Population clustering as a signal for deconfinement in accreting compact stars

We study the evolution of the rotation frequency for accreting compact stars. The discontinuous change of the moment of inertia of a rapidly rotating star due to the possible quark core appearance entails a characteristic change in the spin evolution. Numerical solutions have been performed using a model equation of state describing the deconfinement phase transition. Trajectories of spin evolution are discussed in the angular velocity - baryon number plane (phase diagram) for different accretion scenarios defined by the initial values of mass and magnetic field of the star, as well as mass accretion rate and magnetic field decay time. We observe a characteristic increase in the waiting time when a configuration enters the quark core regime. Overclustering of the population of Z sources of LMXBs in the phase diagram is suggested as a direct measurement of the critical line for the deconfinement phase transition since it is related to the behaviour of the moment of inertia of the compact star.