Gravitational Radiation from Coalescing Binary Neutron Stars. III: Simulations from Equilibrium Model

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Abstract
We have performed numerical simulation of coalescence of binary neutron stars from an equilibrium model using a Newtonian hydrodynamics code including a back reaction potential. We adopt a new back reaction potential proposed by Blanchet, Damour and Schäfer, in which only the third time derivative of quandrupole moment is used to obtain better numerical accuracy. We use the Cartesian coordinate system (x, y, z) with a typical number of grids 141 ×141 ×131 under the assumption of the reflection symmetry with respect to z=0 plane. We performed 3 calculations, one of which is the same problem as Paper II concerned, where a different radiation reaction formalism was applied, in order to examine the effect of a radiation formalism. We found that the results are essentially the same except for a slight difference on the flux and the density contours. The other two calculations are started when two neutron stars of each mass 1.49 M⊙ just touch with each other in rotational equilibrium. One of them concerns coalescence of the neutron stars initiated by the angular momentum loss due to the gravitational radiation. The radiated energy is 4.2% of the rest mass. In the final stage of the numerical calculation the central part is not still axisymmetric and the luminosity decreases very slowly. The ratio of the rotational energy to gravitational energy T/W is 0.114 and a/m is 0.33 in the final stage while a/m is 0.64 at first. In the other calculation, we include in the initial data the approaching velocity of each neutron star due to the quasi-stationary evolution of the binary through emission of the gravitational radiation. The radiated energy amounts to 3% of the rest mass. The system in the final stage is almost axisymmetric with T/W=0.136 and a/m=0.38 in consequence of a large angular momentum loss at the early time. The maximum amplitude of the gravitational radiation h is ∼5 ×10-21 for a hypothetical coalescence event at a distance of 10 Mpc. In the final stage of both calculations all the matter seems to be inside the Schwarzschild radius and the final destiny of the system will be a slowly rotating Kerr black hole.

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