Phase transitions in rotating neutron stars cores: back bending, stability, corequakes, and pulsar timing

The back-bending phenomenon for compact stars is studied by means of analytical equations of state, for both constant-pressure phase transitions and the transitions through the mixed-phase region. We restrict ourselves to the case of normal rotating configurations, with baryon mass below the maximum allowable baryon mass for non-rotating stars. We use high-precision 2-D multi-domain spectral code LORENE to search the parameter space for possible instability regions, and possible changes in the stability character of rotating stars with phase transitions in their cores. Conditions on the density jump in constant-pressure phase transitions, leading to the existence of the unstable segments in the evolutionary sequences of spinning down isolated normal neutron stars, are derived. Conjectures concerning the existence of two disjoint families of non-rotating and rotating stationary configurations of neutron stars are formulated. Particular case of EOSs leading to marginal instability of static and rotating configurations is also studied: marginal instability point in non-rotating configurations continues to exist in all evolutionary spin-down tracks. The fate of rotating stars entering the region of instability is discussed. The change in radius, energy release, and spin-up associated with the corequake in rotating neutron star, triggered by the instability, are calculated. The energy release is found to be very weakly dependent on the angular momentum