Neutrino Observatories Can Characterize Cosmic Sources and Neutrino Properties

Neutrino telescopes that measure relative fluxes of ultrahigh-energy $\nu_{e}, \nu_{\mu}, \nu_{\tau}$ can give information about the location and characteristics of sources, about neutrino mixing, and can test for neutrino instability and for departures from CPT invariance in the neutrino sector. We investigate consequences of neutrino mixing for the neutrino flux arriving at Earth, and consider how terrestrial measurements can characterize distant sources. We contrast mixtures that arise from neutrino oscillations with those signaling neutrino decays. We stress the importance of measuring $\nu_{e}, \nu_{\mu}, \nu_{\tau}$ fluxes in neutrino observatories.