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

TL;DR

This paper presents a simulation showing that the magnetic field weakening in millisecond pulsars results from a geometric screening mechanism during accretion, aligning with observed magnetic field reductions.

Contribution

It introduces a novel geometric model explaining magnetic field screening in pulsars, quantitatively matching observed field weakening in millisecond pulsars.

Findings

Magnetic field decreases by a geometric factor before freezing.

Field diminution factor of 10^3 to 10^4 matches observations.

Screening mechanism depends on initial polar cap width.

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, for the first time, that the field decreases by a purely geometric factor $\sin^{-7/2} \theta_{\rm P,i}$ before freezing to an asymptotic value, where $ \theta_{\rm P,i}$ is the initial angular width of the polar cap. If $ \theta_{\rm P,i}$ lies in the range $5^o$--$10^o$, then the magnetic field diminution factor turns out to be $\sim 10^3$--$10^4$ in conformity with observational data.