Plasma Bremsstrahlung Recombination Neutrinos

Plasma-Neutrinos: An electromagnetic wave entering a sufficiently dense plasma generates collective oscillations of the electrons. In turn, these oscillations of a charged medium generate the emission of electromagnetic waves. A plasmon is the quantum of energy associated to these waves. They propagate in various directions and their sum has to be taken. According to (9.51), associated to each plasmon there is probability of emission of veve.

The energy loss by plasma-neutrino dominates at high densities, in the degenerate domain of the plane log T vs. log q (Fig. 9.11). The emission rate first increases with density (Fig. 9.8), because a higher q favors collective plasma oscillations, in this regime at a given q the v emission rate increases with about T4 because of the behavior of P(veve)/Py. Then, the curves go through a maximum and decline for higher densities, because the domains of a Coulomb liquid and then of ionic Coulomb crystal are entered (Sect. 7.6.4).

Bremsstrahlung Neutrinos: The process is the inverse of the hyperbolic or freefree transitions (Sect. 8.4). An electron slowed down in the Coulomb field of a charged nucleus emits electromagnetic radiation with a probability (9.51) of a pair veve emission (Fig. 9.10).

The emission rates behave like Z2/A, where Z and A are the atomic number and the atomic mass, so that bremsstrahlung v emission is more important for heavy elements. At high densities, the v-emission goes like ~ q T6. Figure 9.9 compares the emission rates of bremsstrahlung neutrinos with the sum of photo-, pair-, plasma-

Fig. 9.10 Schematic illustration of the emission of bremsstrahlung neutrinos

log T

log T

Fig. 9.11 The domains of the plane log T vs. log q where the different processes of neutrino emissions dominate. The dotted line indicates the Fermi temperature Tp (see 7.146 and following remark), to the right of it (in the gray area) matter is degenerate. "rec" indicates neutrino from the recombination process. Adapted from N. Itoh et al. [269]

Fig. 9.11 The domains of the plane log T vs. log q where the different processes of neutrino emissions dominate. The dotted line indicates the Fermi temperature Tp (see 7.146 and following remark), to the right of it (in the gray area) matter is degenerate. "rec" indicates neutrino from the recombination process. Adapted from N. Itoh et al. [269]

neutrinos. Bremsstrahlung neutrinos dominate at very high densities in a significant domain for C detonation and e capture (Fig. 26.10) and also in a small domain of moderate T and q, however there the rates are so low that this is of no significance for evolution.

Recombination Neutrinos: A free electron in the continuum makes a transition to a bound atomic state, in a process which is the inverse of the photoionization or bound-free transitions (Sect. 8.3). Recombination neutrinos dominate at low T and q (Fig. 9.11), i.e., for T < 108 K for pure 56Fe, for T < 2 x 107 K for pure 12C, but they never dominate for helium or hydrogen. On the whole, the emission rates are very low and they have little significance.

There are other neutrino emission processes. The Urca process consists of an e~ capture by a nucleus with ve emission followed (e.g., after some convective transport) by a ยก5 decay with ve emission. There are also synchrotron neutrinos: an electron moving in a strong field may emit a ve ve pair instead of a photon. However, only the photo-, pair-, plasma- and bremsstrahlung-neutrino processes play a significant role in stellar evolution.

Part III

Hydrodynamical Instabilities and Transport Processes

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