  This paper describes the response of the IceCube neutrino telescope located
at the geographic South Pole to outbursts of MeV neutrinos from the core
collapse of nearby massive stars. IceCube was completed in December 2010
forming a lattice of 5160 photomultiplier tubes that monitor a volume of ~ 1
cubic kilometer in the deep Antarctic ice for particle induced photons. The
telescope was designed to detect neutrinos with energies greater than 100 GeV.
Owing to subfreezing ice temperatures, the photomultiplier dark noise rates are
particularly low. Hence IceCube can also detect large numbers of MeV neutrinos
by observing a collective rise in all photomultiplier rates on top of the dark
noise. With 2 ms timing resolution, IceCube can detect subtle features in the
temporal development of the supernova neutrino burst. For a supernova at the
galactic center, its sensitivity matches that of a background-free
megaton-scale supernova search experiment. The sensitivity decreases to 20
standard deviations at the galactic edge (30 kpc) and 6 standard deviations at
the Large Magellanic Cloud (50 kpc). IceCube is sending triggers from potential
supernovae to the Supernova Early Warning System. The sensitivity to neutrino
properties such as the neutrino hierarchy is discussed, as well as the
possibility to detect the neutronization burst, a short outbreak of electron
neutrinos released by electron capture on protons soon after collapse.
Tantalizing signatures, such as the formation of a quark star or a black hole
as well as the characteristics of shock waves, are investigated to illustrate
IceCube's capability for supernova detection.
