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.Comment: invited talk at Yukawa Internatinal Seminar (YKIS99) 17 pages, 11 figures, for associated movie files, see http://astro.sc.niigata-u.ac.jp/~oohara/ykis99

Gauge-Invariant Gravitational Wave Extraction from Coalescing Binary Neutron Stars

We report application of a method for extracting gravitational waves to three-dimensional numerical simulation on coalescing binary neutron stars. We found the extracted wave form includes the componets corresponding to the quadrupole part in the Newtonian potential of the background metric, if it is monitored at a position not far from the central stars. We present how to eliminate it.Comment: 6 pages, 5 figure

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 $\Gamma=3$. 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.Comment: 16 pages(11 figures). To appear in Prog. Theor. Phys. vol.98(1997

Truncated post-Newtonian neutron star model

As a preliminary step towards simulating binary neutron star coalescing problem, we test a post-Newtonian approach by constructing a single neutron star model. We expand the Tolman-Oppenheimer-Volkov equation of hydrostatic equilibrium by the power of $c^{-2}$, where $c$ is the speed of light, and truncate at the various order. We solve the system using the polytropic equation of state with index $\Gamma=5/3, 2$ and 3, and show how this approximation converges together with mass-radius relations. Next, we solve the Hamiltonian constraint equation with these density profiles as trial functions, and examine the differences in the final metric. We conclude the second `post-Newtonian' approximation is close enough to describe general relativistic single star. The result of this report will be useful for further binary studies. (Note to readers) This paper was accepted for publication in Physical Review D. [access code dsj637]. However, since I was strongly suggested that the contents of this paper should be included as a section in our group's future paper, I gave up the publication.Comment: 5 pages, RevTeX, 3 eps figs, epsf.sty, accepted for publication in PRD (Brief Report), but will not appea