IceCube collaboration has seen an unexpected population of high energy
neutrinos compatible with an astrophysical origin. We consider two categories
of events that can help to diagnose cosmic neutrinos: double pulse, that may
allow us to clearly discriminate the cosmic component of tau neutrinos;
cascades with deposited energy above 2 PeV, including events produced by
electron antineutrinos at the Glashow resonance, that can be used to
investigate the neutrino production mechanisms. We show that one half of the
double pulse signal is due to the neutrinos spectral region already probed by
IceCube. By normalizing to HESE data, we find that 10 more years are required
to obtain 90% probability to observe a double pulse. The cascades above 2 PeV
provide us a sensitive probe of the high energy tail of the neutrino spectrum
and are potentially observable, but even in this case, the dependence on type
of the source is mild. In fact we find that pp or p{\gamma} mechanisms give a
difference in the number of cascades above 2 PeV of about 25 % that can be
discriminated at 2{\sigma} in about 50 years of data taking.Comment: 20 pages, 7 figures, accepted for publication in EPJ