Gravitational lensing of gravitational waves: a statistical perspective

Abstract

In this paper, we study the strong gravitational lensing of gravitational waves (GWs) from a statistical perspective, with particular focus on the high frequency GWs from stellar binary black hole coalescences. These are most promising targets for groundbased detectors such as Advanced Laser Interferometer Gravitational Wave Observatory (aLIGO) and the proposed Einstein Telescope (ET) and can be safely treated under the geometrical optics limit for GW propagation. We perform a thorough calculation of the lensing rate, by taking account of effects caused by the ellipticity of lensing galaxies, lens environments, and magnification bias. We find that in certain GW source rate scenarios, we should be able to observe strongly lensed GW events once per year (∼ 1 yr −1 ) in the aLIGO survey at its design sensitivity; for the proposed ET survey, the rate could be as high as ∼ 80 yr −1 . These results depend on the estimate of GW source abundance, and hence can be correspondingly modified with an improvement in our understanding of the merger rate of stellar binary black holes. We also compute the fraction of four-image lens systems in each survey, predicting it to be ∼ 30 per cent for the aLIGO survey and ∼ 6 per cent for the ET survey. Finally, we evaluate the possibility of missing some images due to the finite survey duration, by presenting the probability distribution of lensing time delays. We predict that this selection bias will be insignificant in future GW surveys, as most of the lens systems (∼ 90 per cent) will have time delays less than ∼ 1 month, which will be far shorter than survey durations.

Strong gravitational lensing of explosive transients

“…estimates of z max for the Advanced LIGO design sensitivity [210]. This result indicates that, albeit the probability is not very high, it may be possible to detect strongly lensed gravitational waves of binary black hole mergers in Advanced LIGO, which is broadly consistent with more detailed calculations (e.g., [123,379]). Finally, we discuss typical magnifications of strongly lensed explosive transients detected in surveys.…”

Gravitational wave interference via gravitational lensing: Measurements of luminosity distance, lens mass, and cosmological parameters

“…Then by [45], the lensing cross section and thus the optical depth would be about 12 to 14 orders of magnitude smaller than those considered in Refs. [5,33,43,44], so the lensing rate for the beat is much less than the predicted values quoted above.…”

Detecting lensing-induced diffraction in astrophysical gravitational waves

“…We further note that theoretically we expect a fraction ∼ 10 −3 among the sources from cosmological distances z s ∼ 1-2 should be strongly lensed by an intervening galaxy [12,15,85,86]. In this case, GWs associated with each macro image propagate through the halo of the lens galaxy and hence has an enhanced probability of intersecting a low mass halo as a substructure.…”