61 research outputs found
Probing the Binary Black Hole Merger Regime with Scalar Perturbations
We present results obtained by scattering a scalar field off the curved
background of a coalescing binary black hole system. A massless scalar field is
evolved on a set of fixed backgrounds, each provided by a spatial hypersurface
generated numerically during a binary black hole merger. We show that the
scalar field scattered from the merger region exhibits quasinormal ringing once
a common apparent horizon surrounds the two black holes. This occurs earlier
than the onset of the perturbative regime as measured by the start of the
quasinormal ringing in the gravitational waveforms. We also use the scalar
quasinormal frequencies to associate a mass and a spin with each hypersurface,
and observe the compatibility of this measure with the horizon mass and spin
computed from the dynamical horizon framework.Comment: 10 Pages and 6 figure
Numerical stability of a new conformal-traceless 3+1 formulation of the Einstein equation
There is strong evidence indicating that the particular form used to recast
the Einstein equation as a 3+1 set of evolution equations has a fundamental
impact on the stability properties of numerical evolutions involving black
holes and/or neutron stars. Presently, the longest lived evolutions have been
obtained using a parametrized hyperbolic system developed by Kidder, Scheel and
Teukolsky or a conformal-traceless system introduced by Baumgarte, Shapiro,
Shibata and Nakamura. We present a new conformal-traceless system. While this
new system has some elements in common with the
Baumgarte-Shapiro-Shibata-Nakamura system, it differs in both the type of
conformal transformations and how the non-linear terms involving the extrinsic
curvature are handled. We show results from 3D numerical evolutions of a
single, non-rotating black hole in which we demonstrate that this new system
yields a significant improvement in the life-time of the simulations.Comment: 7 pages, 2 figure
Binary Black Holes: Spin Dynamics and Gravitational Recoil
We present a study of spinning black hole binaries focusing on the spin
dynamics of the individual black holes as well as on the gravitational recoil
acquired by the black hole produced by the merger. We consider two series of
initial spin orientations away from the binary orbital plane. In one of the
series, the spins are anti-aligned; for the second series, one of the spins
points away from the binary along the line separating the black holes. We find
a remarkable agreement between the spin dynamics predicted at 2nd
post-Newtonian order and those from numerical relativity. For each
configuration, we compute the kick of the final black hole. We use the kick
estimates from the series with anti-aligned spins to fit the parameters in the
\KKF{,} and verify that the recoil along the direction of the orbital angular
momentum is and on the orbital plane ,
with the angle between the spin directions and the orbital angular
momentum. We also find that the black hole spins can be well estimated by
evaluating the isolated horizon spin on spheres of constant coordinate radius.Comment: 15 pages, 10 figures, replaced with version accepted for publication
in PR
Gravitational recoil from spinning binary black hole mergers
The inspiral and merger of binary black holes will likely involve black holes
with both unequal masses and arbitrary spins. The gravitational radiation
emitted by these binaries will carry angular as well as linear momentum. A net
flux of emitted linear momentum implies that the black hole produced by the
merger will experience a recoil or kick. Previous studies have focused on the
recoil velocity from unequal mass, non-spinning binaries. We present results
from simulations of equal mass but spinning black hole binaries and show how a
significant gravitational recoil can also be obtained in these situations. We
consider the case of black holes with opposite spins of magnitude
aligned/anti-aligned with the orbital angular momentum, with the
dimensionless spin parameters of the individual holes. For the initial setups
under consideration, we find a recoil velocity of V = 475 \KMS a.
