Different‎ Magnetic Field ‎Distributions‎ in Deformed Neutron Stars‎

Abstract

‎In this work, we review the formalism which would allow us to model magnetically deformed neutron stars. We study the effect of different magnetic field configurations on the equation of state (EoS) and ‎the ‎structure of such stars. ‎For this aim‎, the EoS of magnetars is acquired by using the lowest order constraint variational (LOCV) method ‎‎and ‎employing‎ the AV18 potential‎.‎ We ‎show ‎how ‎the ‎magnetic ‎field ‎varies ‎from ‎the ‎‎surface ‎to ‎the ‎center ‎of ‎neutron‎ ‎star ‎by ‎using ‎various ‎exponential ‎and ‎polynomial ‎profiles ‎and ‎compare ‎their ‎results.‎‎In addition‎, ‎global properties of neutron stars ‎are‎ obtained within two formalisms‎. ‎The first formalism is described by considering the pressure into two directions and the deformation of neutron stars is governed by anisotropies in‎ ‎the equation of state‎‎. The second formalism for investigating macroscopic properties of magnetars is gained by treating the nonuniform pressure as a perturbation to the total pressure and expanding metric and pressure up to the quadrupole term in spherical ‎harmonics.‎Afterwards‎, ‎we include three nucleon interactions (TNI) to ‎the ‎EoS‎ and apply this model to represent our results for both exponential and polynomial magnetic field profiles.‎The maximum gravitational mass is obtained ‎in ‎the ‎range ‎of ‎(‎1.7‎1-1.80)‎ M. ‎and ‎(‎2.13‎‎-‎2.1‎9)‎‎‎ M.‎ for ‎the EoS without and with TNI ‎contribution‎, respectively.