Isospin- and momentum-dependent effective interactions for the baryon octet and the properties of hybrid stars

The isospin- and momentum-dependent MDI interaction, which has been extensively used in intermediate-energy heavy-ion reactions to study the properties of asymmetric nuclear matter, is extended to include the nucleon-hyperon and hyperon-hyperon interactions by assuming the same density, momentum, and isospin dependence as for the nucleon-nucleon interaction. The parameters in these interactions are determined from the empirical hyperon single-particle potentials in symmetric nuclear matter at saturation density. The extended MDI interaction is then used to study in the mean-field approximation the equation of state of hypernuclear matter and also the properties of hybrid stars by including the phase transition from hypernuclear matter to quark matter at high densities. In particular, the effects of attractive and repulsive $\Sigma$N interactions and different values of symmetry energies on the hybrid star properties are investigated.

Figure 1

Single-particle potentials for particles at rest in symmetric nuclear matter as functions of density.

Figure 2

Single-particle potentials in symmetric nuclear matter at saturation density ${\rho }_0$ as functions of particle momentum. The Schrödinger equivalent potential obtained by Hama and co-workers [64, 65] from the nucleon-nucleus scattering data is shown by stars for comparison. $\Sigma$(A) and $\Sigma$(R) are for the MDI-Hyp-A and MDI-Hyp-R interactions, respectively.

Figure 3

Symmetry potentials of nucleons and $\Sigma$ and $\Xi$ hyperons in asymmetric nuclear matter at saturation density $\rho ={\rho }_0$. $\Sigma (\text{A})$ and $\Sigma (\text{R})$ are for the MDI-Hyp-A and MDI-Hyp-R interactions, respectively.

Figure 4

Symmetry potentials of nucleons and $\Sigma$ and $\Xi$ hyperons in asymmetric nuclear matter at density $\rho =3{\rho }_0$. $\Sigma (\text{A})$ and $\Sigma (\text{R})$ are for the MDI-Hyp-A and MDI-Hyp-R interactions, respectively. Note that different scales are used for $x=0$ (left panel) and $x=-1$ (right panel).

Figure 5

Pressure as functions of baryon density $\rho$ for the hadron phase (solid line), mixed phase (dotted line), and quark phase (dashed line). The pressure of the quark matter that is in chemical equilibrium with the hadronic matter as a function of the baryon density of the hadronic matter is denoted by the dash-dotted line, whose intersection with the solid line gives the low-density boundary of the hadron-quark phase transition.

Figure 6

Particle fractions in hypernuclear matter for the MDI-Hyp interaction with $x=0$ [(a) and (c)] and $x=-1$ [(b) and (d)] as well as with attractive [(a) and (b)] and repulsive [(c) and (d)] $\Sigma$$N$ interactions.

Figure 7

Same as Fig. 6 for the chemical potentials in hypernuclear matter.

Figure 8

Equation of state of pure nuclear matter and hypernuclear matter from the MDI-Hyp interaction with $x=0$ and $x=-1$ as well as with attractive (upper panel) and repulsive (lower panel) $\Sigma N$ interactions.

Figure 9

Particle fractions in hypernuclear matter with the presence of hadron-quark phase transition from the MDI-Hyp-R interaction with $x=0$ [(a) and (c)] and $x=-1$ [(b) and (d)] for the hadron phase and the MIT bag model for the quark phase. Results from $B^{1/4}=180$ MeV [(a) and (b)] and $170$ MeV [(c) and (d)] are shown for comparison.

Figure 10

Same as Fig. 9 for the equation of state.

Figure 11

The hybrid star mass as a function of radius (left panel) and central density (right panel) based on the MDI-Hyp interaction with $x=0$ and $x=-1$. Results from attractive and repulsive $\Sigma N$ interactions are shown for comparison. Results from a pure nucleonic approach are also displayed.

Figure 12

The hybrid star mass as a function of radius (left panel) and central density (right panel) in the presence of the hadron-quark phase transition. Results from the MDI-Hyp-R interaction for the hadron phase with $x=0$ and $x=-1$ and the MIT bag model for the quark phase with $B^{1/4}=180$ and $170$ MeV are shown for comparison. Results from a pure nucleonic approach are also displayed.