The mixed phase quark core in massive hybrid stars

TL;DR

This work investigates mixed-phase quark cores in massive hybrid stars by coupling a relativistic mean-field description of hadronic matter with an NJL model for quark matter and applying Gibbs construction for the hadron–quark mixed phase. By varying the repulsive vector coupling $G_V$ and using stiff-to-soft hadronic EOSs (e.g., NL3L-50, BigApple, TM1e), the authors study how EOS stiffness affects the onset densities, the extent of the mixed phase, and the maximum stellar mass. They find that a mixed-phase core of about $5$ km (approximately $R_{MP}^{\max}/R_{\max} \approx 0.4$) can exist in a $2~M_\odot$ star under certain conditions, but no sizable pure quark core with $R_{MP}^{\max}/R_{\max} \gtrsim 0.5$ is realized; the maximum mass is more influenced by the hadronic EOS and the peak $c_s^2$ than by the mixed-phase details. Overall, the results indicate that large mixed-phase cores are unlikely within the examined RMF–NJL framework, highlighting the critical role of the EOS’s maximum sound speed in governing massive hybrid-star properties.

Abstract

We investigate the properties of hybrid star and the mixed phase core to explore the radius ratio of the mixed phase in hybrid star. In the context of observed massive neutron stars (NSs), we examine the internal structure, phase transitions, and the impacts of the equation of state (EOS) in maximum hybrid star. We investigate the stiffness changes in the EOS during the hadron-quark phase transition within the hybrid stars. The relativistic mean-field (RMF) model is used to describe hadronic matter, while to the represent quark matter, the Nambu-Jona-Lasinio (NJL) model is applied. We explore the strength of vector coupling in quark matter, which delays the onset density of the mixed phase and reduces the size of the mixed-phase core in a hybrid star, but does not exhibit a clear correlation with the central density. In a hybrid star with a maximum mass of approximately 2 solar masses ($M_\odot$), a mixed-phase core of $\sim$5 km may exist, comprising about $40\%$ of the total radius. However, our results do not support the existence of a sizable quark core containing the mixed phase ($R_{\rm{MP}}>1/2~R_{\rm{total}}$) for the maximum-mass hybrid star or for a 2~$M_\odot$ massive star.

Figures (9)

• Figure 1: The phase transition density $n_b(1)$, $n_b(2)$ and the center density $n_c$ of the maximum-mass NS as a function of baryon number density $n_b$ with different values of $G_V$.
• Figure 2: Pressures $P$ as a function of the number density $n_b$ obtained using different parameter sets as NL3L-50, BigApple, and TM1e. The results for the hadronic phase, mixed phase (MP), and quark phase (QP) are represented by dash-dot lines, solid lines and dashed lines, respectively. Additionally, the strength of the vector coupling is varied with values $G_V=0,\ 0.1\ G_S,\ 0.2\ G_S$, which are depicted by red, blue, and green lines, respectively.
• Figure 3: The squared sound velocity $c_s^2$ (upper panel) and the polytropic index $\gamma$ (lower panel) as functions of the baryon number density $n_b$ with varying vector couplings $G_V=0,\ 0.1\ G_S,\ 0.2\ G_S$. The labels are consistent with those in Fig. \ref{['fig:2nbp']}. Additionally, in the upper panel, a short dashed line is utilized to represent the conformal limit with $c_s^2=1/3$. In the lower panel, $\gamma=1.75$ (short dashed line) serves as reference value to distinguish the nucleon degree of freedom from non-nuclear degrees of freedom.
• Figure 4: The mass-radius relations (left panel) and mass-central density $n_c$ relations (right panel) of hybrid stars with different model parameters. The results from pure hadronic EOS (dash-dot lines) are compared with those including hadron-quark phase transition for different vector couplings. The shaded areas correspond to simultaneous measurements of the mass and radius range from NICER for PSR J0030+0451 Riley2019Miller2019 and PSR J0740+6620 Riley2021Miller2021, respectively. The radius constraint $R_{1.4}\leq13.6~\rm{km}$ is presented with light grey Annala2018. The hypothesis that the second component of GW190814 is a NS is also depicted Abbott2020.
• Figure 5: The dimensionless tidal deformability as a function of NS mass. The purple vertical line indicates the tidal deformability constraint at 1.4 $M_\odot$ from GW170817 event with $\Lambda_{1.4}=190^{+390}_{-120}$Abbott2018. The shaded areas correspond to the mass constraints from PSR J0740+6620 and GW190814 event Fonseca2021Abbott2020, respectively.