The Landau level-superfluid modified factor and the overal soft X/γ-ray efficiency coefficient of a magnetar

Abstract

As soon as the energy of electrons near the Fermi surface are higher than $Q$, the threshold energy of inverse $\beta-$ decay, the electron capture process will dominate. The resulting high-energy neutrons will destroy anisotropic ${}^3P_2$ neutron superfluid Cooper pairs. By colliding with the neutrons produced in the process $n+ (n\uparrow n\downarrow)\longrightarrow n+ n+ n$, the kinetic energy of the outgoing neutrons will be transformed into thermal energy. The transformed thermal energy would transported from the star interior to the star surface by conduction, then would be transformed into radiation energy as soft X-rays and gamma-rays. After a highly efficient modulation within the pulsar magnetosphere, the surface thermal emission (mainly soft X/$\gamma$-ray emission) has been shaped into a spectrum with the observed characteristics of magnetars. By introducing two important parameters: Landau level-superfluid modified factor and effective X/$\gamma$-ray coefficient, we numerically simulate the process of magnetar cooling and magnetic field decay, and then compute magnetars' soft X/$\gamma$-ray luminosities $L_{X}$. Further, we obtain aschematic diagrams of $L_{X}$ as a function of magnetic field strength $B$. The observations are compared with the calculations.