# Effect of strong magnetic fields on the crust-core transition and inner crust of neutron stars

## TL;DR

This paper investigates how intense magnetic fields influence the crust-core transition in neutron stars by analyzing the dynamical instability regions and the effects of Landau levels and nucleon magnetic moments.

## Contribution

It introduces a formalism using the Vlasov equation to study the impact of strong magnetic fields on neutron star crusts, highlighting the significance of anomalous magnetic moments.

## Key findings

- Strong magnetic fields significantly alter the crust-core transition region.
- The opening of Landau levels causes a succession of stable and unstable regions.
- Anomalous magnetic moments become important for fields above 10^{15} G.

## Abstract

The Vlasov equation is used to determine the dispersion relation for the eigenmodes of magnetized nuclear and neutral stellar matter, taking into account the anomalous magnetic moment of nucleons. The formalism is applied to the determination of the dynamical spinodal section, a quantity that gives a good estimation of the crust-core transition in neutron stars. We study the effect of strong magnetic fields, of the order of $10^{15}-10^{17}$ G, on the extension of the crust of magnetized neutron stars. The dynamical instability region of neutron-proton-electron ($npe$) matter at subsaturation densities is determined within a relativistic mean field model. It is shown that a strong magnetic field has a large effect on the instability region, defining the crust-core transition as a succession of stable and unstable regions due to the opening of new Landau levels. The effect of the anomalous magnetic moment is non-negligible for fields larger than 10$^{15}$ G. The complexity of the crust at the transition to the core and the increase of the crust thickness may have direct impact on the properties of neutrons stars related with the crust.