Hybrid compact stars with finite strange quark mass and dark energy: implications for astrophysical observations

TL;DR

The paper investigates hybrid compact stars composed of three-flavor quark matter with finite strange-quark mass $m_s$ admixed with dark energy, modeled via the MIT bag EoS and a linear dark-energy EoS $p^{de}=\omega\rho^{de}$ coupled through $\rho^{de}=\beta\rho^Q$. Using the Finch–Skea metric, the authors derive analytic interior solutions and apply causality and energy conditions to constrain $\beta$, $\omega$, and $m_s$, obtaining a maximum mass near $2.012\,M_\odot$ and radii around 11 km for favorable parameters. They show that increasing the dark-energy fraction $\beta$ softens the EoS, reducing $M_{max}$ and $R_{max}$, while central densities rise; the model remains stable under TOV equilibrium, Abreu cracking criterion, adiabatic index tests, and small radial oscillations. The framework yields radii and tidal deformabilities ($\Lambda$, $k_2$) compatible with observational constraints (e.g., GW170817), and can accommodate several observed compact stars, suggesting dark energy components may play a role in the structure of dense compact objects. Overall, the work demonstrates that a physically viable hybrid star with finite $m_s$ and dark energy can account for observed masses and radii while satisfying fundamental stability and causality requirements.

Abstract

In this work, a detailed investigation of compact stars composed of deconfined quark matter with finite strange quark mass ($m_s \neq 0$) admixed with dark energy is presented. The quark sector is modeled using the MIT bag model equation of state, while the dark energy component obeys a linear equation of state, $p^{de} = ωρ^{de}$ with $ω$ in the range $-1\leqω\leq-frac{1}{3}$. The stellar configuration is explored within the Finch-Skea ansatz for the $g_{rr}$ metric potential. A coupling between quark matter and dark energy is introduced through $ρ^{de} =βρ^Q$, where $β$ represents the dark energy coupling parameter. Causality restricts $β$ within $0<β<-\frac{1}{3ω}$. The structural features of such compact stars are analysed by varying $β$ in this range. Solving the Tolman-Oppenheimer-Volkoff equations yields a maximum mass of $2.012~M_{\odot}$ with a radius of about 11 km. For a fixed $ω$, both mass and radius decrease as $β$ increases. The model satisfies causality, energy and stability conditions, ensuring physical acceptability. Finally, the framework is applied to estimate radii of compact star candidates identified as strange quark stars with dark energy, showing good agreement with observational data.

Figures (28)

• Figure 1: Variation of $E_B$ with coupling parameter $\beta$ for $m_s=100~MeV$ and $\omega=-1$. The solid, dashed and dotdashed lines represent different bag value as $B_g=57.55~MeV/fm^3$, $60~MeV/fm^3$ and $70~MeV/fm^3$.
• Figure 2: Variation of $E_B$ with coupling parameter $\beta$ for $m_s=100~MeV$ and $\omega=-\frac{1}{3}$. The solid, dashed and dotdashed lines represent different bag value as $B_g=57.55~MeV/fm^3$, $60~MeV/fm^3$ and $70~MeV/fm^3$.
• Figure 3: Mass-radius variation for different value of $\beta$ for $m_s=100~MeV$ and $B_g=60~MeV/fm^3$. The solid and dashed lines represent $\omega=-1$ and $-\frac{1}{3}$ respectively. The black dots represent the maximum mass value for each curve.
• Figure 4: Plot of maximum mass with total central density ($\rho^{total}$) for different value of $\beta$ with $m_s=100~MeV$ and $B_g=60~MeV/fm^3$. The solid and dashed lines represent $\omega=-1$ and $-\frac{1}{3}$ respectively.
• Figure 5: Variation of maximum mass with the percentage of dark energy for $B_g=60~MeV/fm^3$. Here, the black and red lines represent the corresponding variation for a parametric choice of $m_s=100~MeV$ and $120~MeV$, respectively. Also the solid and dashed lines represent the choice of $\omega=-1$ and $\omega=-\frac{1}{3}$, respectively.