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

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 ± 0.03. 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.