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

TL;DR

This study explains the high braking indices of two magnetars by modeling the decrease in their inclination angles using a double magnetic-dipole approach, revealing their internal magnetic evolution.

Contribution

It introduces a double magnetic-dipole model to account for high braking indices in magnetars, emphasizing magnetic inclination angle evolution as a key factor.

Findings

Magnetic inclination angles decrease over time in the studied magnetars.

The ratio of magnetic moments, η, is significantly higher in magnetars than in typical pulsars.

The model aligns with observed high braking indices by linking magnetic evolution to spin-down behavior.

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.