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 $n=3.15\pm 0.03$. 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.

5 pages, 2 figures, PASJ in press