Modeling, detection and characterization of eccentric compact binary coalescence

Eliu Huerta National Center for Supercomputing Applications (NCSA)

University of Illinois at Urbana-Champaign

NCSA: Bhanu Agarwal, Daniel George, Roland Haas, Miguel Holgado, Diyu Luo, Wei Ren, Erik Wessel Cambridge: Chris Moore and Alvin Chua CITA: Prayush Kumar and Harald Pfeiffer

AEI: Ian Hinder

Aspen Center for Astrophysics, The Dawning Era of Gravitational-Wave Astrophysics, February 2017

E.A. Huerta et al., Phys. Rev. D 95, 024038 (2017) Daniel George, E.A. Huerta, arXiv:1701.00008

E.A. Huerta et al., in preparation

Outline

Motivation

State-of-the-art in inspiral-merger-ringdown (IMR) eccentric compact binary coalescence (eCBC) source modeling

Second generation of IMR eCBC waveform models: combining analytical and numerical relativity with machine learning

Detection and characterization of eCBC: introducing a new paradigm in gravitational wave astrophysics

Motivation

Advanced LIGO (aLIGO) has established itself as an astronomical observatory: the dark sector of the Universe is at our fingertips

Enable discovery, expand the science reach of gravitational wave astrophysics by extracting as much information as possible from aLIGO data

Nature is oblivious to our assumptions. Innovate to confirm/rule out the existence of eCBC populations (Carl Rodriguez, Bence Kocsis, Zsolt Frei)

Gravitational wave astrophysics informs astrophysical theory — current detections have reshaped our expectations and knowledge of compact binary

populations

State-of-the-art

• E. A. Huerta et al., Phys. Rev. D 95, 024038 (2017) introduced the first eccentric IMR waveform model that captures the effect of orbital eccentricity throughout the merger of eccentric, non-spinning compact binary sources.

• Key features:

• Reproduces state-of-the-art quasi-circular waveform models in the zero eccentricity limit

• Captures the effect of orbital eccentricity throughout the merger phase

• Ready-to-use for large scale data analysis studies

Hybrid Inspiral Framework

Conservative Dynamics

Derived from a 3PN Hamiltonian

Incorporate quasi-circular self-force corrections to the binding

energy of compact binaries (up to 6PN order)

Radiative Dynamics

Energy and angular momentum fluxes

Recast expressions using a gauge-invariant

expansion parameter

Derive higher-order eccentric PN corrections both for instantaneous and hereditary terms

Incorporate higher-order quasi-circular corrections to the fluxes from black hole perturbation theory

(up to 6PN order)

E.A. Huerta et al., Phys. Rev. D 95, 024038 (2017)

Merger waveform modelAssume that moderately eccentric systems circularize prior to the merger event

E.A. Huerta et al., Phys. Rev. D 95, 024038 (2017)

e0 at fGW = 15Hz

Merger waveform model

Catalog of NR simulations to calibrate a phenomenological merger waveform Generic Implicit Rotating Source (gIRS) Model

E.A. Huerta et al., Phys. Rev. D 95, 024038 (2017)

Hybrid Inspiral Scheme Analytical Merger Waveform

Overlap between IMR ax templatesand non-spinning SEOBNRv2 templates.

e0 at fGW = 14Hz.Overlap between e ! 0 IMR ax templatesand non-spinning SEOBNRv2 templates.

Filtering from fGW = 15HzaLIGO’s design sensitivity.

E.A. Huerta et al., Phys. Rev. D 95, 024038 (2017)

DRAFT

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DRAFT

DRAFT

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The effect of orbital eccentricity in amplitude and phase is captured

throughout the merger

E.A. Huerta et al., Phys. Rev. D 95, 024038 (2017)

Detection of eCBCFitting Factor (FF) calculations

1.5M SEOBNRv2 spin-aligned templatese0 at fGW = 14Hz.

Filtering from fGW = 15Hz using aLIGO’s design sensitivity.

E.A. Huerta et al., Phys. Rev. D 95, 024038 (2017)

Detection of eCBCFitting Factor (FF) calculations

1.5M SEOBNRv2 spin-aligned templatese0 at fGW = 14Hz.

Filtering from fGW = 15Hz using aLIGO’s design sensitivity.

E.A. Huerta et al., Phys. Rev. D 95, 024038 (2017)

1.5M templates to get convergent

results!!!

Unfeasible in low latency

State-of-the-art

• Key areas of improvement for eCBC waveform modeling:

• Merger evolution

• Amplitude evolution

• Improve accuracy of IMR eCBC model in the quasi-circular limit: waveform inaccuracies vs effect of eccentricity for nearly quasi-circular CBC

Second generation of IMR eCBC waveforms

Use hybrid inspiral framework from Phys. Rev. D 95, 024038 (2017)

Improve modeling of amplitude evolution by including higher-order PN corrections

Develop a new merger waveform using machine learning

E. A. Huerta et al., in preparation

Gaussian Process Regression• Gaussian Process Regression (GPR) has been used by Cambridge University’s

gravitational wave team in the context of source modeling and parameter estimation

• Moore et al PRL 113, 251101 (2014)

• Moore et al Phys. Rev. D 93, 064001 (2016)

• See Dan Holz’s group work on GPR.

