54 research outputs found
The Asymptotic Falloff of Local Waveform Measurements in Numerical Relativity
We examine current numerical relativity computations of gravitational waves,
which typically determine the asymptotic waves at infinity by extrapolation
from finite (small) radii. Using simulations of a black hole binary with
accurate wave extraction at , we show that extrapolations from the
near-zone are self-consistent in approximating measurements at this radius,
although with a somewhat reduced accuracy. We verify that is the
dominant asymptotic contribution to the gravitational energy (as required by
the peeling theorem) but point out that gauge effects may complicate the
interpretation of the other Weyl components
Energetics and phasing of nonprecessing spinning coalescing black hole binaries
We present an improved numerical relativity (NR) calibration of the new
effective-one-body (EOB) model for coalescing non precessing spinning black
hole binaries recently introduced by Damour and Nagar [Physical Review D 90,
044018 (2014)]. We do so by comparing the EOB predictions to both the phasing
and the energetics provided by two independent sets of NR data covering mass
ratios and dimensionless spin range . One set of data is a subset of the Simulating eXtreme Spacetimes (SXS)
catalog of public waveforms; the other set consists of new simulations obtained
with the Llama code plus Cauchy Characteristic Evolution. We present the first
systematic computation of the gauge-invariant relation between the binding
energy and the total angular momentum, , for a large sample of,
spin-aligned, SXS and Llama data. The dynamics of the EOB model presented here
involves only two free functional parameters, one () entering the
non spinning sector, as a 5PN effective correction to the interaction
potential, and one ( in the spinning sector,
as an effective next-to-next-to-next-to-leading order correction to the
spin-orbit coupling. These parameters are determined (together with a third
functional parameter entering the waveform) by
comparing the EOB phasing with the SXS phasing, the consistency of the
energetics being checked afterwards. The quality of the analytical model for
gravitational wave data analysis purposes is assessed by computing the EOB/NR
faithfulness. Over the NR data sample and when varying the total mass between
20 and 200~ the EOB/NR unfaithfulness (integrated over the NR
frequency range) is found to vary between and with a
median value of .Comment: 26 pages, 27 figures, results improved with respect to first versio
Initial data transients in binary black hole evolutions
We describe a method for initializing characteristic evolutions of the
Einstein equations using a linearized solution corresponding to purely outgoing
radiation. This allows for a more consistent application of the characteristic
(null cone) techniques for invariantly determining the gravitational radiation
content of numerical simulations. In addition, we are able to identify the {\em
ingoing} radiation contained in the characteristic initial data, as well as in
the initial data of the 3+1 simulation. We find that each component leads to a
small but long lasting (several hundred mass scales) transient in the measured
outgoing gravitational waves.Comment: 18 pages, 4 figure
General relativistic null-cone evolutions with a high-order scheme
We present a high-order scheme for solving the full non-linear Einstein
equations on characteristic null hypersurfaces using the framework established
by Bondi and Sachs. This formalism allows asymptotically flat spaces to be
represented on a finite, compactified grid, and is thus ideal for far-field
studies of gravitational radiation. We have designed an algorithm based on
4th-order radial integration and finite differencing, and a spectral
representation of angular components. The scheme can offer significantly more
accuracy with relatively low computational cost compared to previous methods as
a result of the higher-order discretization. Based on a newly implemented code,
we show that the new numerical scheme remains stable and is convergent at the
expected order of accuracy.Comment: 24 pages, 3 figure
The final spin from the coalescence of aligned-spin black-hole binaries
Determining the final spin of a black-hole (BH) binary is a question of key
importance in astrophysics. Modelling this quantity in general is made
difficult by the fact that it depends on the 7-dimensional space of parameters
characterizing the two initial black holes. However, in special cases, when
symmetries can be exploited, the description can become simpler. For black-hole
binaries with unequal masses but with equal spins which are aligned with the
orbital angular momentum, we show that the use of recent simulations and basic
but exact constraints derived from the extreme mass-ratio limit allow to model
this quantity with a simple analytic expression. Despite the simple dependence,
the expression models very accurately all of the available estimates, with
