arXiv subjects

Takashi Nakamura

Publications and source records attributed to Takashi Nakamura.

At least 145 records · Page 8Linked to original sources

arXiv2000

Feasibility of Reconstructing the Quintessential Potential Using SNIa Data

We investigate the feasibility of the method for reconstructing the equation of state and the effective potential of the quintessence field from SNIa data. We introduce a useful functional form to fit the luminosity distance with good accuracy (the relative error is less than 0.1%). We assess the ambiguity in reconstructing the equation of state and the effective potential which originates from the uncertainty in $Ω_M$. We find that the equation of state is sensitive to the assumed $Ω_M$, while the shape of the effective potential is not. We also demonstrate the actual reconstruction procedure using the data created by Monte-Carlo simulation. Future high precision measurements of distances to thousands of SNIa could reveal the shape of the quintessential potential.

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arXiv2000

Determining the Equation of State of the Expanding Universe Using a New Independent Variable

To determine the equation of state of the universe, we propose to use a new independent variable $R\equiv (H_0/c)(d_L(z)/(1+z))$, where $H_0$ and $d_L(z)$ are the present Hubble parameter and the luminosity distance, respectively. For the flat universe suggested from the observation of the anisotropy of cosmic microwave background, the density and the pressure are expressed as $ρ/ρ_0=4(df/dR)^2/f^6$ and $p/ρ_0=-4/3(d^2f/dR^2)/f^5$ where $ρ_0$ is the present density and $f(R)=1/\sqrt{1+z(R)}$. In $(R, f)$ plane the sign as well as the strength of the pressure is in proportion to the curvature of the curve $f(R)$. We propose to adopt a Pade-like expression of $f(R)=1/\sqrt{u}$ with $u\equiv 1+\sum\limits_{n=1}^{N}u_nR^n$. For flat $Λ$ model the expansion up to N=7 has at most an error $< 0.2%$ for $z < 1.7$ and any value of $Λ$. We also propose a general method to determine the equation of state of the universe which has $N-1$ free parameters. If the number of parameters are smaller than $N-1$, there is a consistency check of the equation of state so that we may confirm or refute each model.

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arXiv2000

Possible direct method to determine the radius of a star from the spectrum of gravitational wave signals

We computed the spectrum of gravitational waves from a dust disk star of radius R inspiraling into a Kerr black hole of mass M and specific angular momentum a. We found that when R is much larger than the wave length of the quasinormal mode, the spectrum has several peaks and the separation of peaks $Δω$ is proportional to $R^{-1}$ irrespective of M and a. This suggests that the radius of the star in coalescing binary black hole - star systems may be determined directly from the observed spectrum of gravitational wave. This also suggests that the spectrum of the radiation may give us important information in gravitational wave astronomy as in optical astronomy.

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arXiv2000

Response of Interferometric Detectors to Scalar Gravitational Waves

We rigorously analyze the frequency response functions and antenna sensitivity patterns of three types of interferometric detectors to scalar mode of gravitational waves which is predicted to exist in the scalar-tensor theory of gravity. By a straightforward treatment, we show that the antenna sensitivity pattern of the simple Michelson interferometric detector depends strongly on the wave length $λ_{\rm SGW}$ of the scalar mode of gravitational waves if $λ_{\rm SGW}$ is comparable to the arm length of the interferometric detector. For the Delay-Line and Fabry-Perot interferometric detectors with arm length much shorter than $λ_{\rm SGW}$, however, the antenna sensitivity patterns depend weakly on $λ_{\rm SGW}$ even though $λ_{\rm SGW}$ is comparable to the effective path length of those interferometers. This agrees with the result obtained by Maggiore and Nicolis.

gr-qc↗

arXiv2000

Multiple Sub-Jet Model of Gamma Ray Bursts and Possible Origin of X-ray Precursors and Post-cursors

We assume that internal shocks of Gamma Ray Bursts (GRBs) consist of multiple sub-jets with a collimation half-angle $\sim {\rm several }\timesγ_i^{-1}$, where $γ_i$ is the Lorenz factor of each sub-jet. If by chance a sub-jet is first emitted off-axis from the line of sight, the observed peak energy can be in the X-ray region. Next if by chance a subsequent sub-jet is emitted along the line of sight, then the peak energy will be in the gamma ray region and the gamma ray may arrive after the X-ray precursor from the former sub-jet depending on parameters. This model predicts a new class of GRBs with extremely weak and short gamma ray emission but X-ray precursor and/or post-cursor as well as an afterglow.

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arXiv2000

Equilibrium sequences of irrotational binary polytropic stars : The case of double polytropic stars

Solutions to equilibrium sequences of irrotational binary polytropic stars in Newtonian gravity are expanded in a power of $ε=a_0/R$, where R and $a_0$ are the orbital separation of the binary system and the radius of each star for $R=\infty$. For each order of $ε$, we should solve ordinary differential equations for arbitrary polytropic indices n. We show solutions for polytropic indices n= 0.5, 1, 1.5 and 2 up to $ε^6$ orders. Our semi-analytic solutions can be used to check the validity of numerical solutions.

