[Paper Review] Ferromagnetic Phase Transitions in Neutron Stars

J. P. W. Diener|arXiv (Cornell University)|May 31, 2013

Pulsars and Gravitational Waves Research18 references3 citations

TL;DR

This paper investigates ferromagnetic phase transitions in neutron star matter using Quantum Hadrodynamics with explicit baryon magnetic dipole and charge-magnetic field couplings. It finds that the ferromagnetic field undergoes abrupt jumps at specific densities due to Landau level transitions, significantly affecting neutron star magnetism without substantially altering the mass-radius relation.

ABSTRACT

The ferromagnetic phase in pure neutron matter as well as charge neutral, beta-equilibrated nuclear matter is considered. We employ Quantum Hadrodynamics, a relativistic field theory description of nuclear matter with meson degrees of freedom, and include couplings between the baryon (proton and neutron) magnetic dipole moment as well as between their charge and the magnetic field in the Lagrangian density describing such a system. We vary the strength of the baryon magnetic dipole moment till a non-zero value of the magnetic field, for which the total energy density of the magnetised system is at a minimum, is found. The system is then assumed to be in the ferromagnetic state. The ferromagnetic equation of state is employed to study matter in the neutron star interior. We find that as the density increases the ferromagnetic field does not increase continuously, but exhibit sudden rapid increases. These sudden increases in the magnetic field correspond to shifts between different configurations of the charged particle's Landau levels and can have significant observational consequences for neutron stars. We also found that although the ferromagnetic phase softens the neutron star equation of state it does not significantly alter the star's mass-radius relationship. The properties of magnetised symmetric nuclear matter were also studied. We confirm that magnetised matter tends to be more proton-rich but become more weakly bound for stronger magnetic fields. We show that the behaviour of the compressibility of nuclear matter is influenced by the Landau quantisation and tends to have an oscillatory character as it increases with the magnetic field. The symmetry energy also exhibits similar behaviour.

Motivation & Objective

• To explore the emergence of ferromagnetism in dense neutron matter under extreme magnetic fields.
• To model how baryon magnetic dipole moments and charge-magnetic field couplings influence the equation of state in neutron stars.
• To determine the conditions under which a spontaneous magnetisation arises in neutron star interiors.
• To assess the observational implications of ferromagnetic transitions for magnetars and other neutron star phenomena.
• To analyze the role of Landau quantisation in modifying compressibility and symmetry energy in magnetised nuclear matter.

Proposed method

• Employing Quantum Hadrodynamics (QHD), a relativistic field theory with meson exchange, to describe nuclear interactions in neutron matter.
• Including explicit couplings between baryon magnetic dipole moments and the magnetic field, and between baryon charge and the electromagnetic field in the Lagrangian.
• Using the relativistic mean-field (RMF) approximation to solve for the ground state and self-consistently determine the magnetic field configuration.
• Varying the baryon magnetic dipole moment strength to identify the minimum energy state with non-zero magnetic field, indicating ferromagnetic order.
• Calculating particle densities, energy density, pressure, and scalar densities in the presence of Landau quantisation for charged fermions.
• Applying the resulting ferromagnetic equation of state to neutron star interiors and analyzing its impact on mass-radius and emission properties.

Experimental results

Research questions

• RQ1 Under what conditions does a spontaneous ferromagnetic phase transition occur in pure neutron matter?
• RQ2 How do Landau level transitions influence the behavior of the magnetic field in dense, magnetised neutron star matter?
• RQ3 What is the impact of ferromagnetism on the neutron star equation of state and its mass-radius relationship?
• RQ4 How does Landau quantisation affect the compressibility and symmetry energy in magnetised nuclear matter?
• RQ5 What are the observational consequences of abrupt magnetic field jumps in neutron stars, particularly in magnetars?

Key findings

• The ferromagnetic magnetic field exhibits sudden, rapid increases at specific densities due to transitions between Landau level configurations, rather than a continuous rise.
• These abrupt field jumps are directly linked to changes in the quantum number distribution of charged particles in Landau levels, indicating a phase-like transition.
• Although the ferromagnetic phase softens the equation of state, it does not significantly alter the neutron star mass-radius relationship.
• Magnetised symmetric nuclear matter becomes more proton-rich and less bound as the magnetic field strength increases.
• The compressibility of nuclear matter shows oscillatory behavior with increasing magnetic field due to Landau quantisation effects.
• The symmetry energy also exhibits oscillatory variations with magnetic field strength, reflecting the influence of Landau level quantisation on the nuclear interaction.