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Probing quark matter is one of the important tasks in the studies of neutron stars (NS). Some works explicitly consider the existence of quark matter in the appearance of hybrid star (HS) or pure quark star (QS). In the present work, we study the roto-chemical heating with accretion in HS and QS, and compare their chemical evolution and cooling features with pure NS. Different from HS and NS, there are two jumps in the chemical evolution of QS, which results from the fast direct Urca (Durca) reaction causing the fast recovery to chemical balance. However, the sudden change in the chemical evolution doesn’t provide an obvious heating effect in the thermal evolution. Differently, the roto-chemical heating effect appears both in the accretion phase and spin-down phase of the HS, and the heating platform in the accretion phase relies on the accretion rate. Larger accretion rate results in larger chemical deviation, higher and longer heating platform, and earlier appearance of the heating effect. Interestingly, with the disappearance of the heating effect in the accretion phase, the surface temperature drops fast, which is another possibility of the rapid cooling trend of the NS in Cas A. Furthermore, the surface temperature of the QS is obviously lower than the HS and NS, which is a latent candidate for the explanation of the old classical pulsar J2144-3933 with the lowest known surface temperature.

Roto-Chemical Heating with Fall-Back Disk Accretion in the Neutron Stars Containing Quark Matter