Direct URCA process in neutron stars with strong magnetic fields

We calculate the emissivity for the direct URCA process in strongly magnetized, degenerate matter in neutron stars, under $\beta $-equilibrium. We show that, if the magnetic field is large enough for protons and electrons to be confined to the ground Landau levels, the field-free threshold condition on proton concentration no longer holds, and direct URCA reactions are open for an arbitrary proton concentration. Direct URCA process leads to an early phase of fast neutron star cooling. This circumstance allows us to constrain the initial magnetic field inside observed pulsars.