2019PASP..131e4201W

The young pulsar PSR J1640-4631 is the first pulsar reported with a high braking index, n = 3.15 ± 0.03, and has attracted extensive attention. In this work, by inputting the equation of state, we obtain two typical and feasible ranges of the electrical conductivity in the crust of PSR J1640-4631. Then, by considering the effects of general relativity, we formulate the induction equation and use it to investigate the decay of crustal magnetic fields within two scenarios: pure Ohmic decay, and the combination of Ohmic decay and Hall drift. In the former scenario, we calculate the current magnetic field decay rates as dB_p/dt ∼ (0.78-1.00) x 10⁷ G yr^–1 and dB_t/dt ∼ (0.82-1.05) x 10⁸ G yr^–1 for the poloidal and toroidal parts, respectively, and estimate the current magnetic energy decay rate as L_B ∼ (0.95-1.22) x 10³² erg s^–1. In the latter scenario, the combination of Ohmic decay and Hall drift accelerates the decay of magnetic fields, and we calculate the current magnetic field decay rates as dB_p/dt ∼ (1.26-1.47) x 10⁷ G yr^–1, and dB_t/dt ∼ (1.32-1.54) x 10⁸ G yr^–1 for the poloidal and toroidal parts, respectively, and estimate the current magnetic energy decay rate as L_B ∼ (1.86-2.18) x 10³² erg s^–1. It is found that the recalculated value of the braking index n of the star is lower than its observed value, which implies that other factors influence the spin-down evolution. The current magnetic energy decay rates calculated in both scenarios are far less than the isotropic soft X-ray luminosity obtained from Chandra+NuStar telescopes. The observed soft X-ray flux in the (2-10) keV band is F_X ∼ 1.8(4) x 10^–13 erg cm^–2 s^–1, which corresponds to a high surface temperature, T ∼ 1.54(6) x 10⁶ K. The observed X-ray flux of the star could be caused by the decay of a multipolar magnetic field near the pole, which is strong enough to activate the slot-gap mechanism. The high surface temperature of the star is attributed either to magnetic spot formation or thermoplastic wave heating due to the decay of the toroidal field near the pole. Our results could be useful in interpreting the high soft X-ray flux from high magnetic field pulsars.