Summary: ASTR 3730: Problem Set 2
(due Tuesday September 20th
(1) The collapse of the core of a massive star in a Type 2 supernova results in the
formation of a neutron star and the release of large numbers of neutrinos.
Neutrinos have a very small cross-section for interaction with matter, but the
high densities encountered during stellar collapse mean that there can be
circumstances where the neutrinos become temporarily trapped before they
scatter and escape.
(i) Consider a static star of mass M, radius r, made up of particles with
mass mn. If the cross-section for interaction between neutrinos and
matter is , derive an expression for the radius of a star that is just
optically thick to neutrino emission from the core.
(ii) Evaluate this radius for a star of mass M = 1.4 MSun, assuming a
neutrino-matter cross-section = 10-44
(2) Suppose some impulsive process releases a burst of radiation (photons or
neutrinos) at the center of a star of radius r. The optical depth between the
surface and the center is >> 1. Estimate the characteristic time scale of the