Quasiequilibrium Initial Data Research Articles

New code for equilibriums and quasiequilibrium initial data of compact objects. IV. Rotating relativistic stars with mixed poloidal and toroidal magnetic fields

A new code for computing fully general relativistic solutions of strongly magnetized rapidly rotating compact stars is developed as a part of the COCAL (Compact Object CALculator) code. The full set of Einstein's equations, Maxwell's equations and magnetohydrodynamic equations are consistently solved assuming perfect conductivity, stationarity, and axisymmetry, and strongly magnetized solutions associated with mixed poloidal and toroidal components of magnetic fields are successfully obtained in generic (non-circular) spacetimes. We introduce the formulation of the problem and the numerical method in detail, then present examples of extremely magnetized compact star solutions and their convergence tests. It is found that, in extremely magnetized stars, the stellar matter can be expelled from the region of strongest toroidal fields. Hence we conjecture that a toroidal electro-vacuum region may appear inside of the extremely magnetized compact stars, which may seem like the neutron star becoming the strongest toroidal solenoid coil in the universe.

Horizon surface gravity in corotating black hole binaries

For binary systems of corotating black holes, the zeroth law of black hole mechanics states that the surface gravity is constant over each component of the horizon. Using the approximation of a conformally flat spatial metric, we compute sequences of quasi-equilibrium initial data for corotating black hole binaries with irreducible mass ratios in the range . For orbits outside the innermost stable one, the surface gravity is found to be constant on each component of the apparent horizon at the sub-percent level. We compare those numerical results to the analytical predictions from post-Newtonian theory at the fourth (4PN) order and from black hole perturbation theory to linear order in the mass ratio. We find a remarkably good agreement for all mass ratios considered, even in the strong-field regime. In particular, our findings confirm that the domain of validity of black hole perturbative calculations appears to extend well beyond the extreme mass-ratio limit.

New code for equilibriums and quasiequilibrium initial data of compact objects. III. Axisymmetric and triaxial rotating stars

We introduce new code for stationary and axisymmetric equilibriums, as well as for triaxial quasiequilibrium initial data, of single rotating relativistic stars. The new code is developed as a part of our versatile initial data code for compact objects, Compact Object CALculator (cocal). In computing strong gravitational fields, the waveless formulation is incorporated into the cocal code on top of the previously developed Isenberg-Wilson-Mathews formulation (conformally flat thin-sandwich formulation). Also introduced is a new differential rotation law that contains two parameters to control an angular velocity profile and a transition from uniform to differential rotation. We present convergence tests and solution sequences for both uniformly and differentially rotating equilibriums of stationary axisymmetric compact stars, as well as for quasiequilibrium initial data of uniformly rotating triaxial (nonaxisymmetric) compact stars. We also show comparisons of uniformly rotating axisymmetric solutions computed with three different codes: cocal, lorene, and the RNS code.

New code for quasiequilibrium initial data of binary neutron stars: Corotating, irrotational, and slowly spinning systems

We present the extension of our cocal---Compact Object CALculator---code to compute general-relativistic initial data for binary compact-star systems. In particular, we construct quasiequilibrium initial data for equal-mass binaries with spins that are either aligned or antialigned with the orbital angular momentum. The Isenberg-Wilson-Mathews formalism is adopted and the constraint equations are solved using the representation formula with a suitable choice of a Green's function. We validate the new code with solutions for equal-mass binaries and explore its capabilities for a wide range of compactnesses, from a white dwarf binary with compactness $\ensuremath{\sim}1{0}^{\ensuremath{-}4}$, up to a highly relativistic neutron-star binary with compactness $\ensuremath{\sim}0.22$. We also present a comparison with corotating and irrotational quasiequilibrium sequences from the spectral code lorene [Taniguchi and Gourgoulhon, Phys. Rev. D 66, 104019 (2002)] and with different compactness, showing that the results from the two codes agree to a precision of the order of 0.05%. Finally, we present equilibria for spinning configurations with a nuclear-physics equation of state in a piecewise polytropic representation.

