Computing the Complete Gravitational Wavetrain from Relativistic Binary Inspiral

We present a new method for generating the nonlinear gravitational wavetrain from the late inspiral (pre-coalescence) phase of a binary neutron star system by means of a numerical evolution calculation in full general relativity. In a prototype calculation, we produce 214 wave cycles from corotating polytropes, representing the final part of the inspiral phase prior to reaching the ISCO. Our method is based on the inequality that the orbital decay timescale due to gravitational radiation is much longer than an orbital period and the approximation that gravitational radiation has little effect on the structure of the stars. We employ quasi-equilibrium sequences of binaries in circular orbit for the matter source in our field evolution code. We compute the gravity-wave energy flux, and, from this, the inspiral rate, at a discrete set of binary separations. From these data, we construct the gravitational waveform as a continuous wavetrain. Finally, we discuss the limitations of our current calculation, planned improvements, and potential applications of our method to other inspiral scenarios.Comment: 4 pages, 4 figure

The Moment of Inertia of the Binary Pulsar J0737-3039A: Constraining the Nuclear Equation of State

We construct numerical models of the newly discovered binary pulsar J0737-3039A, both with a fully relativistic, uniformly rotating, equilibrium code that handles arbitrary spins and in the relativistic, slow-rotation approximation. We compare results for a representative sample of viable nuclear equations of state (EOS) that span three, qualitatively different, classes of models for the description of nuclear matter. A future dynamical measurement of the neutron star's moment of inertia from pulsar timing data will impose significant constraints on the nuclear EOS. Even a moderately accurate measurement (<~ 10 %) may be able to rule out some of these competing classes. Using the measured mass, spin and moment of inertia to identify the optimal model computed from different EOSs, one can determine the pulsar's radius.Comment: 4 pages, ApJL in pres

Black hole puncture initial data with realistic gravitational wave content

We present improved post-Newtonian-inspired initial data for non-spinning black-hole binaries, suitable for numerical evolution with punctures. We revisit the work of Tichy et al. [W. Tichy, B. Bruegmann, M. Campanelli, and P. Diener, Phys. Rev. D 67, 064008 (2003)], explicitly calculating the remaining integral terms. These terms improve accuracy in the far zone and, for the first time, include realistic gravitational waves in the initial data. We investigate the behavior of these data both at the center of mass and in the far zone, demonstrating agreement of the transverse-traceless parts of the new metric with quadrupole-approximation waveforms. These data can be used for numerical evolutions, enabling a direct connection between the merger waveforms and the post-Newtonian inspiral waveforms.Comment: 13 pages, 7 figures; replaced with published versio

Learning about compact binary merger: the interplay between numerical relativity and gravitational-wave astronomy

Activities in data analysis and numerical simulation of gravitational waves have to date largely proceeded independently. In this work we study how waveforms obtained from numerical simulations could be effectively used within the data analysis effort to search for gravitational waves from black hole binaries. We propose measures to quantify the accuracy of numerical waveforms for the purpose of data analysis and study how sensitive the analysis is to errors in the waveforms. We estimate that ~100 templates (and ~10 simulations with different mass ratios) are needed to detect waves from non-spinning binary black holes with total masses in the range 100 Msun < M < 400 Msun using initial LIGO. Of course, many more simulation runs will be needed to confirm that the correct physics is captured in the numerical evolutions. From this perspective, we also discuss sources of systematic errors in numerical waveform extraction and provide order of magnitude estimates for the computational cost of simulations that could be used to estimate the cost of parameter space surveys. Finally, we discuss what information from near-future numerical simulations of compact binary systems would be most useful for enhancing the detectability of such events with contemporary gravitational wave detectors and emphasize the role of numerical simulations for the interpretation of eventual gravitational-wave observations.Comment: 19 pages, 12 figure

Collapse of a Magnetized Star to a Black Hole

We study of the collapse of a magnetized spherical star to a black hole in general relativity theory. The matter and gravitational fields are described by the exact Oppenheimer-Snyder solution for the collapse of a spherical, homogeneous dust ball. We adopt a ``dynamical Cowling approximation'' whereby the matter and the geometry (metric), while highly dynamical, are unaffected by the electromagnetic fields. The matter is assumed to be perfectly conducting and threaded by a dipole magnetic field at the onset of collapse. We determine the subsequent evolution of the magnetic and electric fields without approximation; the fields are determined analytically in the matter interior and numerically in the vacuum exterior. We apply junction conditions to match the electromagnetic fields across the stellar surface. We use this model to experiment with several coordinate gauge choices for handling spacetime evolution characterized by the formation of a black hole and the associated appearance of singularities. These choices range from ``singularity avoiding'' time coordinates to ``horizon penetrating'' time coordinates accompanied by black hole excision. The later choice enables us to integrate the electromagnetic fields arbitrarily far into the future. At late times the longitudinal magnetic field in the exterior has been transformed into a transverse electromagnetic wave; part of the electromagnetic radiation is captured by the hole and the rest propagates outward to large distances. The solution we present for our simple scenario can be used to test codes designed to treat more general evolutions of relativistic MHD fluids flowing in strong gravitational fields in dynamical spacetimes.Comment: 22 pages, 12 figures; scheduled for March 10 issue of Ap

Why Solve the Hamiltonian Constraint in Numerical Relativity?

