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 the quadrupole moment of a magnetic mountain , most notably sinking into the crust .