Cooling of hybrid stars with spin down compression

We study the cooling of hybrid stars coupled with spin-down. Due to the spin-down of hybrid stars, the interior density continuously increases and different neutrino reactions may be triggered (from the modified Urca process to the quark and nucleon direct Urca process) at different stages of evolution. We calculate the rate of neutrino emissivity of different reactions and simulate the cooling curves of the rotational hybrid stars. The results show that the cooling curves of hybrid stars clearly depend on a magnetic field if the direct Urca reactions occur during the spin-down. Comparing the results of the rotational star model with the transitional static model, we find the cooling behavior of the rotational model is more complicated; the temperature of the star is higher, especially when direct Urca reactions appear in the process of rotation. Then, we find that the predicted temperatures of some rotating hybrid stars are compatible with the pulsar's data which are in contradiction with the results of the transitional method.