Hybrid Quark Stars with Quark-Quark Phase Transitions

TL;DR

This work investigates hybrid quark stars (HybQS) formed by phase transitions between different quark matter phases within absolutely stable quark matter. It develops a parameterized interacting quark matter EOS and employs Maxwell constructions to build HybQS models with sharp QM–QM transitions between crust and core, then maps the resulting $M$–$R$ phase diagrams and tests viability against the constraints $M_{ m TOV}\gtrsim 2\,M_\odot$ and $\Lambda_{1.4M_\odot}<800$, identifying regions that admit twin-star solutions. The authors show that flavor-changing QM–QM transitions can produce twin stars and that color superconductivity expands the viable parameter space, enabling additional HybQS branches. They further demonstrate that QM–QM transitions can perturb postmerger GW signatures by breaking the approximate $f_{\rm peak}$–$\Lambda_{1.35M_\odot}$ relation, through shifts in the $f$-mode frequencies, suggesting observable pathways to identify HybQS in future detections. Overall, the study reveals new possibilities for compact-star interiors and outlines concrete directions for incorporating more realistic QCD physics and data-driven analyses.

Abstract

We explore the possibility of phase transitions between different quark matter phases occurring within quark stars, giving rise to the hybrid quark stars (HybQSs). First, we obtain the generic phase diagram of possible mass-radius relation forms for the HybQSs. Then, utilizing a well-established general parameterization of interacting quark matter, we construct quark star models featuring sharp first-order quark-quark phase transitions of various types, in contrast to the hadron-quark transition in conventional hybrid stars. We systematically investigate how recent observations, such as the pulsar mass measurement $M_{\rm TOV}\gtrsim2M_{\odot}$ and the GW170817's tidal deformability bound $Λ_{1.4M_{\odot}}<800$, constrain the viable parameter space. We also identified twin stars in some of the HybQS parameter space. Furthermore, we found that the quark-quark phase transitions in hybrid quark stars may also cause the deviation from the approximate universal relation between the dominant postmerger frequency $f_{\rm peak}$ and tidal deformability $Λ_{1.35M_{\odot}}$, which was previously believed to only be caused by the hadron-quark phase transitions in hybrid neutron stars. This work unveils new possibilities of phase transitions and the resulting new types of compact stars in realistic astrophysical scenarios.

Figures (7)

• Figure 1: Phase diagram for the mass-radius relation of HybQS branches. The red line corresponds to Eq. (\ref{['critical_rho']}). In (a), we fix the parameters as $B$ = 50 MeV/fm$^3$ and $c_{s}^{2}$ = 1/3. In (b), we fix the parameters as $B$ = 50 MeV/fm$^3$ and $c_{s}^{2}$ = 1. The mass–radius relations for regions A, B, C, and D are presented in Figs. \ref{['MITCSS_MR']} (a), (b), (c) and (d), respectively.
• Figure 2: $M$-$R$ relations of typical HybQS examples in different regions of Fig. \ref{['MITCSS_phasediagram']}. The insets on the left present enlarged views of the vicinity of the phase transition points, with the phase transition points indicated by blue dots. (a), (b), (c) and (d) correspond to regions A, B, C and D in Fig. \ref{['MITCSS_phasediagram']}, respectively.
• Figure 3: (a) $M$-$R$ relations of HybQS benchmark examples with unpaired 2$f$ to unpaired 3$f$ phase transition. (b) related parameter space, where the cross markers correspond to the same-color $M$-$R$ in (a). In (b), the gray dashed contour encloses the parameter space consistent with theoretical considerations. The red line corresponds to the $M_{\rm TOV} = 2\,M_\odot$ constraint, below which one has $M_{\rm TOV} \gtrsim 2\,M_\odot$, while the blue line represents the $\Lambda_{1.4M_{\odot}} = 800$ constraint, above which one has $\Lambda_{1.4M_{\odot}} < 800$. The enclosed yellow region indicates the intersection of these two observational constraints, highlighting the parameter space simultaneously satisfying both.
• Figure 4: (a) $M$-$R$ relations of HybQS benchmark examples with unpaired 2$f$ to 2SC+s or to CFL phase transition (these two cases have the same results). (b) The related viable parameter space (yellow-shaded region), where the cross markers correspond to the same-color $M$-$R$ in (a). In (b), the line-color convention follows that of Fig. \ref{['udQMtoSQM']}b. Each panel is obtained by fixing one of the parameters, with the other two serving as the horizontal and vertical axes. For the top left panel, we choose $\bar{\lambda}_{\rm core}=0.06$, while for the two bottom panels, we choose $B_{\rm crust}=28\rm\, MeV/fm^{3}$ and $B_{\rm core}=65\rm \, MeV/fm^{3}$, respectively.
• Figure 5: Parameter space of HybQSs with the 2SC to 2SC+s (top three rows) and the 2SC to CFL (bottom three rows) transitions. Each panel is obtained by fixing two of the parameters of ($B_{\rm crust}$, $B_{\rm core}$, $\bar{\lambda}_{\rm crust}$, $\bar{\lambda}_{\rm core}$)=(50 MeV/fm$^{3}$, 65 MeV/fm$^{3}$, 0.1, 0.01), with the other two serving as the horizontal and vertical axes correspondingly. The line-color convention follows that of Fig. \ref{['udQMtoSQM']}b, with the additional red arrows in the bottom-left panels helping clarify the $M_{\rm TOV} \gtrsim 2M_{\odot}$ directions.