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

TL;DR

This study investigates how hadron-quark phase-transition properties in neutron star mergers imprint on gravitational waves. By constructing 245 hybrid EoS models using three hadronic bases and a constant-speed-of-sound quark phase connected via a Maxwell construction, and by simulating 1.35$M_\odot$–1.35$M_\odot$ binaries with a relativistic SPH code including thermal effects, the authors map the dependence of the postmerger frequency shift $\Delta f_\text{peak}$ on the onset density $n_\text{on}$, density jump $\Delta n$, and quark stiffness $c_s^2$. They find that the latent heat (via $\Delta n$) dominates the impact on $f_\text{peak}$, while the stiffness of quark matter plays a smaller role, and they provide an empirical formula for $\Delta f_\text{peak}$ to translate a future detection into constraints on the phase-transition properties. The results offer a framework for constraining high-density QCD phase structure from gravitational-wave observations, while highlighting limitations related to finite-temperature treatment, construction type, and fixed binary mass. This work lays the groundwork for using postmerger GW signals to probe the hadron-quark phase transition in dense matter and to guide future multi-messenger constraints.

Abstract

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.

Figures (12)

• Figure 1: Minimum speed of sound squared in the quark phase required to obtain a maximum neutron star mass $M_\mathrm{max}\geq 2~M_\odot$ color-coded as a function of onset density and density jump of the phase transition for hybrid models based on the hadronic SFHo (left panel), DD2F (middle panel) and DD2 (right panel) models. The stiffness of the hadronic models increases from left to right. In each panel the dashed line encloses the region where the requirement $M_\mathrm{max}\geq 2~M_\odot$ cannot be fulfilled. Black symbols mark EoS models for which we perform simulations of binary NS mergers in this work with plus signs indicating models that promptly collapse to a black hole at merger for all $c_s^2\leq 1$. For EoSs with the highest simulated $n_\mathrm{on}$ and beyond, the phase transition does not have an impact on the GW signal anymore.
• Figure 2: Mass-radius curves of cold neutron stars for a selection of hybrid EoSs we employ in this study based on a constant speed of sound model (colored). Each column shows results from hybrid models based on a different underlying hadronic model (black). The top row displays curves of hybrid models with a single onset density of the phase transition of $2\times n_\mathrm{sat}$ (SFHO), $2\times n_\mathrm{sat}$ (DD2F) and $1.8\times n_\mathrm{sat}$ (DD2). The numbers indicate the density jump $\Delta n$ at the phase transition in units of nuclear saturation density. The bottom row shows hybrid models at a constant speed of sound of $c_s^2=0.7$ in the quark phase. The stiffness of the hadronic phase increases from left to right.
• Figure 3: Shift of the dominant postmerger gravitational-wave frequency $f_\mathrm{peak}$ in merger simulations using SFHo-based hybrid EoSs compared to $f_\mathrm{peak}$ predicted by Eq. \ref{['eq:fpeak_lambda']} based on the tidal deformability of the inspiraling stars (i.e. assuming a hadronic EoS) as a function of the onset density, density jump and stiffness of the quark phase. The dashed line marks the central density of the inspiraling purely hadronic stars, i.e. for SFHo. Hence, models at smaller values of $n_\mathrm{on}$ contain quark matter before merging, whereas models to the right of the dashed line are purely hadronic during the inspiral.
• Figure 4: Same as Fig. \ref{['fig:df_DD2F']}, but for DD2F-based models.
• Figure 5: Same as Fig. \ref{['fig:df_DD2F']}, but for DD2-based models.