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.

💡 Research Summary

The paper investigates how a phase transition in the dense core of an isolated, rotating neutron star can be triggered by the back‑bending instability that arises as the star loses angular momentum. Using three‑dimensional general‑relativistic hydrodynamic simulations, the authors follow the evolution of a marginally stable, rigidly rotating configuration as it migrates to a new stable equilibrium. The migration is accompanied by a “mini‑collapse” of the core, the creation of a modest amount of differential rotation, and large‑amplitude bulk pulsations that persist until the star settles.

Two families of equations of state (EOS) are examined. The first is a simple analytic model that introduces a mixed hadron‑quark phase over an intermediate pressure interval and pure quark matter at the highest densities. The second is a microphysical EOS that incorporates a first‑order phase transition caused by kaon (K⁻) condensation, producing a sharp density jump at the edge of the exotic core. Both EOS feature a softening of the pressure–density relation at supranuclear densities, which is the key ingredient that generates the back‑bending segment of the mass‑radius curve and the associated instability.

In the simulations the star is initially set in a rigid‑rotation state. Angular momentum loss is imposed artificially to mimic electromagnetic spin‑down, driving the model toward the unstable branch. Once the critical point is reached, the central density rises sharply, the core contracts, and the phase transition proceeds. The collapse is modest (a few percent reduction in radius) but sufficient to excite the fundamental f‑mode and several pressure p‑modes. The rapid change in the moment‑of‑inertia distribution also induces a small differential rotation profile, with the inner core rotating slightly faster than the outer layers.

Gravitational‑wave (GW) emission is computed from the quadrupole formula. In models with the mixed hadron‑quark EOS, the excited modes can resonate with the GW frequency, leading to a significant amplification of the signal—up to an order of magnitude larger than in a purely hadronic star undergoing a similar spin‑down. The GW spectrum is dominated by a narrow peak around 1–3 kHz, corresponding to the f‑mode frequency of the post‑migration configuration.

For the kaon‑condensation EOS, the presence of a sharp density jump at the core boundary introduces a very efficient dissipation channel. As the star pulsates, matter repeatedly crosses the phase‑boundary, converting kinetic energy into heat and damping the oscillations on a timescale of a few milliseconds. This “density‑jump dissipation” overwhelms other damping mechanisms such as bulk viscosity in the exotic phase, GW back‑reaction, or numerical viscosity. Consequently, the GW signal from a kaon‑condensation star is short‑lived and weaker, despite the larger initial amplitude of the pulsations.

The authors explore the astrophysical relevance of these findings. Young, highly magnetized neutron stars (magnetars) are identified as the most promising candidates because their rapid spin‑down can bring them into the back‑bending regime within a few years after birth. For such objects located within ~10 kpc, the predicted GW strain (h ≈ 10⁻²³–10⁻²⁴) lies within the sensitivity band of current interferometers for a short burst, and would be comfortably detectable by third‑generation detectors (Einstein Telescope, Cosmic Explorer). The presence or absence of a long‑lived GW tail could therefore serve as a diagnostic of the underlying EOS: a persistent tail would hint at a smooth softening (mixed phase), whereas a rapid cutoff would point to a first‑order transition with a density discontinuity.

In summary, the study demonstrates that a core phase transition can drive a dynamic migration of a rotating neutron star, producing observable GW signatures that encode detailed information about the high‑density EOS. The work highlights the importance of including realistic phase‑transition physics and differential rotation in neutron‑star modeling, and it provides a concrete roadmap for using future GW observations to probe the exotic states of matter that may exist in the hearts of neutron stars.