31 research outputs found
Extrapolating gravitational-wave data from numerical simulations
Two complementary techniques are developed for obtaining the asymptotic form
of gravitational-wave data at large radii from numerical simulations, in the
form of easily implemented algorithms. It is shown that, without extrapolation,
near-field effects produce errors in extracted waveforms that can significantly
affect LIGO data analysis. The extrapolation techniques are discussed in the
context of Newman--Penrose data applied to extrapolation of waveforms from an
equal-mass, nonspinning black-hole binary simulation. The results of the two
methods are shown to agree within error estimates. The various benefits and
deficiencies of the methods are discussed.Comment: Added missing references; refined data. Version accepted in Phys.
Rev.
Measuring orbital eccentricity and periastron advance in quasicircular black hole simulations
We compare different methods of computing the orbital eccentricity of quasicircular binary black-hole systems using the orbital variables and gravitational-wave phase and frequency. For eccentricities of about a per cent, most methods work satisfactorily. For small eccentricity, however, the gravitational-wave phase allows a particularly clean and reliable measurement of the eccentricity. Furthermore, we measure the decay of the orbital eccentricity during the inspiral and find reasonable agreement with post-Newtonian results. Finally, we measure the periastron advance of nonspinning binary black holes, and we compare them to post-Newtonian approximations. With the low uncertainty in the measurement of the periastron advance, we positively detect deviations between fully numerical simulations and post-Newtonian calculations
Reducing orbital eccentricity of precessing black-hole binaries
Building initial conditions for generic binary black-hole evolutions without
initial spurious eccentricity remains a challenge for numerical-relativity
simulations. This problem can be overcome by applying an eccentricity-removal
procedure which consists in evolving the binary for a couple of orbits,
estimating the eccentricity, and then correcting the initial conditions. The
presence of spins can complicate this procedure. As predicted by post-Newtonian
theory, spin-spin interactions and precession prevent the binary from moving
along an adiabatic sequence of spherical orbits, inducing oscillations in the
radial separation and in the orbital frequency. However, spin-induced
oscillations occur at approximately twice the orbital frequency, therefore they
can be distinguished from the initial spurious eccentricity, which occurs at
approximately the orbital frequency. We develop a new removal procedure based
on the derivative of the orbital frequency and find that it is successful in
reducing the eccentricity measured in the orbital frequency to less than 0.0001
when moderate spins are present. We test this new procedure using
numerical-relativity simulations of binary black holes with mass ratios 1.5 and
3, spin magnitude 0.5 and various spin orientations. The numerical simulations
exhibit spin-induced oscillations in the dynamics at approximately twice the
orbital frequency. Oscillations of similar frequency are also visible in the
gravitational-wave phase and frequency of the dominant mode.Comment: 17 pages, 11 figures, fixed typo
High-accuracy comparison of numerical relativity simulations with post-Newtonian expansions
Numerical simulations of 15 orbits of an equal-mass binary black hole system
are presented. Gravitational waveforms from these simulations, covering more
than 30 cycles and ending about 1.5 cycles before merger, are compared with
those from quasi-circular zero-spin post-Newtonian (PN) formulae. The
cumulative phase uncertainty of these comparisons is about 0.05 radians,
dominated by effects arising from the small residual spins of the black holes
and the small residual orbital eccentricity in the simulations. Matching
numerical results to PN waveforms early in the run yields excellent agreement
(within 0.05 radians) over the first cycles, thus validating the
numerical simulation and establishing a regime where PN theory is accurate. In
the last 15 cycles to merger, however, {\em generic} time-domain Taylor
approximants build up phase differences of several radians. But, apparently by
coincidence, one specific post-Newtonian approximant, TaylorT4 at 3.5PN order,
agrees much better with the numerical simulations, with accumulated phase
differences of less than 0.05 radians over the 30-cycle waveform.
Gravitational-wave amplitude comparisons are also done between numerical
simulations and post-Newtonian, and the agreement depends on the post-Newtonian
order of the amplitude expansion: the amplitude difference is about 6--7% for
zeroth order and becomes smaller for increasing order. A newly derived 3.0PN
amplitude correction improves agreement significantly ( amplitude
difference throughout most of the run, increasing to 4% near merger) over the
previously known 2.5PN amplitude terms.Comment: Updated to agree with published version (various minor
clarifications; added description of AH finder in Sec IIB; added discussion
of tidal heating in Sec VC
Periastron Advance in Spinning Black Hole Binaries: Gravitational Self-Force from Numerical Relativity
We study the general relativistic periastron advance in spinning black hole
binaries on quasi-circular orbits, with spins aligned or anti-aligned with the
orbital angular momentum, using numerical-relativity simulations, the
post-Newtonian approximation, and black hole perturbation theory. By imposing a
symmetry by exchange of the bodies' labels, we devise an improved version of
the perturbative result, and use it as the leading term of a new type of
expansion in powers of the symmetric mass ratio. This allows us to measure, for
the first time, the gravitational self-force effect on the periastron advance
of a non-spinning particle orbiting a Kerr black hole of mass M and spin S =
-0.5 M^2, down to separations of order 9M. Comparing the predictions of our
improved perturbative expansion with the exact results from numerical
simulations of equal-mass and equal-spin binaries, we find a remarkable
agreement over a wide range of spins and orbital separations.Comment: 18 pages, 12 figures; matches version to appear in Phys. Rev.
