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Takashi Nakamura

Publications and source records attributed to Takashi Nakamura.

156 records · Page 9Linked to original sources
arXiv1998

Location of the innermost stable circular orbit of binary neutron stars in the post Newtonian approximations of general relativity

In this paper, we present results obtained from our recent studies on the location of the innermost stable circular orbit (ISCO) for binary neutron stars (BNSs) in several levels of post Newtonian (PN) approximations. We reach the following conclusion at present: (1) even in the Newtonian case, there exists the ISCO for binary of sufficiently stiff equation of state (EOS). If the mass and the radius of each star are fixed, the angular velocity at the ISCO $Ω_{ISCO}$ is larger for softer EOS: (2) when we include the first PN correction, there appear roughly two kinds of effects. One is the effect to the self-gravity of each star of binary and the other is to the gravity acting between two stars. Due to the former one, each star of binary becomes compact and the tidal effect is less effective. As a result, $Ω_{ISCO}$ tends to be increased. On the other hand, the latter one has the property to destabilize the binary orbit, and $Ω_{ISCO}$ tends to be decreased. If we take into account both effects, however, the former effect is stronger than the latter one, and $Ω_{ISCO}$ becomes large with increase of the 1PN correction: (3) the feature mentioned above is more remarkable for softer EOS if the mass and radius are fixed. This is because for softer EOS, each star has the larger central density and is susceptible to the GR correction: (4) there has been no self consistent calculation including all the 2PN effects and only exist studies in which one merely includes the effect of the 2PN gravity acting between two stars. In this case, the effect has the property to destabilize the binary orbit, so that $Ω_{ISCO}$ is always smaller than that for the Newtonian case. If we include the PN effect of the self-gravity to each star, $Ω_{ISCO}$ will increase.

gr-qc↗
arXiv1997

Numerical study on the hydrodynamic instability of binary stars in the first post Newtonian approximation of general relativity

We present numerical results on the hydrodynamic stability of coalescing binary stars in the first post Newtonian(1PN) approximation of general relativity. We pay particular attention to the hydrodynamical instability of corotating binary stars in equilibrium states assuming the stiff polytropic equation of state with the adiabatic constant $Γ=3$. In previous 1PN numerical studies on corotating binary stars in equilibrium states, it was found that along the sequence of binary stars as a function of the orbital separation, they have the energy and/or angular momentum minima where the secular instability sets in, and that with increase of the 1PN correction, the orbital separation at these minima decreases while the angular velocity there increases. In this paper, to know the location of the innermost stable circular orbit(ISCO), we perform numerical simulations and find where the hydrodynamical instability along the corotating sequences of binary sets in. From the numerical results, we found that the dynamical stability limit seems to exist near the energy and/or angular momentum minima not only in the Newtonian, but also in the 1PN cases. This means that the 1PN effect of general relativity increases the angular frequency of gravitational waves at the ISCO.

gr-qc↗
arXiv1997

Gravitational Waves from Coalescing Black Hole MACHO Binaries

If MACHOs are black holes of mass about 0.5 solar mass, they must have been formed in the early universe when the temperature was about 1 GeV. We estimate that in this case in our galaxy's halo out to about 50kpc there exist about half billion black hole binaries whose coalescence times are comparable to the age of the universe, so that the coalescence rate will be about five hundredth events/year/galaxy. This suggests that we can expect a few events/year within 15Mpc. The gravitational waves from such coalescing black hole MACHOs can be detected by the first generation of interferometers in the LIGO/VIRGO/TAMA/GEO network. Therefore, the existence of black hole MACHOs can be tested within the next five years by gravitational waves.

astro-ph↗
arXiv1997

Cosmology with x-matter

Motivated by the possibility of $H_0t_0 > 1$ where $H_0$ and $t_0$ are the Hubble parameter and the age of the universe, respectively, we investigate the cosmology including x-matter. x-matter is expressed by the equation of state $p_x=w_0ρ_{x0} + c_s^2(ρ_x-ρ_{x0})$, where $p_x$, $ρ_x$ and $ρ_{x0}$ are the pressure, the density of x-matter and the density at present, respectively. $w_0$ and $c_s^2$ are functions of $ρ_x$ in general. x-matter has the most general form of the equation of state which is characterized by 1)violation of strong energy condition at present for $w_0 < -1/3$ ; 2) locally stable (i.e. $c_s^2\geq 0$); 3)causality is guaranteed ($c_s\leq 1$). Considering the case that $w_0$ and $c_s^2$ are constants, we find that there is a large parameter space of $(w_0,c_s^2,Ω_{x0})$ in which the model universe is consistent with the age of the universe and the observations of distant Type I supernovae.

