  The flavor composition of high-energy astrophysical neutrinos is a rich
observable. However, present analyses cannot effectively distinguish particle
showers induced by $\nu_e$ versus $\nu_\tau$. We show that this can be
accomplished by measuring the intensities of the delayed, collective light
emission from muon decays and neutron captures, which are, on average, greater
for $\nu_\tau$ than for $\nu_e$. This new technique would significantly improve
tests of the nature of astrophysical sources and of neutrino properties. We
discuss the promising prospects for implementing it in IceCube and other
detectors.
