Application of a two dipole model to PSR J1640-4631, a pulsar with an anomalous braking index

TL;DR

This paper models the high braking index of PSR J1640-4631 using a two-dipole approach, explaining the decrease in magnetic inclination angle through magnetic interactions and rotation effects.

Contribution

It introduces a two-dipole model to explain the magnetic inclination angle evolution in PSR J1640-4631, linking magnetic interactions to the observed braking index.

Findings

Magnetic moments tend to align with the spin axis, reducing the inclination angle.

The model explains the high braking index through magnetic inclination evolution.

Pulse profile suggests a low rate of change in the inclination angle.

Abstract

Recent timing observation provides an intriguing result for the braking index of the X-ray pulsar PSR J1640-4631, which has a measured braking index $n=3.15\pm0.03$. The decrease of the inclination angle between between the spin axis and the magnetic axis can be responsible for such a high braking index. However, the physical mechanisms causing the change of the magnetic inclination angle have not been fully understood. In this Letter, we apply a two-dipole model given by Hamil et al (2016) to explain the decrease of the magnetic inclination angle of PSR J1640-4631. The rotation effect of a charged sphere and the magnetization of ferromagnetically ordered material produce magnetic moments $M_{1}$ and $M_{2}$, respectively. There exist a minimum of the potential energy for the magnetic moment $M_{2}$ in the magnetic field of $M_{1}$, hence the $M_{2}$ will freely rotate around the minimum energy position (i. e equilibrium position), similar to a simple pendulum. Our calculation indicate the magnetic moment $M_{2}$ would evolve towards alignment with the spin axis for PSR J1640-4631, and cause the magnetic inclination angle to decrease. The single peak in the pulse profile favors a relatively low change rate of the magnetic inclination angle.