Explaining high-braking indice of magnetars SGR 0501+4516 and 1E 2259+586 using the double magnetic-dipole model

Abstract

In this paper, we attribute high braking indices $n>3$ of two magnetars SGR 0501$+$4516 and 1E 2259$+$586 to the decrease in their inclination angles using the double magnetic-dipole model proposed by Hamil et al.(2016). In this model, there are two magnetic moments inside a neutron star, one is generated by the rotation effect of a charged sphere, $M_1$, and the other is generated by the magnetization of ferromagnetically ordered material, $M_2$. Our calculations indicate that the magnetic moment $M_2$ would evolve towards alignment with the spin axis of the two magnetars, and cause their magnetic inclination angles to decrease. We also define a ratio $\eta =M_2/M_1$, which reflects the magnetization degree, and find that the values of $\eta$ of the two magnetars are about two-orders of magnitude higher than that of rotationally powered pulsar PSR J1640-4631 with $n=3.15(3)$, assuming that they have the same rate of decrease in their inclination angles.

6 pages,3 figures,5 tables. arXiv admin note: text overlap with arXiv:1909.01699 by other authors

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