2017ApJ...849...19G

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 , 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 a reliable nuclear equation of state, we estimate the pulsar's initial spin period, P₀∼(17–44) ms, corresponding to the moment of inertia I∼(0.8–2.1)×10⁴⁵ g cm². Assuming that PSR J1640-4631 has experienced a long-term exponential decay of the dipole magnetic field, we calculate the true age t_age, the effective magnetic field decay timescale τ_D, and the initial surface dipole magnetic field at the pole B_p(0) of the pulsar to be 2900-3100 yr, 1.07(2)×10⁵ yr, and (1.84–4.20)×10¹³ 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_p/dt∼-(1.66–3.85)×10⁸ 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.