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

Coincidence analysis to search for inspiraling compact binaries using TAMA300 and LISM data

Japanese laser interferometric gravitational wave detectors, TAMA300 and LISM, performed a coincident observation during 2001. We perform a coincidence analysis to search for inspiraling compact binaries. The length of data used for the coincidence analysis is 275 hours when both TAMA300 and LISM detectors are operated simultaneously. TAMA300 and LISM data are analyzed by matched filtering, and candidates for gravitational wave events are obtained. If there is a true gravitational wave signal, it should appear in both data of detectors with consistent waveforms characterized by masses of stars, amplitude of the signal, the coalescence time and so on. We introduce a set of coincidence conditions of the parameters, and search for coincident events. This procedure reduces the number of fake events considerably, by a factor $\sim 10^{-4}$ compared with the number of fake events in single detector analysis. We find that the number of events after imposing the coincidence conditions is consistent with the number of accidental coincidences produced purely by noise. We thus find no evidence of gravitational wave signals. We obtain an upper limit of 0.046 /hours (CL $= 90$) to the Galactic event rate within 1kpc from the Earth. The method used in this paper can be applied straightforwardly to the case of coincidence observations with more than two detectors with arbitrary arm directions.Comment: 28 pages, 17 figures, Replaced with the version to be published in Physical Review