Quasiequilibrium sequences of synchronized and irrotational binary neutron stars in general relativity: Method and tests

Abstract

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

Various features of quasiequilibrium sequences of binary neutron stars in general relativity

“…We have developed a numerical code for computing quasiequilibrium sequences of binary neutron stars through the series of works [24,25,34,35]. In the present article, we have presented the results of relativistic computations of both synchronized and irrotational rotation states, for polytropic equations of state with several adiabatic indices.…”

“…[34] and [24], hereafter Paper I and II respectively). We refer the interested reader to those articles and simply summarize here the basic assumptions, the basic equations and our numerical method.…”

“…Various approaches to compute binary neutron star models in the hydrodynamical inspiral phase have been considered: (i) (semi-)analytical [19,20] and (ii) numerical [21,22,23,24,25] in Newtonian gravity, (iii) (semi-)analytical [26,27,28,29] and (iv) numerical [30] in the post-Newtonian approximation, and (v) numerical in the framework of general relativity [31,32,33,34,35,36,37,38,39,40]. Binary neutron stars gradually decrease their orbital separations as a result of the emission of gravitational radiation.…”

Are neutron stars crushed? Gravitomagnetic tidal fields as a mechanism for binary-induced collapse

“…The French [23,24,49,50] and Japanese [26,27] numerical groups also make these assumptions but do not see compression. Further, Wilson [51] examined the head-on collision of two NSs using both the SCF/quasi-equilibrium conditions and in full general relativity.…”

Bowen-York-type initial data for binaries with neutron stars

“…The method has been used for BBHs by Grandclément et al [9], for DNS by Gourgoulhon et al [10], and for BH-NS binaries by Etienne et al [11]. The key in those studies was the identification of a helical Killing vector field, so the initial data are approximately time-symmetric, ensuring that the compact objects are in a quasi-circular orbit.…”