Quasi-geometrical optics approximation in gravitational lensing

Takahashi, Ryuichi

doi:10.1051/0004-6361:20040212

Cited by 35 publications

(27 citation statements)

References 20 publications

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“…Nakamura (1998) discussed the diffraction effect on lensing magnifications for inspiraling binaries induced by intervening compact objects. Wave effects in the gravitational lensing of GWs have been discussed linked to several topics (e.g., Baraldo et al 1999;Takahashi & Nakamura 2003;Takahashi 2004;Takahashi et al 2005;Suyama et al 2005Suyama et al , 2006Yoo et al 2007;Sereno et al 2010;Yoo et al 2013;Cao et al 2014). Figure 1 shows a lensing configuration with an observer, a lens, and a source in a nearly straight line.…”

Section: Derivation Of the Arrival Time Differencementioning

confidence: 99%

Arrival Time Differences Between Gravitational Waves and Electromagnetic Signals Due to Gravitational Lensing

Takahashi

2017

ApJ

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In this study, we demonstrate that general relativity predicts arrival time differences between gravitational wave (GW) and electromagnetic (EM) signals caused by the wave effects in gravitational lensing. The GW signals can arrive earlier than the EM signals in some cases if the GW/EM signals have passed through a lens, even if both signals were emitted simultaneously by a source. GW wavelengths are much larger than EM wavelengths; therefore, the propagation of the GWs does not follow the laws of geometrical optics, including the Shapiro time delay, if the lens mass is less than approximately 10 5 M ⊙ (f /Hz) −1 , where f is the GW frequency. The arrival time difference can reach ∼ 0.1 s (f /Hz) −1 if the signals have passed by a lens of mass ∼ 8000M ⊙ (f /Hz) −1 with the impact parameter smaller than the Einstein radius; therefore, it is more prominent for lower GW frequencies. For example, when a distant super massive black hole binary (SMBHB) in a galactic center is lensed by an intervening galaxy, the time lag becomes of the order of 10 days. Future pulsar timing arrays including SKA (the Square Kilometre Array) and X-ray detectors may detect several time lags by measuring the orbital phase differences between the GW/EM signals in the SMBHBs. Gravitational lensing imprints a characteristic modulation on a chirp waveform; therefore, we can deduce whether a measured arrival time lag arises from intrinsic source properties or gravitational lensing. Determination of arrival time differences would be extremely useful in multimessenger observations and tests of general relativity.

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Section: Derivation Of the Arrival Time Differencementioning

confidence: 99%

Arrival Time Differences Between Gravitational Waves and Electromagnetic Signals Due to Gravitational Lensing

Takahashi

2017

ApJ

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“…There have been few motivations for a long time to consider the lensing effect on gravitational waves. Until recently, the authors in [3,4] realized that the gravitational lensing effect on gravitational waves should be described by wave dynamics instead of optics approximation. The features of wave dynamics make the fraction of lensed events larger than that optics approximation has ever predicted.…”

Section: Introductionmentioning

confidence: 99%

“…This fact motivated many authors to study lensing effects on gravitational waves in the past decade [3][4][5][6][7][8][9][10][11][12][13][14][15][16]. As noted in [4], the lensing effect is very important for the space-based gravitational wave detector LISA [17]. Even for the coming generations of ground-based gravitational wave detectors such as Advanced LIGO and Einstein telescope (ET), lensing effects are also nonnegligible.…”

Section: Introductionmentioning

confidence: 99%

Gravitational lensing effects on parameter estimation in gravitational wave detection with advanced detectors

Cao

Wang

2014

Phys. Rev. D

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The gravitational lensing effect is important to the detection of electromagnetic signals in astrophysics. The gravitational wave lensing effect has also been found significant to gravitational wave detection in the past decade. Recent analysis shows that the lensing events for advanced detectors could be quite plausible. The black holes in our MilkyWay Galaxy may play the role of lens objects. These facts motivate us to study the lensing effects on gravitational wave signals for advanced detectors. Taking advanced LIGO and Einstein Telescope for examples, we investigate the lensing effects on the parameter extraction of gravitational wave signals. Using the Markov chain Monte Carlo simulation together with matched filtering methods, we find that the lensing effect for a lens object with small mass is negligible. But when the mass of the lens object increases to larger than 1000M⊙ the lensing effect becomes important. Using the template without lensing corrections would result in loss of signal detections. In contrast if we consider templates with lensing effects, the lensed signal may provide much information about the lens black hole. These facts may give us a new way to determine the parameters of the lensing object. For example, this kind of signal may also help us estimate the mass and the distance of the supermassive black hole hosted at the center of our Galaxy

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“…This integral is carried out over the optical axis. Due to the fact that we limit our analysis to the case in which the wave length, λ, of the gravitational wave is larger than the Schwarzschild radius of the thin lens, we must use wave optics instead of geometric optics, as in Takahashi (2004). In this framework, the change in the amplitude is quantified via the enhancement factor or complex amplification factor (Nakamura & Deguchi 1999):…”

Section: Generalmentioning

confidence: 99%

Gravitational Wave Enhancement as a Tool to Distinguish Dark Matter Halo Profiles

Castillo

Calcaneo-Roldan

2019

RMxAA

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The recent success of the dark matter model has proven to be an invaluable tool for describing the formation, evolution and stability of galaxies. In this work we study the enhancement function, F , of the gravitational lensing of gravitational waves by galactic dark matter halos and show how this function may be used to distinguish between halo models. In particular we compare an isothermal sphere with an NFW type density distribution, both of which are assumed to be spherically symmetric, and find that our technique clearly distinguishes between the models.

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Quasi-geometrical optics approximation in gravitational lensing

Cited by 35 publications

References 20 publications

Arrival Time Differences Between Gravitational Waves and Electromagnetic Signals Due to Gravitational Lensing

Arrival Time Differences Between Gravitational Waves and Electromagnetic Signals Due to Gravitational Lensing

Gravitational lensing effects on parameter estimation in gravitational wave detection with advanced detectors

Gravitational Wave Enhancement as a Tool to Distinguish Dark Matter Halo Profiles

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