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We investigate properties of strange quark matter in the framework of SU(3)Nambu--Jona-Lasinio(NJL) model with vector interaction under strong magneticfields. The effects of vector-isoscalar and vector-isovector interaction on theequation of state of strange quark matter are investigated, and it is foundthat the equation of state is not sensitive to the vector-isovectorinteraction, however, a repulsive interaction in the vector-isoscalar channelgives a stiffer equation of state for cold dense quark matter. In the presenceof magnetic field, gluons will be magnetized via quark loops, and thecontribution from magnetized gluons to the equation of state is also estimated.The sound velocity square is a quantity to measure the hardness or softness ofdense quark matter, and in the NJL model without vector interaction at zeromagnetic field the sound velocity square is always less than 1/3. It is foundthat a repulsive vector-isoscalar interaction and a positive pressurecontribution from magnetized gluons can enhance the sound velocity square,which can even reach 1. To construct quark magnetars under strong magneticfields, we consider anisotropic pressures and use a density-dependent magneticfield profile to mimic the magnetic field distribution in a quark star. We alsoanalyze the parameter region for the magnitude of vector-isoscalar interactionand the contribution from magnetized gluons in order to produce 2 solar massquark magnetars.

Quark magnetar in three-flavor Nambu--Jona-Lasinio model with vector interaction and magnetized gluon potential