astro-ph↗
arXiv1997

Scalar gravitational wave from Oppenheimer-Snyder collapse in scalar- tensor theories of gravity

Unlike general relativity, scalar-tensor theories of gravity predict scalar gravitational waves even from a spherically symmetric gravitational collapse. We solve numerically the generation and propagation of the scalar gravitational wave from a spherically symmetric and homogeneous dust collapse under the approximation that we can neglect the back reaction of the scalar wave on the space-time, and examine how the amplitude, characteristic frequency and wave form of the observed scalar gravitational wave depend on the initial radius and mass of the dust and parameters contained in the theory. In the Brans-Dicke theory, through the observation of the scalar gravitational wave, it is possible to determine the initial radius and mass and a parameter contained in the theory. In the scalar-tensor theories, it would be possible to get the information of the first derivative of the coupling function contained in the theory because the wave form of the scalar gravitational wave greatly depends on it.

gr-qc↗
arXiv1996

The Minimum Mass of the First Stars and the Anthropic Principle

The lower limit of the mass of the first stars suggested recently may imply the formation of massive stars of mass greater than 8 solar mass irrespective of the details of the initial mass function. The production of heavy metals from the first stars will ensure a requisite for the existence of life without the anthropic principle.

astro-ph↗
arXiv1996

Fragmentation of the Primordial Gas Clouds and the Lower Limit on the Mass of the First Stars

We discuss the fragmentation of primordial gas clouds in the universe after decoupling. Comparing the time scale of collapse with that of fragmentation, we obtain the typical mass of a fragment both numerically and analytically. It is shown that the estimated mass gives the minimum mass of a fragment which is formed from the primordial gas cloud and is essentially determined by the Chandrasekhar mass.

astro-ph↗
arXiv1996

Innermost Stable Circular Orbit of Coalescing Neutron Star-Black Hole Binary --- Generalized Pseudo-Newtonian Potential Approach ---

The innermost stable circular orbits (ISCO) of coalescing neutron star-black hole binary are studied taking into account both the tidal and relativistic effects. We adopt the generalized pseudo-Newtonian potential to mimic the general relativistic effects of gravitation. It is found that the separation of the neutron star and the black hole at the ISCO is greater than that obtained by using either the Newtonian potential or the second post-Newtonian equation of motion of point mass. In equal mass cases, it is found that for $\bar{a}/m_1 > 3.5$ with $\bar{a}$ and $m_1$ being the mean radius and the mass of the neutron star, the tidal effect dominates the stability of the binary system while for $\bar{a}/m_1 < 3.5$, the relativistic effect, i.e. the fact that the interaction potential has unstable orbit, does.

astro-ph↗
arXiv1995

Volume Expansion Rate and The Age of The Universe

Under four assumptions such that 1) Einstein's theory of gravity is correct, 2) existence of foliation by geodesic slicing, 3) the trace of the extrinsic curvature, $K$, is negative at the present time in observed region, that is, the observed universe is now expanding, 4) the strong energy condition is satisfied, we show that $H_{v0} t_{0} \leq 1$, where $H_v \equiv - K/3$ agrees with the Hubble parameter in the case of a homogeneous and isotropic universe, and $t_0$ is the age of the Universe. If $H_{v0} t_0 > 1$ is confirmed observationally, at least one of the four assumptions is incorrect.

astro-ph↗
arXiv1995

The Microlensing and Halo Models of the Galaxy

We investigated the dependence of the optical depth $τ$ of the microlensing events on model parameters of the Galactic halo. We only consider Galactic mass models in which the rotation curve inside the Sun is compatible with the observation and LMC is bound to the Galaxy. It is found that $τ$ varies up to a factor 2.5 from the standard spherical and flat rotation halo model. This implies that only the most centrally concentrated halo model can be consistent with the observation if the halo consists of only MACHOs. We also calculate the power $x$ of IMF of MACHO consistent with Tyson's CCD survey as well as Bahcall \etal's observation by {\em HST}. It is found that $x$ is greater than 5.

astro-ph↗
arXiv1995

Hubble Parameter in Void Universe

We investigate the distance-redshift relation in the simple void model. As discussed by Moffat and Tatarski, if the observer stays at the center of the void, the observed Hubble parameter is not so different from the background Hubble parameter. However, if the position of observer is off center of the void, we must consider the peculiar velocity correction which is measured by the observed dipole anisotropy of cosmic microwave background. This peculiar velocity correction for the redshift is crucial to determine the Hubble parameter and we shall discuss this effect. Further the results of Turner et al by the N-body simulation will be also considered.

astro-ph↗