We propose a simple but useful parametrization of the flavor composition of ultrahigh-energy neutrino fluxes produced from distant astrophysical sources: $\phi^{ }_e : \phi^{ }_\mu : \phi^{ }_\tau = \sin^2 \xi \cos^2 \zeta : \cos^2 \xi \cos^2 \zeta : \sin^2 \zeta$. We show that it is possible to determine or constrain $\xi$ and $\zeta$ by observing two independent neutrino flux ratios at the second-generation neutrino telescopes, provided three neutrino mixing angles and the Dirac CP-violating phase have been well measured in neutrino oscillations. Any deviation of $\zeta$ from zero will signify the existence of cosmic $\nu^{ }_\tau$ and $\bar{ \nu}^{ }_\tau$ neutrinos at the source, and an accurate value of $\xi$ can be used to test both the conventional mechanism and the postulated scenarios for cosmic neutrino production.
Categories: astro-ph hep-ex hep-ph