Keisuke Taniguchi

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 binaries are studied taking into account both 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 innermost stable circular orbit is greater than that obtained by using either the Newtonian potential (i.e., the case in which only the tidal interaction is included) or the second post· Newtonian equation of motion of a point mass (i.e., the case in which the effect of general relativity is taken into account but the tidal force is neglected). In equal mass cases, it is found that for a/m[~3.5 with a and m[ being the mean radius and the mass of the neutron star, the tidal effect dominates the stability of the binary system, while for a/m[ ~3.5, the relativistic effect, i.e., the fact that the interaction potential has an unstable orbit, does. The effect of the circulation is also studied by comparing the Roche ellipsoids (REs) with the irrotational Roche· Riemann ellipsoids (IRREs). In the IRREs case, which are believed to be the case of coalescing binary neutron stars, it is found that in the equal mass binary case, the orbital frequency is 495 Hz at the ISCO.

Irrotational and Incompressible Ellipsoids in the First Post-Newtonian Approximation of General Relativity

First post-Newtonian (lPN) hydrostatic equations for an irrotational fluid which have been recently derived are solved for an incompressible star. The 1PN configurations are expressed as a deformation of the Newtonian irrotational Riemann ellipsoid using Lagrangian displacement vectors introduced by Chandrasekhar. For the 1PN solutions, we also calculate the luminosity of gravitational waves in the 1PN approximation using the Blanchet-Damour formalism. It is found that the solutions of the 1PN equations exhibit singularities at points where the axial ratios of semi-axes are 1 : 0.5244 : 0.6579 and 1 : 0.2374 : 0.2963, and the singularities seem to show that at the points, the irrotational Riemann ellipsoid is unstable to the deformation induced by the effect of general relativity. For stable cases (a2/al > 0.5244, where al and a2 are the semi-major and minor axes, respectively) we find that when increasing the 1PN correction, the angular velocity and total angular momentum increase, while the total energy and luminosity of gravitational waves decrease. These 1PN solutions will be useful when examining the accuracy of numerical code for obtaining relativistic irrotational stars. We also investigate the validity of an ellipsoidal approximation, in which a 1PN solution is obtained assuming an ellipsoidal figure and neglecting the deformation. It is found that for a2/al > 0.7, the ellipsoidal approximation gives a fairly accurate result for the energy, angular momentum, and angular velocity, although in the approximation we cannot find the singularities.

Gravitational radiation from corotating binary neutron stars of incompressible fluid in the first post-Newtonian approximation of general relativity

We analytically study gravitational radiation from corotating binary neutron stars composed of an incompressible, homogeneous fluid in circular orbits. The energy and the angular momentum loss rates are derived up to the first post-Newtonian (1PN) order beyond the quadrupole approximation including effects of the finite size of each of the binary stars. It is found that the leading term of finite size effects in the 1PN order is only

Chapter 5. Location of the Innermost Stable Circular Orbit of Binary Neutron Stars in the Post Newtonian Approximations of General Relativity

{O(GM}_{*}{/c}^{2}{a}_{*})

Irrotational and Incompressible Binary Systems in the First Post-Newtonian Approximation of General Relativity

smaller than that in Newtonian order, where

The Relation between Seismic Activities and Earth Tides in the Case of the Matsushiro Earthquake Swarm

{\mathrm{GM}}_{*}{/c}^{2}{a}_{*}

Microseismicity Induced by Heavy Rainfall Around Flooded Vertical Ore Veins

means the ratio of the gravitational radius to the mean radius of each binary star, and the 1PN term acts to decrease the Newtonian finite size effect in gravitational radiation.

BEHAVIOR OF FRACTURED ZONES AT THE YAMASAKI FAULT FOR TELESEISMIC SURFACE WAVES

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

Black hole-neutron star binaries in numerical relativity

\Omega_{ISCO}

Irrotational Binary Systems with the Polytropic Equation of State

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,