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arXiv2000

Density Distribution and Shape of Galactic Dark Halo Can be Determined by Low Frequency Gravitational Waves ?

Under the assumption that the Milky Way's dark halo consists of primordial black hole MACHOs (PBHMACHOs), the mass density of the halo can be measured by the low frequency gravitational waves ($10^{-3} Hz \siml ν_{gw} \siml 10^{-1}$ Hz) from PBHMACHO binaries whose fraction is $\sim 10^{-6}$. We find that ten years observation by LISA will detect $\sim 700$ PBHMACHO binaries and enable us to determine the power index of the density profile within 10% (20%) and the core radius within 25% (50%) in about 90% (99%) confidence level, respectively. The axial ratios of the halo may also be determined within $\sim 10%$. LISA and OMEGA may give us an unique observational method to determine the density profile and the shape of the dark halo to open a new field of observational astronomy.

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arXiv1999

3D General Relativistic Simulations of Coalescing Binary Neutron Stars

We develop a 3 dimensional computer code to study a coalescing neutron star binary. The code can currently follow the evolution up to two stars begin to merge from two spherical stars of mass 1 solar mass and radius 8.9km with separation 35.4km. As for coordinate conditions, we use conformal slicing and pseudo-minimal distortion conditions. The evolution equations for the metric is integrated using the CIP method while the van Leer's scheme is used to integrate the equations for the matter. We present a few results of our simulations including gravitational radiation.

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arXiv1999

Almost analytic solutions to equilibrium sequences of irrotational binary polytropic stars for n=1

A solution to an equilibrium of irrotational binary polytropic stars in Newtonian gravity is expanded in a power of ε=a_0/R, where R and a_0 are the separation of the binary system and the radius of each star for R=\infty. For the polytropic index n=1, the solutions are given almost analytically up to order ε^6. We have found that in general an equilibrium solution should have the velocity component along the orbital axis and that the central density should decrease when R decreases. Our almost analytic solutions can be used to check the validity of numerical solutions.

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arXiv1999

Low frequency gravitational waves from black hole MACHO binaries

The intensity of low frequency gravitational waves from black hole MACHO binaries is studied. First we estimate the gravitational wave background produced by black hole MACHO binaries in the Milky Way halo as well as the cosmological gravitational wave background produced by the extragalactic black hole MACHO binaries. It is found that the cosmological gravitational wave background due to black hole MACHO binaries is larger than the halo background unless an extreme model of the halo is assumed, while it is smaller than the background due to close white dwarf binaries at $ν_{gw} \siml 10^{-2.5}$ Hz if the actual space density of white dwarfs is maximal. This cosmological background due to black hole MACHO binaries is well below the observational constraints from the pulsar timing, quasar proper motions and so on. We find that one year observation by LISA will be able to detect gravitational waves from at least several hundreds of nearby independent black hole MACHO binaries whose amplitudes exceed these backgrounds. This suggests that LISA will be able to pin down various properties of primordial black hole MACHOs together with the results of LIGO-VIRGO-TAMA-GEO network. Furthermore, it may be possible to draw a map of the mass distribution of our halo, since LISA can determine the position and the distance to individual sources consisted of black hole MACHO binaries. Therefore, LISA may open a new field of the gravitational wave astronomy.

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arXiv1999

Off-axis Emission from the Beamed Afterglow of Gamma Ray Bursts and a Possible Interpretation of Slowly Declining X-Ray Afterglow of GRB980425

A formula for off-axis emissions from the beamed afterglow of GRBs in a synchrotron model is derived. The formula is applied to an inhomogeneous circumstellar matter obeying n proportional to 1/r**2 suggested for SN1998bw/GRB980425. The slow decline rate as well as the X-ray flux similar to the observed values are obtained for appropriate choice of the parameters so that the association of GRB980425 with SN1998bw is further strengthened.

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arXiv1999

Determining the Equation of State of the Expanding Universe: Inverse Problem in Cosmology

Even if the luminosity distance as a function of redshift is obtained accurately using, for example, Type Ia supernovae, the equation of state of the Universe cannot be determined uniquely but depends on one free parameter $Ω_{k0} ={k}/(a_0^2H_0^2)$, where $a_0$ and $H_0$ are the present scale factor and the Hubble parameter, respectively. This degeneracy might be resolved if, for example, the time variations of the redshift of quasars are measured as proposed recently by Loeb. Therefore the equation of state of the Universe (or the metric of the universe) might be determined without any theoretical assumption on the matter content of the Universe in future.

