Constraining high-energy cosmic neutrino sources: Implications and prospects

We consider limits on the local ($z=0$) density (n₀) of extragalactic neutrino sources set by the nondetection of steady high-energy neutrino sources producing 50 TeV muon multiplets in the present IceCube data, taking into account the redshift evolution, luminosity function, and neutrino spectrum of the sources. We show that the lower limit depends moderately on source spectra and strongly on redshift evolution. We find n₀10^-8--10^-7 Mpc^-3 for standard candle sources evolving rapidly, nₛ∝(1+z)³, and n₀10^-6--10^-5 Mpc^-3 for nonevolving sources. The corresponding upper limits on their neutrino luminosity are L_ν_μᵉᶠᶠ10⁴²--10⁴³ erg s^-1 and L_ν_μᵉᶠᶠ10⁴¹--10⁴² erg s^-1, respectively. Applying these results to a wide range of classes of potential sources, we show that powerful ``blazar'' jets associated with active galactic nuclei are unlikely to be the dominant sources. For almost all other steady candidate source classes (including starbursts, radio galaxies, and galaxy clusters and groups), an order of magnitude increase in the detector sensitivity at ~0.1--1 PeV will enable a detection (as point sources) of the few brightest objects. Such an increase, which may be provided by next-generation detectors like IceCube-Gen2 and an upgraded KM3NET, can improve the limit on n₀ by more than 2 orders of magnitude. Future gamma-ray observations (by Fermi, the High-Altitude Water Cherenkov Observatory, and the Cherenkov Telescope Array) will play a key role in confirming the association of the neutrinos with their sources.