Magnetically Confined Mountains on Accreting Neutron Stars in General Relativity

TL;DR

This paper develops a general relativistic model of magnetically confined mountains on neutron stars, showing that relativistic effects decrease magnetic deformation and dipole screening compared to Newtonian predictions.

Contribution

It introduces a relativistic formulation and numerical solutions for neutron star mountains, extending previous Newtonian models and quantifying the impact of relativity on magnetic structure.

Findings

Relativistic corrections reduce magnetic deformation.

Dipole moment screening is about three times less.

Mountain scale height decreases by approximately 40%.

Abstract

The general relativistic formulation of the problem of magnetically confined mountains on neutron stars is presented, and the resulting equations are solved numerically, generalising previous Newtonian calculations. The hydromagnetic structure of the accreted matter and the subsequent magnetic burial of the star's magnetic dipole moment are computed. Overall, it is observed that relativistic corrections reduce the hydromagnetic deformation associated with the mountain. The magnetic field lines are curved more gently than in previous calculations, and the screening of the dipole moment is reduced. Quantitatively, it is found that the dimensionless dipole moment ($m_{\rm d}$) depends on the accreted mass ($M_{\rm a}$) as $m_{\rm d} = -3.2\times10^{3}M_{\rm a}/M_\odot + 1.0$, implying approximately three times less screening compared to the Newtonian theory. Additionally, the characteristic scale height of the mountain, governing the gradients of quantities like pressure, density, and magnetic field strength, reduces by approximately $40\%$ for an isothermal equation of state.