Quadrupole moment of a magnetically confined mountain on an accreting neutron star: effect of the equation of state

TL;DR

This study extends models of magnetically confined mountains on neutron stars to include various realistic equations of state, revealing significant reductions in ellipticity and implications for gravitational wave detection and neutron star properties.

Contribution

It introduces adiabatic equations of state into magnetic mountain models, showing their effects on ellipticity and magnetic dipole moments, and compares results with observational constraints.

Findings

Ellipticity decreases significantly with realistic equations of state.

Models are consistent with current LIGO upper limits.

Spin distribution simulations better match observations with adiabatic models.

Abstract

Magnetically confined mountains on accreting neutron stars are promising sources of continuous-wave gravitational radiation and are currently the targets of directed searches with long-baseline detectors like the Laser Interferometer Gravitational Wave Observatory (LIGO). In this paper, previous ideal-magnetohydrodynamic models of isothermal mountains are generalized to a range of physically motivated, adiabatic equations of state. It is found that the mass ellipticity drops substantially, from \epsilon ~ 3e-4 (isothermal) to \epsilon ~ 9e-7 (non-relativistic degenerate neutrons), 6e-8 (relativistic degenerate electrons) and 1e-8 (non-relativistic degenerate electrons) (assuming a magnetic field of 3e12 G at birth). The characteristic mass M_{c} at which the magnetic dipole moment halves from its initial value is also modified, from M_{c}/M_{\sun} ~ 5e-4 (isothermal) to M_{c}/M_{\sun} ~ 2e-6, 1e-7, and 3e-8 for the above three equations of state, respectively. Similar results are obtained for a realistic, piecewise-polytropic nuclear equation of state. The adiabatic models are consistent with current LIGO upper limits, unlike the isothermal models. Updated estimates of gravitational-wave detectability are made. Monte Carlo simulations of the spin distribution of accreting millisecond pulsars including gravitational-wave stalling agree better with observations for certain adiabatic equations of state, implying that X-ray spin measurements can probe the equation of state when coupled with magnetic mountain models.