Supermassive black hole mergers producing kicks of this magnitude could result
in the ejection from the cores of dwarf galaxies of the final hole produced by
the collision.Comment: 8 pages, 8 figures, replaced with version accepted for publication in
Ap
Approximate Analytical Solutions to the Initial Data Problem of Black Hole Binary Systems
We present approximate analytical solutions to the Hamiltonian and momentum
constraint equations, corresponding to systems composed of two black holes with
arbitrary linear and angular momentum. The analytical nature of these initial
data solutions makes them easier to implement in numerical evolutions than the
traditional numerical approach of solving the elliptic equations derived from
the Einstein constraints. Although in general the problem of setting up initial
conditions for black hole binary simulations is complicated by the presence of
singularities, we show that the methods presented in this work provide initial
data with and norms of violation of the constraint equations
falling below those of the truncation error (residual error due to
discretization) present in finite difference codes for the range of grid
resolutions currently used. Thus, these data sets are suitable for use in
evolution codes. Detailed results are presented for the case of a head-on
collision of two equal-mass M black holes with specific angular momentum 0.5M
at an initial separation of 10M. A straightforward superposition method yields
data adequate for resolutions of , and an "attenuated" superposition
yields data usable to resolutions at least as fine as . In addition, the
attenuated approximate data may be more tractable in a full (computational)
exact solution to the initial value problem.Comment: 6 pages, 5 postscript figures. Minor changes and some points
clarified. Accepted for publication in Phys. Rev.
Constant Crunch Coordinates for Black Hole Simulations
We reinvestigate the utility of time-independent constant mean curvature
foliations for the numerical simulation of a single spherically-symmetric black
hole. Each spacelike hypersurface of such a foliation is endowed with the same
constant value of the trace of the extrinsic curvature tensor, . Of the
three families of -constant surfaces possible (classified according to their
asymptotic behaviors), we single out a sub-family of singularity-avoiding
surfaces that may be particularly useful, and provide an analytic expression
for the closest approach such surfaces make to the singularity. We then utilize
a non-zero shift to yield families of -constant surfaces which (1) avoid the
black hole singularity, and thus the need to excise the singularity, (2) are
asymptotically null, aiding in gravity wave extraction, (3) cover the
physically relevant part of the spacetime, (4) are well behaved (regular)
across the horizon, and (5) are static under evolution, and therefore have no
``grid stretching/sucking'' pathologies. Preliminary numerical runs demonstrate
that we can stably evolve a single spherically-symmetric static black hole
using this foliation. We wish to emphasize that this coordinatization produces
-constant surfaces for a single black hole spacetime that are regular,
static and stable throughout their evolution.Comment: 14 pages, 9 figures. Formatted using Revtex4. To appear Phys. Rev. D
2001, Added numerical results, updated references and revised figure
Superkicks in Hyperbolic Encounters of Binary Black Holes
Generic inspirals and mergers of binary black holes produce beamed emission
of gravitational radiation that can lead to a gravitational recoil or kick of
the final black hole. The kick velocity depends on the mass ratio and spins of
the binary as well as on the dynamics of the binary configuration. Studies have
focused so far on the most astrophysically relevant configuration of
quasi-circular inspirals, for which kicks as large as 3,300 km/s have been
found. We present the first study of gravitational recoil in hyperbolic
encounters. Contrary to quasi-circular configurations, in which the beamed
radiation tends to average during the inspiral, radiation from hyperbolic
encounters is plunge dominated, resulting in an enhancement of preferential
beaming. As a consequence, it is possible to achieve kick velocities as large
as 10,000 km/s.Comment: 4 pages, 5 figures, 1 tabl
Analysis of ``Gauge Modes'' in Linearized Relativity
By writing the complete set of (ADM) equations for linearized waves,
we are able to demonstrate the properties of the initial data and of the
evolution of a wave problem set by Alcubierre and Schutz. We show that the
gauge modes and constraint error modes arise in a straightforward way in the
analysis, and are of a form which will be controlled in any well specified
convergent computational discretization of the differential equations.Comment: 11pages LaTe
Introduction to Isolated Horizons in Numerical Relativity
We present a coordinate-independent method for extracting mass (M) and
angular momentum (J) of a black hole in numerical simulations. This method,
based on the isolated horizon framework, is applicable both at late times when
the black hole has reached equilibrium, and at early times when the black holes
are widely separated. We show how J and M can be determined in numerical
simulations in terms of only those quantities which are intrinsic to the
apparent horizon. We also present a numerical method for finding the rotational
symmetry vector field (required to calculate J) on the horizon.Comment: 14 pages, revtex4, 7 figures. Final PRD versio
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