Thermodynamics of the Neutrino Gas in a Plasma

Physics – Plasma Physics

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Scientific paper

The interaction of neutrinos with a plasma can be of great importance for the description of some catastrophic events, such as supernova explosions. For instance, during the formation of a neutron star, neutrinos νe and antineutrinos barνe are unable to leave the star. The neutrino escape timescale exceeds the characteristic dynamical timescale, and an equilibrium state is reached, which includes the neutrino concentrations. A detailed knowledge of the transport properties of the neutrinos in these environments must consider the neutrino-plasma weak coupling. We describe here the influence of a background unmagnetized plasma in the thermodynamical properties of the neutrino gas, when the weak interaction of the neutrino gas with the plasma electrons is taken into account. The mechanism by which equilibrium can be established consists in the absorption and emission of νe and barνe by matter. In this case, the number of neutrinos is conserved and the chemical potential is zero. It is also assumed that the νe has a rest mass. The free energy of the neutrino gas is calculated explicitly, thus allowing the derivation of all the relevant thermodynamical quantities. The equation of state of the neutrino gas in the plasma is also derived for several relevant astrophysical processes.

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