Quark matter and quark stars in strong magnetic fields at finite temperature within the confined-isospin-density-dependent mass model

We study the properties of strange quark matter (SQM) and quark stars (QSs) in strong magnetic fields within the extended confined isospin-density-dependent mass (CIDDM) model including the temperature dependence of the equivalent mass for quarks. The quark symmetry energy, quark symmetry free energy, and the equation of state (EOS) of SQM in constant magnetic fields at finite temperature are investigated, and it is found that including the temperature dependence in CIDDM model and considering strong magnetic fields can both significantly influence the properties of the SQM and the maximum mass of quark stars. Using the density-dependent magnetic field and assuming two extreme cases for the magnetic field orientation in QSs (the radial orientation in which the local magnetic fields are along the radial direction and the transverse orientation in which the local magnetic fields are randomly oriented but perpendicular to the radial orientation), we analyze the mass-radius relations for different stages of the protoquark stars (PQSs) along the star evolution. Our results indicate that the maximum mass of magnetized PQSs may depend on not only the strength distribution and the orientation of the magnetic fields inside the PQSs, but also the heating process and the cooling process in the star evolution.