In a superhigh magnetic field, direct Urca reactions can proceed for an arbitrary proton concentration. Since only the electrons with high energy E (E > Q, Q is the threshold energy of inverse β-decay) at large Landau levels can be captured, we introduce the Landau level effect coefficient q and the effective electron capture rate eff . By using eff , the values of L X and L ν are calculated, where L X and L ν are the average neutrino luminosity of AXPs and the average X-ray luminosity of AXPs L X , respectively. The complete process of electron capture inside a magnetar is simulated numerically.

In this paper, we consider the effect of Landau levels on the decay of superhigh magnetic fields of magnetars. Applying 3 P 2 anisotropic neutron superfluid theory yield a second-order differential equation for a superhigh magnetic field B and its evolutionary timescale t. The superhigh magnetic fields may evolve on timescales ∼ (10 6 − 10 7 ) yrs for common magnetars. According to our model, the activity of a magnetar may originate from instability caused by the high electron Fermi energy.

There is accumulating evidence that scalar fields may exist in nature. The gravitational collapse of a boson cloud leads to the formation of a boson star just like white dwarfs and neutron stars. In general, as one of the candidates of dark matter, a boson star holds a stable configuration and has deserved intensive attention and extensive research in the past 50 years. At first, we analyze the ground state solutions for a Boson-Fermi system using the metric tensor in the Newtonian approximation, then analyze the configuration of a star composed of bosons and fermions. At last, for the purpose of investigating the equilibrium geometry of a Boson-Fermi system, we construct the virial equations of a boson-Fermi system with different orders. In our future work, we will explore the equilibrium configuration and the stability of a Boson-Fermi star and how a scalar field affects the pressure of the system using higher-order virial equations of fluid motions. KEYWORDSboson-fermion star -complex scale fields -fluid boson stars -gravity theories

To date, the observational determination of braking indexes of magnetars is still an open question due to the lack of longterm radio emission and strong timing noise. Based on the assumption that the real ages of magnetars are the ages of their host supernova remnants (SNRs), expanding diffuse gaseous nebulae resulting from explosions of massive stars, we obtain the sizes of the braking index n for 11 magnetar candidates with SNRs. According to our calculations, the magnetar braking indexes will be constrained within the range of about 1-40, assuming the measurements of SNRs are reliable. We also investigate the frequency parameters of magnetars with associated SNRs, and estimate possible wind luminosities for magnetars with n < 3 and magnetic field decay rates for magnetars with n > 3.

In this paper, an approximate method of calculating the Fermi energy of electrons (E F (e)) in a high-intensity magnetic field, based on the analysis of the distribution of a neutron star magnetic field, has been proposed. In the interior of a neutron star, different forms of intense magnetic field could exist simultaneously and a high electron Fermi energy could be generated by the release of magnetic field energy. The calculation results show that: E F (e) is related to density ρ, the mean electron number per baryon Y e and magnetic field strength B.