Comprehensive survey of hybrid equations of state in neutron star mergers and constraints on the hadron-quark phase transition

We perform an extensive study of equation of state (EoS) models featuring a phase transition from hadronic to deconfined quark matter in neutron star merger simulations. We employ three different hadronic EoSs, a constant speed of sound parameterization for the quark phase and a Maxwell construction to generate a large sample of hybrid EoS models. We systematically vary the onset density and density jump of the phase transition as well as the quark matter stiffness and simulate binary neutron star mergers to infer how the properties of the phase transition affect the gravitational-wave signal. In total we simulate mergers with 245 different hybrid EoS models. In particular, we explore in which scenarios a phase transition would be detectable by a characteristically increased postmerger gravitational-wave frequency compared to an estimate from the inspiral signal assuming a purely hadronic EoS. We find that the density jump at the transition (latent heat) has the largest impact on the gravitational-wave frequencies, while the influence of the stiffness of quark matter is smaller. We quantify which range of phase transition properties would be compatible with a certain magnitude or absence of the gravitational-wave postmerger frequency shift. By means of these dependencies, a future detection will thus directly yield constraints on the allowed features of the hadron-quark phase transition.

💡 Research Summary

This paper presents a comprehensive, systematic investigation into how a phase transition from hadronic to deconfined quark matter manifests in gravitational-wave (GW) signals from binary neutron star mergers. The core objective is to quantify the impact of specific phase transition properties on post-merger GW frequencies and establish a framework for constraining these properties from future observations.

The methodology is built on three pillars. First, the authors construct a large suite of hybrid equation of state (EoS) models. They use three different hadronic EoSs (DD2, DD2F, SFHo) as a base, model the quark phase with a constant speed of sound parameterization, and connect the phases via a Maxwell construction. This approach allows independent variation of three key parameters: the transition onset density (n_on), the density jump at the transition (Δn, related to latent heat), and the stiffness of quark matter (c_s^2). Thermal effects crucial for merger dynamics are incorporated via an effective scheme.

Second, the team performs an extensive set of numerical simulations. They simulate the mergers of two 1.35 solar mass neutron stars for a total of 245 distinct hybrid EoS models, using a general relativistic smoothed particle hydrodynamics code.

Third, they analyze the results by focusing on the dominant post-merger GW frequency (f_peak). They define a key observable: the frequency shift Δf_peak = f_peak,hybrid - f_peak,had. Here, f_peak,hybrid is measured from the simulation, while f_peak,had is the frequency predicted by an established empirical relation between f_peak and the tidal deformability (Λ) for purely hadronic EoSs. A significant positive Δf_peak indicates a phase transition that softens the EoS and makes the remnant more compact.

The main findings are:

1. The density jump Δn (latent heat) has the most pronounced effect on Δf_peak. A larger Δn leads to a stronger frequency increase, providing a clearer observational signature.
2. The stiffness of quark matter (c_s^2) has a comparatively smaller influence on the GW frequency.
3. The onset density n_on is critical for detectability. If n_on is too high, the amount of quark matter produced in the remnant is small, resulting in a negligible Δf_peak and creating a “masquerade problem” where the hybrid system is indistinguishable from a purely hadronic one.
4. The existence of massive ~2 solar mass neutron stars imposes stringent astrophysical constraints on the hybrid EoS parameter space, ruling out combinations of very high n_on and large Δn unless the quark matter is extremely stiff (c_s^2 near 1).
5. For each family of hybrid models (based on a specific hadronic EoS), the authors provide a fitting formula that quantifies Δf_peak as a function of n_on, Δn, and c_s^2. This creates a direct inverse mapping: a future measurement of Δf_peak from a GW detection can be used to constrain the allowed region of phase transition parameters.

In conclusion, this work demonstrates that post-merger GWs are a sensitive probe of the high-density QCD phase diagram. By systematically scanning the parameter space of hybrid EoSs, it moves beyond studies of individual models and establishes quantitative relationships between microphysical transition properties and macroscopic GW observables. It provides a crucial interpretative tool for extracting physics from the post-merger GW signals expected with next-generation detectors.