First law of mechanics for black hole binaries with spins

We use the canonical Hamiltonian formalism to generalize to spinning point particles the first law of mechanics established for binary systems of nonspinning point masses moving on circular orbits [A. Le Tiec, L. Blanchet, and B. F. Whiting, Phys. Rev. D 85, 064039 (2012)]. We find that the redshift observable of each particle is related in a very simple manner to the canonical Hamiltonian and, more generally, to a class of Fokker-type Hamiltonians. Our results are valid through linear order in the spin of each particle, but hold also for quadratic couplings between the spins of different particles. The knowledge of spin effects in the Hamiltonian allows us to compute spin-orbit terms in the redshift variable through 2.5PN order, for circular orbits and spins aligned or anti-aligned with the orbital angular momentum. To describe extended bodies such as black holes, we supplement the first law for spinning point-particle binaries with some ``constitutive relations'' that can be used for diagnosis of spin measurements in quasi-equilibrium initial data.

New code for equilibriums and quasiequilibrium initial data of compact objects. II. Convergence tests and comparisons of binary black hole initial data

COCAL is a code for computing equilibriums or quasiequilibrium initial data of single or binary compact objects based on finite difference methods. We present the results of supplementary convergence tests of COCAL code using time symmetric binary black hole data (Brill-Lindquist solution). Then, we compare the initial data of binary black holes on the conformally flat spatial slice obtained from COCAL and KADATH, where KADATH is a library for solving a wide class of problems in theoretical physics including relativistic compact objects with spectral methods. Data calculated from the two codes converge nicely towards each other, for close as well as largely separated circular orbits of binary black holes. Finally, as an example, a sequence of equal mass binary black hole initial data with corotating spins is calculated and compared with data in the literature.

New code for equilibriums and quasiequilibrium initial data of compact objects

We present a new code, named COCAL - Compact Object CALculator, for the computation of equilibriums and quasiequilibrium initial data sets of single or binary compact objects of all kinds. In the cocal code, those solutions are calculated on one or multiple spherical coordinate patches covering the initial hypersurface up to the asymptotic region. The numerical method used to solve field equations written in elliptic form is an adaptation of self-consistent field iterations in which Green's integral formula is computed using multipole expansions and standard finite difference schemes. We extended the method so that it can be used on a computational domain with excised regions for a black hole and a binary companion. Green's functions are constructed for various types of boundary conditions imposed at the surface of the excised regions for black holes. The numerical methods used in cocal are chosen to make the code simpler than any other recent initial data codes, accepting the second order accuracy for the finite difference schemes. We perform convergence tests for time symmetric single black hole data on a single coordinate patch, and binary black hole data on multiple patches. Then, we apply the code to obtain spatially conformally flat binary black hole initial data using boundary conditions including the one based on the existence of equilibrium apparent horizons.

Binary-black-hole initial data with nearly extremal spins

There is a significant possibility that astrophysical black holes with nearly extremal spins exist. Numerical simulations of such systems require suitable initial data. In this paper, we examine three methods of constructing binary-black-hole initial data, focusing on their ability to generate black holes with nearly extremal spins: (i) Bowen-York initial data, including standard puncture data (based on conformal flatness and Bowen-York extrinsic curvature), (ii) standard quasiequilibrium initial data (based on the extended-conformal-thin-sandwich equations, conformal flatness, and maximal slicing), and (iii) quasiequilibrium data based on the superposition of Kerr-Schild metrics. We find that the two conformally flat methods (i) and (ii) perform similarly, with spins up to about 0.99 obtainable at the initial time. However, in an evolution, we expect the spin to quickly relax to a significantly smaller value around 0.93 as the initial geometry relaxes. For quasiequilibrium superposed Kerr-Schild data [method (iii)], we construct initial data with initial spins as large as 0.9997. We evolve superposed Kerr-Schild data sets with spins of 0.93 and 0.97 and find that the spin drops by only a few parts in ${10}^{4}$ during the initial relaxation; therefore, we expect that superposed Kerr-Schild initial data will allow evolutions of binary black holes with relaxed spins above 0.99. Along the way to these conclusions, we also present several secondary results: the power-law coefficients with which the spin of puncture initial data approaches its maximal possible value; approximate analytic solutions for large spin puncture data; embedding diagrams for single spinning black holes in methods (i) and (ii); nonunique solutions for method (ii). All of the initial-data sets that we construct contain subextremal black holes, and when we are able to push the spin of the excision boundary surface into the superextremal regime, the excision surface is always enclosed by a second, subextremal apparent horizon. The quasilocal spin is measured by using approximate rotational Killing vectors, and the spin is also inferred from the extrema of the intrinsic scalar curvature of the apparent horizon. Both approaches are found to give consistent results, with the approximate-Killing-vector spin showing the least variation during the initial relaxation.

