Estimation of Electrical Conductivity and Magnetization Parameter of Neutron Star Crusts and Applied to the High-Braking-Index Pulsar PSR J1640-4631

Abstract

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 ω B τ is defined as the ratio of the Ohmic timescale τ O h m to the Hall drift timescale τ H a l l . During the first several million years, the inner temperature of the newly born neutron star cools from T = 10 9 K to T = 1.0 × 10 8 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 B = 1.0 × 10 13 G and B = 1.0 × 10 14 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: ω B τ ≃ ( 1 − 50 ) B 0 / ( 10 13 G) by using numerical simulations. It was found when B ≤ 10 15 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 P 0 , the initial dipole magnetic field B 0 , the Ohm dissipation timescale τ O h m and Hall drift timescale τ H a l l . 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.

The dissipation of toroidal magnetic fields and spin‐down evolution of young and strongly magnetized pulsars

“…The magnetization parameter, ω B τ , is defined as the ratio of the ohmic timescale τ Ohm to the Hall drift timescale τ Hall , where ω B is the electron gyrofrequency, and τ is the electron relaxation time. We calculated the crust conductivity of NSs and gave a general expression of ω B τ for young pulsars (Wang et al 2020). It was found that, when B ≤ 10 15 G, the conductivity increases slightly with the increase in the magnetic field strength B due to the quantum effects, the enhanced B has a small effect on the matter in the low‐density regions of the crust and has almost no influence on the matter in the high‐density regions.…”

The fundamental plane of black hole activity for quiescent sources

“…Dong et al (2014)) found that both “outliers” of BH XRBs and bright AGNs follow a steeper fundamental plane of black hole activity. Coriat et al (2011) argued that the two fundamental planes are regulated by radiatively inefficient (e.g., ADAF) and radiatively efficient accretion processes (e.g., SSD + corona), respectively, if we assume the jet launching and radio radiation behave identically (see also, Deng et al 2020; Gao et al 2011a; Fu et al 2020; Li et al 2016; Zhu et al 2016; Wang et al 2020).…”

Investigation of magneto‐thermal evolution of AXP 1E 2259 + 586

“…Recently, we have adopted 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 B = 1.0 × 10 13 G and B = 1.0 × 10 14 G, four different temperatures, T , and two different impurity concentration parameters, Q , and then calculated the conductivity of the inner crust of NSs and gave a general expression of magnetization parameter for young pulsars by using numerical simulations, where ω B is the electron gyro‐frequency, and τ is the electron relaxation time (Wang et al 2020, Gao et al 2021). It was found that when B ≤ 10 15 G, the conductivity increases slightly with the increase in the magnetic field strength due to the quantum effects, the enhanced magnetic field strength has a small effect on the matter in the low−density regions of the crust, and almost has no influence on the matter in the high−density regions.…”

“…The effect of Hall drift depends on the initial field strength and structure and how fast the NS cools. During the Hall drift stage, the toroidal field is strongly rearranged and dissipated, after this stage, the long‐term evolution seems to select, generally, a predominantly quadrupolar/octupolar structure concentrated in the inner crust and which tends to be stronger close to the poles (Deng et al 2020; Fu et al 2020; Gao et al 2017a, 2017b, 2017c, 2019a, 2019b; Li et al 2016; Wang et al 2020).…”