[Paper Review] Magnetic Collapse of a Neutron Gas: No Magnetar Formation

A. Pérez Martı́nez, Hugo Pérez Rojas+1 more|ArXiv.org|Nov 30, 2000

Atomic and Subatomic Physics Research2 references3 citations

TL;DR

This paper proposes that a strongly magnetized neutron gas in neutron stars can undergo transverse collapse due to anisotropic pressure induced by magnetic fields, preventing magnetar formation. When magnetic pressure exceeds equatorial pressure at critical field strengths (~10^15 G), the star collapses into a hybrid or strange star, not a magnetar, setting a density-dependent upper limit on observable magnetic fields in pulsars.

ABSTRACT

A degenerate neutron gas in equilibrium with a background of electrons and protons in a magnetic field exerts its pressure anisotropically, having a smaller value perpendicular than along the magnetic field. For critical fields the magnetic pressure may produce the vanishing of the equatorial pressure of the neutron gas, and the outcome could be a transverse collapse of the star. This fixes a limit to the fields to be observable in stable pulsars as a function of their density. The final structure left over after the implosion might be a mixed phase of nucleons and meson ($π^{\pm,0},κ^{\pm,0}$) condensate (a strange star also likely) or a black string, but no magnetar at all.

Motivation & Objective

• To investigate whether extreme magnetic fields in neutron stars can trigger gravitational collapse due to anisotropic pressure.
• To determine the critical magnetic field strength at which transverse collapse of a neutron gas becomes unavoidable.
• To explore the final state of such collapsed stars, particularly whether magnetars can form under these conditions.
• To derive the equation of state for a degenerate neutron gas in a strong magnetic field, accounting for Landau quantization and magnetic moment alignment.
• To establish a density-dependent upper bound on observable magnetic fields in stable pulsars.

Proposed method

• Model a relativistic degenerate neutron gas in equilibrium with electrons and protons under a strong external magnetic field B.
• Use the Dirac equation with anomalous magnetic moment to derive the energy spectrum of neutrons in a magnetic field, including Landau level quantization.
• Compute the thermodynamic potential Ωn from the partition function, incorporating contributions from both spin states (η = ±1) and magnetic field dependence.
• Derive the neutron number density Nn and magnetization Mn via functional derivatives of Ωn with respect to chemical potential and magnetic field.
• Analyze the equation of state and pressure anisotropy, particularly the perpendicular (equatorial) pressure, to identify collapse conditions.
• Evaluate the condition where magnetic pressure exceeds equatorial pressure, leading to transverse collapse, using the critical field condition B ≤ Bc.

Experimental results

Research questions

• RQ1 At what magnetic field strength does the equatorial pressure of a neutron gas vanish, triggering transverse collapse?
• RQ2 Can magnetars form in neutron stars with magnetic fields up to 10^15 G, given quantum effects on degenerate neutron gas?
• RQ3 What is the final stable configuration of a neutron star after magnetic collapse—hybrid star, strange star, or black string?
• RQ4 How does the equation of state of a magnetized neutron gas differ from the isotropic case, and what role does Landau quantization play?
• RQ5 What upper limit does magnetic collapse impose on the observable magnetic fields in neutron stars as a function of density?

Key findings

• Transverse collapse occurs when the magnetic pressure exceeds the equatorial pressure of the neutron gas, which happens at critical magnetic fields B ~ 10^15 G for typical neutron star densities.
• The collapse is driven by anisotropic pressure due to Landau quantization and magnetic moment alignment, leading to vanishing perpendicular pressure.
• The final remnant after collapse is not a magnetar, but likely a hybrid star with nucleons and meson condensates (π±,0, κ±,0) or a strange star.
• The model predicts a density-dependent upper limit on observable magnetic fields in pulsars, preventing the formation of stable magnetars.
• Magnetic field lines are expelled beyond the Alfvén radius rA during the collapse, dissipating flux and reducing B below the QED limit (~10^13 G), preventing re-emergence of ultra-strong fields.
• The process is analogous to solar flares or coronal mass ejections, where magnetic energy is rapidly released, leaving behind a remnant with a canonical field strength.