Low density instability in relativistic mean field models

The effects of symmetry energy softening of relativistic mean field (RMF) models on the properties of matter with neutrino trapping are investigated. It is found that the effects are less significant than those in the case without neutrino trapping. The weak dependence of the equation of state on the symmetry energy is shown as the main reason for this finding. Using different RMF models the dynamical instabilities of uniform matters, with and without neutrino trapping, have been also studied. The interplay between the dominant contribution of the variation of matter composition and the role of effective masses of mesons and nucleons leads to higher critical densities for matter with neutrino trapping. Furthermore, the predicted critical density is insensitive to both the number of trapped neutrinos as well as the RMF model used in the investigation. It is also found that additional nonlinear terms in the Horowitz-Piekarewicz and Furnstahl-Serot-Tang models prevent another kind of instability, which occurs at relatively high densities, because the effective σ meson mass in their models increases as a function of matter density.

Figure 1

Binding energy per nucleon (upper left panel) and the neutrino electron fraction (upper right panel) as a function of the baryon density, as well as the EOS as functions of baryon density (lower left panel) and energy density (lower right panel) according to RMF models. The curves are obtained by using $Y_{l_e}=0.3$.

Figure 2

$\Delta E_2/A,\Delta E_1/A,$ and${\alpha }^2$ as a function of the ratio between baryon and nuclear saturation densities for matters with and without neutrino trapping (NT). The $\mathrm{G}{2}^{*}$ parameter set and $Y_{l_e}=0.3$ are used in obtaining these results.

Figure 3

$\Delta E_2/A$ and $\Delta E_1/A$ as a function of the ratio between baryon and nuclear saturation densities for matters with and without neutrino trapping (NT), obtained by using G2, $\mathrm{G}{2}^{*}$, Z271, $\mathrm{Z}{271}^{*}$, and NL3 parameter sets. All curves are obtained with $Y_{l_e}=0.3$.

Figure 4

${\alpha }^2$ as a function of the ratio between baryon and nuclear saturation densities for matters with and without neutrino trapping (NT). The results are obtained by using G2, $\mathrm{G}{2}^{*}$, Z271, $\mathrm{Z}{271}^{*}$, and NL3 parameter sets and $Y_{l_e}=0.3$.

Figure 5

Symmetry energy as a function of the ratio between baryon and nuclear saturation densities for G2, $\mathrm{G}{2}^{*}$, Z271, $\mathrm{Z}{271}^{*}$, and NL3 parameter sets.

Figure 6

Same as Fig. 1, but here the $Y_{l_e}$ is varied and the $\mathrm{G}{2}^{*}$ parameter set is used.

Figure 7

$\Delta E_2/A,\Delta E_1/A,$ and α as a function of the ratio between baryon density and nuclear saturation density for matter with neutrino trapping (NT) obtained by using the $\mathrm{G}{2}^{*}$ parameter set but with varied $Y_{l_e}$.

Figure 8

Critical densities for the Z271, $\mathrm{Z}{271}^{*}$, G2, and $\mathrm{G}{2}^{*}$ parameter sets as a function of the neutrino fraction in matter.

Figure 9

Same as in Fig. 8, but for the NL3 parameter set.

Figure 10

Effective masses of the nucleon and $\sigma ,\omega ,$ and ρ mesons as a function of the baryon density. Note that several lines coincide.