Z-bursts from the Virgo cluster

Abstract

Resonant annihilation of ultrahigh energy cosmic neutrinos ($\mathrm{UHEC}\ensuremath{\nu}$) on the cosmic neutrino background ($\mathrm{C}\ensuremath{\nu}\mathrm{B}$) into $Z$ bosons---the $Z$-burst mechanism---and its associated absorption and emission phenomenology provide a unique, albeit indirect, probe of the $\mathrm{C}\ensuremath{\nu}\mathrm{B}$ in its present state. In this paper, we examine the implications of gravitational clustering of the $\mathrm{C}\ensuremath{\nu}\mathrm{B}$ in nearby galaxy clusters for the $Z$-burst phenomenology. In particular, we study the emission features of the $Z$-decay products originating from the Virgo cluster, and the potential of future cosmic ray experiments to observe clustering-enhanced $Z$-burst rates. We find that a detector with an exposure equivalent to three years of observations at the Extreme Universe Space Observatory (EUSO) will very likely measure these enhanced rates together with the associated $\mathrm{UHEC}\ensuremath{\nu}$ flux, provided that the latter saturates current observational limits and the neutrino masses are quasidegenerate, ${m}_{{\ensuremath{\nu}}_{i}}\ensuremath{\gtrsim}0.1\text{ }\text{ }\mathrm{eV}$. In the case of $\mathrm{UHEC}\ensuremath{\nu}$ fluxes below the electromagnetic cascade limit, or a hierarchical neutrino mass spectrum, an experimental sensitivity exceeding that of EUSO by at least 2 orders of magnitude is required to detect the clustering enhancements with any certainty.