33 research outputs found
Spin-orbit interactions in black-hole binaries
We perform numerical simulations of black-hole binaries to study the exchange
of spin and orbital angular momentum during the last, highly nonlinear, stages
of the coalescence process. To calculate the transfer of angular momentum from
orbital to spin, we start with two quasi-circular configurations, one with
initially non-spinning black holes, the other with corotating black holes. In
both cases the binaries complete almost two orbits before merging. We find
that, during these last orbits, the specific spin (a/m) of each horizon
increases by only 0.012 for the initially non-spinning configuration, and by
only 0.006 for the initially corotating configuration. By contrast, the
corotation value for the specific spin should increase from 0.1 at the initial
proper separation of 10M to 0.33 when the proper separation is 5M. Thus the
spin-orbit coupling is far too weak to tidally lock the binary to a corotating
state during the late-inspiral phase. We also study the converse transfer from
spin into orbital motion. In this case, we start the simulations with parallel,
highly-spinning non-boosted black holes. As the collision proceeds, the system
acquires a non-head-on orbital motion, due to spin-orbit coupling, that leads
to the radiation of angular momentum. We are able to accurately measure the
energy and angular momentum losses and model their dependence on the initial
spins.Comment: This version corrects two typos in Eq (4) and Table I present in the
published versio
The last orbit of binary black holes
We have used our new technique for fully numerical evolutions of orbiting
black-hole binaries without excision to model the last orbit and merger of an
equal-mass black-hole system. We track the trajectories of the individual
apparent horizons and find that the binary completed approximately one and a
third orbits before forming a common horizon. Upon calculating the complete
gravitational radiation waveform, horizon mass, and spin, we find that the
binary radiated 3.2% of its mass and 24% of its angular momentum. The early
part of the waveform, after a relatively short initial burst of spurious
radiation, is oscillatory with increasing amplitude and frequency, as expected
from orbital motion. The waveform then transitions to a typical `plunge'
waveform; i.e. a rapid rise in amplitude followed by quasinormal ringing. The
plunge part of the waveform is remarkably similar to the waveform from the
previously studied `ISCO' configuration. We anticipate that the plunge
waveform, when starting from quasicircular orbits, has a generic shape that is
essentially independent of the initial separation of the binary.Comment: 5 pages, 5 figures, revtex
Accurate Evolutions of Orbiting Black-Hole Binaries Without Excision
We present a new algorithm for evolving orbiting black-hole binaries that
does not require excision or a corotating shift. Our algorithm is based on a
novel technique to handle the singular puncture conformal factor. This system,
based on the BSSN formulation of Einstein's equations, when used with a
`pre-collapsed' initial lapse, is non-singular at the start of the evolution,
and remains non-singular and stable provided that a good choice is made for the
gauge. As a test case, we use this technique to fully evolve orbiting
black-hole binaries from near the Innermost Stable Circular Orbit (ISCO)
regime. We show fourth order convergence of waveforms and compute the radiated
gravitational energy and angular momentum from the plunge. These results are in
good agreement with those predicted by the Lazarus approach.Comment: 4 pages, revtex4, 3 figs, references added, typos fixe
A time-domain fourth-order-convergent numerical algorithm to integrate black hole perturbations in the extreme-mass-ratio limit
We obtain a fourth order accurate numerical algorithm to integrate the
Zerilli and Regge-Wheeler wave equations, describing perturbations of
nonrotating black holes, with source terms due to an orbiting particle. Those
source terms contain the Dirac's delta and its first derivative. We also
re-derive the source of the Zerilli and Regge-Wheeler equations for more
convenient definitions of the waveforms, that allow direct metric
reconstruction (in the Regge-Wheeler gauge).Comment: 30 pages, 12 figure
On computations of angular momentum and its flux in numerical relativity
The purpose of this note is to point out ambiguities that appear in the
calculation of angular momentum and its radiated counterpart when some simple
formulae are used to compute them. We illustrate, in two simple different
examples, how incorrect results can be obtained with them. Additionally, we
discuss the magnitude of possible errors in well known situations.Comment: 8 pages. Minor improvements . To appear in Class. Quantum Gra
Accurate black hole evolutions by fourth-order numerical relativity
We present techniques for successfully performing numerical relativity
simulations of binary black holes with fourth-order accuracy. Our simulations
are based on a new coding framework which currently supports higher order
finite differencing for the BSSN formulation of Einstein's equations, but which
is designed to be readily applicable to a broad class of formulations. We apply
our techniques to a standard set of numerical relativity test problems,
demonstrating the fourth-order accuracy of the solutions. Finally we apply our
approach to binary black hole head-on collisions, calculating the waveforms of
gravitational radiation generated and demonstrating significant improvements in
waveform accuracy over second-order methods with typically achievable numerical
resolution.Comment: 17 pages, 25 figure
Momentum constraint relaxation
Full relativistic simulations in three dimensions invariably develop runaway
modes that grow exponentially and are accompanied by violations of the
Hamiltonian and momentum constraints. Recently, we introduced a numerical
method (Hamiltonian relaxation) that greatly reduces the Hamiltonian constraint
violation and helps improve the quality of the numerical model. We present here
a method that controls the violation of the momentum constraint. The method is
based on the addition of a longitudinal component to the traceless extrinsic
curvature generated by a vector potential w_i, as outlined by York. The
components of w_i are relaxed to solve approximately the momentum constraint
equations, pushing slowly the evolution toward the space of solutions of the
constraint equations. We test this method with simulations of binary neutron
stars in circular orbits and show that effectively controls the growth of the
aforementioned violations. We also show that a full numerical enforcement of
the constraints, as opposed to the gentle correction of the momentum relaxation
scheme, results in the development of instabilities that stop the runs shortly.Comment: 17 pages, 10 figures. New numerical tests and references added. More
detailed description of the algorithms are provided. Final published versio
Toward a dynamical shift condition for unequal mass black hole binary simulations
Moving puncture simulations of black hole binaries rely on a specific gauge
choice that leads to approximately stationary coordinates near each black hole.
Part of the shift condition is a damping parameter, which has to be properly
chosen for stable evolutions. However, a constant damping parameter does not
account for the difference in mass in unequal mass binaries. We introduce a
position dependent shift damping that addresses this problem. Although the
coordinates change, the changes in the extracted gravitational waves are small.Comment: 15 pages, submitted to CQG for NRDA 2009 conference proceeding
Gravitational perturbations of Schwarzschild spacetime at null infinity and the hyperboloidal initial value problem
We study gravitational perturbations of Schwarzschild spacetime by solving a
hyperboloidal initial value problem for the Bardeen-Press equation.
Compactification along hyperboloidal surfaces in a scri-fixing gauge allows us
to have access to the gravitational waveform at null infinity in a general
setup. We argue that this hyperboloidal approach leads to a more accurate and
efficient calculation of the radiation signal than the common approach where a
timelike outer boundary is introduced. The method can be generalized to study
perturbations of Kerr spacetime using the Teukolsky equation.Comment: 14 pages, 9 figure