Effects of quark-matter symmetry energy on hadron-quark coexistence in neutron-star matter

We examine the effects of the isovector-vector coupling and hypercharge-vector coupling in quark matter on hadron-quark coexistence in neutron-star matter. The relativistic mean field theory with the TM1 parameter set and an extended TM1 parameter set are used to describe hadronic matter, and the Nambu-Jona-Lasinio model with scalar, isoscalar-vector, isovector-vector, and hypercharge-vector couplings is used to describe deconfined quark matter. The hadron-quark phase transition is constructed via the Gibbs conditions for phase equilibrium. The isovector-vector and hypercharge-vector couplings in quark matter enhance the symmetry energy and hypercharge symmetry energy in neutron-star matter, while their effects are found to be suppressed at high densities by the strange quarks. As a result, the hadron-quark mixed phase shrinks with only isovector-vector coupling and moves to higher density with isovector-vector and hypercharge-vector couplings. The maximum mass of neutron star increases slightly with isovector-vector and hypercharge-vector couplings.

Figure 1

Symmetry energy as a function of the baryon number density for the pure hadronic phase (black lines) and the pure quark phase (blue lines) with different vector couplings.

Figure 2

Pressures as a function of the baryon number density for the pure hadronic phase (dash-dotted lines), the mixed phase (dashed lines), and the pure quark phase (solid lines).

Figure 3

Energy density per baryon as a function of the baryon number density for the hadronic, mixed, and quark phases. The left panel is a local enlargement of the right panel. Open circles (squares, triangles) label the transition points for $G_3=G_8=0$ ($G_3=G_8=1.5G_0$, $G_3=G_8=10G_0$).

Figure 4

The left panel shows the relation between the chemical potential of neutron and electron. The right panel is the electron chemical potential as a function of baryon number density for different phases.

Figure 5

The isospin asymmetry and hypercharge fraction for $(G_3/G_0,G_8/G_0)=(0,0),(1.5,0),(1.5,1.5),(10,0)$, and (10,10).

Figure 6

Particle number fractions for the pure hadronic phase (dash-dotted lines), the mixed phase (dashed lines), and the pure quark phase (solid lines). The fractions of $u$, $d$, and $s$ quarks are labeled by green (middle), blue (upper), red (lower) solid lines in the pure quark phase and green (lower), blue (upper), red (middle) dashed lines in the mixed phase.

Figure 7

The left panel plots mass-radius relations of neutron stars for different EOS. The solid lines and the dash-dotted lines (dashed lines) show the results without and with isovector-vector coupling and hypercharge-vector coupling respectively. The right panel shows maximum mass as a function of neutron-star central density.