Neutron Star Cooling on Strong Magnetic Field : Neutrino -Antineutrino Pair Emission and Direct Urca Processes

We study neutrino and anti-neutrino emissions through the v (v) over bar -pair emission and the direct Urca processes in the strong magnetic field, The strong magnetic fields supply additional momentum and the neutrino emissivity and largely enhance the emissivity. We solve exact wave functions for protons and electrons in the states described with Landau levels. Both processes in strong magnetic fields are expected to contribute significantly to the cooling of the magnetars.