Question

Consider the final iron core of a massive star with a mass M Fe = 1.5M and
radius R Fe = 3 × 10 8 cm. When this core collapses, the initial collapse stops when the central
core with a mass M core = 0.7M reaches a density ρ = 3 × 10 13 g cm −3 . At this density the
core bounces, which drives a shock with an energy E bounce = 10 51 erg into the infalling outer
core.
(a) Estimate the energy that is required to photo-dissociate 0.1 M of Fe into neutrons
and protons. Compare this energy to the bounce shock energy and comment on the fate
of the shock. Remember that ∼0.8% of the rest mass energy of protons is released in the
conversion 56p → 56 Fe.
(b) In the proto-neutron star (with an initial radius 3 × 10 6 cm), the mean free path
of neutrinos is l ν = 30 cm. Estimate the diffusion time for neutrinos to escape from the
proto-neutron star and hence estimate the neutrino luminosity during the initial neutron-
star cooling phase.
(c) Assuming that 5–10% of the neutrino luminosity is absorbed by the infalling outer
core, estimate how long it takes to absorb enough neutrino energy to reverse the infall of the
outer core and drive a successful supernova explosion with a typical explosion energy of 10 51
erg. Compare this time to the dynamical (free-fall) timescale of the proto-neutron star.

Answer 1

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