Dynamic migration of rotating neutron stars due to a phase transition instability

Using numerical simulations based on solving the general relativistic hydrodynamic equations, we study the dynamics of a phase transition in the dense core of isolated rotating neutron stars, triggered by the back bending instability reached via angular momentum loss. In particular, we investigate the dynamics of a migration from an unstable configuration into a stable one, which leads to a mini-collapse of the neutron star and excites sizeable pulsations in its bulk until it acquires a new stable equilibrium state. We consider equations of state with softening at high densities, a simple analytic one with a mixed hadron-quark phase in an intermediate pressure interval and pure quark matter at very high densities, and a microphysical one that has a first-order phase transition, originating from kaon condensation. Although the marginally stable initial models are rigidly rotating, we observe that during the collapse (albeit little) differential rotation is created. We analyze the emission of gravitational radiation, which in some models is amplified by mode resonance effects, and assess its prospective detectability by interferometric detectors. We expect that the most favorable conditions for dynamic migration exist in very young magnetars. We find that the damping of the post-migration pulsations strongly depends on the character of the equation of state softening. The damping of pulsations in the models with the microphysical equation of state is caused by dissipation associated with matter flowing through the density jump at the edge of the dense core. If at work, this mechanism dominates over all other types of dissipation, like bulk viscosity in the exotic-phase core, gravitational radiation damping, or numerical viscosity.