Improved estimate of the detectability of gravitational radiation from a magnetically confined mountain on an accreting neutron star

Abstract

We give an improved estimate of the detectability of gravitational waves from magnetically confined mountains on accreting neutron stars. The improved estimate includes the following effects for the first time: three-dimensional hydromagnetic ("fast") relaxation, three-dimensional resistive ("slow") relaxation, realistic accreted masses $M_a \la 2 \times 10^{-3} M_\odot$, (where the mountain is grown ab initio by injection), and verification of the curvature rescaling transformation employed in previous work. Typically, a mountain does not relax appreciably over the lifetime of a low-mass X-ray binary. The ellipticity reaches $\epsilon \approx 2 \times 10^{-5}$ for $M_a=2\times 10^{-3} M_\odot$. The gravitational wave spectrum for triaxial equilibria contains an additional line, which, although weak, provides valuable information about the mountain shape. We evaluate the detectability of magnetic mountains with Initial and Advanced LIGO. For a standard, coherent matched filter search, we find a signal-to-noise ratio of $d = 28 (M_a/10^{-4} M_\odot) (1+5.5 M_a/10^{-4} M_\odot)^{-1} (D/10 \mathrm{kpc})^{-1} (T_0/14 \mathrm{d})^{1/2}$ for Initial LIGO, where $D$ is the distance and $T_0$ is the observation time. From the nondetection of gravitational waves from low-mass X-ray binaries to date, and the wave strain limits implied by the spin frequency distribution of these objects (due to gravitational wave braking), we conclude that there are other, as yet unmodelled, physical effects that further reduce he quadrupole moment of a magnetic mountain, most notably sinking into the crust.