Why do millisecond pulsars have weaker magnetic fields compared to ordinary pulsars?

Abstract

Millisecond pulsars, with magnetic fields weaker by three to four orders compared to those of ordinary pulsars, are presumed to be neutron stars spun up by binary accretion. We expect the magnetic field to get screened by the accreted material. Our simulation of this screening mechanism shows that the field decreases by a purely geometric factor sin^−7/2 θ_P,i before freezing to an asymptotic value, where θ_P,i is the initial angular width of the polar cap. If θ_P,i lies in the range 5-10°, then the magnetic field diminution factor turns out to be ~ 10³-10⁴, in conformity with observational data.