Population Clustering as a Signal for Deconfinement in Accreting Compact Stars

Abstract

We study the evolution of the rotation frequency of compact stars with mass accretion. The discontinuous change of the moment of inertia of a fastly rotating star due to the possible quark core appearance entails a characteristic change of spin evolution. Numerical solutions have been performed using a model equation of state describing the deconfinement phase transition as constrained by the conservation of total baryon number and electric charge. A phase diagram for compact stars in the angular velocity - baryon number plane is obtained with a dividing line for quark core configurations. Trajectories of spin evolution in this diagram are studied for different accretion scenarios defined by the initial mass and magnetic field of the star, the 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 correlated to a maximum in the moment of inertia of the compact star.