Investigations of the Ohmic Decay and the Soft X-Ray Emission of the High-braking-index Pulsar PSR J1640-4631
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) × 107 G yr-1 and dB t /dt ∼ (0.82-1.05) × 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) × 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) × 107 G yr-1, and dB t /dt ∼ (1.32-1.54) × 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) × 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+N uStar telescopes. The observed soft X-ray flux in the (2-10) keV band is F X ∼ 1.8(4) × 10-13 erg cm-2 s-1, which corresponds to a high surface temperature, T ∼ 1.54(6) × 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.