Hybrid protoneutron stars with the Dyson-Schwinger quark model

We study the hadron-quark phase transition at finite temperature in the interior of protoneutron stars, combining the Dyson-Schwinger model for quark matter with the Brueckner-Hartree-Fock approach for hadronic matter. We discuss the dependence of the results on different nuclear three-body forces and on details of the quark model. A maximum mass exceeding two solar masses can only be obtained with a strong three-body force and suitable parameter values in the Dyson-Schwinger model. With a hybrid configuration, the maximum mass of protoneutron stars is larger than that of cold neutron stars, such that a delayed collapse might be possible in principle.

Figure 1

Quark number density (upper panel), pressure ${\tilde{P}}_q$ (central panel), and entropy density (lower panel) for massless quarks at finite chemical potentials and temperatures. Different curves correspond to different values of the parameter $\alpha =2$ (dotted blue lines), 4 (dashed red lines), $\infty$ (solid black lines) and different temperatures $T=0$ (thin lines), $T=40\mathrm{MeV}$ (thick lines). All $s_{u,d}(\mu ,T=0)=0$.

Figure 2

Same as Fig. 1, but for strange quarks with $m_s=115\mathrm{MeV}$.

Figure 3

Baryon density (upper panels) and pressure (lower panels) as function of the baryon chemical potential for cold untrapped matter (left panels), untrapped matter at $T=40\mathrm{MeV}$ (central panels), and trapped matter at $T=40\mathrm{MeV}$ (right panels). See text for details.

Figure 4

Pressure vs baryon density of NS matter with the Gibbs phase transition construction for different models. Phenomenological (upper panels) or microscopic (lower panels) TBF are used for the hadronic EOS. The pure hadron or quark phases are marked with thin curves and the mixed phase region with thick curves. The pure quark phase regions with the DSM in the upper panel and with DS2 in the lower panel lie beyond the range we plot.

Figure 5

NS gravitational mass vs central baryon density. Phenomenological (upper panels) or microscopic (lower panels) TBF are used for the hadronic EOS.