We calculate the mass-radius relationship of quark stars with the magnetized density- dependent quark mass model in this work, considering two magnetic field geometries： a statistically isotropic, tangled field and a force-free configuration. In both cases, magnetic field production decreases in the case of maximum quark star mass. Furthermore, a tangled, isotropic magnetic field has a relatively smaller impact on the mass and radius, compared to the force-free configuration, which implies that the geometry of the interior magnetic field is at least as important as the field strength itself when the influ- ence of the strong magnetic field on the mass and radius is assessed.
We have recently shown that, as a compact star containing mixed-phase matter slows down, the compression can cause deconfinement phase transition, and thus enhance the chemical deviations and raise the chemical heating eiYiciency. In a previous study, only the direct Urca processes in nucleon and quark matter were considered. In this work, we extend the previous analysis to the case where the much slower modified Urca processes operate in nucleon matter. We find a fast promotion in the surface effective temperature of hybrid stars, and that the cooling process is dominated by both the nucleon and quark channels.
