Quarkyonic stars with isospin-flavor asymmetry

We suggest an extension to isospin asymmetric matter of the quarkyonic model from McLerran and Reddy [Phys. Rev. Lett. 122, 122701 (2019)]. This extension allows us to construct the $\beta$ equilibrium between quarks, nucleons, and leptons. The concept of quarkyonic matter originates from the large number of color limit for which nucleons have the correct degrees of freedom near the Fermi surface—reflecting the confining forces—while deep inside the Fermi sea quarks appear naturally. In isospin-asymmetric matter, we suggest to implement this concept within a global isoscalar relation between the shell gaps differentiating the nucleon and the quark sectors. In addition, we impose the conservation of the isospin-flavor asymmetry for the nucleon and the quark components. Within this model, several quarkyonic stars are constructed on top of the SLy4 model for the nucleon sector, producing a bump in the sound speed. As a consequence, quarkyonic stars are systematically bigger and have a larger maximum mass than the associated neutron stars. This model also predicts a lower proton fraction at $\beta$ equilibrium, which potentially quenches fast cooling in massive compact stars.

Figure 1

Schematic views of the different Fermi seas at stake in quarkyonic matter for SM (left) and AM (right). Quarks occupy deep states inside their Fermi spheres while nucleons occupy the shells close to their Fermi levels.

Figure 2

Baryon chemical potential ${\mu }_B$, energy per particle $E_B/A$, pressure $P_B$, and sound speed ${(v_{s,B}/c)}^2$ in symmetric (SM, ${\delta }_N=0.0$, dashed lines), asymmetric (AM, ${\delta }_N=0.5$, dashed-dotted lines), and neutron matter (NM, ${\delta }_N=1.0$, dotted lines) for ${\mathrm{\Lambda }}_{\mathrm{Qyc}}=250\mathrm{MeV}$ and ${\kappa }_{\mathrm{Qyc}}=0.3$. For all figures shown hereafter, the quarkyonic model (green lines) is compared with the Skyrme SLy4 model (magenta lines).

Figure 3

Particle fractions at $\beta$ equilibrium for the SLy4 nucleon model and the quarkyonic model taking ${\mathrm{\Lambda }}_{\mathrm{Qyc}}=250\mathrm{MeV}$ and ${\kappa }_{\mathrm{Qyc}}=0.3$.

Figure 4

Comparison of the proton fraction at $\beta$ equilibrium in the pure nucleonic model with the prediction of the quarkyonic model for various sets of the parameters (${\mathrm{\Lambda }}_{\mathrm{Qyc}}, {\kappa }_{\mathrm{Qyc}}$): (250,0.3), (270,0.3), and (250,0.2). (left) As a function of the particle density in ${\text{fm}}^{-3}$, (right) as a function of the energy density ${\rho }_B{c}^2$ in MeV ${\text{fm}}^{-3}$.

Figure 5

Neutron chemical potential ${\mu }_n$, total energy per particle $E_{\mathrm{tot}}/A$, total pressure $P_{\mathrm{tot}}$, and total sound speed ${(v_{s,tot}/c)}^2$ at $\beta$ equilibrium for the parameters (${\mathrm{\Lambda }}_{\mathrm{Qyc}}, {\kappa }_{\mathrm{Qyc}}$), see caption of Fig. 4 for more details.

Figure 6

Neutron-star properties (mass $M$, radius $R$, tidal deformability ${\mathrm{\Lambda }}_{GW}$, central density $n_c$, binding energy $E_{\mathrm{bind}}=M_b-M$, where $M_b$ is the baryon mass, and the moment of inertia $I$) for quarkyonic matter with different ${\mathrm{\Lambda }}_{\mathrm{Qyc}}$ and ${\kappa }_{\mathrm{Qyc}}$, see caption of Fig. 4 for more details. The solid circle represents the dURAC threshold.

Figure 7

Compactness $(M/M_{\odot })/(R/\text{km})$ as function of the mass $M/M_{\odot }$ (left) and radius (right) for various sets of the parameters ${\mathrm{\Lambda }}_{\mathrm{Qyc}}$ and ${\kappa }_{\mathrm{Qyc}}$, see caption of Fig. 4 for more details.

Figure 8

Gravitational redshift $z_{\mathrm{surf}}$ as function of the mass $M/M_{\odot }$ (left) and radius (right) for various sets of the parameters ${\mathrm{\Lambda }}_{\mathrm{Qyc}}$ and ${\kappa }_{\mathrm{Qyc}}$, see caption of Fig. 4 for more details.

Figure 9

Mass-radius relation for SLy4-soft nuclear interaction and for the quarkyonic model with various sets of the parameters ${\mathrm{\Lambda }}_{\mathrm{Qyc}}$ and ${\kappa }_{\mathrm{Qyc}}$, see caption of Fig. 4 for more details.