Diffraction in gravitational lensing for compact objects of low mass

Deguchi, Shuji; Watson, William D.

doi:10.1086/164389

Cited by 93 publications

(98 citation statements)

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“…In this case the Fresnel radius does not change but the typical separation of the image from the lens is given by the Einstein radius r E ≈ √ 4GM r, where M is the mass of the lens. Then the ratio between r E and r F is given by r E /r F = GM/λ, which leads to the usual criterion that the diffraction effect becomes important when λ > ∼ GM [1,2,3,4,5]. From the above formula (31), we can read that the leading order corrections scales like ∝ λ/r.…”

Section: Quasi-geometrical Optics Approximationmentioning

confidence: 99%

“…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%

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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: Quasi-geometrical Optics Approximationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Exact wave propagation in a spacetime with a cosmic string

2006

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“…The parameter y measures the number of Fresnel zones [22,23] contributing to the lensing effect: when y ∼ ∞ geometrical optics applies, while for y ∼ 1 severe effects of diffraction occur and more precise solutions of the wave equation are required.…”

Section: Diffraction Limitmentioning

confidence: 99%

Increase of the Number of Detectable Gravitational Waves Signals Due to Gravitational Lensing

Varvella

Angonin

Tourrenc

2004

General Relativity and Gravitation

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This article deals with the gravitational lensing (GL) of gravitational waves (GW). We compute the increase in the number of detected GW events due to GL. First, we check that geometrical optics is valid for the GW frequency range on which Earth-based detectors are sensitive, and that this is also partially true for what concerns the future space-based interferometer LISA. To infer this result, both the diffraction parameter and a cut-off frequency are computed. Then, the variation in the number of GW signals is estimated in the general case, and applied to some lens models: point mass lens and singular isothermal sphere (SIS profile). An estimation of the magnification factor has also been done for the softened isothermal sphere and for the King profile. The results appear to be strongly model-dependent, but in all cases the increase in the number of detected GW signals is negligible. The use of time delays among images is also investigated.

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“…However, for the gravitational lensing of gravitational waves the wavelength is long so that the geometrical optics approximation is not valid in some cases. As shown by several authors (Ohanian 1983;Bliokh & Minakov 1975;Bontz & Haugan 1981;Thorne 1983;Deguchi & Watson 1986), if the wavelength λ is larger than the Schwarzschild radius of the lens mass M, the diffraction effect becomes important. Thus, the diffraction effect is important for a lens mass smaller than 10 8 M (λ/1AU), where 1 AU is the wavelength for the planned laser interferometer space antenna (LISA: Bender et al 2000).…”

Section: Introductionmentioning

confidence: 96%

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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Diffraction in gravitational lensing for compact objects of low mass

Cited by 93 publications

References 0 publications

Exact wave propagation in a spacetime with a cosmic string

Exact wave propagation in a spacetime with a cosmic string

Increase of the Number of Detectable Gravitational Waves Signals Due to Gravitational Lensing

Quasi-geometrical optics approximation in gravitational lensing

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