A new numerical method for constructing quasi-equilibrium sequences of irrotational binary neutron stars in general relativity

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  • 20 August 1999
Abstract
We propose a new numerical method to compute quasi-equilibrium sequences of general relativistic irrotational binary neutron star systems. It is a good approximation for an inspiraling binary neutron star system just before the coalescence as a result of gravitational wave emission that (1) the binary star system is irrotational, and (2) the binary star system is in quasi-equilibrium. We can introduce the velocity potential for such irrotational flow field, which satisfies an elliptic PDE with a Neumann type boundary condition at the stellar surface. For the treatment of general relativistic gravity, we use the Wilson--Mathews formulation. In this formulation, the basic equations are expressed by a system of PDEs. We have developed a method to solve them with appropriate boundary conditions. We have checked the reliability of our new code by comparing our results with those of other computations available. By using this code, we have obtained quasi-equilibrium sequences of irrotational binary star systems with strong gravity as models for final states of real evolution of binary neutron star systems just before coalescence. Analysis of our quasi-equilibrium sequences of binary star systems shows that the systems may not suffer from dynamical instability of the orbital motion and that the maximum density does not increase substantially.

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