Magnetic field decay in black widow pulsars

We study in this work the evolution of the magnetic field in `redback-black widow' pulsars. Evolutionary calculations of these `spider' systems suggest that first the accretion operates in the redback stage, and later the companion star ablates matter due to winds from the recycled pulsar. It is generally believed that mass accretion by the pulsar results in a rapid decay of the magnetic field when compared to the rate of an isolated neutron star. We study the evolution of the magnetic field in black widow pulsars by solving numerically the induction equation using the modified Crank-Nicolson method with intermittent episodes of mass accretion on to the neutron star. Our results show that the magnetic field does not fall below a minimum value ('bottom field') in spite of the long evolution time of the black widow systems, extending the previous conclusions for much younger low-mass X-ray binary systems. We find that in this scenario, the magnetic field decay is dominated by the accretion rate, and that the existence of a bottom field is likely related to the fact that the surface temperature of the pulsar does not decay as predicted by the current cooling models. We also observe that the impurity of the pulsar crust is not a dominant factor in the decay of magnetic field for the long evolution time of black widow systems. (AU)