Neutrino Properties and Their Role in Astrophysics and Cosmology

Abstract

The present chapter provides an overview of the role of neutrinos and their properties in various circumstances of astrophysics and cosmology. The first section discusses solar neutrinos and their production in nuclear fusion. We then turn to the role of neutrinos in stellar supernova explosions, and the production of neutrinos of high energy neutrinos by the interactions of primary cosmic rays in the Earth atmosphere, the so-called atmospheric neutrinos. We also cover the flavor composition of high energy neutrinos from astrophysical sources, the role of neutrinos as hot dark matter and in lepto- and baryogenesis .

Problems

12.1

Neutrino Sphere in Core Collapse Supernovae

(a) Estimate the matter density at the neutrino sphere in a core collapse supernova. Assume that the scale height of the matter distribution is $R\simeq 10$ km, use the typical neutrino scattering cross section $\sigma _\nu \sim 10^{-43}\,(E_\nu /\mathrm{MeV})^2\,\mathrm{cm}^{-2}$ as a function of neutrino energy discussed in Sect. 1.3 and use $E_\nu \simeq 16$ MeV, as indicated by supernova simulations.

(b) The neutrino emission can approximately be described by a thermal distribution with a certain temperature $T_\nu$. Assuming a temperature profile that increases with decreasing radius, determine the relative ordering of the temperatures of electron neutrinos, electron-antineutrinos and muon and tau neutrinos at the neutrino sphere. Hint: These three neutrino flavors have different characteristic interaction cross sections and rates.

12.2

Stability of Neutron Stars

Neutron stars consist mostly of neutrons which as is well known decay in vacuum. What prevents neutrons to decay in neutron stars? Estimate the ratio of the number of protons and electrons to the number of nucleons that follows from the stability of the neutrons.

12.3

Pulsar Kicks

Imagine how the mixing of active neutrinos with sterile neutrinos in a hot neutron star after the explosion of a core collapse supernova can lead to asymmetric emission of sterile neutrinos and thus to pulsar kicks. Hints: Use the fact that pulsars carry strong magnetic fields which polarize electrons and induce a correlation of the momentum of active neutrinos produced through charged current interactions with the magnetic field direction upon production. Why does this in itself not lead to anisotropic emission of active neutrinos? How can mixing with sterile neutrinos lead to asymmetric emission?