Probing CP violation in neutrino oscillations with neutrino telescopes

Measurements of flavor ratios of astrophysical neutrino fluxes are sensitive to the two yet unknown mixing parameters $\theta_{13}$ and $\delta$ through the combination $\sin\theta_{13}\cos\delta$. We extend previous studies by considering the possibility that neutrino fluxes from more than a single type of sources will be measured. We point out that, if reactor experiments establish a lower bound on $\theta_{13}$, then neutrino telescopes might establish an upper bound on $|\cos\delta|$ that is smaller than one, and by that prove that CP is violated in neutrino oscillations. Such a measurement requires several favorable ingredients to occur: (i) $\theta_{13}$ is not far below the present upper bound; (ii) The uncertainties in $\theta_{12}$ and $\theta_{23}$ are reduced by a factor of about two; (iii) Neutrino fluxes from muon-damped sources are identified, and their flavor ratios measured with accuracy of order 10% or better. For the last condition to be achieved with the planned km^3 detectors, the neutrino flux should be close to the Waxman-Bahcall bound. It motivates neutrino telescopes that are effectively about 10 times larger than IceCube for energies of O(100 TeV), even at the expense of a higher energy threshold.