In a recent letter, Physics Letters B 767 (2017) 247–252, we presented a an SU(2) NJL model with a coupling wich depends on the magnetic field in order to calculate the neutral pion mass at T = 0. In this work, we improve our model by adding the strange quark, the Polyakov loop and finite temperature. We then build a thermomagnetic dependence for the G and K couplings of the SU(3) PNJL model by fitting lattice QCD calculations for the average and the difference of u and d quark condensates under a strong magnetic field. With the new couplings, we compute several thermodynamic quantities and generate an equation of state for magnetized quark matter which we use to determine the mass-radius relation for compact stars from the integration of the TOV equations.
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