  We discuss the diffuse flux of electron neutrinos and antineutrinos from
cosmological failed supernovae, stars that collapse directly into a black hole,
with no explosion. This flux has a hotter energy spectrum compared to regular,
neutron-star forming collapses, and therefore it dominates the total diffuse
flux from core collapses above 20-45 MeV of neutrino energy. Reflecting the
features of the originally emitted neutrinos, the flux of nu_e and anti-nu_e at
Earth is larger for larger survival probability of these species, and for
stiffer equations of state of nuclear matter. In the energy window 19-29 MeV,
the flux from failed supernovae is susbtantial, ranging from 7% to a dominant
fraction of the total flux from all core collapses. It can be as large as phi =
0.38 s^{-1} cm^{-2} for anti-nu_e (phi = 0.28 s^{-1} cm^{-2} for nue),
normalized to a local rate of core collapses of R_{cc}(0)=10^{-4} yr^{-1}
Mpc^{-3}. In 5 years, a 0.45 Mt water Cherenkov detector should see 5-65 events
from failed supernovae, while up to 160 events are expected for the same mass
with Gadolinium addition. A 0.1 Mt liquid argon experiment should record 1-11
events. Signatures of neutrinos from failed supernovae are the enhancement of
the total rates of events from core collapses (up to a factor of 2) and the
appearance of high energy tails in the event spectra.
