Abstract:
This paper reports on our effort in modeling realistic astrophysical neutron star binaries in general relativity. We analyze under what conditions the conformally flat quasiequilibrium (CFQE) approach can generate ``astrophysically relevant'' initial data, by developing an analysis that determines the violation of the CFQE approximation in the evolution of the binary described by the full Einstein theory. We show that the CFQE assumptions significantly violate the Einstein field equations for corotating neutron stars at orbital separations nearly double that of the innermost stable circular orbit (ISCO) separation, thus calling into question the astrophysical relevance of the ISCO determined in the CFQE approach. With the need to start numerical simulations at large orbital separation in mind, we push for stable and long term integrations of the full Einstein equations for the binary neutron star system. We demonstrate the stability of our numerical treatment and analyze the stringent requirements on resolution and size of the computational domain for an accurate simulation of the system.

Abstract:
We analyze the stability of relativistic, quasi-equilibrium binary neutron stars in synchronous circular orbit. We explore stability against radial collapse to black holes prior to merger, and against orbital plunge. We apply theorems based on turning points along uniformly rotating sequences of constant angular momentum and rest mass to locate the onset of secular instabilities. We find that inspiraling binary neutron stars are stable against radial collapse to black holes all the way down to the innermost stable circular orbit.

Abstract:
One often-used approximation in the study of binary compact objects (i.e., black holes and neutron stars) in general relativity is the instantaneously circular orbit assumption. This approximation has been used extensively, from the calculation of innermost circular orbits to the construction of initial data for numerical relativity calculations. While this assumption is inconsistent with generic general relativistic astrophysical inspiral phenomena where the dissipative effects of gravitational radiation cause the separation of the compact objects to decrease in time, it is usually argued that the timescale of this dissipation is much longer than the orbital timescale so that the approximation of circular orbits is valid. Here, we quantitatively analyze this approximation using a post-Newtonian approach that includes terms up to order ({Gm/(rc^2)})^{9/2} for non-spinning particles. By calculating the evolution of equal mass black hole / black hole binary systems starting with circular orbit configurations and comparing them to the more astrophysically relevant quasicircular solutions, we show that a minimum initial separation corresponding to at least 6 (3.5) orbits before plunge is required in order to bound the detection event loss rate in gravitational wave detectors to < 5% (20%). In addition, we show that the detection event loss rate is > 95% for a range of initial separations that include all modern calculations of the innermost circular orbit (ICO).

Abstract:
Two relations, the virial relation $M_{\rm ADM}=M_{\rm K}$ and the first law in the form $\delta M_{\rm ADM}=\Omega \delta J$, should be satisfied by a solution and a sequence of solutions describing binary compact objects in quasiequilibrium circular orbits. Here, $M_{\rm ADM}$, $M_{\rm K}$, $J$, and $\Omega$ are the ADM mass, Komar mass, angular momentum, and orbital angular velocity, respectively. $\delta$ denotes an Eulerian variation. These two conditions restrict the allowed formulations that we may adopt. First, we derive relations between $M_{\rm ADM}$ and $M_{\rm K}$ and between $\delta M_{\rm ADM}$ and $\Omega \delta J$ for general asymptotically flat spacetimes. Then, to obtain solutions that satisfy the virial relation and sequences of solutions that satisfy the first law at least approximately, we propose a formulation for computation of quasiequilibrium binary neutron stars in general relativity. In contrast to previous approaches in which a part of the Einstein equation is solved, in the new formulation, the full Einstein equation is solved with maximal slicing and in a transverse gauge for the conformal three-metric. Helical symmetry is imposed in the near zone, while in the distant zone, a waveless condition is assumed. We expect the solutions obtained in this formulation to be excellent quasiequilibria as well as initial data for numerical simulations of binary neutron star mergers.

Abstract:
In numerical evolutions of binary black holes (BBH) it is desirable to easily control the orbital eccentricity of the BBH, and the number of orbits completed by the binary through merger. This paper presents fitting formulae that allow to choose initial-data parameters for generic precessing BBH resulting in an orbital eccentricity $\sim 10^{-4}$, and that allow to predict the number of orbits to merger. We further demonstrate how these fits can be used to choose initial-data parameters of desired non-zero eccentricity. For both usage scenarios, no costly exploratory BBH evolutions are necessary, but both usage scenarios retain the freedom to refine the fitted parameters further based on the results of BBH evolutions. The presented fitting formulas are based on 729 BBH configurations which are iteratively reduced to eccentricity $\lesssim 10^{-4}$, covering mass-ratios between 1 and 8 and spin-magnitude up to 0.5. 101 of these configurations are evolved through the BBH inspiral phase.

