The favoured twin: on the dynamical response of twin stars to perturbations

If a strong first-order phase transition takes place at sufficiently high rest-mass densities in the equation of state (EOS) modelling compact stars, a new branch will appear in the mass-radius sequence of stable equilibria. This branch will be populated by stars comprising a quark-matter core and a hadronic-matter envelope, i.e., hybrid stars, which represent twin-star'' solutions to equilibria having the same mass but a fully hadronic EOS. While both branches are stable to linear perturbations, it is unclear which of the twin solutions is the favoured’’ one, that is, which of the two configurations is expected to be found in nature. We assess this point by performing a large campaign of general-relativistic simulations aimed at assessing the response of compact stars on the two branches to perturbations of various strength. In this way, we find that, independently of whether the stars populate the hadronic or the twin branch, their response is characterised by a critical-perturbation strength such that the star will oscillate on the original branch for subcritical perturbations and migrate to the neighbouring branch for supercritical perturbations while conserving rest-mass. Because the critical values are different for stars with the same rest-mass but sitting on either branch, it is possible to define as favoured the part of the branch that has the largest critical perturbation, thus correcting the common wisdom that stellar models on the twin branch are the favoured ones. Interestingly, we show that the binding energies on the two branches can be used to deduce without simulations which of the stellar configurations is more likely to be found in nature.

💡 Research Summary

The paper tackles a long‑standing question in neutron‑star physics: when a strong first‑order phase transition (PT) to quark matter creates a “twin‑star” configuration—two distinct equilibrium solutions (a purely hadronic branch, HB, and a hybrid or twin branch, TB) with the same gravitational mass—which of the two is more likely to be realized in nature. While linear perturbation theory guarantees that both branches are stable, the authors investigate the nonlinear response to finite‑amplitude disturbances using a large suite of general‑relativistic hydrodynamic simulations.

They adopt a piecewise‑polytropic equation of state (EOS) that reproduces a Maxwell‑type PT: low‑density hadronic polytropes (i = 1–3), a narrow transition region with an almost vanishing but non‑zero sound speed (i = 4), and high‑density quark‑matter polytropes (i = 5–6). This EOS yields a mass‑radius curve featuring an overlapping “twin region” where HB and TB coexist for the same rest mass (M_b). Two representative models with M_b = 1.4 M_⊙ are selected: HB·1.4 (radius ≈ 13.9 km, purely hadronic) and TB·1.4 (radius ≈ 11.7 km, hybrid).

Numerical experiments are performed with the 1‑D GR1D code (and spot‑checked with the 3‑D WhiskyTHC code) at 100 m resolution, imposing an inward radial velocity perturbation v_r = –λ c on the initially static star. By varying λ, they identify a critical perturbation amplitude λ_crit for each branch. If λ < λ_crit, the star remains on its original branch, executing small‑amplitude f‑mode oscillations that damp due to numerical viscosity. If λ > λ_crit, the star migrates to the neighboring equilibrium branch while conserving rest mass: a HB star compresses into a TB configuration, and a TB star expands into a HB configuration.

Crucially, λ_crit differs between the two branches for the same M_b. The branch with the larger λ_crit can withstand stronger disturbances and is therefore defined as the “favoured” branch. The authors show that this asymmetry is directly linked to the binding‑energy difference ΔE_bind = E_bind(TB) – E_bind(HB). When ΔE_bind < 0 (TB more tightly bound), the twin branch is energetically preferred; when ΔE_bind > 0, the hadronic branch is favoured. This provides a simple, EOS‑based criterion to predict the preferred configuration without running costly simulations.

The study demonstrates that nonlinear stability considerations break the degeneracy of twin solutions and that the preferred branch can be identified from static properties (mass, radius, binding energy). The findings have immediate implications for interpreting neutron‑star mass‑radius measurements, gravitational‑wave observations of binary mergers (where tidal deformabilities depend on the branch), and for constraining the high‑density EOS. The authors suggest future work should incorporate rotation, magnetic fields, and fully three‑dimensional dynamics to assess how robust the λ_crit criterion remains under more realistic astrophysical conditions.