We present a numerical method to compute quasiequilibrium configurations of close binary neutron stars in the pre-coalescing stage. A hydrodynamical treatment is performed under the assumption that the flow is either rigidly rotating or irrotational. The latter state is technically more complicated to treat than the former one (synchronized binary), but is expected to represent fairly well the late evolutionary stages of a binary neutron star system. As regards the gravitational field, an approximation of general relativity is used, which amounts to solving five of the ten Einstein equations (conformally flat spatial metric). The obtained system of partial differential equations is solved by means of a multi-domain spectral method. Two spherical coordinate systems are introduced, one centered on each star; this results in a precise description of the stellar interiors. Thanks to the multi-domain approach, this high precision is extended to the strong field regions. The computational domain covers the whole space so that exact boundary conditions are set to infinity. Extensive tests of the numerical code are performed, including comparisons with recent analytical solutions. Finally a constant baryon number sequence (evolutionary sequence) is presented in details for a polytropic equation of state with γ = 2. PACS number(s): 04.25. Dm, 04.40.Dg, 97.60.Jd, 02.70.Hm

No abstract

No abstract

A multidomain spectral method for computing very high precision three-dimensional stellar models is presented. The boundary of each domain is chosen in order to coincide with a physical discontinuity ͑e.g., the star's surface͒. In addition, a regularization procedure is introduced to deal with the infinite derivatives on the boundary that may appear in the density field when stiff equations of state are used. Consequently all the physical fields are smooth functions on each domain and the spectral method is absolutely free of any Gibbs phenomenon, which yields to a very high precision. The power of this method is demonstrated by direct comparison with analytical solutions such as MacLaurin spheroids and Roche ellipsoids. The relative numerical error is revealed to be of the order of 10 Ϫ10 . This approach has been developed for the study of relativistic inspiralling binaries. It may be applied to a wider class of astrophysical problems such as the study of relativistic rotating stars too.