[Paper Review] MHD instabilities in accretion mounds on neutron star binaries

Dipanjan Mukherjee, D. Bhattacharya+1 more|arXiv (Cornell University)|Apr 26, 2013

High-pressure geophysics and materials3 citations

TL;DR

This study investigates magnetohydrodynamic (MHD) instabilities in accretion mounds on neutron star binaries using numerical solutions of the Grad-Shafranov equation and 3D MHD simulations with the PLUTO code. It finds that pressure-driven instabilities disrupt mounds above a threshold mass (~5×10⁻¹³ M☉), leading to finger-like structures and limiting long-term magnetic field burial through diamagnetic screening.

ABSTRACT

We have numerically solved the Grad-Shafranov equation for axisymmetric static MHD equilibria of matter confined at the polar cap of neutron stars. From the equilibrium solutions we explore the stability of the accretion mounds using the PLUTO MHD code. We find that pressure driven modes disrupt the equilibria beyond a threshold mound mass, forming dynamic structures, as matter spreads over the neutron star surface. Our results show that local variation of magnetic field will significantly affect the shape and nature of the cyclotron features observed in the spectra of High Mass X-ray Binaries.

Motivation & Objective

• To model the magnetostatic equilibrium of accretion mounds on neutron stars using the Grad-Shafranov equation with a realistic equation of state for dense Fermi plasma.
• To investigate the stability of these equilibria against MHD instabilities, particularly pressure-driven modes, under varying mound masses and magnetic field curvatures.
• To assess the implications of MHD instabilities for the long-term evolution of neutron star magnetic fields and the observed cyclotron resonance scattering features (CRSF) in high-mass X-ray binaries.
• To determine the threshold mound mass and plasma beta (β) at which MHD instabilities become dominant, limiting field line distortion and diamagnetic screening.

Proposed method

• Solved the axisymmetric Grad-Shafranov equation for magnetostatic equilibrium, incorporating a relativistic Fermi gas equation of state (p ∝ ρ⁵/³) to accurately model high-density plasma near the neutron star surface.
• Used the PLUTO MHD code to perform 3D non-axisymmetric simulations of perturbed equilibrium solutions to study the growth of MHD instabilities over time.
• Defined mound height as a function of magnetic flux function Z₀(ψ), with field lines and pressure gradients computed from the GS solution to model realistic mound geometry.
• Tracked the evolution of density and magnetic field magnitude over time, identifying the onset of finger-like instabilities at radial edges of the mound.
• Computed plasma β (ratio of plasma to magnetic pressure) for different mound masses to compare with theoretical instability thresholds (e.g., Litwin et al. 2001).
• Performed simulations across varying mound masses (from ~6.8×10⁻¹³ M☉ to ~10⁻¹² M☉) to identify the critical mass threshold for instability.

Experimental results

Research questions

• RQ1 At what mound mass does MHD instability first disrupt the magnetostatic equilibrium of an accretion mound on a neutron star?
• RQ2 How do local magnetic field distortions caused by accreted matter affect the shape and variability of cyclotron resonance scattering features (CRSF) in high-mass X-ray binaries?
• RQ3 To what extent do MHD instabilities limit the long-term magnetic field burial via diamagnetic screening in neutron stars?
• RQ4 What is the growth timescale of pressure-driven MHD instabilities in accretion mounds, and how does it vary with mound mass and field curvature?
• RQ5 How does the plasma beta (β) at the instability threshold compare with theoretical predictions (e.g., β ~ 260)?

Key findings

• MHD instabilities disrupt accretion mound equilibria when the mound mass exceeds ~5×10⁻¹³ M☉, corresponding to a mound of ~45 m in height.
• The maximum plasma β in the stable 45 m mound is ~293, which is close to the theoretical instability threshold of β ~ 260 predicted by Litwin et al. (2001).
• For larger mounds (~10⁻¹² M☉), MHD instabilities grow rapidly, developing finger-like channels at the radial edges within a few Alfvén times (~2.8×10⁻³ s).
• Smaller mounds (e.g., 50 m, ~6.8×10⁻¹³ M☉) exhibit slower instability growth, with timescales about ten times longer than larger mounds.
• Significant magnetic field distortion extends up to ~1 km above the mound, with field strength deviating by >10% from the dipolar field even at 500 m height.
• MHD instabilities severely limit the formation of large-scale diamagnetic screening currents, thereby constraining the long-term burial of neutron star magnetic fields.