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Computation of Gravitational Waveforms from Compact Binaries Mark A. Scheel Caltech Saul A. Teukolsky, PRAC PI Blue Waters Symposium, June 5 2018 Simulations of eXtreme Spacetimes collaboration www.black-holes.org Mark A. Scheel (Caltech)

SLIDE 1

Computation of Gravitational Waveforms from Compact Binaries

Mark A. Scheel

Caltech

Saul A. Teukolsky, PRAC PI

Blue Waters Symposium, June 5 2018 Simulations of eXtreme Spacetimes collaboration www.black-holes.org

Mark A. Scheel (Caltech) BBH Initial Data Comparison Jun 05 2018 1 / 22

SLIDE 2

Outline

(past) Introduction and Motivation (present) Black-hole binaries: SpEC code (future) Neutron-star binaries: SpECTRE code

Mark A. Scheel (Caltech) BBH Initial Data Comparison Jun 05 2018 2 / 22

SLIDE 3

1. Introduction and Motivation

Mark A. Scheel (Caltech) BBH Initial Data Comparison Jun 05 2018 3 / 22

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Gravitational Waves

Ripples in spacetime curvature caused by moving mass-energy. Predicted by Einstein, 1916 Waves interact with matter weakly: direct detection difficult.

Mark A. Scheel (Caltech) BBH Initial Data Comparison Jun 05 2018 4 / 22

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LIGO: Laser Interferometer Gravitational Wave Observatory

Mark A. Scheel (Caltech) BBH Initial Data Comparison Jun 05 2018 5 / 22

SLIDE 6

First direct detection of gravitational waves: Sep. 14, 2015

Phys. Rev. Lett. 116, 061102 (2016)

Source: 2 colliding black holes, 109 ly away Black hole masses: 35 M⊙, 30 M⊙ Max power in waves: 4 × 1049 watts Total energy in waves: 5 × 1054 ergs First strong-gravity test of general relativity

Mark A. Scheel (Caltech) BBH Initial Data Comparison Jun 05 2018 6 / 22

SLIDE 7

2017 Nobel Prize in Physics

Rai Weiss Kip Thorne Barry Barish “for decisive contributions to the LIGO detector and the observation of gravitational waves”

Mark A. Scheel (Caltech) BBH Initial Data Comparison Jun 05 2018 7 / 22

SLIDE 8

Q. How do we know waves come from black holes?
A. Compare signals with detailed predictions of general relativity.

Mark A. Scheel (Caltech) BBH Initial Data Comparison Jun 05 2018 8 / 22

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Q. How do we know waves come from black holes?
A. Compare signals with detailed predictions of general relativity.

Numerical relativity: solving Einstein’s equations on a computer.

Phys. Rev. Lett. 116, 061102 (2016)

Mark A. Scheel (Caltech) BBH Initial Data Comparison Jun 05 2018 8 / 22

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Need to simulate binaries with many parameters

7-dimensional parameter space: spin vectors and mass ratio.

1 2

M M

2 1

χ χ

Different parameters give different gravitational wave signals

Mark A. Scheel (Caltech) BBH Initial Data Comparison Jun 05 2018 9 / 22

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2. Black-hole binaries and SpEC

Mark A. Scheel (Caltech) BBH Initial Data Comparison Jun 05 2018 10 / 22

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SpEC: Spectral Einstein Code

Einstein’s Eqs: 50 coupled nonlinear 1st order PDEs Spectral multidomain method MPI parallelism Grid distorts to follow horizons p refinement, basic h refinement

Mark A. Scheel (Caltech) BBH Initial Data Comparison Jun 05 2018 11 / 22

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SpEC Simulations

1 2

M M

2 1

χ χ

Cost of one simulation:

“Easy” parameters: 4 days on 3 Blue Waters nodes. “Hard” parameters: few months on 3–5 Blue Waters nodes. (scaling limited by MPI approach with heterogeneous load)

Run 100s of simulations simultaneously cover parameter space.

Mark A. Scheel (Caltech) BBH Initial Data Comparison Jun 05 2018 12 / 22

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Results: Waveform Catalog

Spin χB

0.0 0.2 0.4 0.6 0.8 1.0

Spin χA

0.0 0.2 0.4 0.6 0.8 1.0

M a s s R a t i

2 4 6 8

Arrows = spin directions

1882 simulations shown, 542 on Blue Waters (+640 on Blue Waters in progress) Publicly available www.black-holes.org/waveforms

339 public now 1882 by end of summer

Used by LIGO scientists, dozens of

ther researchers.

