Stability of the neutron-proton-electron matter under strong magnetic fields: The covariant Vlasov approach

The neutron-proton-electron matter under a strong magnetic field is studied in the context of the covariant Vlasov approach. We use a Walecka-type hadronic model and the dispersion relations for the longitudinal and transverse modes are obtained. The instability regions for longitudinal and transverse modes are also studied. The crust-core transition of a magnetized neutron star is discussed.

Figure 1

Dynamical spinodals for the NL3 (top) and the FSU (bottom) parametrization, for several values of the magnetic field and for a moment transfer $k=75\mathrm{MeV}$. The black curve corresponds to the $B=0$ results.

Figure 2

Dynamical spinodals for the NL3 (top) and the FSU (bottom) parametrizations, for different moment transfer $k$ and for magnetic field $B={10}^{17}\mathrm{G}$. The black curve corresponds to the $B=0$ results.

Figure 3

Largest growth rate $\mathrm{\Gamma }=\left|\omega \right|$ (top), the corresponding half-wavelength (middle), the neutron-proton density fluctuation ratio versus density, and the electron-proton density fluctuation ratio (bottom) versus density for different magnetic-field intensities and matter with $y_p=0.035$ for FSU (left), and with $y_p=0.02$ for NL3 (right). The black curve corresponds to the $B=0$ results.

Figure 4

Dynamical spinodals for npe matter subjected to an external magnetic field. The spinodal sections for both longitudinal (blue) and transverse modes (green) are given for $k=100$ MeV and (a) $B=2.2\times {10}^{16}$ G, (b) $B=4.4\times {10}^{17}$ G, (c) $B=4.4\times {10}^{18}$ G. The black curve corresponds to the $B=0$ results.