Effects of the symmetry energy on the kaon condensates in the quark-meson coupling model

In this work we investigate protoneutron star properties within a modified version of the quark-meson coupling (QMC) model that incorporates an $\omega \text{−}\rho$ interaction plus kaon condensed matter at finite temperature. Fixed entropy and trapped neutrinos are taken into account. Our results are compared with the ones obtained with the GM1 parametrization of the nonlinear Walecka model for similar values of the symmetry energy slope. Contrary to GM1, within the QMC model the formation of low mass black holes during cooling are not probable. It is shown that the evolution of the protoneutron star may include the melting of the kaon condensate driven by the neutrino diffusion, followed by the formation of a second condensate after cooling. The signature of this complex process could be a neutrino signal followed by a gamma ray burst. We have seen that both models can, in general, describe very massive stars.

Figure 1

Equation of states for the QMC model and $L=70.05$ MeV for three situations of interest in the star evolution.

Figure 2

(a) Nucleon effective mass and (b) radius for the QMC model and $L=70.05$ MeV for three situations of interest in the star evolution.

Figure 3

Particle fractions obtained with the QMC model for $T=10$ MeV, $L=93.5$ MeV (thick line), and $L=70.5$ MeV (thin line).

Figure 4

Warm matter with trapped neutrinos, $S=1$ and $Y_l=0.4$. (a) Particle fractions versus the baryonic density within QMC for two different values of the slope $L$. (b) Kaon fraction for both QMC and GM1.

Figure 5

Kaon effective mass versus density in $\beta$-equilibrium matter for different values of the entropy per baryon $S$ and the slope $L$. Matter for $S=1$ contains trapped neutrinos with $Y_l=0.4$ and all other curves were obtained for neutrino free matter.

Figure 6

Neutrino chemical potential versus baryon density for $\beta$-equilibrium matter at $S=1$ with the lepton fraction $Y_l=0.4$. Results for GM1 and QMC are shown for three different values of $L$.

Figure 7

Temperature versus density for neutrino free matter with $S=2$ and matter with neutrino trapped matter with $S=1$.

Figure 8

Mass-radius profiles for stars with $S=1$ and fixed lepton fraction $Y_l=0.4$ (red full lines), $S=2$ and neutrino free matter (green dashed lines), and cold matter (blue dotted lines), for different values of the symmetry energy slope: $L=59$ (thick), 70 (medium), and 93 (thin) MeV, with (a) QMC and (b) GM1. The black dots indicate the onset of kaon condensate.

Figure 9

Baryonic versus gravitacional masses for stars with $S=1$ and fixed lepton fraction $Y_l=0.4$ (top dashed curve), $S=2$ and neutrino free matter (middle full curve), and cold matter (bottom dotted curve), for (a) and (c) $L=93.5$ MeV and (b) and (d) $L=59.3$ MeV. The results were obtained with (a) and (b) QMC and (c) and (d) GM1. The black full dots indicate the minimal mass configuration which contains a kaon condensate in the core, and the red asterisks the minimal configuration with a fraction ${10}^{-8}$ or larger of thermal kaons.