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

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 ε drops substantially, from ε≈ 3 × 10−4 (isothermal) to ε≈ 9 × 10−7 (non‐relativistic degenerate neutrons), 6 × 10−8 (relativistic degenerate electrons) and 1 × 10−8 (non‐relativistic degenerate electrons) (assuming a magnetic field of 1012.5 G at birth). The characteristic mass Mc at which the magnetic dipole moment halves from its initial value is also modified, from Mc/M⊙≈ 5 × 10−4 (isothermal) to Mc/M⊙≈ 2 × 10−6, 1 × 10−7, and 3 × 10−8 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.

Gravitational Wave Astrophysics

“…In Figs. 6 and 7 we show the results obtained by Haskell et al (in preparation) for the model E equation of state of Priymak et al (2011). The critical mass depends on the assumed background field of the systems and we consider two possibilities, a background field of B D 10 12 G and one of B D 10 10 G. The latter may be a more realistic limit, given that Grad-Shafranov simulations show that the external dipole can be quenched by Haskell et al (in preparation) for the GW emission from known LMXBs, given a magnetic mountain with a background magnetic field of B D 10 10 G or B D 10 12 G. We consider the case in which the mountain is stable in-between outbursts and can thus be built gradually over the life time of the system.…”

“…The situation is even more interesting in accreting systems, in which, although the magnetic field is globally much weaker than in magnetars, the accretion process can lead to material spreading equatorially and compressing the field, making it locally strong enough to sustain a sizeable mountain (Melatos and Payne 2005;Payne and Melatos 2004;Priymak et al 2011).…”

“…After matter is accreted at the magnetic poles it spreads towards the equator, compressing the field and leading to an overall suppression of the large-scale dipolar structure, but also to local enhancements that can support a sizeable mountain (Melatos and Payne 2005;Payne and Melatos 2004;Vigelius and Melatos 2009b). Given an amount of accreted mass M a , the mass quadrupole is given by Shibazaki et al (1989) and Priymak et al (2011):…”

Gravitational Waves from Rapidly Rotating Neutron Stars

“…After matter is accreted at the magnetic poles it spreads towards the equator, compressing the field and leading to an overall suppression of the large-scale dipolar structure, but also to local enhancements that can support a sizeable mountain [46,56,67]. Given an amount of accreted mass M a , the mass quadrupole is given by [62,58]:…”

First all-sky search for continuous gravitational waves from unknown sources in binary systems

“…Many mechanisms have been proposed where gravitational wave emission continues after accretion of material has subsided. For instance, the magnetic field of the neutron star can guide the accretion flow to "hot spots" which could build up the neutron star ellipticity close to that allowed by the maximum breaking strain of the crust [18], with possibly sustained localized mass accumulation [19], depending on nuclear equation of state [20], material sinking [21], resistive relaxation [22] and magnetic bottling stability [23]. In addition, magnetic fields could create nonaxisymmetric deformations of the neutron star interior [24], or r-mode oscillations of the neutron star might be sustained, causing the star to emit gravitational waves [25,26].…”