Self-bound quark stars with a first-order two-to-three flavor phase transition

TL;DR

This work advances the study of self-bound quark stars by employing a flavor-dependent quark-mass density–dependent (QMDD) model with an excluded-volume correction. It maps zero-pressure stability in the $(a,C)$ parameter space, identifies scenarios with both two-flavor ud matter and a first-order $ud\to uds$ transition to a three-flavor core, and computes cold, $\beta$-equilibrated TOV sequences to confront masses, radii, tidal deformabilities, and moments of inertia with multimessenger constraints. A key finding is that intermediate excluded-volume strength ($\kappa\approx0.3$) often reconciles $M_{\max}\gtrsim 2\,M_\odot$ with radius and GW170817 constraints, and that three EOS-insensitive universal relations (I–C, $\Lambda$–C, and $\mathcal{C}$–$\mathcal{C}_B$) largely erase explicit $\kappa$-dependence in dimensionless form. These universal trends, together with clear quark-hadron discrimination via $M$, $R$, $I$, and $\Lambda$, provide practical priors and diagnostics for interpreting compact-star data in multimessenger astronomy.

Abstract

We investigate self-bound quark stars in a flavor-dependent quark-mass density-dependent (QMDD) model with an excluded-volume correction. We chart the parameter space at zero pressure to identify self-bound regimes, including cases with a first-order $ud \to uds$ transition, and construct cold, $β$-equilibrated stellar sequences via the Tolman-Oppenheimer-Volkoff equations. The excluded-volume parameter $κ$ controls the stiffness of the equation of state and thus masses, radii, tidal deformabilities, and moments of inertia. Intermediate repulsion typically reconciles $M_{\max} \gtrsim 2\,M_\odot$ with current radius/tidal constraints, with hybrid self-bound objects more compatible than pure strange-quark stars. We identify three EOS-insensitive trends $-$ dimensionless moment of inertia vs. compactness, tidal deformability vs. compactness, and gravitational vs. baryonic compactness $-$ whose explicit $κ$-dependence largely disappears in dimensionless form (the first two being notably tighter than the third). These results provide model-guided priors and tools for discriminating between hadronic and self-bound EOS families with multimessenger data.

Figures (12)

• Figure 1: Stability window of the flavor-dependent QMDD model in the $(a,C)$ plane. The black (red) curve corresponds to $e_{ud}^0=930\,\mathrm{MeV}$ ($e_{uds}^0=930\,\mathrm{MeV}$); points lying below the respective curve yield self-bound $ud$ ($uds$) matter at $p=0$. Points above both 930 MeV curves correspond to hybrid quark-hadronic matter. The indigo line marks $e_{ud}^0=e_{uds}^0$. The orange line indicates $c_s^0=c$; to its right the $p\!\to\!0$ limit is acausal.
• Figure 2: Gibbs free energy per baryon for two- ($ud$) and three-flavor ($uds$) bulk quark matter. Curves correspond to the parameter sets (a)–(d) defined in Fig. \ref{['fig:1']} and three representative excluded-volume strengths $\kappa$ (0, intermediate, high). At $p=0$, $G/n_B$ is independent of $\kappa$. Crossings between $ud$ and $uds$ branches (when present) indicate a first-order $ud\!\to\!uds$ transition.
• Figure 3: Total pressure $p$ versus energy density $\epsilon$ for the same parameter sets as Fig. \ref{['fig:2']}. A constant-pressure plateau with a discontinuous jump in $\epsilon$ appears when a first-order $ud\!\to\!uds$ transition occurs; each curve crosses $p=0$ at finite $\epsilon$.
• Figure 4: Sound speed $c_s$ (in units of $c$) versus baryon number density $n_B$ for the same parameter sets as Fig. \ref{['fig:2']}. The horizontal line marks the conformal limit $1/\sqrt{3}$; curves end at their zero-pressure points.
• Figure 5: (a) Schematic mass–radius diagram of self-bound stars. The magenta curve shows self-bound strange-quark-matter configurations, the blue curve shows self-bound $ud$ stars, and the bicolor (magenta–blue) curve displays the sequence of self-bound hybrid stars analyzed in this work. (b) Representation of the internal composition of the models on the $M$–$R$ curves in panel (a), indicating regions of $uds$ matter (magenta) and $ud$ matter (blue).