Statistical constraints on binary black hole inspiral dynamics

Galley, Chad R.; Herrmann, Frank; Silberholz, John; Tiglio, Manuel; Guerberoff, Gustavo

doi:10.1088/0264-9381/27/24/245007

Cited by 13 publications

(21 citation statements)

References 25 publications

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“…While the work presented here is limited to the nonprecessing case, our results provide the first hints, together with [24] for precessing inspiral dynamics (see also [12]), [22] for quasi-normal mode ringing, and studies using a Singular Value Decomposition (SVD) technique [23,34,35] that a full representation of the eightparameter space of inspiral-merger-ringdown waveforms (either numerical, Effective-One-Body, or phenomenological ones) might actually be achievable with a relatively compact reduced basis. If this is the case, then there is hope that the number of simulations needed to represent the space of precessing binary inspirals might be relatively small (perhaps, on the order of several thousand for advanced LIGO but not orders of magnitude larger than this), thus allowing for a tractable number of numerical simulations if the parameters are chosen with malice of forethought from our reduced basis studies.…”

Section: Discussionsupporting

confidence: 54%

“…For the non-precessing inspiral waveforms, we find a very moderate increase in the number of RB elements as the dimensionality of the parameter space is increased from 2D to 4D. While this number could and might change significantly for precessing binaries, former results in [24] show dimensionality reduction in the precessing case (with respect to the spin dynamics).…”

Section: Introductionmentioning

confidence: 71%

“…But if it holds, the curse of dimensionality might be beaten. In fact, indications that the problem, in the presence of precession, is amenable to dimensional reduction, have already been found through a Principal Component Analysis of the precessing dynamics of compact binary inspirals [24]. There it was found that for the case of a random selection of precessing binaries with the same total mass there are three combinations of spin orientations that are semi-conserved (in a statistical sense) throughout the inspiral.…”

Section: Resultsmentioning

confidence: 99%

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Towards beating the curse of dimensionality for gravitational waves using reduced basis

2012

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Using the Reduced Basis approach, we efficiently compress and accurately represent the space of waveforms for non-precessing binary black hole inspirals, which constitutes a four dimensional parameter space (two masses, two spin magnitudes). Compared to the non-spinning case, we find that only a marginal increase in the (already relatively small) number of reduced basis elements is required to represent any non-precessing waveform to nearly numerical round-off precision. Most parameters selected by the algorithm are near the boundary of the parameter space, leaving the bulk of its volume sparse. Our results suggest that the full eight dimensional space (two masses, two spin magnitudes, four spin orientation angles on the unit sphere) may be highly compressible and represented with very high accuracy by a remarkably small number of waveforms, thus providing some hope that the number of numerical relativity simulations of binary black hole coalescences needed to represent the entire space of configurations is not intractable. Finally, we find that the distribution of selected parameters is robust to different choices of seed values starting the algorithm, a property which should be useful for indicating parameters for numerical relativity simulations of binary black holes. In particular, we find that the mass ratios m1/m2 of non-spinning binaries selected by the algorithm are mostly in the interval [1, 3] and that the median of the distribution follows a power-law behavior ∼ (m1/m2) −5.25 .

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Section: Discussionsupporting

confidence: 54%

Section: Introductionmentioning

confidence: 71%

Section: Resultsmentioning

confidence: 99%

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Towards beating the curse of dimensionality for gravitational waves using reduced basis

2012

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“…While we may assume that η and | S i | remain essentially constant throughout inspiral and merger, the spin directions generally evolve, so a useful parameterization of the system should take care to distinguish components of the spin-direction space with physically distinct effects on the waveforms [11].…”

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confidence: 99%

Mergers of black-hole binaries with aligned spins: Waveform characteristics

et al. 2011

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We conduct a descriptive analysis of the multipolar structure of gravitational-radiation waveforms from equal-mass aligned-spin mergers, following an approach first presented in the complementary context of nonspinning black holes of varying mass ratio [1]. We find that, as with the nonspinning mergers, the dominant waveform mode phases evolve together in lock-step through inspiral and merger, supporting the previous waveform description in terms of an adiabatically rigid rotator driving gravitational-wave emission -an implicit rotating source (IRS). We further apply the latetime merger-ringdown model for the rotational frequency introduced in [1], along with an improved amplitude model appropriate for the dominant (2, ±2) modes. This provides a quantitative description of the merger-ringdown waveforms, and suggests that the major features of these waveforms can be described with reference only to the intrinsic parameters associated with the state of the final black hole formed in the merger. We provide an explicit model for the merger-ringdown radiation, and demonstrate that this model agrees to fitting factors better than 95% with the original numerical waveforms for system masses above ∼ 150M⊙. This model may be directly applicable to gravitational-wave detection of intermediate-mass black hole mergers.

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“…Work over the last few years has shown that gravitational waveforms exhibit redundancy in the parameter space [37][38][39][40][41][42], suggesting that the amount of information necessary to represent a fiducial waveform model is smaller than might be anticipated. This reduction can be captured accurately using only a remarkably few number m of representative waveforms.…”

Section: Introductionmentioning

confidence: 99%

Fast Prediction and Evaluation of Gravitational Waveforms Using Surrogate Models

et al. 2014

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We propose a solution to the problem of quickly and accurately predicting gravitational waveforms within any given physical model. The method is relevant for both real-time applications and more traditional scenarios where the generation of waveforms using standard methods can be prohibitively expensive. Our approach is based on three offline steps resulting in an accurate reduced order model in both parameter and physical dimensions that can be used as a surrogate for the true or fiducial waveform family. First, a set of m parameter values is determined using a greedy algorithm from which a reduced basis representation is constructed. Second, these m parameters induce the selection of m time values for interpolating a waveform time series using an empirical interpolant that is built for the fiducial waveform family. Third, a fit in the parameter dimension is performed for the waveform's value at each of these m times. The cost of predicting L waveform time samples for a generic parameter choice is of order OðmL þ mc fit Þ online operations, where c fit denotes the fitting function operation count and, typically, m ≪ L. The result is a compact, computationally efficient, and accurate surrogate model that retains the original physics of the fiducial waveform family while also being fast to evaluate. We generate accurate surrogate models for effective-one-body waveforms of nonspinning binary black hole coalescences with durations as long as 10 5 M, mass ratios from 1 to 10, and for multiple spherical harmonic modes. We find that these surrogates are more than 3 orders of magnitude faster to evaluate as compared to the cost of generating effective-one-body waveforms in standard ways. Surrogate model building for other waveform families and models follows the same steps and has the same low computational online scaling cost. For expensive numerical simulations of binary black hole coalescences, we thus anticipate extremely large speedups in generating new waveforms with a surrogate. As waveform generation is one of the dominant costs in parameter estimation algorithms and parameter space exploration, surrogate models offer a new and practical way to dramatically accelerate such studies without impacting accuracy.

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Statistical constraints on binary black hole inspiral dynamics

Cited by 13 publications

References 25 publications

Towards beating the curse of dimensionality for gravitational waves using reduced basis

Towards beating the curse of dimensionality for gravitational waves using reduced basis

Mergers of black-hole binaries with aligned spins: Waveform characteristics

Fast Prediction and Evaluation of Gravitational Waveforms Using Surrogate Models

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