Quark matter under strong magnetic fields in the Nambu–Jona-Lasinio model

In the present work we use the large-${N}_{c}$ approximation to investigate quark matter described by the SU(2) Nambu--Jona-Lasinio model subject to a strong magnetic field. The Landau levels are filled in such a way that usual kinks appear in the effective mass and other related quantities. $\ensuremath{\beta}$ equilibrium is also considered and the macroscopic properties of a magnetar described by this quark matter is obtained. Our study shows that the magnetar masses and radii are larger if the magnetic field increases but only very large fields ($\ensuremath{\geqslant}{10}^{18}$ G) affect the equation of state in a non-negligible way.