The Dipole Magnetic Field and Spin-down Evolutions of The High Braking Index Pulsar PSR J1640-4631

Abstract

In this work, we interpreted the high braking index of PSR J1640$-$4631 with a combination of the magneto-dipole radiation and dipole magnetic field decay models. By introducing a mean rotation energy conversion coefficient $\overline{\zeta }$, the ratio of the total high-energy photon energy to the total rotation energy loss in the whole life of the pulsar, and combining the pulsar's high-energy and timing observations with reliable nuclear equation of state, we estimate the pulsar's initial spin period, $P_0\sim (17-44)$ ms, corresponding to the moment of inertia $I\sim (0.8-2.1)\times 10^{45}$ g cm${}^2$. Assuming that PSR J1640$-$4631 has experienced a long-term exponential decay of the dipole magnetic field, we calculate the true age $t_{\mathrm{age}}$, the effective magnetic field decay timescale ${\tau }_D$, and the initial surface dipole magnetic field at the pole $B_p(0)$ of the pulsar to be $(2900-3100)$ yrs, $1.07(2)\times 10^5$ yrs, and $(1.84-4.20)\times 10^{13}$ G, respectively. The measured braking index of $n=3.15(3)$ for PSR J1640$-$4631 is attributed to its long-term dipole magnetic field decay and a low magnetic field decay rate, $d{B}_{\mathrm{p}}/dt\sim -(1.66-3.85)\times 10^8$ G yr${}^{-1}$. Our model can be applied to both the high braking index ($n>3$) and low braking index ($n<3$) pulsars, tested by the future polarization, timing, and high-energy observations of PSR J1640$-$4631.

Correspoding to the publication version: 2017, ApJ, 849, 19 (12pp)

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