Thermodynamical instabilities under strong magnetic fields

The thermodynamical instabilities of low densities in the $np$ matter and $npe$ matter are studied within several relativistic nuclear models under some values of magnetic fields. The results are compared between each other and the effects of the symmetry energy slope at saturation density on the instability are investigated. The instability regions can exhibit bands due to the presence of Landau levels for very strong magnetic fields of the order of ${10}^{17}$ G, while for weaker magnetic fields, the bands are replaced by many diffused or scattered pieces. It also shows that the proton fraction in the inner crust of neutron stars may be complex under strong magnetic fields.

Figure 1

Symmetry energy versus density for several relativistic models.

Figure 2

The instability region with several values of magnetic fields for FSUGold model for $np$ matter (top panels) and $npe$ matter (bottom panels). Spinodal section with no magnetic fields is also shown with the red curve for comparison.

Figure 3

The same as in Fig. 2 but for IUFSU model.

Figure 4

The same as in Fig. 2 but for FSU2 model.

Figure 5

The same as in Fig. 2 but for NL3 model.

Figure 6

Neutron densities for the termination of unstable region in the case when no proton is present versus magnetic fields for different $L$ with the parameters given in Table 2 and the other parameters the same as IUFSU model.

Figure 7

$\delta {\rho }_p^{-}/\delta {\rho }_n^{-}$ versus density for several relativistic models with $B=5\times {10}^{17}$ G for proton fraction $y_p=0.02$ (top panels) and 0.05 (bottom panels), respectively. The $B=0$ results are also given for $np$ matter (thick black curves) and $npe$ matter (thin black curves).

Figure 8

The same as in Fig. 7 but with $B=8\times {10}^{16}$ G.

Figure 9

The same as in Fig. 7 but with $B=1\times {10}^{16}$ G.