First Results from the Numerical Relativity/ Analytical Relativity - - PowerPoint PPT Presentation

First Results from the Numerical Relativity/ Analytical Relativity Collaboration

Ian Hinder

• n behalf of the NR/AR collaboration

18th September 2013 NRDA meeting, Majorca Max Planck Institute for Gravitational Physics, Potsdam, Germany

Introduction

• Motivations: Gravitational wave templates for Advanced LIGO/Virgo for high-

mass Binary Black Hole (BBH) systems; specifically spinning

• BBH inspiral, merger and ringdown waveform
• Early inspiral: analytic approximations
• Late inspiral, merger and ringdown: Numerical Relativity (NR) simulations
• GW searches: NR simulations expensive; need approximate models

500 1000 1500 2000

• 0.2

0.0 0.2 0.4 t h

Pool resources of 13 NR groups to construct family of NR simulations to calibrate/tune analytic approximations for late inspiral and merger

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Participants

• Florida Atlantic University
• University of Jena
• University of Cardiff
• Caltech
• Cornell
• University of Urbino
• University of Syracuse
• University of Maryland
• University of Mississippi
• Instituto Superior Técnico, Lisbon
• Canadian Institute for Theoretical Astrophysics
• Albert Einstein Institute
• Louisiana State University
• Georgia Institute of Technology
• University of Illinois at Urbana Champaign
• Institut des Hautes Études Scientifiques
• NASA Goddard Spaceflight Center
• University of the Balearic Islands, Palma
• Rochester Institute of Technology
• Institute of Space Sciences, Barcelona
• Computation: 11M CPU hours from NSF on Kraken + time on groups’ own machines

FAU FAU Jena Jena Palma Palma Cardiff Cardiff NASA Goddard NASA Goddard RIT RIT Caltech Caltech Cornell Cornell CITA CITA AEI AEI LSU LSU Georgia Tech Georgia Tech Illinois Illinois Maryland Maryland IHES IHES Urbino Urbino Syracuse Syracuse ISS ISS Mississippi Mississippi IST IST

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Χ1 m1 Χ2 m2 D

Parameter space

• Stage 1:

Basic coverage q = 1, 2, 3, mild spins

• Stage 2:

Additional precessing configurations

• Stage 3:

More challenging configurations

• Higher mass ratios

(q ≫10)

• Low #orbits, large

spins (|χ| > 0.95)

• Long (> 40 orbits)

# BHs spinning Spin Alignment Spins 1 Aligned 0, ±0.3, ±0.6 2 Aligned Equal 2 Aligned Unequal (0.4,0.6,0.8) 2 Aligned χ1+χ2 = 0 1 Misaligned 2 Misaligned 2 Misaligned χ1+χ2 fixed, vary orientation

Configurations in Stage 1

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Targets for NR simulations

• Computational cost vs accuracy/realism/density of parameter space
• Studies carried out to set targets to ensure simulations are useful
• ~20 usable GW cycles
• Eccentricity:
• Brown and Zimmerman 2010: e ≲ 0.05 for detection
• Aim for e < 0.002 as conservative target
• Phase error Δϕ(t) < 0.25 radians up to t | ωgw = 0.2/M (< 1 orbit before merger)
• Relative amplitude error ΔA/A < 0.01

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Summary of the State of the Art

• arXiv:1307.5307v1: Error-analysis and comparison to analytical models of

numerical waveforms produced by the NRAR Collaboration

• Uniform description of methods and techniques used in NR
• A complete recipe for computing “ready-to-use” strain waveforms from NR
• First time such an extensive and detailed uniform error analysis

methodology has been applied to such a diverse data set in NR

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Analysis “Pipeline”

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Run Simulations Commit to repository Analyse waveforms

multiple resolutions, eccentricity reduction, error control, etc

Check Psi4 -> h

waveforms, horizon masses, spins, trajectories metadata (based on NINJA)

Extrapolate h in r Export AR repository

2 resolutions Waveform

}

2 orders Error estimate Df and DA Finite-resolution Finite radius Strain conversion

Combine errors

NR Groups NRAR Analysis Code

Extrapolation

• NR waveforms computed at finite radius; typically only valid as r → Infinity.

Introduces error (e.g. 0.1 radians, 20% in amplitude) too large to ignore: Extrapolate.

• Identified criteria for which extraction radii to choose:
• At least 5 radii, spanning at least a factor of 3 in radius
• Error estimate for extrapolation needs to take into account datasets with

“good radii”, and assign small errors, as well as “bad radii” and assign best error estimates possible

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R σR(q) ⌘ min(|Rp(q) Rp+1(q)| + |Rp+1(q) Rp+2(q)|, |Rp(q) R0(q)|) ,

How do NR waveforms compare with targets?

