Neutrino pair synchrotron radiation from relativistic electrons in strong magnetic fields

The emissivity for the neutrino pair synchrotron radiation in strong magnetic fields has been calculated both analytically and numerically for high densities and moderate temperatures, as can be found in neutron stars. Under these conditions, the electrons are relativistic and degenerate. We give here our results in terms of an universal function of a single variable. For two different regimes of the electron gas we present a simplified calculation and compare our results to those of Kaminker et al. Agreement is found for the classical region, where many Landau levels contribute to the emissivity , but some differences arise in the quantum regime. One finds that the emissivity for neutrino pair synchrotron radiation is competitive, and can be dominant, with other neutrino processes for magnetic fields of the order $B \sim 10^{14} - 10^{15} G $.This indicates the relevance of this process for some astrophysical scenarios, such as neutron stars and supernovae.