As a rapidly rotating neutron star spins down due to the loss of its angular momentum, its central density increases and the nuclear matter in its core converts to quark matter, which leads to a drastic decrease of the stellar moment of inertia, and even results in an era of spin-up of the pulsar (Glendenning, Pei, & Weber 1997). We find that given a certain equation of state in the liquid core, even if the backbending of the moment of inertia as a function of the rotating frequency occurs, an increase of the total moment of inertia by only 1% could carry adequate angular momentum and stop the star spin-up. This small discrepancy in the total moment of inertia might be due to the different properties of subnuclear matter in the crust, especially to different transition density and pressure at the inner boundary of the solid crust between various models. The strong dependence of the phenomenon of back-bending on the physical state of the crust provides, in principle, a new observational approach to check and constrain theories on subnuclear matter.
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