A core-collapse releases a total neutrino energy of

PHYSICS · Multi-part · Fermi University Physics · Particle Physics & Quantum Fields · Astrophysics & Cosmology · Stellar death and compact objects

Stars from the Inside, Ch Stellar explosions: core collapse, the neutrino-driven shock, radioactive light and remnants

Problem

A core-collapse releases a total neutrino energy of 3×1046 J3\times10^{46}\,\mathrm{J}, shared roughly equally among the six neutrino species (electron, muon and tau neutrinos and their antiparticles). Water-Cherenkov detectors record this burst mainly through inverse beta decay, νˉe+p→n+e+\bar\nu_e + p \to n + e^+, on the free protons (hydrogen nuclei) of the water. Take the mean νˉe\bar\nu_e energy to be 15 MeV15\,\mathrm{MeV}, the interaction cross-section at this energy to be σ≈2×10−45 m2\sigma \approx 2\times10^{-45}\,\mathrm{m^2}, and the distance to the Large Magellanic Cloud to be D=51.4 kpcD = 51.4\,\mathrm{kpc}. The Kamiokande II detector's fiducial mass was M=2140M = 2140 tonnes of water (1 tonne=103 kg1\,\mathrm{tonne} = 10^3\,\mathrm{kg}); each water molecule (molar mass 18 g mol−118\,\mathrm{g\,mol^{-1}}) contributes two free protons as targets. Emission may be treated as instantaneous and isotropic. ((a)) Estimate the number of νˉe\bar\nu_e-proton interactions expected in Kamiokande II. ((b)) Comment on how this compares with the roughly dozen events Kamiokande II actually recorded from SN 1987A.

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