errors of a couple of percent at most. We also discuss how to use the fit to
predict when a Schwarzschild BH is produced by the merger of two spinning BHs,
when the total angular momentum of the spacetime ``flips'' sign, or under what
conditions the final BH is ``spun-up'' by the merger. Finally, suggest an
extension of the fit to include unequal-spin binaries, thus potentially
providing a complete description of the final spin from the coalescence of
generic black-hole binaries with spins aligned to the orbital angular momentum.Comment: Version matching the published one; small changes throughout to fit
space constraints; corrects error in vii) about spin-up/dow
Spin Diagrams for Equal-Mass Black-Hole Binaries with Aligned Spins
Binary black-hole systems with spins aligned with the orbital angular
momentum are of special interest as they may be the preferred end-state of the
inspiral of generic supermassive binary black-hole systems. In view of this, we
have computed the inspiral and merger of a large set of binary systems of
equal-mass black holes with spins aligned with the orbital angular momentum but
otherwise arbitrary. By least-square fitting the results of these simulations
we have constructed two "spin diagrams" which provide straightforward
information about the recoil velocity |v_kick| and the final black-hole spin
a_fin in terms of the dimensionless spins a_1 and a_2 of the two initial black
holes. Overall they suggest a maximum recoil velocity of |v_kick|=441.94 km/s,
and minimum and maximum final spins a_fin=0.3471 and a_fin=0.9591,
respectively.Comment: 4 pages, 3 figs; small changes matching published versio
Gravitational-wave detectability of equal-mass black-hole binaries with aligned spins
Binary black-hole systems with spins aligned or anti-aligned to the orbital
angular momentum provide the natural ground to start detailed studies of the
influence of strong-field spin effects on gravitational wave observations of
coalescing binaries. Furthermore, such systems may be the preferred end-state
of the inspiral of generic supermassive binary black-hole systems. In view of
this, we have computed the inspiral and merger of a large set of binary systems
of equal-mass black holes with spins parallel to the orbital angular momentum
but otherwise arbitrary. Our attention is particularly focused on the
gravitational-wave emission so as to quantify how much spin effects contribute
to the signal-to-noise ratio, to the horizon distances, and to the relative
event rates for the representative ranges in masses and detectors. As expected,
the signal-to-noise ratio increases with the projection of the total black hole
spin in the direction of the orbital momentum. We find that equal-spin binaries
with maximum spin aligned with the orbital angular momentum are more than
"three times as loud" as the corresponding binaries with anti-aligned spins,
thus corresponding to event rates up to 30 times larger. We also consider the
waveform mismatch between the different spinning configurations and find that,
within our numerical accuracy, binaries with opposite spins S_1=-S_2 cannot be
distinguished whereas binaries with spin S_1=S_2 have clearly distinct
gravitational-wave emissions. Finally, we derive a simple expression for the
energy radiated in gravitational waves and find that the binaries always have
efficiencies E_rad/M > 3.6%, which can become as large as E_rad/M = 10% for
maximally spinning binaries with spins aligned with the orbital angular
momentum.Comment: 18 pages, 11 figures, matches published versio
Comparing Gravitational Waveform Extrapolation to Cauchy-Characteristic Extraction in Binary Black Hole Simulations
We extract gravitational waveforms from numerical simulations of black hole
binaries computed using the Spectral Einstein Code. We compare two extraction
methods: direct construction of the Newman-Penrose (NP) scalar at a
finite distance from the source and Cauchy-characteristic extraction (CCE). The
direct NP approach is simpler than CCE, but NP waveforms can be contaminated by
near-zone effects---unless the waves are extracted at several distances from
the source and extrapolated to infinity. Even then, the resulting waveforms can
in principle be contaminated by gauge effects. In contrast, CCE directly
provides, by construction, gauge-invariant waveforms at future null infinity.
We verify the gauge invariance of CCE by running the same physical simulation
using two different gauge conditions. We find that these two gauge conditions
produce the same CCE waveforms but show differences in extrapolated-
waveforms. We examine data from several different binary configurations and
measure the dominant sources of error in the extrapolated- and CCE
waveforms. In some cases, we find that NP waveforms extrapolated to infinity
agree with the corresponding CCE waveforms to within the estimated error bars.
However, we find that in other cases extrapolated and CCE waveforms disagree,
most notably for "memory" modes.Comment: 26 pages, 20 figure
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