Quarkyonic matter state of neutron stars

This work extends our previous study of isospin symmetric quarkyonic matter to quarkyonic neutron matter which might be relevant to the inner cores of neutron stars. The vector-isovector $\rho$ mesons are introduced to the model mainly to account for isospin density interactions, just like the $\omega$ meson for baryon density interactions. The modified Lagrangian still preserves approximate chiral symmetry which could be significantly broken at lower density. New free parameters are fixed by adopting the experimental constraints on the symmetry energy and its slope at saturation density. Eventually, the pressure, mass-radius relation, and tidal deformability are explored in advance for the quarkyonic neutron stars. While the pressure and tidal deformability are well consistent with experimental and observational restrictions, the mass-radius relation is unable to reproduce the observed two solar mass of PSR $\mathrm{J}0740+6620$.

Figure 1

The symmetry energy $E_{\mathrm{sym}}(n_{\mathrm{B}})$ (upper panel) and its slope $L_{\mathrm{sym}}(n_{\mathrm{B}})\equiv 3n_0\frac{\partial E_{\mathrm{sym}}(n_{\mathrm{B}})}{\partial n_{\mathrm{B}}}$ (lower panel) as functions of the baryon density $n_{\mathrm{B}}$ for the quarkyonic neutron matter.

Figure 2

Upper panel: the densities $n_{\mathrm{B}},n_{\mathrm{I}}$, and $n_{\mathrm{B}}^{\mathrm{q}}$ as functions of the baryon chemical potential ${\mu }_{\mathrm{B}}$; lower panel: the order parameters $⟨\sigma ⟩,⟨{\omega }_0⟩$, and $⟨{\rho }_0^3⟩$ as functions of the corresponding baryon density $n_{\mathrm{B}}$.

Figure 3

Pressure (red dotted in upper panel) and sound velocity (lower panel) as functions of baryon density $\rho$ or $n_{\mathrm{B}}$. The upper panel is adjusted from the plot given in Ref. [15].

Figure 4

Upper panel: the mass-radius relations of quarkyonic neutron stars (red dashed line) and pure neutron stars (black solid line), lower panel: the tidal deformability of quarkyonic neutron stars (red dashed line) with the constraint from GW170817 (black error bar).