Wave Effects in the Gravitational Lensing of Gravitational Waves from Chirping Binaries

By Ryuichi Takahashi, Takashi Nakamura. 2003

298 citations recorded by the source corpus.

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.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/51eacde4f25b354e31dbf1bd5dfc476adc2f1aa3

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Citations in the corpus

GW231123: A Binary Black Hole Merger with Total Mass 190–265 M⊙ (2025, unknown): “GWs can also undergo wave-optics lensing (Takahashi & Nakamura 2003) when they encounter smaller objects ( 10 2 –10 6 M ⊙ for signals in the LVK band).”
Unveiling the gravitational universe at μ-Hz frequencies (2019, background): “These wave effects can help identify the properties of the gravitational lens as the source’s frequency increases toward coalescence [249].”
Search for Gravitational Lensing Signatures in LIGO-Virgo Binary Black Hole Events (2019, background): “…wave optics effects are produced due to the superposition of several lensed wavefronts with variable magnifications and time-delays (Ohanian 1974; Bliokh & Minakov 1975; Bontz & Haugan 1981; Thorne 1983; Deguchi & Watson 1986; Nakamura 1998; Takahashi & Nakamura 2003a; Christian et al. 2018).”
Constraints on the Cosmic Expansion History from GWTC–3 (2021, background): “…masses) of a GW source in the absence of an EM counterpart, is the possible lensing of the GW signal due to the intervening matter distribution (Schneider et al. 1992; Bartelmann 2010; Nakamura 1998; Wang et al. 1996; Takahashi & Nakamura 2003; Dai et al. 2017; Broadhurst et al. 2018; Diego 2019).”
Gravitational lensing of gravitational waves: A statistical perspective (2018, background): “This is known as the geometrical optics approximation to GW propagation (Takahashi & Nakamura 2003).”
Using Gravitational-Wave Standard Sirens (2005, background): “GWs are lensed by intervening matter exactly as electromagnetic waves are lensed (Marković 1993; Wang et al. 1996; Takahashi & Nakamura 2003).”