Equilibrium configurations of relativistic stars with purely toroidal magnetic fields: Effects of realistic equations of state

We investigate equilibrium sequences of relativistic stars containing purely toroidal magnetic fields with four kinds of realistic equations of state (EOS) of SLy, FPS, Shen, and LS. We numerically construct thousands of equilibrium configurations in order to study the effects of the realistic EOSs. Particularly, we pay attention to the equilibrium sequences of constant baryon mass and/or constant magnetic flux, which model evolutions of an isolated neutron star, losing angular momentum via gravitational waves. Important properties obtained in this study are summarized as follows. (1) Unlike the polytropic EOS, it is found for the realistic EOSs that the maximum masses do not monotonically increase with the field strength along the constant magnetic flux sequences. (2) The dependence of the mass-shedding angular velocity on the EOSs is determined from that of the nonmagnetized case. The stars with Shen (FPS) EOS reach the mass-shedding limit at the smallest (largest) angular velocity, while the stars with SLy or Lattimer-Swesty EOSs take the moderate values. (3) For the supramassive sequences, the equilibrium configurations are found to be generally oblate for the realistic EOSs in sharp contrast to the polytropic stars. For FPS (LS) EOS, the parameter region which permits the prolately deformed stars is widest (narrowest). For SLy and Shen EOS, it is in medium. Furthermore, the angular velocities Ω_up, above which the stars start to spin up as they lose angular momentum, are found to depend sharply on the realistic EOSs. Our analysis indicates that the hierarchy of this spin-up angular velocity is Ω_up,SLy > Ω _up,FPS > Ω_up,LS > Ω_up,Shen, and this relation holds even if the sequences have strong magnetic fields. Our results suggest that the relativistic stars containing purely toroidal magnetic fields will be a potential source of gravitational waves and the EOSs within such stars can be constrained by observing the angular velocity, the gravitational wave, and the signature of the spin-up.