E_\nu \sim 0.1E$ and figure out which energies the target photons must have to produce pions with a proton of a given energy E.

(b) How does this result Eq. (9.14) change for a source optically thick to the reaction $p+\gamma \rightarrow N+\pi ?$