On the weak magnetic field of millisecond pulsars: Does it decay before accretion?

Millisecond pulsars are old, fast spinning neutron stars thought to have evolved from classical pulsars in binary systems, where the rapid rotation is caused by the accretion of matter and angular momentum from their companion. During this transition between classical and millisecond pulsars, there is a magnetic field reduction of around 4 orders of magnitude, which is not well understood. According to the standard scenario, the magnetic field is reduced as a consequence of accretion, either through ohmic dissipation or through screening by the accreted matter. We explored an alternative hypothesis in which the magnetic field is reduced through ambipolar diffusion before the accretion. This is particularly effective during the long epoch in which the pulsar has cooled, but has not yet started accreting. This makes the final magnetic field dependent on the evolution time of the companion star and thus its initial mass. We use observed binary systems to constrain the time available for the magnetic field decay based on the current pulsar companion: a helium white dwarf, a carbon-oxygen white dwarf, or another neutron star. Based on a simplified model without baryon pairing, we show that the proposed process agrees with the general distribution of observed magnetic field strengths in binaries, but is not able to explain some mildly recycled pulsars where no significant decay appears to have occurred. We discuss the possibility of other formation channels for these systems and the conditions under which the magnetic field evolution would be set by the neutron star crust rather than the core.