Mark A. Scheel (Caltech) BBH Initial Data Comparison Jun 05 2018 13 / 22

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Results: Waveform Catalog

Numerical relativity waveform: SXS:BBH:0305 from our catalog.

Phys. Rev. Lett. 116, 061102 (2016)

Mark A. Scheel (Caltech) BBH Initial Data Comparison Jun 05 2018 14 / 22

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Results: Surrogate waveform models

Run many simulations sampling 7d parameter space. Build fast interpolant that can be evaluated for any parameters.

1 2

M M

2 1

χ χ 10−5 10−4 10−3 10−2 10−1 100 Mismatch 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Case density

NR resolution Surrogate Cross-validation IMRPhenomPv2 SEOBNRv3

Mark A. Scheel (Caltech) BBH Initial Data Comparison Jun 05 2018 15 / 22

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Results: Surrogate waveform models

Run many simulations sampling 7d parameter space. Build fast interpolant that can be evaluated for any parameters.

1 2

M M

2 1

χ χ 10−5 10−4 10−3 10−2 10−1 100 Mismatch 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Case density

NR resolution Surrogate Cross-validation IMRPhenomPv2 SEOBNRv3

744 simulations (540 on Blue Waters) M1/M2 ≤ 2, χ ≤ 0.8. Publicly available. Improvements in progress. . .

Blackman+, Phys. Rev.D 96, 024058 (2017)

Mark A. Scheel (Caltech) BBH Initial Data Comparison Jun 05 2018 15 / 22

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3. Neutron star binaries and SpECTRE

Mark A. Scheel (Caltech) BBH Initial Data Comparison Jun 05 2018 16 / 22

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Aug 8, 2017 – LIGO detects neutron star binary

ApJ. Lett. 848:L13 (2017)

Seen electromagnetically (visible, gamma-ray, . . . ) as well! Dawn of multimessenger astronomy!

Mark A. Scheel (Caltech) BBH Initial Data Comparison Jun 05 2018 17 / 22

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Simulating neutron-star collisions

More difficult than black holes. Must include General relativity Hydrodynamics Magnetic fields Realistic equations of state Neutrino transport SpEC can do binary neutron stars (finite-volume hydro + spectral GR) SpEC (and other codes) not quite accurate enough for LIGO.

Mark A. Scheel (Caltech) BBH Initial Data Comparison Jun 05 2018 18 / 22

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SpECTRE — a new relativistic astrophysics code

Build on SpEC, but key differences: Discontinuous Galerkin methods. Task-based parallelism (using Charm++ infrastructure). Local timestepping.

I[0] I[1] I[3] I[2] D[2] D[0] D[1] D[3] D[4]

Global Object Space

I[0] I[1] I[2] I[3] D[1] D[2] D[3] D[4] D[0]

Runtime System View

D[0] D[1] D[4] D[3] I[1] I[2] I[3] I[0] D[2]

e C

e 1 C

e 2

Charm RTS Charm RTS Charm RTS

Interconnect Computational Domain

Still under development

Mark A. Scheel (Caltech) BBH Initial Data Comparison Jun 05 2018 19 / 22

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SpECTRE: RHMD test problem: asynchronous execution

example on 12 cores

Kidder+, J. Comp. Phys. 335, 84 (2017)

time processor utilization Blue = volume terms Red = interface fluxes Yellow = limiter White = idle

Mark A. Scheel (Caltech) BBH Initial Data Comparison Jun 05 2018 20 / 22

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SpECTRE: RMHD test problem: strong scaling

Kidder+, J. Comp. Phys. 335, 84 (2017)

Mark A. Scheel (Caltech) BBH Initial Data Comparison Jun 05 2018 21 / 22

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Summary

Numerical solutions of Einstein’s equations ⇒ understand gravitational wave data. Current simulations: SpEC:

Designed for binary black-hole problems. 100s of simulations on Blue Waters for gravitational wave science.

Next-generation code: SpECTRE:

Motivated by problems involving neutron stars. Task-based parallelism. Test problems scale to all of Blue Waters.

Mark A. Scheel (Caltech) BBH Initial Data Comparison Jun 05 2018 22 / 22

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