arXiv subjects

Ryuichi Takahashi

Publications and source records attributed to Ryuichi Takahashi.

83 records · Page 5Linked to original sources

arXiv2006

Exact Wave Propagation in a Spacetime with a Cosmic String

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} {(G μ)}^{-2}λ\sim 150 {\rm Mpc} (λ/{\rm 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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arXiv2005

Classifying the Future of Universes with Dark Energy

We classify the future of the universe for general cosmological models including matter and dark energy. If the equation of state of dark energy is less then -1, the age of the universe becomes finite. We compute the rest of the age of the universe for such universe models. The behaviour of the future growth of matter density perturbation is also studied. We find that the collapse of spherical overdensity region is greatly changed if the equation of state of dark energy is less than -1.

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arXiv2005

Scattering of Gravitational Waves by the Weak Gravitational Fields of Lens Objects

We consider the scattering of the 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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arXiv2005

Wave propagation in a weak gravitational field and the validity of the thin lens approximation

Wave effects can be important for the gravitational lensing of gravitational waves. In such a case, wave optics must be used in stead of geometric optics. We consider a plane wave entering a lens object and solve numerically the wave equation for three lens models: the uniform density sphere, the singular isothermal sphere, and the Hernquist model. By comparing our numerical solutions with the analytical solutions under the thin lens approximation, we evaluate the error of this approximation. The results show that the relative error of the thin lens approximation is small if the geometrical thickness of the lens is much smaller than the distance between the lens and the observer.

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arXiv2004

Determination of the equation of the state of the Universe using ~ 0.1 Hz Gravitational Wave Detectors

We show that ten(one) years operation of the ultimate DECIGO (DECihertz Interferometer Gravitational wave Observatory) can determine the cosmic equation of the state with such accuracy that 0.06%(3%), 0.08%(4%) and 0.06%(3%) for $Ω_m$, $Ω_w$ and $w$, respectively. In more realistic case of practical DECIGO or BBO (Big Bang Observer), $w$ will be determined within $\sim 10%$ by ten years observation assuming the flat universe model. Hence, the DECIGO or BBO will give an independent determination of the cosmic equation of the state.

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arXiv2004

Quasi-geometrical Optics Approximation in Gravitational Lensing

The gravitational lensing of gravitational waves should be treated in the wave optics instead of the geometrical optics when the wave length $λ$ of the gravitational waves is larger than the Schwarzschild radius of the lens mass $M$. The 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 $λ\to 0$, 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. By analyzing 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 cuspy (or singular) density profile at the center $ρ(r) \propto r^{-α}$ ($0 < α\leq 2$), the diffracted image is formed at the lens center with the magnification $μ\sim (λ/M)^{3-α}$.

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arXiv2003

Deci hertz Laser Interferometer can determine the position of the Coalescing Binary Neutron Stars within an arc minute a week before the final merging event to Black Hole

It may be possible to construct a laser interferometer gravitational wave antenna in space with $h_{rms}\sim 10^{-23}$ at $ f\sim 0.1{\rm Hz}$ in $\sim 2020$. This deci hertz antenna may be called DECIGO/BBO,which stand for DECi hertz Interferometer Gravitational wave Observatory and Big Bang Observer, respectively. The analysis of 1-10 years observational data of the coalescing binary neutron stars or black holes at the distance of $\sim$ 300Mpc will give us the spatial position within $\sim$ an arc minute and the time of the coalescence within $\sim 0.1$ sec beforehand. With the knowledge of the accurate position and the time of final merging event, the follow up simultaneous observation using high frequency ($ f\sim 100{\rm Hz}$) gravitational wave antennae as well as electro-magnetic wave antennae from the radio frequency to the ultra high energy gamma ray will reveal the physics in the enigmatic event of the coalescence and the formation of the black hole.

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arXiv2003

Wave Effects in Gravitational Lensing of Gravitational Waves from Chirping Binaries

In the gravitational lensing of gravitational waves, the wave optics should be used instead of the geometrical optics when the wavelength $λ$ of the gravitational waves is longer than the Schwarzschild radius of the lens mass $M_L$. For the gravitational lensing of the chirp signals from the coalescence of the super massive black holes at the redshift $z_S\sim 1$ relevant to LISA, the wave effects become important for the lens mass smaller than $\sim 10^8 M_{\odot}$. 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 within $\sim 0.1% [(S/N)/10^3]^{-1}$ for the lens mass larger than $10^8 M_{\odot}$ and $\gsim 10% [(S/N)/10^3]^{-1}$ for the lens mass smaller than $10^7 M_{\odot}$ due to 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 can not be determined. While in the wave optics cases we find that the lens mass can be determined even for $M_L < 10^8 M_{\odot}$. 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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arXiv2002

Lens Model Degeneracy and Cosmological Tests by Strong Gravitational Lensing

We estimate the sensitivity of lensing observables to the parameters in the lens model (isothermal sphere/Navarro-Frenk-White profile) parameters and to cosmological parameters. We find that the observables are primarily dependent on the lens model parameters, while the dependence on cosmological parameters is minor (especially so for the dark energy parameters). We demonstrate the lens model degeneracy by deriving both the projected mass density profile and the circular velocity profile. We also identify a possible source of the problem of fitting the averaged mass profile of CL 0024+1654 with the Navarro-Frenk-White profile.

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arXiv2002

Parameter estimation for Galactic binaries by LISA

We calculate how accurately parameters of the short-period binaries $(10^{-4} {Hz} \lsim f\lsim 10^{-2} {Hz})$ will be determined from the gravitational waves by LISA. In our analysis the chirp signal ${\dot f}$ is newly included as a fitting parameters and dependence on observational period or wave frequency is studied in detail. Implications for gravitational wave astronomy are also discussed quantitatively.

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arXiv2001

Gravitational Lens Statistics and The Density Profile of Dark Halos

We investigate the influence of the inner profile of lens objects on gravitational lens statistics taking into account of the effect of magnification bias and both the evolution and the scatter of halo profiles. We take the dark halos as the lens objects and consider the following three models for the density profile of dark halos; SIS (singular isothermal sphere), the NFW (Navarro Frenk White) profile, and the generalized NFW profile which has a different slope at smaller radii. The mass function of dark halos is assumed to be given by the Press-Schechter function. We find that magnification bias for the NFW profile is order of magnitude larger than that for SIS. We estimate the sensitivity of the lensing probability of distant sources to the inner profile of lenses and to the cosmological parameters. It turns out that the lensing probability is strongly dependent on the inner density profile as well as on the cosmological constant. We compare the predictions with the largest observational sample, the Cosmic Lens All-Sky Survey. The absence or presence of large splitting events in larger surveys currently underway such as the 2dF and SDSS could set constraints on the inner density profile of dark halos.

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