Abstract
In the gravitational lensing of gravitational waves, wave optics should be used instead of geometrical optics when the wavelength λ of the gravitational waves is longer than the Schwarzschild radius of the lens mass ML. For gravitational lensing of chirp signals from the coalescence of supermassive black holes at redshift zS ~ 1 relative to the Laser Interferometer Space Antenna, the wave effects become important for a lens mass smaller than ~108 M☉. For such cases, we compute how accurately we can extract the mass of the lens and the source position from the lensed signal. We consider two simple lens models: the point-mass lens and the SIS (singular isothermal sphere). We find that the lens mass and the source position can be determined to within ~0.1% of [(S/N)/103]-1 for a lens mass larger than 108 M☉ and ≳10% of [(S/N)/103]-1 for a lens mass smaller than 107 M☉ because of the diffraction effect, where S/N is the signal-to-noise ratio of the unlensed chirp signals. For the SIS model, if the source position is outside the Einstein radius, only a single image exists in the geometrical optics approximation, so that the lens parameters cannot be determined, while in the wave optics cases we find that the lens mass can be determined even for ML < 108 M☉. For the point-mass lens, one can extract the lens parameters even if the source position is far outside the Einstein radius. As a result, the lensing cross section is an order of magnitude larger than that for the usual strong lensing of light.
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