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Astron. Astrophys. 328, 409-418 (1997)

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1. Introduction

In this article, we study the synchrotron emission of neutrino pairs by relativistic, degenerate electrons in strong magnetic fields,


This emission can be an important source of neutrino energy losses from the crusts of magnetized cooling neutron stars (NSs) as well as (in a modified form) from the superfluid NS cores.

The process has been considered by several authors starting from the pioneering article by Landstreet (1967). The adequate quasiclassical formalism was developed by Kaminker, Levenfish & Yakovlev (1991, hereafter KLY) who presented also critical analysis of preceding work. KLY carried out detailed analytic and numerical analysis of the case in which the electrons populated many Landau levels and the main contribution into the synchrotron emission came from high cyclotron harmonics. They also considered briefly the opposite case of the superstrong magnetic field which suppresses greatly the contribution from all harmonics. In that case, only the first harmonics actually survives (although exponentially damped).

Exact quantum formalism of the neutrino synchrotron emission was developed by Kaminker et al. (1992a). Kaminker & Yakovlev (1993) considered the synchrotron process in the nondegenerate electron gas. Recently Kaminker et al. (1997) have analyzed how the synchrotron emission is modified in the superconducting NS cores where the initially uniform magnetic field splits into fluxoids. In a recent article, Vidaurre et al. (1995) have reconsidered the results of KLY claiming them to be inaccurate.

In the present article, we continue to study the neutrino synchrotron radiation from the degenerate magnetized electron gas. The emphasis is made upon the case in which the electron transitions associated with one or several lowest cyclotron harmonics are most important. This case has not been studied attentively earlier. We calculate the neutrino emissivity numerically using the exact quantum formalism (Sect. 2, Appendix A). We also use the quasiclassical approach (Sect. 3, Appendix B), combine our new results with those by KLY and propose an analytic fit that describes accurately all the neutrino synchrotron radiation regimes in a strongly degenerate, relativistic electron gas in which the electrons occupy many Landau levels. Another limiting case in which the electrons populate the ground level alone is considered in Appendix C. In Sect. 3 we present also critical discussion of the results by Vidaurre et al. (1995). In Sect. 4 we show the importance of the neutrino synchrotron emission in the NS interiors.

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© European Southern Observatory (ESO) 1997

Online publication: March 24, 1998