We study the emission of neutrinos , resulting from the scattering of electrons off magnetic flux tubes ( fluxoids ) in the neutron star cores with superfluid ( superconducting ) protons .
In the absence of proton superfluidity ( T \geq T _ { cp } ) , this process transforms into the well known electron synchrotron emission of neutrino pairs in a locally uniform magnetic field B , with the neutrino energy loss rate Q proportional to B ^ { 2 } T ^ { 5 } .
For temperatures T not much below T _ { cp } , the synchrotron regime ( Q \propto T ^ { 5 } ) persists and the emissivity Q can be amplified by several orders of magnitude due to the appearance of the fluxoids and associated enhancement of the field within them .
For lower T , the synchrotron regime transforms into the bremsstrahlung regime ( Q \propto T ^ { 6 } ) similar to the ordinary neutrino-pair bremsstrahlung of electrons which scatter off atomic nuclei .
We calculate Q numerically and represent our results through a suitable analytic fit .
In addition , we estimate the emissivities of two other neutrino-production mechanisms which are usually neglected – neutrino-pair bremsstrahlung processes due to electron-proton and electron-electron collisions .
We show that the electron-fluxoid and electron-electron scattering can provide the main neutrino production mechanisms in the neutron star cores with highly superfluid protons and neutrons at T \raise 1.29 pt \hbox { $ < $ \kern - 7.5 pt \raise - 4.73 pt \hbox { $ \sim$ } } 5 \times 10 ^ { 8 } K. The electron-fluxoid scattering is significant if the initial , locally uniform magnetic field B \raise 1.29 pt \hbox { $ > $ \kern - 7.5 pt \raise - 4.73 pt \hbox { $ \sim$ } } 10 ^ { 13 } G .