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

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5. Conclusions

We have considered the synchrotron neutrino-pair emission of electrons from a dense magnetized plasma. We developed a computer code (Sect. 2) which calculates the synchrotron emission in the presence of quantizing magnetic fields for a wide range of conditions at which the electrons can be weakly as well as strongly degenerate and/or relativistic. We have also calculated the synchrotron emissivity in the quasiclassical approximation (Sect. 3) for strongly degenerate, relativistic electrons which populate many Landau levels. We have paid special attention to the case in which the main contribution into the synchrotron neutrino emission comes from the fundamental or several low cyclotron harmonics. This case has not been analyzed properly earlier by KLY and Vidaurre et al. (1995). We have obtained a simple analytic expression (16) which fits accurately our quasiclassical results in wide ranges of densities, temperatures, and magnetic fields. In Sect. 4 we have demonstrated that the synchrotron neutrino emissivity gives considerable or even dominant contribution into the neutrino emissivity at [FORMULA]  G in moderate-density and/or high-density layers of the NS crusts, depending on temperature and magnetic field. Let us notice, that the neutrino emissivities plotted in Figs. 5- 8 are appropriate for cooling neutron stars rather than for newly born or merging neutron stars. Since the neutrino radiation from a cooling neutron star is too weak to be detected with modern neutrino observatories we do not calculate the spectrum of emitted neutrinos.

Our results indicate that the neutrino synchrotron emission should be taken into account in the cooling theories of magnetized neutron stars. It can be important during initial cooling phase (t = 10-1000  yrs after the neutron star birth). At this stage, the thermal relaxation of internal stellar layers is not achieved (e.g., Nomoto & Tsuruta 1987, Lattimer et al. 1994) and local emissivity from different crustal layers can affect this relaxation and observable surface temperature.

The synchrotron process in the crust can also be significant at the late neutrino cooling stages ([FORMULA]  yrs, [FORMULA]  K), in the presence of strong magnetic fields [FORMULA]  G. The synchrotron emission can be the dominant neutrino production mechanism in the neutron star crust, while the neutrino luminosity from the stellar core may be not too high, at this cooling stage, and quite comparable with the luminosity from the crust.

It is worthwhile to mention that the synchrotron emission can be important also in the superfluid neutron star cores (Kaminker et al. 1997). A strong superfluidity of neutrons and protons suppresses greatly (e.g., Yakovlev & Levenfish 1995) the traditional neutrino production mechanisms such as Urca processes or nucleon-nucleon bremsstrahlung. The superfluidity (superconductivity) of protons splits an initial, locally uniform magnetic field of the neutron star core into fluxoids - thin magnetic threads of quantized magnetic flux. This process modifies the neutrino synchrotron process (Kaminker et al. 1997) amplifying it just after the superconductivity onset and making it significant since the traditional neutrino generation mechanisms are suppressed. It has been shown that this modified neutrino synchrotron process can dominate over other mechanisms if the initially uniform magnetic field in the NSs core is [FORMULA]  G and if [FORMULA]  K. These fields and temperatures are quite consistent with the results of the present article: similar conditions are necessary for the synchrotron emission to dominate over other neutrino production mechanisms in the NS crust by the end of the neutrino cooling stage. If so, the total neutrino luminosity (from the stellar crust and core) can be governed by internal stellar magnetic fields which can affect the neutron star cooling. We plan to study this cooling in a future article.

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© European Southern Observatory (ESO) 1997

Online publication: March 24, 1998