Relativistic numerical model for close neutron-star binaries

Abstract

We describe a numerical method for calculating the (3+1) dimensional general relativistic hydrodynamics of a coalescing neutron-star binary system. The relativistic field equations are solved at each time slice with a spatial 3-metric chosen to be conformally flat. Against this solution to the general relativistic field equations the hydrodynamic variables and gravitational radiation are allowed to respond. The gravitational radiation signal is derived via a multipole expansion of the metric perturbation to the hexadecapole (l = 4) order including both mass and current moments and a correction for the slow motion approximation. Using this expansion, the effect of gravitational radiation on the system evolution can also be recovered by introducing an acceleration term in the matter evolution. In the present work we illustrate the method by applying this model to evaluate various orbits of two neutron stars with a gravitational mass of 1.45 M⊙ near the time of the final merger. We discuss the evidence that, for a realistic neutron star equation of state, general relativistic effects may cause the stars to individually collapse into black holes prior to merging. Also, the strong fields cause the last stable orbit to occur at a larger separation distance and lower frequency than previously estimated.PACS Numbers: 04.20.Jb, 04.30.+x, 47.75+f,, 95.30.Lz, 95.30.Sf 97.60.Jd,

Irrotational binary neutron stars in quasiequilibrium

“…The Einstein field equations are solved by imposing a conformally flat condition (CFC) on the three metric [1,2]. That is, the spatial three metric is constrained to be represented by a position dependent conformal factor φ 4 times the Kronecker delta, γ ij = φ 4 δ ij .…”

“…The physical processes occurring during the last orbits of a neutron-star binary are a subject of intense current debate [1][2][3][4][5][6][7][8][9][10][11]. In part, this recent surge in interest stems from relativistic numerical hydrodynamic simulations in which it has been noted [1][2][3] that as the stars approach each other their interior density increases.…”

“…In part, this recent surge in interest stems from relativistic numerical hydrodynamic simulations in which it has been noted [1][2][3] that as the stars approach each other their interior density increases. Indeed, for an appropriate mass and equation of state, previous numerical simulations indicated that binary neutron stars might collapse individually toward black holes seconds prior to merger.…”

Astrophysics in 1997

“…Wilson et al (1996) are said to have greatly overestimated the effects, but their response was not presented. Three seems to us to be just the right number for brown dwarf candidates in the Pleiades (Martin et al 1996), the number of plots of warm and cool spots in the microwave background radiation that agree (Inman et al 1997), the number of independent sightings of the halo around NGC 5907 that seems to trace its dark matter distribution (Rudy et al 1997), the number of pulsars whose optical colors look like synchrotron radiation (Nasuti et al 1997), the number of spectroscopic binaries whose component spectra have been separated by tomography (Liu et al 1997a), and the number of soft X-ray transients with neutron star components and optical identifications (Wachter 1997).…”

Gravitational Waves from Relativistic Neutron-Star Mergers with Microphysical Equations of State

“…Based on a set of simulated binary merger models [7], we identify characteristic features of the simulated GW signals and link them to the merger properties. The simulations were carried out with our relativistic smoothed particle hydrodynamics (SPH) code [10,11], which solves the relativistic hydrodynamics equations together with the Einstein field equation in the conformally flat ap- proximation [CFC; 12,13]. The simulations were started from a stable equilibrium configuration slightly outside the innermost stable circular orbit and the corresponding initial data were generated by relaxing the fluid to a velocity field that includes the orbital motion and the proper spins of the NSs.…”