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

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 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, Stone, and Stone (2016, Phys. Rev. D. 94, 063012) 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 exists 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 indicates that 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 for the magnetic inclination angle. [ABSTRACT FROM AUTHOR]