Dynamical instabilities of warm $\mathit{npe}$ matter: $\delta$ meson effects

The effects of $\delta$ mesons on the dynamical instabilities of cold and warm nuclear and stellar matter at subsaturation densities are studied in the framework of relativistic mean-field hadron models $(\mathrm{NL}3$, $\mathrm{NL}\rho$, and $\mathrm{NL}\rho \delta )$ with the inclusion of the electromagnetic field. The distillation effect and the spinodals for all the models considered are discussed. The crust-core transition density and pressure are obtained as a function of temperature for $\beta$-equilibrium matter with and without neutrino trapping. An estimation of the size of the clusters formed in the nonhomogeneous phase and the corresponding growth rates are made. It is shown that cluster sizes increase with temperature. The effects of the $\delta$ meson on the instability region are larger for low temperatures, very asymmetric matter, and densities close to the spinodal surface. It increases the distillation effect above $~0.4{\rho }_0$ and has the opposite effect below that density.

Figure 1

The ratio of the proton over the neutron density fluctuations [Eq. (C3)] for NL$\rho \delta$ (dot-dashed) and NL$\rho$ (continuous line) plotted for $y_p=0.2$ at $T=5$ MeV for (a) $\rho =0.2{\rho }_0$ (black), $\rho =0.3{\rho }_0$ (green), and $\rho =0.5{\rho }_0$ (blue) as a function of the wave vector $\mathbf{k}$ and for (b) $k=10$ MeV (black), $k=50$ MeV (green), and $k=100$ MeV (blue) as a function of the density, $\rho$.

Figure 2

Spinodals [Eq. (16), with $\omega =0$] for $k=75$ MeV (black) for NL3 (dashed) and $k=100$ MeV (green) for NL$\rho \delta$ (dot-dashed) and NL$\rho$ (continuous line) at $T=0$ (a), $T=10$ (b), and $T=12$ MeV (c). The lines that cross the spinodals are the EOS in $\beta$ equilibrium [Eq. (9)] for $\mathit{npe}$ (neutrino-free, $Y_{\nu }=0$) and with trapped neutrinos for a lepton fraction $Y_l=0.4$ (red and blue, respectively), as indicated.

Figure 3

The crossing densities at the crust-core transition for $\beta$-equilibrium stellar matter with trapped neutrinos ($Y_l=0.4$) for NL3 (blue, dashed), NL$\rho \delta$ (green, dot-dashed), and NL$\rho$ (black, continuous line) as a function of temperature.

Figure 4

$\beta$-equilibrium neutrino-free matter at $T=0$ MeV: (a) the growth rates as a function of density, (b) the corresponding size of the clusters for NL3 (blue, dashed), NL$\rho \delta$ (green, dot-dashed), and NL$\rho$ (black, continuous line).

Figure 5

$\beta$-equilibrium neutrino-trapped matter $(Y_l=0.4)$: growth rates at (a) $T=5$, (b) $T=10$, and (c) $T=12$ MeV and corresponding size of the clusters at (d) $T=5$, (e) $T=10$, and (f) $T=12$ MeV for NL3 (blue, dashed), NL$\rho \delta$ (green, dot-dashed), and NL$\rho$ (black, continuous line).