Quark magnetar in three-flavor Nambu–Jona-Lasinio model under strong magnetic fields with two types of vector interactions

We investigate the properties of strange quark matter (SQM) and quark stars (QSs) in the framework of SU(3) Nambu–Jona-Lasinio (NJL) model with two types of vector interactions under strong magnetic fields: (1) the flavor-dependent repulsion among u, d, and s quarks with the coupling constant GV, and (2) the universal repulsion and the vector-isovector interaction with the coupling constants gV and GIV. The effects of the two types of vector interactions on the constituent quark mass, vacuum quark mass, quark chemical potential, and quark fraction in SQM under strong magnetic fields are studied, and the results indicate that these physical quantities for SQM are all sensitive to the two types of vector interactions in NJL model under magnetic fields. Using a density-dependent magnetic field profile which is introduced to describe the magnetic field strength distribution inside the magnetars, we calculate the properties of spherical QSs by using two extreme cases for the orientation of the magnetic field inside the stars, i.e., the radial orientation in which the magnetic fields are along the radial direction in stars, and the transverse orientation in which the magnetic fields are randomly oriented in the plane which is perpendicular to the radial direction. Our results indicate that the maximum mass of QSs may dependent on both the strength distribution and the orientation of the magnetic fields inside QSs by using SU(3) NJL model.