Estimation of Electrical Conductivity and Magnetization Parameter of Neutron Star Crusts and Applied to the High-Braking-Index Pulsar PSR J1640-4631 - Hui Wang (Universe, 2020)
Young pulsars are thought to be highly magnetized neutron stars (NSs). The crustal magnetic field of a NS usually decays at different timescales in the forms of Hall drift and Ohmic dissipation. The magnetization parameter <semantics> ω B τ </semantics> is defined as the ratio of the Ohmic timescale <semantics> τ O h m </semantics> to the Hall drift timescale <semantics> τ H a l l </semantics> . During the first several million years, the inner temperature of the newly born neutron star cools from <semantics> T = 10 9 <mspace width="0.166667em"></mspace> </semantics> K to <semantics> T = 1 . 0 × 10 8 <mspace width="0.166667em"></mspace> </semantics> K, and the crustal conductivity increases by three orders of magnitude. In this work, we adopt a unified equations of state for cold non-accreting neutron stars with the Hartree–Fock–Bogoliubov method, developed by Pearson et al. (2018), and choose two fiducial dipole magnetic fields of <semantics> B = 1 . 0 × 10 13 <mspace width="0.166667em"></mspace> </semantics> G and <semantics> B = 1 . 0 × 10 14 <mspace width="0.166667em"></mspace> </semantics> G, four different temperatures, T, and two different impurity concentration parameters, Q, and then calculate the conductivity of the inner crust of NSs and give a general expression of magnetization parameter for young pulsars: <semantics> ω B τ ≃ ( 1 − 50 ) B 0 / ( 10 13 <mspace width="0.166667em"></mspace> </semantics> G) by using numerical simulations. It was found when <semantics> B ≤ 10 15 </semantics> G, due to the quantum effects, the conductivity increases slightly with the increase in the magnetic field, the enhanced magnetic field has a small effect on the matter in the low-density regions of the crust, and almost has no influence the matter in the high-density regions. Then, we apply the general expression of the magnetization parameter to the high braking-index pulsar PSR J1640-4631. By combining the observed arrival time parameters of PSR J1640-4631 with the magnetic induction equation, we estimated the initial rotation period <semantics> P 0 </semantics> , the initial dipole magnetic field <semantics> B 0 </semantics> , the Ohm dissipation timescale <semantics> τ O h m </semantics> and Hall drift timescale <semantics> τ H a l l </semantics> . We model the magnetic field evolution and the braking-index evolution of the pulsar and compare the results with its observations. It is expected that the results of this paper can be applied to more young pulsars.