  Times of arrival of high energy neutrinos encode information about their
sources. We demonstrate that the energy-dependence of the onset time of
neutrino emission in advancing relativistic jets can be used to extract
important information about the supernova/gamma-ray burst progenitor structure.
We examine this energy and time dependence for different supernova and
gamma-ray burst progenitors, including red and blue supergiants, helium cores,
Wolf-Rayet stars, and chemically homogeneous stars, with a variety of masses
and metallicities. For choked jets, we calculate the cutoff of observable
neutrino energies depending on the radius at which the jet is stalled. Further,
we exhibit how such energy and time dependence may be used to identify and
differentiate between progenitors, with as few as one or two observed events,
under favorable conditions.
