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

Takahashi, Ryuichi; Nakamura, Takashi

doi:10.1086/377430

Cited by 285 publications

(470 citation statements)

References 36 publications

(78 reference statements)

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“…More precisely, if the wavelength becomes comparable or longer than the Schwarzschild radius of the lens object, the diffraction effect becomes important and as a result the magnification factor approaches unity [1,2,3,4,5]. Mainly due to the possibility that the wave effects could be observed by future gravitational wave observations, several authors [6,7,8,9,10,11,12,13,14,15] have studied wave effects in gravitational lensing in recent years.…”

Section: Introductionmentioning

confidence: 99%

Exact wave propagation in a spacetime with a cosmic string

2006

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We present exact solutions of the massless Klein-Gordon equation in a spacetime in which an infinite straight cosmic string resides. The first solution represents a plane wave entering perpendicular to the string direction. We also present and analyze a solution with a static point-like source. In the short wavelength limit these solutions approach the results obtained by using the geometrical optics approximation: magnification occurs if the observer lies in front of the string within a strip of angular width 8πGµ, where µ is the string tension. We find that when the distance from the observer to the string is less than 10 −3 (Gµ) −2 λ ∼ 150Mpc(λ/AU)(Gµ/10 −8 ) −2 , where λ is the wave length, the magnification is significantly reduced compared with the estimate based on the geometrical optics due to the diffraction effect. For gravitational waves from neutron star(NS)-NS mergers the several lensing events per year may be detected by DECIGO/BBO.

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Section: Introductionmentioning

confidence: 99%

Exact wave propagation in a spacetime with a cosmic string

2006

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“…This lens model is most frequently used in wave optics in gravitational lensing of gravitational waves (Nakamura 1998;Ruffa 1999;De Paolis et al 2001Zakharov & Baryshev 2002;Takahashi & Nakamura 2003;Yamamoto 2003;Varvella et al 2003;Seto 2004). The amplification factor F of Eq.…”

Section: Point Mass Lensmentioning

confidence: 99%

“…and the deflection potential is ψ(x) = x. The SIS model is used for more realistic lens objects than the point mass lens, such as galaxies, star clusters and dark halos (Takahashi & Nakamura 2003). In this model F is numerically computed in Eq.…”

Section: Singular Isothermal Spherementioning

confidence: 99%

Quasi-geometrical optics approximation in gravitational lensing

Takahashi¹

2004

A&A

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Abstract. The gravitational lensing of gravitational waves should be treated in wave optics instead of geometrical optics when the wave length λ of the gravitational waves is larger than the Schwarzschild radius of the lens mass M. Wave optics is based on the diffraction integral which represents the amplification of the wave amplitude by lensing. We study the asymptotic expansion of the diffraction integral in the powers of the wave length λ. The first term, arising from the short wavelength limit λ → 0, corresponds to the geometrical optics limit. The second term, being of the order of λ/M, is the leading correction term arising from the diffraction effect. Analysing this correction term, we find that (1) the lensing magnification µ is modified to µ (1 + δ), where δ is of the order of (λ/M) 2 , and (2) if the lens has a cuspy (or singular) density profile at center ρ(r) ∝ r −α (0 < α ≤ 2), the diffracted image is formed at the lens center with magnification µ ∼ (λ/M) 3−α .

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“…4.7 and 7, using the diffraction integral under the thin lens approximation. Recently, several authors have been studying wave optics in the gravitational lensing of gravitational waves using this integral (Nakamura 1998;Nakamura & Deguchi 1999;Ruffa 1999;Takahashi & Nakamura 2003;Yamamoto 2003;Macquart 2004;Takahashi 2004). In this letter, we present another method to derive the solution of Eq.…”

Section: Introductionmentioning

confidence: 99%

Scattering of gravitational waves by the weak gravitational fields of lens objects

Takahashi

Suyama

Michikoshi

2005

A&A

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Abstract.We consider the scattering of gravitational waves by the weak gravitational fields of lens objects. We obtain the scattered gravitational waveform by treating the gravitational potential of the lens to first order, i.e. using the Born approximation. We find that the effect of scattering on the waveform is roughly given by the Schwarzschild radius of the lens divided by the wavelength of gravitational wave for a compact lens object. If the lenses are smoothly distributed, the effect of scattering is of the order of the convergence field κ along the line of sight to the source. In the short wavelength limit, the amplitude is magnified by 1 + κ, which is consistent with the result in weak gravitational lensing.

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

Cited by 285 publications

References 36 publications

Exact wave propagation in a spacetime with a cosmic string

Exact wave propagation in a spacetime with a cosmic string

Quasi-geometrical optics approximation in gravitational lensing

Scattering of gravitational waves by the weak gravitational fields of lens objects

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