Abstract:
We perform magnetohydrodynamic simulations in full general relativity (GRMHD) of a binary black hole-neutron star on a quasicircular orbit that undergoes merger. The binary mass ratio is 3:1, the black hole initial spin parameter $a/m=0.75$ ($m$ is the black hole Christodoulou mass) aligned with the orbital angular momentum, and the neutron star is an irrotational $\Gamma=2$ polytrope. About two orbits prior to merger (at time $t=t_B$), we seed the neutron star with a dynamically weak interior dipole magnetic field that extends into the stellar exterior. At $t=t_B$ the exterior has a low-density atmosphere with constant plasma parameter $\beta\equiv P_{\rm gas}/P_{\rm mag}$. Varying $\beta$ at $t_B$ in the exterior from $0.1$ to $0.01$, we find that at a time $\sim 4000{\rm M} \sim 100(M_{\rm NS}/1.4M_\odot)$ms [M is the total (ADM) mass] following the onset of accretion of tidally disrupted debris, magnetic winding above the remnant black hole poles builds up the magnetic field sufficiently to launch a mildly relativistic, collimated outflow - an incipient jet. The duration of the accretion and the lifetime of the jet is $\Delta t\sim 0.5(M_{\rm NS}/1.4M_\odot)$s. Our simulations furnish the first explicit examples in GRMHD which show that a jet can emerge following a black hole - neutron star merger.

Abstract:
We present a numerical scheme that solves the initial value problem in full general relativity for a binary neutron star in quasi-equilibrium. While Newtonian gravity allows for a strict equilibrium, a relativistic binary system emits gravitational radiation, causing the system to lose energy and slowly spiral inwards. However, since inspiral occurs on a time scale much longer than the orbital period, we can adopt a quasi-equilibrium approximation. In this approximation, we integrate a subset of the Einstein equations coupled to the equations of relativistic hydrodynamics to solve the initial value problem for binaries of arbitrary separation, down to the innermost stable orbit.

Abstract:
The innermost stable circular orbits (ISCO) of coalescing neutron star-black hole binary are studied taking into account both the tidal and relativistic effects. We adopt the generalized pseudo-Newtonian potential to mimic the general relativistic effects of gravitation. It is found that the separation of the neutron star and the black hole at the ISCO is greater than that obtained by using either the Newtonian potential or the second post-Newtonian equation of motion of point mass. In equal mass cases, it is found that for $\bar{a}/m_1 > 3.5$ with $\bar{a}$ and $m_1$ being the mean radius and the mass of the neutron star, the tidal effect dominates the stability of the binary system while for $\bar{a}/m_1 < 3.5$, the relativistic effect, i.e. the fact that the interaction potential has unstable orbit, does.

Abstract:
We develop a method to compute low-eccentricity initial data of binary neutron stars required to perform realistic simulations in numerical relativity. The orbital eccentricity is controlled by adjusting the orbital angular velocity of a binary and incorporating an approaching relative velocity of the neutron stars. These modifications improve the solution primarily through the hydrostatic equilibrium equation for the binary initial data. The orbital angular velocity and approaching velocity of initial data are updated iteratively by performing time evolutions over ~3 orbits. We find that the eccentricity can be reduced by an order of magnitude compared to standard quasicircular initial data, specifically from ~0.01 to <~0.001, by three successive iterations for equal-mass binaries leaving ~10 orbits before the merger.

Abstract:
We report on the first calculations of fully relativistic binary circular orbits to span a range of separation distances from the innermost stable circular orbit (ISCO), deeply inside the strong field regime, to a distance ($\sim$ 200 km) where the system is accurately described by Newtonian dynamics. We consider a binary system composed of two identical corotating neutron stars, with 1.43 $M_\odot$ gravitational mass each in isolation. Using a conformally flat spatial metric we find solutions to the initial value equations that correspond to semi-stable circular orbits. At large distance, our numerical results agree exceedingly well with the Newtonian limit. We also present a self consistent determination of the ISCO for different stellar masses.