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arXiv1998

A Way to 3D Numerical Relativity --- Coalescing Binary Neutron Stars ---

One of the most promising sources of gravitational radiation is coalescence of binary neutron stars or black holes. In order to study gravitational radiation at the merging phase of coalescing binary neutron stars which is called the last three-milliseconds, full general relativistic simulations are required. Since coalescence of binary stars is a completely non-axisymmetric and 3 dimensional (in space) event, which needs great powers of computers, we have to develop a method of 3D numerical relativity using a vector-parallel supercomputer. As a first step of this final goal, we started simulations using post-Newtonian hydrodynamics including radiation reaction of gravitational waves from 1989. They gave a lot of perspectives on coalescing events and gravitational radiation from them. Next we started to attack 3D, fully relativistic simulations. First, basic equations on the (3+1)-formalism of the Einstein equations are shown. As for gauge conditions, we use conformal time slicing and psuedo minimal distortion condtions at present. For these conditions as well as to solve initial value equations, we should solve some elliptic partial differential equations. It consumes the greatest part of CPU time. We show recent results of test simulations on coalescing binary neutron stars.

gr-qc↗

arXiv1998

The Luminosity Distance, the Equation of State, and the Geometry of the Universe

The second derivative of the luminosity distance with respect to the redshift is written in terms of the deceleration parameter $q_0$. We point out that the third derivative contains the information regarding the sound speed of cosmic matter as well as the curvature of the universe. We restrict physically possible parameter ranges of the coefficients. It is found that there is a relation between the coefficients in a flat universe model with matter such that $c_{s0}(1+w_{\rm x0})=0$ ($c_{s0}$ is the total sound speed of the matter component and $w_{\rm x0}$=$p_{\rm x0}/ρ_{\rm x0}$).

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arXiv1998

Observational tests of x-matter models

We study gravitational lensing statistics, matter power spectra and the angular power spectra of the cosmic microwave background (CMB) radiation in x-matter models. We adopt an equation-of-state of x-matter which can express a wide range of matter from the pressureless dust to the cosmological constant. A new ingredient in this model is the sound speed of the x-component in addition to the equation-of-state $w_0=p_{x0}/ρ_{x0}$. Except for the cosmological constant case, the perturbations of x-matter itself are considered. Our primary interest is in the effect of non-zero sound speed on the structure formation and the CMB spectra. It is found that there exist parameter ranges where x-matter models are consistent with all current observations. The x-matter generally leaves imprints in the CMB anisotropy and the matter power spectrum, which should be detectable in future observations.

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arXiv1998

A Model for Non High Energy Gamma Ray Bursts and Sources of Ultra High Energy Cosmic Rays

As a progenitor of NHE (Non High Energy) GRBs, we propose a (C+O) star and a neutron star (black hole) close binary system. Since the (C+O) star is tidally locked, a new born pulsar should be a milli second pulsar (MSP). Dynamo will generate a superstrong magnetic field(SSM). The beam of the energy from the super strongly magnetized milli second pulsar can punch a hole in the supernova ejecta . Then the beam of gamma rays flows out of the ejecta. If we observe this beam from the lateral direction, it will be NHE-GRB. In this model the pulsar with the spin period about 1sec should exist in SN1998bw so that the searches for this pulsar in all the wave length are urgent. SSM-MSPs can accelerate protons up to Ultra High Energy. If a few percent of the beam energy of SSM-MSP in NHE-GRB event is in the form of UHECRs, the flux of the observed UHECRs can be explained. Then along the direction of each UHECR, a supernova remnant should be found. It is suggested that NHE-GRB is the progenitor of the soft gamma ray repeater which has also the superstrong magnetic field and is in the supernova remnant.

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arXiv1998

Black Hole Binary Formation in the Expanding Universe --- Three Body Problem Approximation ---

We study black hole MACHO binary formation through three-body interactions in the early universe at $t\sim 10^{-5}$s. The probability distribution functions of the eccentricity and the semimajor axis of binaries as well as of the coalescence time are obtained assuming that the black holes are randomly formed in space. We confirm that the previous order-of-magnitude estimate for the binary parameters is valid within $\sim 50%$ error. We find that the coalescence rate of the black hole MACHO binaries is $\sim 5 \times 10^{-2} \times 2^{\pm 1}$ events/year/galaxy taking into consideration several possible factors which may affect this estimate. This suggests that the event rate of coalescing binary black holes will be at least several events per year within 15 Mpc. The first LIGO/VIRGO interferometers in 2001 will be able to verify whether the MACHOs are black holes or not.

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arXiv1998

Expected EAGLE event rate towards the Magellanic Clouds

We propose to search for MACHOs by observing EAGLE (Extremely Amplified Gravitational LEnsing) events of a majority of dim stars. This search is independent of the usual one. For the detection limit of EAGLE (about 20 mag), about 100 f (τ^{LMC} / 3 \times 10^{-7}) (100 days / ) EAGLE events/y are expected to result from all the dim stars in LMC. Here τ^{LMC} and are the optical depth and the average duration of microlensing events, respectively, while f (0 < f < 1) is a parameter depending on the unknown stellar luminosity function. The observed mean duration of EAGLE events also depends on the luminosity function and is (0.01 - 0.4) times the usual duration of microlensing events, which corresponds to (1 - 30) days. The follow-up observation using larger telescopes may enable us to determine the impact parameter and the true duration of the event. If f is determined by another independent method, we can also determine τ^{LMC}. Even if f is undetermined, the detection of EAGLE events strongly suggest that MACHOs are not due to variable source stars, since EAGLE events are due to the dim main-sequence stars. Although for the SMC, the event rate is smaller by a factor of about 7, it is still a substantial number (about 13 f (τ^{SMC} / 3 \times 10^{-7} (100 days / ) events/y).

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