The indefinite sign of the Hamiltonian constraint means that solutions to Einstein's equations must achieve a delicate balance--often among numerically large terms that nearly cancel. If numerical errors cause a violation of the Hamiltonian constraint, the failure of the delicate balance could lead to qualitatively wrong behavior rather than just decreased accuracy. This issue is different from instabilities caused by constraint-violating modes. Examples of stable numerical simulations of collapsing cosmological spacetimes exhibiting local mixmaster dynamics with and without Hamiltonian constraint enforcement are presented.Comment: Submitted to a volume in honor of Michael P. Ryan, Jr. Based on talk given at GR1

Head-on collisions of binary white dwarf--neutron stars: Simulations in full general relativity

We simulate head-on collisions from rest at large separation of binary white dwarf -- neutron stars (WDNSs) in full general relativity. Our study serves as a prelude to our analysis of the circular binary WDNS problem. We focus on compact binaries whose total mass exceeds the maximum mass that a cold degenerate star can support, and our goal is to determine the fate of such systems. A fully general relativistic hydrodynamic computation of a realistic WDNS head-on collision is prohibitive due to the large range of dynamical time scales and length scales involved. For this reason, we construct an equation of state (EOS) which captures the main physical features of NSs while, at the same time, scales down the size of WDs. We call these scaled-down WD models "pseudo-WDs (pWDs)". Using pWDs, we can study these systems via a sequence of simulations where the size of the pWD gradually increases toward the realistic case. We perform two sets of simulations; One set studies the effects of the NS mass on the final outcome, when the pWD is kept fixed. The other set studies the effect of the pWD compaction on the final outcome, when the pWD mass and the NS are kept fixed. All simulations show that 14%-18% of the initial total rest mass escapes to infinity. All remnant masses still exceed the maximum rest mass that our cold EOS can support (1.92 solar masses), but no case leads to prompt collapse to a black hole. This outcome arises because the final configurations are hot. All cases settle into spherical, quasiequilibrium configurations consisting of a cold NS core surrounded by a hot mantle, resembling Thorne-Zytkow objects. Extrapolating our results to realistic WD compactions, we predict that the likely outcome of a head-on collision of a realistic, massive WDNS system will be the formation of a quasiequilibrium Thorne-Zytkow-like object.Comment: 24 pages, 14 figures, matches PRD published version, tests of HRSC schemes with piecewise polytropes adde

Scattering of particles by neutron stars: Time-evolutions for axial perturbations

The excitation of the axial quasi-normal modes of a relativistic star by scattered particles is studied by evolving the time dependent perturbation equations. This work is the first step towards the understanding of more complicated perturbative processes, like the capture or the scattering of particles by rotating stars. In addition, it may serve as a test for the results of the full nonlinear evolution of binary systems.Comment: 7 pages, 5 figures, Phys. Rev. D in pres

Binary-induced collapse of a compact, collisionless cluster

We improve and extend Shapiro's model of a relativistic, compact object which is stable in isolation but is driven dynamically unstable by the tidal field of a binary companion. Our compact object consists of a dense swarm of test particles moving in randomly-oriented, initially circular, relativistic orbits about a nonrotating black hole. The binary companion is a distant, slowly inspiraling point mass. The tidal field of the companion is treated as a small perturbation on the background Schwarzschild geometry near the hole; the resulting metric is determined by solving the perturbation equations of Regge and Wheeler and Zerilli in the quasi-static limit. The perturbed spacetime supports Bekenstein's conjecture that the horizon area of a near-equilibrium black hole is an adiabatic invariant. We follow the evolution of the system and confirm that gravitational collapse can be induced in a compact collisionless cluster by the tidal field of a binary companion.Comment: 9 Latex pages, 14 postscript figure

Strange matter in rotating compact stars

We have constructed equations of state involving various exotic forms of matter with large strangeness fraction such as hyperon matter, Bose-Einstein condensates of antikaons and strange quark matter. First order phase transitions from hadronic to antikaon condensed and quark matter are considered here. The hadronic phase is described by the relativistic field theoretical model. Later those equations of state are exploited to investigate models of uniformly rotating compact stars. The effect of rotation on the third family branch for the equation of state involving only antikaon condensates is investigated. We also discuss the back bending phenomenon due to a first order phase transition from $K^-$ condensed to quark matter.Comment: 8 pages, 4 figures; Plenary talk delivered at Strangeness in Quark Matter (SQM) 2004 held in Cape Town, South Africa from 15-20 September; Accepted for publication in the proceedings in Journal of Physics