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Constraining High-Energy Cosmic Neutrino Sources: Implications and Prospects

We consider limits on the local ($z=0$) density ($n_0$) of extragalactic neutrino sources set by the nondetection of steady high-energy neutrino sources producing $\gtrsim50$ 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 $n_0\gtrsim{10}^{-8}-{10}^{-7}~{\rm Mpc}^{-3}$ for standard candle sources evolving rapidly, $n_s\propto{(1+z)}^3$, and $n_0\gtrsim{10}^{-6}-{10}^{-5}~{\rm Mpc}^{-3}$ for nonevolving sources. The corresponding upper limits on their neutrino luminosity are $L_{ν_μ}^{\rm eff}\lesssim10^{42}-10^{43}~{\rm erg}~{\rm s}^{-1}$ and $L_{ν_μ}^{\rm eff}\lesssim10^{41}-10^{42}~{\rm erg}~{\rm s}^{-1}$, 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 $\sim0.1-1$ 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 $n_0$ by more than two orders of magnitude. Future gamma-ray observations (by Fermi, HAWC and CTA) will play a key role in confirming the association of the neutrinos with their sources.