The Energy-loss Rate of Neutrinos in the Urca Process of Strange Quark Matter in Weak and Ultra-strong Magnetic Fields

The influence of magnetic field on the energy-loss rate of neutrinos in the direct Urca process of quarks in the model of strange stars is investigated in this article. First, an improvement is made on the method of approximate calculation in the case of weak field, which can be extended to other processes of weak interactions. Then, a rigorous calculation is made for ultra-strong magnetic fields, of the energy-loss rate of neutrinos in the Urca process. The result shows that the emissivity strongly depends on the magnetic field, being directly proportional to the square of the magnetic field strength. More importantly, the dependence on temperature is different in the cases of strong and weak or null magnetic fields.