General relativistic simulations of magnetized binary neutron star mergers

Binary neutron stars (NSNS) are expected to be among the leading sources of gravitational waves observable by ground-based laser interferometers and may be the progenitors of short-hard gamma-ray bursts. We present a series of general relativistic NSNS coalescence simulations both for unmagnetized and magnetized stars. We adopt quasiequilibrium initial data for circular, irrotational binaries constructed in the conformal thin-sandwich (CTS) framework. We adopt the BSSN formulation for evolving the metric and a high-resolution shock-capturing scheme to handle the magnetohydrodynamics. Our simulations of unmagnetized binaries agree with the results of Shibata, Taniguchi and Ury\ifmmode \bar{u}\else \={u}\fi{} [M. Shibata, K. Taniguchi, and K. Ury\ifmmode \bar{u}\else \={u}\fi{}, Phys. Rev. D 68, 084020 (2003).]. In cases in which the mergers result in a prompt collapse to a black hole, we are able to use puncture gauge conditions to extend the evolution and determine the mass of the material that forms a disk. We find that the disk mass is less than 2% of the total mass in all cases studied. We then add a small poloidal magnetic field to the initial configurations and study the subsequent evolution. For cases in which the remnant is a hypermassive neutron star, we see measurable differences in both the amplitude and phase of the gravitational waveforms following the merger. For cases in which the remnant is a black hole surrounded by a disk, the disk mass and the gravitational waveforms are about the same as the unmagnetized cases. Magnetic fields substantially affect the long-term, secular evolution of a hypermassive neutron star (driving ``delayed collapse'') and an accretion disk around a nascent black hole.

Post-Newtonian diagnosis of quasiequilibrium configurations of neutron star–neutron star and neutron star–black hole binaries

We use a post-Newtonian diagnostic tool to examine numerically generated quasiequilibrium initial data sets for nonspinning double neutron star and neutron star-black hole binary systems. The post-Newtonian equations include the effects of tidal interactions, parametrized by the compactness of the neutron stars and by suitable values of 'apsidal' constants, which measure the degree of distortion of stars subjected to tidal forces. We find that the post-Newtonian diagnostic agrees well with the double neutron star initial data, typically to better than half a percent except where tidal distortions are becoming extreme. We show that the differences could be interpreted as representing small residual eccentricity in the initial orbits. In comparing the diagnostic with preliminary numerical data on neutron star-black hole binaries, we find less agreement.

Eccentricity content of binary black hole initial data

Using a post-Newtonian diagnostic tool developed by Mora and Will, we examine numerically generated quasiequilibrium initial data sets that have been used in recently successful numerical evolutions of binary black holes through plunge, merger and ringdown. We show that a small but significant orbital eccentricity is required to match post-Newtonian and quasiequilibrium calculations. If this proves to be a real eccentricity, it could affect the fine details of the subsequent numerical evolutions and the predicted gravitational waveforms.

Can a combination of the conformal thin-sandwich and puncture methods yield binary black hole solutions in quasiequilibrium?

We consider combining two important methods for constructing quasiequilibrium initial data for binary black holes: the conformal thin-sandwich formalism and the puncture method. The former seeks to enforce stationarity in the conformal three-metric and the latter attempts to avoid internal boundaries, like minimal surfaces or apparent horizons. We show that these two methods make partially conflicting requirements on the boundary conditions that determine the time slices. In particular, it does not seem possible to construct slices that are quasistationary and that avoid physical singularities while simultaneously are connected by an everywhere positive lapse function, a condition which must be obtained if internal boundaries are to be avoided. Some relaxation of these conflicting requirements may yield a soluble system, but some of the advantages that were sought in combining these approaches will be lost.