http://arxiv.org/abs/1709.03459
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 phonon 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 inertial of momentum $I\sim (0.8-2.1)\times 10^{45}$ 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 $t_{\rm age}$, the effective magnetic field decay timescale $\tau_{\rm D}$, and the initial surface dipole magnetic field at the pole $B_{p}(0)$ of the pulsar to be $(2900-3100)$ yrs, $1.07(2)\times10^{5}$ yrs, and $(1.84-4.20)\times10^{13}$ 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, $dB_{\rm p}/dt\sim -(1.66-3.85)\times10^{8}$ 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.
Z. Gao, N. Wang, H. Shan, et. al.
Tue, 12 Sep 17
4/71
Comments: Submmotted to ApJ after considering referee’s suggestions