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10 20 30 40

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

0.01 0.1 1 0.001 0.01 0.1

at ω22, ref at ω22, ref (aligned) early inspiral

Δφ (radians) usable GW cycles ΔA/A JCP FAU GATech RIT Lean AEI PC SXS UIUC

Target # meeting tar # meeting target ≥20 cycles 23/25 23/25 ΔΦ < 0.25 25/25 17/25 ΔA/A < 0.01 19/25 16/25 Inspiral Premerger Finite radius Finite resolution

Cross-validation

• Different codes (“A” = AEI and “U” = UIUC): same waveform for cross-check
• Difference between results comparable with error estimate

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500 1000 1500 2000 10-3 10-2 10-1 Ht-r*LêM Amplitude difference AA-AU DAA

2 + DAU 2

500 1000 1500 10-2 10-1 100 101 Ht-r*LêM Phase difference fA-fU DfA

2 + DfU 2

Analytic Models

• Effective-one-body (EOB)
• Mainly SEOBNRv1: aligned spin only (no precession)
• For q = 10, also looked at non-spinning EOBNRv2 and IHES-EOB
• Phenomenological (frequency-domain)
• Mainly IMRPhenomB
• None of these models calibrated to waveforms produced by NRAR

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Criteria

• Ineffectualness
• Detection
• Very expensive to compute due to need

to minimise over parameters

• Unfaithfulness
• Parameter estimation
• An upper bound on ineffectualness
• In this work, usually compute unfaithfulness

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¯ E ⌘ 1 max

tc,c,~

• hhNR, hARi

p hhNR, hNRihhAR, hARi ,

¯ F ⌘ 1 max

tc,c

hhNR, hARi p hhNR, hNRihhAR, hARi

hh1, h2i ⌘ 4 Re Z ∞ ˜ h1(f)˜ h∗

2(f)

Sh(f) d f ,

˜ hk(f) = Z ∞

−∞

hk(t) e−2⇡ift dt (k = 1, 2)

Sh: ZERO_DET_HIGH_P

Unfaithfulness: Effective One Body model

• Non-precessing SEOBNRv1 model with non-precessing NR waveforms:
• NB: SEOBNRv1 calibrated with previous simulations (*)
• Few % unfaithfulness also for mildly-precessing NR waveforms

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40 80 120 160 200 0.2% 0.4% 0.6% 0.8% 1%

6: G2+15-60 7: G2+30+00 10: L4 * 12: A1+30+00 13: A1+60+00 16: S1+44+44 * (Calibrated) 17: S1-44-44 * (Calibrated) 18: S1+30+30 19: S2+30+30 24: S3-60+00

40 80 120 160 200 0.1% 0.3% 1% 3% 10% 30%

F

_

2: J2-15+60 4: F3+60+40 5: G1+60+60 8: G2+60+60 14: P1+80-40 15: P1+80+40 20: S3+30+30 25: U1+30+00

SEOBNRv1

M (Msun) M (Msun)

Figure 7. Unfaithfulness ¯ F of the SEOBNRv1 waveform model compared to the

Unfaithfulness: Phenomenological model

• Good agreement for high mass
• Higher unfaithfulness at low masses (expected: templates designed to be

effectual rather than faithful)

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40 80 120 160 200 1% 2% 3%

2: J2-15+60 6: G2+15-60 7: G2+30+00 8: G2+60+60 10: L4 12: A1+30+00 17: S1-44-44 25: U1+30+00

40 80 120 160 200 0.3% 1% 3% 10%

F

_

4: F3+60+40 5: G1+60+60 13: A1+60+00 14: P1+80-40 15: P1+80+40 16: S1+44+44 18: S1+30+30 19: S2+30+30 20: S3+30+30 24: S3-60+00

IMRPhenomB

M (Msun) M (Msun)

• Non-precessing IMRPhenomB model with non-precessing NR waveforms:

Conclusions 1

• 22 waveforms produced by collaboration, +3 contributed
• New waveforms of higher quality than most previously published waveforms
• Parameter space newly explored
• NR groups pushed into unknown territory
• Radial extrapolation requirements clarified
• Challenges in data management
• Generic pipeline can be used easily with new data

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Conclusions 2

• First time to compare previously-calibrated models to new NR data
• Effective One Body model:
• Good towards both low and high total masses
• Ineffectualness < 1% for non-precessing NR waveforms for 100-200 M☉
• Robust when interpolating NR waveforms away from the points where they

were previously calibrated

• Phenomenological models:
• Also have ineffectualness < 1% for non-precessing NR waveforms for

100-200 M☉

• Waveforms have larger unfaithfulness towards low masses

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