Effect of the δ meson on the instabilities of nuclear matter under strong magnetic fields

We study the influence of the isovector-scalar meson on the spinodal instabilities and the distillation effect in asymmetric nonhomogenous nuclear matter under strong magnetic fields of the order of ${10}^{18}\text{−}{10}^{19}$ G. Relativistic nuclear models both with constant couplings (NLW) and with density-dependent parameters (DDRH) are considered. A strong magnetic field can have large effects on the instability regions giving rise to bands of instability and wider unstable regions. It is shown that for neutron-rich matter the inclusion of the δ meson increases the size of the instability region for NLW models and decreases it for the DDRH models. The effect of the δ meson on the transition density to homogeneous $\beta$-equilibrium matter is discussed. The DDRHδ model predicts the smallest transition pressures, about half the values obtained for NLδ.

Figure 1

Symmetry energy for all models used in the present work.

Figure 2

Spinodal section in terms of ${\rho }_p$ versus ${\rho }_n$ for NLρ (thin lines) and NLδ (thick lines) at $T=0$ MeV and for several values of magnetic fields (a) without and (b) with AMM.

Figure 3

Spinodal section in terms of ${\rho }_p$ versus ${\rho }_n$ for TW (thin lines) and DDRHδ (thick lines) models at $T=0$ MeV and for several values of magnetic fields (a) without and (b) with AMM.

Figure 4

Physical quantities at the inner edge of a compact star in the presence of strong magnetic fields: (a) density, (b) proton fraction, and (c) pressure.

Figure 5

$\delta {\rho }_p^{-}/\delta {\rho }_n^{-}$ plotted as a function of the proton fraction with $\rho =0.06$ ${\mathrm{fm}}^{-3}$ for the NLW models [NLρ (thin lines) and NLδ (thick lines)] (left) and DDRH models [TW (thin lines) and DDRHδ (thick lines)] (right) and for several values of the magnetic fields without AMM. The fraction ${\rho }_p/{\rho }_n$ is given by the thin dotted line.