Transformations of asymptotic gravitational-wave data

Boyle, Michael

doi:10.1103/physrevd.93.084031

Cited by 107 publications

(156 citation statements)

References 62 publications

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“…We have verified that our choice of extrapolation order does not significantly affect our results. We have also checked that corrections to the wave modes [90] to account for a small drift in the coordinates of the center of mass have a negligible effect on our results; hence, we present here the uncorrected results.…”

Section: B Simulations Using Pseudospectral Excision Methodsmentioning

confidence: 99%

Targeted numerical simulations of binary black holes for GW170104

Healy¹,

Lange²,

O’Shaughnessy³

et al. 2018

Phys. Rev. D

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In response to LIGO's observation of GW170104, we performed a series of full numerical simulations of binary black holes, each designed to replicate likely realizations of its dynamics and radiation. These simulations have been performed at multiple resolutions and with two independent techniques to solve Einstein's equations. For the nonprecessing and precessing simulations, we demonstrate the two techniques agree mode by mode, at a precision substantially in excess of statistical uncertainties in current LIGO's observations. Conversely, we demonstrate our full numerical solutions contain information which is not accurately captured with the approximate phenomenological models commonly used to infer compact binary parameters. To quantify the impact of these differences on parameter inference for GW170104 specifically, we compare the predictions of our simulations and these approximate models to LIGO's observations of GW170104.

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Section: B Simulations Using Pseudospectral Excision Methodsmentioning

confidence: 99%

Targeted numerical simulations of binary black holes for GW170104

Healy¹,

Lange²,

O’Shaughnessy³

et al. 2018

Phys. Rev. D

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“…For example, quaternions are a special case of the spacetime algebra 45 which allows us to treat boosts and rotations in the same language. This approach was previously used to transform SWSHs under boosts 14 by projecting the spacetime algebra down to quaternion components, and evaluating the SWSHs as functions of those quaternions. This is one example of the power and simplifications that result from defining SWSFs as functions of quaternions.…”

Section: Discussionmentioning

confidence: 99%

“…This approach was developed, though not explored in depth, in previous papers. 13,14 A similar approach was described in depth by Straumann,15 who chose to define SWSHs as functions from SO(3) to a two-dimensional vector space. SO(3) maps to S 2 by rotating the z axis to any point on the sphere (as discussed further in Sec.…”

Section: A Previous Workmentioning

confidence: 99%

“…Both h and a [Eqs. (14) and (18)] involve R quadratically, meaning that R and −R map to the same elements under both maps. Since we have constructed these maps as rotations of vectors, the interpretation is clear: the Spin(3) group we have used is implicitly projected down to SO(3), and the former is a double cover of the latter.…”

Section: Degree Of the Attitude Map And The Domain Of Spin-weightementioning

confidence: 99%

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How should spin-weighted spherical functions be defined?

Boyle

2016

Journal of Mathematical Physics

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Spin-weighted spherical functions provide a useful tool for analyzing tensor-valued functions on the sphere. A tensor field can be decomposed into complex-valued functions by taking contractions with tangent vectors on the sphere and the normal to the sphere. These component functions are usually presented as functions on the sphere itself, but this requires an implicit choice of distinguished tangent vectors with which to contract. Thus, we may more accurately say that spin-weighted spherical functions are functions of both a point on the sphere and a choice of frame in the tangent space at that point. The distinction becomes extremely important when transforming the coordinates in which these functions are expressed, because the implicit choice of frame will also transform. Here, it is proposed that spin-weighted spherical functions should be treated as functions on the spin or rotation groups, which simultaneously tracks the point on the sphere and the choice of tangent frame by rotating elements of an orthonormal basis. In practice, the functions simply take a quaternion argument and produce a complex value. This approach more cleanly reflects the geometry involved, and allows for a more elegant description of the behavior of spin-weighted functions. In this form, the spin-weighted spherical harmonics have simple expressions as elements of the Wigner D representations, and transformations under rotation are simple. Two variants of the angular-momentum operator are defined directly in terms of the spin group; one is the standard angular-momentum operator L, while the other is shown to be related to the spin-raising operator ð. Computer code is also included, providing an explicit implementation of the spin-weighted spherical harmonics in this form.

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“…We then use the fixed frequency integration method of [102] to compute the gravitational wave strain h 2,2 from Ψ 2, 2 4 without taking into account possible drift effects described in [103]. Since the total drift of the BH at AH formation and at the end of the simulation is less than 0.1 M and 0.2 M , respectively, the effect of drift is expected to be less than 1% on the dominant (2, 2) mode.…”

Section: 2mentioning

confidence: 99%

Simulations of inspiraling and merging double neutron stars using the Spectral Einstein Code

et al. 2016

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We present results on the inspiral, merger, and post-merger evolution of a neutron star -neutron star (NSNS) system. Our results are obtained using the hybrid pseudospectral-finite volume Spectral Einstein Code (SpEC). To test our numerical methods, we evolve an equal-mass system for ≈ 22 orbits before merger. This waveform is the longest waveform obtained from fully general-relativistic simulations for NSNSs to date. Such long (and accurate) numerical waveforms are required to further improve semi-analytical models used in gravitational wave data analysis, for example the effective one body models. We discuss in detail the improvements to SpEC's ability to simulate NSNS mergers, in particular mesh refined grids to better resolve the merger and post-merger phases. We provide a set of consistency checks and compare our results to NSNS merger simulations with the independent BAM code. We find agreement between them, which increases confidence in results obtained with either code. This work paves the way for future studies using long waveforms and more complex microphysical descriptions of neutron star matter in SpEC.

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Transformations of asymptotic gravitational-wave data

Cited by 107 publications

References 62 publications

Targeted numerical simulations of binary black holes for GW170104

Targeted numerical simulations of binary black holes for GW170104

How should spin-weighted spherical functions be defined?

Simulations of inspiraling and merging double neutron stars using the Spectral Einstein Code

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