What is the magnetic field distribution for the equation of state of magnetized neutron stars?

TL;DR

This paper provides a realistic, self-consistent calculation of magnetic field profiles inside strongly magnetized neutron stars, revealing a polynomial increase with density rather than the exponential growth previously assumed.

Contribution

It introduces a new polynomial model for magnetic field distribution in neutron stars based on comprehensive microscopic and relativistic modeling.

Findings

Magnetic fields increase polynomially with baryon density.

The new model differs from previous exponential assumptions.

Provides a phenomenological fit for magnetic field profiles.

Abstract

In this Letter, we report a realistic calculation of the magnetic field profile for the equation of state inside strongly magnetized neutron stars. Unlike previous estimates, which are widely used in the literature, we find that magnetic fields increase relatively slowly with increasing baryon chemical potential (or baryon density) of magnetized matter. More precisely, the increase is polynomial instead of exponential, as previously assumed. Through the analysis of several different realistic models for the microscopic description of stellar matter (including hadronic, hybrid and quark models) combined with general relativistic solutions endowed with a poloidal magnetic field obtained by solving Einstein-Maxwell's field equations in a self-consistent way, we generate a phenomenological fit for the magnetic field distribution in the stellar polar direction to be used as input in microscopic calculations.