General relativistic treatment of the thermal, magnetic and rotational evolution of neutron stars with crustal magnetic fields

TL;DR

This paper presents a comprehensive general relativistic model for the thermal, magnetic, and rotational evolution of neutron stars with crustal magnetic fields, considering different equations of state and comparing results with observations.

Contribution

It introduces a fully general relativistic formalism for neutron star evolution, including magnetic and rotational aspects, and assesses the impact of different equations of state on observable properties.

Findings

General relativistic effects decelerate magnetic field decay compared to non-relativistic models.

A not too soft equation of state aligns with observed neutron star periods and cooling behavior.

Crustal magnetic field evolution depends on star compactness and impurity content.

Abstract

We investigate the thermal, magnetic and rotational evolution of isolated neutron stars assuming that the dipolar magnetic field is confined to the crust. Our treatment, for the first time, uses a fully general relativistic formalism not only for the thermal but also for the magnetic part, and includes partial general relativistic effects in the rotational part. Due to the fact that the combined evolution depends crucially upon the compactness of the star, three different equations of state have been employed in the calculations. In the absence of general relativistic effects, while upon increasing compactness a decrease of the crust thickness takes place leading into an accelerating field decay, the inclusion of general relativistic effects intend to ``decelerate this acceleration''. As a consequence we find that within the crustal field hypothesis, a given equation of state is compatible with the observed periods $P$ and period derivative $\dot P$ provided the initial field strength and current location as well as the magnitude of the impurity content are constrained appropriately. Finally, we access the flexibility of the soft, medium and stiff classes of equations of state as candidates in describing the state of the matter in the neutron star interiors. The comparison of our model calculations with observations, together with the consideration of independent information about neutron star evolution, suggests that a not too soft equation of state describes neutron star interiors and its cooling proceeds along the `standard' scenario.