• We have completed the construction of a GPR merger waveform and linked it to our hybrid inspiral waveform

E. A. Huerta et al., in preparation

State-of-the-artHybrid Inspiral

SchemeAnalytical Merger

Waveform

Overlap between e ! 0 IMR ax templatesand non-spinning SEOBNRv2 templates.

Filtering starts at fGW = 15Hzusing design sensitivity for aLIGO.

“While the implicit rotating source (IRS) merger waveform model provides a good description of the merger dynamics in the vicinity of the light-ring, its accuracy deteriorates rapidly several cycles

before merger” (REPLACE IRS-based merger waveform!)

The corrections that have to be implemented to ensure that the minimum overlap between the IMR ax model and SEOBNRv2 are greater than 0.99 over the whole BBH space are within reach with

additional work (this talk!)

E.A. Huerta et al., Phys. Rev. D 95, 024038 (2017)

E.A. Huerta et al., Phys. Rev. D 95, 024038 (2017)

Comparison to state-of-the-art quasi-circular waveforms

No free parameters used for the construction of the model

Combination of PN, self-force, black hole perturbation theory and numerical relativity

GPE merger waveform constructed with numerical simulations

Inspiral evolution was combined with GPR merger waveform

Hybrid inspiral framework encodes the correct physics very late in the inspiral evolution

E. A. Huerta et al., in preparation

DRAFT

NCSA-CAM eCBC waveform The inspiral dynamics of non-spinning, quasi-circular compact binaries can

be accurately described without resorting to phenomenology — no free parameters or re-summations needed

Non-spinning, quasi-circular IMR dynamics is accurately captured by combining our hybrid inspiral framework with a small training set of

numerical relativity waveforms and machine learning

Our new NCSA-CAM also encapsulates the effect of orbital eccentricity throughout the merger

E. A. Huerta et al., in preparation

Validation of NCSA-CAM eCBC waveform with eccentric NR simulations

DRAFT

E. A. Huerta et al., in preparation

DRAFTUncalibrated NCSA-CAM model compared to eccentric NR simulations

Now what?

Basic analysis requires 1.5M+ templates

Extension to spinning, eccentric compact binaries?

What is the status of searches for quasi-circular, spin-aligned binaries? 300k+ templates needed

Is this model sustainable? Open Science Grid up and running in Blue Waters… this can only go so far. ATLAS, NANOGrav taking advantage of this platform

NR and EM followups require rapid and accurate PE results to enable real-time multimessenger astrophysics

Now what?

Matched-filtering searches are computationally expensive

Limited by the number of templates needed to carry out the search

Extension to explore a deeper parameter space is computationally prohibitive

Are we missing astrophysically motivated sources lurking in aLIGO data

Advanced Virgo, KAGRA and LIGO-India will eventually come on-line…

Do we go and seize all HPC and HTC resources to detect and characterize new GW sources?

Deep Neural Networks

RCATJLTHYHATOJ

Deep Neural Networks

RCATJLTHYHATOJ

Deep Neural NetworksDaniel George, E. A. Huerta, arXiv:1701.00008

First scientific application for processing highly noisy time data series

Advantages

Directly processes raw data

Automatically develops optimal strategy

Constant evaluation time no matter the size of the training dataset

Highly non-linear

Optimized hardware for deep learning (GPU)

Features

Does not perform template matching (linear filter)

Learns patters connecting signals

Dimensional reduction

Interpolation

Compact, portable code

Deep Neural NetworksDaniel George, E. A. Huerta, arXiv:1701.00008

First scientific application for processing highly noisy time data series

Deep Neural NetworksDaniel George, E. A. Huerta, arXiv:1701.00008

First scientific application for processing highly noisy time data series

Design of DNN

Used Wolfram Language MXNet

Innovative Systems Lab at NCSA: Tesla, GTX1080 and P100 GPUs

Basic design: 4000 templates

Fully trained DNN is 4MB in size

Deep Neural NetworksDaniel George, E. A. Huerta, arXiv:1701.00008

First scientific application for processing highly noisy time data series Parameter Estimation

Application to eCBCDaniel George, E. A. Huerta, arXiv:1701.00008

DRAFT

Conclusions

New approach to combine an accurate hybrid inspiral framework with a machine learning-based merger waveform

We have introduced the second generation of IMR, non-spinning, eCBC waveforms: no free parameters or re-summations needed. Validated with state-of-the-art quasi-circular

waveforms and eccentric NR simulations

Detection and characterization of moderately eccentric compact sources is now within reach with deep neural networks — stay tuned!

eCBC Team

Acknowledgements

• This research is part of the Blue Waters sustained-petascale computing project, which is supported by the National Science Foundation (awards OCI-0725070 and ACI-1238993) and the state of Illinois. Blue Waters is a joint effort of the University of Illinois at Urbana-Champaign and its National Center for Supercomputing Applications.

• The eccentric numerical relativity simulations used in this article were generated with the open source, community software the Einstein Toolkit.

• Vlad Kindratenko for granting us access to several NVIDIA Tesla, GeForce, and P100 GPUs in the Innovative Systems Lab at NCSA.

• Wolfram Research for developing the software stack used for DNN analysis.