81 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
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
Unambiguous determination of gravitational waveforms from binary black hole mergers
Gravitational radiation is properly defined only at future null infinity
(\scri), but in practice it is estimated from data calculated at a finite
radius. We have used characteristic extraction to calculate gravitational
radiation at \scri for the inspiral and merger of two equal mass non-spinning
black holes. Thus we have determined the first unambiguous merger waveforms for
this problem. The implementation is general purpose, and can be applied to
calculate the gravitational radiation, at \scri, given data at a finite
radius calculated in another computation.Comment: 4 pages, 3 figures, published versio
Neutrino-driven Turbulent Convection and Standing Accretion Shock Instability in Three-Dimensional Core-Collapse Supernovae
We conduct a series of numerical experiments into the nature of
three-dimensional (3D) hydrodynamics in the postbounce stalled-shock phase of
core-collapse supernovae using 3D general-relativistic hydrodynamic simulations
of a - progenitor star with a neutrino leakage/heating scheme. We
vary the strength of neutrino heating and find three cases of 3D dynamics: (1)
neutrino-driven convection, (2) initially neutrino-driven convection and
subsequent development of the standing accretion shock instability (SASI), (3)
SASI dominated evolution. This confirms previous 3D results of Hanke et al.
2013, ApJ 770, 66 and Couch & Connor 2014, ApJ 785, 123. We carry out
simulations with resolutions differing by up to a factor of 4 and
demonstrate that low resolution is artificially favorable for explosion in the
3D convection-dominated case, since it decreases the efficiency of energy
transport to small scales. Low resolution results in higher radial convective
fluxes of energy and enthalpy, more fully buoyant mass, and stronger neutrino
heating. In the SASI-dominated case, lower resolution damps SASI oscillations.
In the convection-dominated case, a quasi-stationary angular kinetic energy
spectrum develops in the heating layer. Like other 3D studies, we
find in the "inertial range," while theory and
local simulations argue for . We argue that
current 3D simulations do not resolve the inertial range of turbulence and are
affected by numerical viscosity up to the energy containing scale, creating a
"bottleneck" that prevents an efficient turbulent cascade.Comment: 24 pages, 15 figures. Accepted for publication in The Astrophysical
Journal. Added one figure and made minor modifications to text according to
suggestions from the refere
Notes on the integration of numerical relativity waveforms
A primary goal of numerical relativity is to provide estimates of the wave
strain, , from strong gravitational wave sources, to be used in detector
templates. The simulations, however, typically measure waves in terms of the
Weyl curvature component, . Assuming Bondi gauge, transforming to the
strain reduces to integration of twice in time. Integrations
performed in either the time or frequency domain, however, lead to secular
non-linear drifts in the resulting strain . These non-linear drifts are not
explained by the two unknown integration constants which can at most result in
linear drifts. We identify a number of fundamental difficulties which can arise
from integrating finite length, discretely sampled and noisy data streams.
These issues are an artifact of post-processing data. They are independent of
the characteristics of the original simulation, such as gauge or numerical
method used. We suggest, however, a simple procedure for integrating numerical
waveforms in the frequency domain, which is effective at strongly reducing
spurious secular non-linear drifts in the resulting strain.Comment: 23 pages, 10 figures, matches final published versio
Dynamics and gravitational wave signature of collapsar formation
We perform 3+1 general relativistic simulations of rotating core collapse in the context of the collapsar model for long gamma-ray bursts. We employ a realistic progenitor, rotation based on results of stellar evolution calculations, and a simplified equation of state. Our simulations track self-consistently collapse, bounce, the postbounce phase, black hole formation, and the subsequent early hyperaccretion phase. We extract gravitational waves from the spacetime curvature and identify a unique gravitational wave signature associated with the early phase of collapsar formatio
Dynamics and Gravitational Wave Signature of Collapsar Formation
We perform 3+1 general relativistic simulations of rotating core collapse in the context of the collapsar model for long gamma-ray bursts. We employ a realistic progenitor, rotation based on results of stellar evolution calculations, and a simplified equation of state. Our simulations track self-consistently collapse, bounce, the postbounce phase, black hole formation, and the subsequent early hyperaccretion phase. We extract gravitational waves from the spacetime curvature and identify a unique gravitational wave signature associated with the early phase of collapsar formation
Characteristic extraction in numerical relativity: binary black hole merger waveforms at null infinity
The accurate modeling of gravitational radiation is a key issue for
gravitational wave astronomy. As simulation codes reach higher accuracy,
systematic errors inherent in current numerical relativity wave-extraction
methods become evident, and may lead to a wrong astrophysical interpretation of
the data. In this paper, we give a detailed description of the
Cauchy-characteristic extraction technique applied to binary black hole
inspiral and merger evolutions to obtain gravitational waveforms that are
defined unambiguously, that is, at future null infinity. By this method we
remove finite-radius approximations and the need to extrapolate data from the
near zone. Further, we demonstrate that the method is free of gauge effects and
thus is affected only by numerical error. Various consistency checks reveal
that energy and angular momentum are conserved to high precision and agree very
well with extrapolated data. In addition, we revisit the computation of the
gravitational recoil and find that finite radius extrapolation very well
approximates the result at \scri. However, the (non-convergent) systematic
differences to extrapolated data are of the same order of magnitude as the
(convergent) discretisation error of the Cauchy evolution hence highlighting
the need for correct wave-extraction.Comment: 41 pages, 8 figures, 2 tables, added references, fixed typos. Version
matches published version
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