Stationary Structures of Irrotational Binary Systems: Models for Close Binary Systems of Compact Stars

We propose a new numerical method to calculate irrotational binary systems composed of compressible gaseous stars in Newtonian gravity. Assuming irrotationality, i.e., vanishing of the vorticity vector everywhere in the star in the inertial frame, we can introduce the velocity potential for the flow field. Using this velocity potential we can derive a set of basic equations for stationary states that consist of (1) the generalized Bernoulli equation, (2) the Poisson equation for the Newtonian gravitational potential, and (3) the equation for the velocity potential with the Neumann-type boundary condition. We succeeded in developing a new code to compute numerically exact solutions to these equations for the first time. Such irrotational configurations of binary systems are appropriate models for realistic neutron star binaries composed of inviscid gases, just prior to coalescence of two stars caused by emission of gravitational waves. Accuracies of our numerical solutions are so high that we can compute reliable models for fully deformed final stationary configurations and hence determine the inner most stable circular orbit of binary neutron star systems under the approximations of weak gravity and inviscid limit

Merger of black hole-neutron star binaries: nonspinning black hole case

We perform a simulation for merger of a black hole (BH)-neutron star (NS) binary in full general relativity preparing a quasicircular state as initial condition. The BH is modeled by a moving puncture with no spin and the NS by the $\Gamma$-law equation of state with $\Gamma=2$. Corotating velocity field is assumed for the NS. The mass of the BH and the rest-mass of the NS are chosen to be $\approx 3.2 M_{\odot}$ and $\approx 1.4 M_{\odot}$ with relatively large radius of the NS $\approx 14$ km. The NS is tidally disrupted near the innermost stable orbit but $\sim 80$ of the material is swallowed into the BH with small disk mass $\sim 0.3M_{\odot}$ even for such small BH mass $\sim 3M_{\odot}$. The result indicates that the system of a BH and a massive disk of $\sim M_{\odot}$ is not formed from nonspinning BH-NS binaries, although a disk of mass $\sim 0.1M_{\odot}$ is a possible outcome.Comment: 5 pages. Phys. Rev. D 74, 121503 (R) (2006

Irrotational and Incompressible Binary Systems in the First Post-Newtonian Approximation of General Relativity

The first post-Newtonian (PN) hydrostatic equations for an irrotational fluid are solved for an incompressible binary system. The equilibrium configuration of the binary system is given by a small deformation from the irrotational Darwin-Riemann ellipsoid which is the solution at Newtonian order. It is found that the orbital separation at the innermost stable circular orbit (ISCO) decreases when one increases the compactness parameter $M_{\ast}/c^2 a_{\ast}$, in which $M_{\ast}$ and $a_{\ast}$ denote the mass and the radius of a star, respectively. If we compare the 1PN angular velocity of the binary system at the ISCO in units of $\sqrt{M_{\ast}/a_{\ast}^3}$ with that of Newtonian order, the angular velocity at the ISCO is almost the same value as that at Newtonian order when one increases the compactness parameter. Also, we do not find the instability point driven by the deformation at 1PN order, where a new sequence bifurcates throughout the equilibrium sequence of the binary system until the ISCO. We also investigate the validity of an ellipsoidal approximation, in which a 1PN solution is obtained assuming an ellipsoidal figure and neglecting the deformation. It is found that the ellipsoidal approximation gives a fairly accurate result for the total energy, total angular momentum and angular velocity. However, if we neglect the velocity potential of 1PN order, we tend to overestimate the angular velocity at the ISCO regardless of the shape of the star (ellipsoidal figure or deformed figure).Comment: 36 pages with 5 figures, revtex, Prog. Theor. Phys. in pres

Quark Matter in Neutron Star Mergers

Binary neutron star mergers are expected to be one of the most promising source of gravitational waves (GW) for the network of laser interferometric and bar detectors becoming operational in the next few years. The merger wave signal is expected to be sensitive to the interior structure of the neutron star (NS). The structure of high density phases of matter is under current experimental investigation in heavy-ion collisions. We investigate the dependence of the merger process and its GW signal on the presence of quarks in these phases by performing numerical simulations, where the smoothed particle hydrodynamics (SPH) method and the conformally flat approximation for the 3-geometry in general relativistic gravity are implemented.Comment: 4 Pages, 4 Figures, Proc. Nuclei in the Cosmos 7, 200

Binary neutron stars: Equilibrium models beyond spatial conformal flatness

Equilibria of binary neutron stars in close circular orbits are computed numerically in a waveless formulation: The full Einstein-relativistic-Euler system is solved on an initial hypersurface to obtain an asymptotically flat form of the 4-metric and an extrinsic curvature whose time derivative vanishes in a comoving frame. Two independent numerical codes are developed, and solution sequences that model inspiraling binary neutron stars during the final several orbits are successfully computed. The binding energy of the system near its final orbit deviates from earlier results of third post-Newtonian and of spatially conformally flat calculations. The new solutions may serve as initial data for merger simulations and as members of quasiequilibrium sequences to generate gravitational wave templates, and may improve estimates of the gravitational-wave cutoff frequency set by the last inspiral orbit.Comment: 4 pages, 6 figures, revised version, PRL in pres

Merger of black hole-neutron star binaries in full general relativity

We present our latest results for simulation for merger of black hole (BH)-neutron star (NS) binaries in full general relativity which is performed preparing a quasicircular state as initial condition. The BH is modeled by a moving puncture with no spin and the NS by the $\Gamma$-law equation of state with $\Gamma=2$ and corotating velocity field as a first step. The mass of the BH is chosen to be $\approx 3.2 M_{\odot}$ or $4.0M_{\odot}$, and the rest-mass of the NS $\approx 1.4 M_{\odot}$ with relatively large radius of the NS $\approx 13$--14 km. The NS is tidally disrupted near the innermost stable orbit but $\sim 80$--90% of the material is swallowed into the BH and resulting disk mass is not very large as $\sim 0.3M_{\odot}$ even for small BH mass $\sim 3.2M_{\odot}$. The result indicates that the system of a BH and a massive disk of $\sim M_{\odot}$ is not formed from nonspinning BH-NS binaries irrespective of BH mass, although a disk of mass $\sim 0.1M_{\odot}$ is a possible outcome for this relatively small BH mass range as $\sim 3$--4$M_{\odot}$. Our results indicate that the merger of low-mass BH and NS may form a central engine of short-gamma-ray bursts.Comment: 14 pages. To appear in a special issue of Classical and Quantum Gravity: New Frontiers in Numerical Relativit

Gravitational wave content and stability of uniformly, rotating, triaxial neutron stars in general relativity

Targets for ground-based gravitational wave interferometers include continuous, quasiperiodic sources of gravitational radiation, such as isolated, spinning neutron stars. In this work we perform evolution simulations of uniformly rotating, triaxially deformed stars, the compressible analogues in general relativity of incompressible, Newtonian Jacobi ellipsoids. We investigate their stability and gravitational wave emission. We employ five models, both normal and supramassive, and track their evolution with different grid setups and resolutions, as well as with two different evolution codes. We find that all models are dynamically stable and produce a strain that is approximately one-tenth the average value of a merging binary system. We track their secular evolution and find that all our stars evolve towards axisymmetry, maintaining their uniform rotation, kinetic energy, and angular momentum profiles while losing their triaxiality.Comment: 12 pages, 5 figure