Lattice QCD constraints on hybrid and quark stars

A QCD-motivated dynamical-quasiparticle model with parameters adjusted to reproduce the lattice-QCD equation of state is extrapolated from the region of high temperatures and moderate baryonic densities to the domain of high baryonic densities and zero temperature. The resulting equation of state matched with realistic hadronic equations of state predicts a phase transition into the quark phase at higher densities than those reachable in neutron star interiors. This excludes the possibility of the existence of hybrid (hadron-quark) stars. Pure quark stars are possible and have low masses, small radii, and very high central densities. Similar results are obtained for a simple bag model with massive quarks, fitted to reproduce the same lattice results. Self-bound quark matter is also excluded within these models. Uncertainties in the present extrapolation are discussed. Comparison with standard bag models is made.

Figure 1

(Color online) Pressure (left panel) and the interaction measure $\varepsilon -3P$ (right panel) scaled by $T^4$ as functions of $T/T_C$ at zero baryon chemical potential $\mu =0$. Solid line corresponds to 1-loop version; dashed line, 2-loop version of the DQ model. The vertically hatched band is the heavy-bag fit with $c=0$ and $c=0.3$ for the top and bottom boundary lines, respectively. The grey band (for P) and the grey line (for $\varepsilon -3P$) represent prediction of the light-bag-155 model. The dash-dotted line corresponds to the light-bag-200 model. Lattice data (triangles and dots) are from Ref. 14.

Figure 2

(Color online) $\Delta P=P(T,\mu )-P(T,\mu =0)$ (left panel) and the baryon density n (right panel) scaled by $T^4$ and $T^3$ as functions of $T/T_c$ at nonzero baryon chemical potentials $\mu =$ 330 and 530 MeV (from bottom to top). Note different scales (left and right, respectively) for $\mu \hspace{1em}=\hspace{1em}330$ and 530 MeV in the right panel. Notation is the same as in Fig. 1.

Figure 3

(Color online) Quark and gluon effective masses (left panel) and bag parameters scaled by $T^4$ (right panel) for the DQ model, cf. Eq. (5), and bag models as functions of $T/T_C$ at zero baryon chemical potential $\mu =0$. Notation is the same as in Fig. 1.

Figure 4

(Color online) Effective quark masses (left panel) and bag parameters (right panel) for the DQ models (curves), cf. Eq. (5), and bag models (horizontal lines) as functions of $n/n_0$ for $T=0$ at β equilibrium. Notation is the same as in Fig. 1.

Figure 5

(Color online) Pressure as a function of the chemical potential (left panel) and $n/n_0$ (right panel) for $T=0$ at β equilibrium. Notation for the quark models is the same as in Fig. 1. Band boundaries for the heavy-bag and light-bag-155 models correspond to $c=0$ and $c=0.3$: from top to bottom in left panel, and from bottom to top in right panel. Hadronic EOS of the conventional Walecka model (hadron W) is displayed by long-dashed line. Two versions of the hadronic model of Ref. 52, i.e., hadron-MW1 and hadron-MW2, are presented by dashed-dotted-dotted and dotted lines, respectively.

Figure 6

(Color online) Pressure vs energy density at $T=0$ in β equilibrium for various EOSs. Band boundaries for the heavy-bag model correspond to $c=0$ and $c=0.3$ (from bottom to top). Notation is the same as in Figs. 1 and 5.

Figure 7

(Color online) Quark star mass-radius relation of pure quark stars for the normal quark phase with $\Delta =0$ (left panel) and the CFL quark phase with $\Delta =100\text{MeV}$ (right panel). Notation is the same as in previous figures. Band boundaries are $c=0$ and $c=0.3$, from bottom to top.

Figure 8

(Color online) Quark star mass vs central density. Notation is the same as in Fig. 7.