New numerical method for constructing quasiequilibrium sequences of irrotational binary neutron stars in general relativity - art. no. 124023

We propose a new numerical method to compute quasi-equilibrium sequences of general relativistic irrotational binary neutron star systems. It is a goo d approximation to assume that (1) the binary star system is irrotational, i.e. the vorticity of the flow field inside component stars vanishes everyw here (irrotational flow), and (2) the binary star system is in quasi-equili brium, for an inspiraling binary neutron star system just before the coales cence as a result of gravitational wave emission. We can introduce the velo city potential for such an irrotational flow field, which satisfies an elli ptic partial differential equation (PDE) with a Neumann type boundary condi tion at the stellar surface. For a treatment of general relativistic gravit y, we use the Wilson-Mathews formulation, which assumes conformal flatness for spatial components of metric. In this formulation, the basic equations are expressed by a system of elliptic PDEs. We have developed a method to s olve these PDEs with appropriate boundary conditions. The method is based o n the established prescription for computing equilibrium states of rapidly rotating axisymmetric neutron stars or Newtonian binary systems. We have ch ecked the reliability of our new code by comparing our results with those o f other computations available. We have also performed several convergence tests. By using this code, we have obtained quasi-equilibrium sequences of irrotational binary star systems with strong gravity as models for final st ates of real evolution of binary neutron star systems just before coalescen ce. Analysis of our quasi-equilibrium sequences of binary star systems show s that the systems may not suffer from dynamical instability of the orbital motion and that the maximum density does not increase as the binary separa tion decreases.