Ineffectiveness of Pad\'e resummation techniques in post-Newtonian approximations
We test the resummation techniques used in developing Pad\'e and Effective
One Body (EOB) waveforms for gravitational wave detection. Convergence tests
show that Pad\'e approximants of the gravitational wave energy flux do not
accelerate the convergence of the standard Taylor approximants even in the test
mass limit, and there is no reason why Pad\'e transformations should help in
estimating parameters better in data analysis. Moreover, adding a pole to the
flux seems unnecessary in the construction of these Pad\'e-approximated flux
formulas. Pad\'e approximants may be useful in suggesting the form of fitting
formulas. We compare a 15-orbit numerical waveform of the Caltech-Cornell group
to the suggested Pad\'e waveforms of Damour et al. in the equal mass,
nonspinning quasi-circular case. The comparison suggests that the Pad\'e
waveforms do not agree better with the numerical waveform than the standard
Taylor based waveforms. Based on this result, we design a simple EOB model by
modifiying the ET EOB model of Buonanno et al., using the Taylor series of the
flux with an unknown parameter at the fourth post-Newtonian order that we fit
for. This simple EOB model generates a waveform having a phase difference of
only 0.002 radians with the numerical waveform, much smaller than 0.04 radians
the phase uncertainty in the numerical data itself. An EOB Hamiltonian can make
use of a Pad\'e transformation in its construction, but this is the only place
Pad\'e transformations seem useful.Comment: 13 pages, 7 figures. added some reference
Measuring orbital eccentricity and periastron advance in quasicircular black hole simulations
We compare different methods of computing the orbital eccentricity of quasicircular binary black-hole systems using the orbital variables and gravitational-wave phase and frequency. For eccentricities of about a per cent, most methods work satisfactorily. For small eccentricity, however, the gravitational-wave phase allows a particularly clean and reliable measurement of the eccentricity. Furthermore, we measure the decay of the orbital eccentricity during the inspiral and find reasonable agreement with post-Newtonian results. Finally, we measure the periastron advance of nonspinning binary black holes, and we compare them to post-Newtonian approximations. With the low uncertainty in the measurement of the periastron advance, we positively detect deviations between fully numerical simulations and post-Newtonian calculations
Numerical simulations with a first order BSSN formulation of Einstein's field equations
We present a new fully first order strongly hyperbolic representation of the
BSSN formulation of Einstein's equations with optional constraint damping
terms. We describe the characteristic fields of the system, discuss its
hyperbolicity properties, and present two numerical implementations and
simulations: one using finite differences, adaptive mesh refinement and in
particular binary black holes, and another one using the discontinuous Galerkin
method in spherical symmetry. The results of this paper constitute a first step
in an effort to combine the robustness of BSSN evolutions with very high
accuracy numerical techniques, such as spectral collocation multi-domain or
discontinuous Galerkin methods.Comment: To appear in Physical Review
High-accuracy numerical simulation of black-hole binaries: Computation of the gravitational-wave energy flux and comparisons with post-Newtonian approximants
Expressions for the gravitational wave (GW) energy flux and center-of-mass
energy of a compact binary are integral building blocks of post-Newtonian (PN)
waveforms. In this paper, we compute the GW energy flux and GW frequency
derivative from a highly accurate numerical simulation of an equal-mass,
non-spinning black hole binary. We also estimate the (derivative of the)
center-of-mass energy from the simulation by assuming energy balance. We
compare these quantities with the predictions of various PN approximants
(adiabatic Taylor and Pade models; non-adiabatic effective-one-body (EOB)
models). We find that Pade summation of the energy flux does not accelerate the
convergence of the flux series; nevertheless, the Pade flux is markedly closer
to the numerical result for the whole range of the simulation (about 30 GW
cycles). Taylor and Pade models overestimate the increase in flux and frequency
derivative close to merger, whereas EOB models reproduce more faithfully the
shape of and are closer to the numerical flux, frequency derivative and
derivative of energy. We also compare the GW phase of the numerical simulation
with Pade and EOB models. Matching numerical and untuned 3.5 PN order
waveforms, we find that the phase difference accumulated until
is -0.12 radians for Pade approximants, and 0.50 (0.45) radians for an EOB
approximant with Keplerian (non-Keplerian) flux. We fit free parameters within
the EOB models to minimize the phase difference, and confirm degeneracies among
these parameters. By tuning pseudo 4PN order coefficients in the radial
potential or in the flux, or, if present, the location of the pole in the flux,
we find that the accumulated phase difference can be reduced - if desired - to
much less than the estimated numerical phase error (0.02 radians).Comment: modified non-Keplerian flux improves agreement with NR; updated error
bound of NR-PN comparison; added ref