First Results from the Numerical Relativity/ Analytical Relativity Collaboration Ian Hinder on behalf of the NR/AR collaboration Max Planck Institute for Gravitational Physics, 18th September 2013 NRDA meeting, Majorca 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 0.4 0.2 0.0 h - 0.2 0 500 1000 1500 2000 t • GW searches: NR simulations expensive; need approximate models Pool resources of 13 NR groups to construct family of NR simulations to calibrate/tune analytic approximations for late inspiral and merger 2
Participants AEI AEI Cardiff Cardiff IHES IHES Jena Jena Syracuse RIT Syracuse RIT Urbino CITA Urbino CITA Cornell Cornell ISS ISS Illinois Illinois Palma Palma NASA Goddard IST NASA Goddard IST Maryland Maryland Mississippi Caltech Mississippi Georgia Tech Caltech Georgia Tech LSU LSU FAU FAU • Florida Atlantic University • Canadian Institute for Theoretical Astrophysics • University of Jena • Albert Einstein Institute • University of Cardi ff • Louisiana State University • Caltech • Georgia Institute of Technology • Cornell • University of Illinois at Urbana Champaign • University of Urbino • Institut des Hautes Études Scientifiques • University of Syracuse • NASA Goddard Spaceflight Center • University of Maryland • University of the Balearic Islands, Palma • University of Mississippi • Rochester Institute of Technology • Instituto Superior Técnico, Lisbon • Institute of Space Sciences, Barcelona • Computation: 11M CPU hours from NSF on Kraken + time on groups’ own machines 3
Parameter space Χ 1 m 1 Χ 2 D • Stage 1: Basic coverage q = 1, 2, 3, mild spins m 2 • Stage 2: Additional precessing configurations • Stage 3: # BHs spinning Spin Alignment Spins More challenging 1 Aligned 0, ±0.3, ±0.6 configurations 2 Aligned Equal • Higher mass ratios 2 Aligned Unequal (0.4,0.6,0.8) (q ≫ 10) 2 Aligned χ 1 + χ 2 = 0 • Low #orbits, large 1 Misaligned spins (| χ | > 0.95) 2 Misaligned • Long (> 40 orbits) χ 1 + χ 2 fixed, vary orientation 2 Misaligned Configurations in Stage 1 4
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 Δ ϕ (t) < 0.25 radians up to t | ω gw = 0.2/M (< 1 orbit before merger) • Relative amplitude error Δ A/A < 0.01 5
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 6
Analysis “Pipeline” NR Groups multiple resolutions, eccentricity reduction, Run Simulations error control, etc waveforms, horizon masses, spins, trajectories Commit to repository metadata (based on NINJA) Analyse waveforms 2 resolutions NRAR Analysis Code } Finite-resolution Check Strain conversion Combine errors Finite radius Psi4 -> h 2 orders Extrapolate h in r Error estimate Waveform Df and DA Export AR repository 7
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 R error estimates possible σ R ( q ) ⌘ min( |R p ( q ) � R p +1 ( q ) | + |R p +1 ( q ) � R p +2 ( q ) | , |R p ( q ) � R 0 ( q ) | ) , 8
How do NR waveforms compare with targets? 40 usable GW cycles Target # meeting tar # meeting target 30 ≥ 20 cycles 23/25 23/25 20 ΔΦ < 0.25 25/25 17/25 10 at ω 22, ref Δ A/A < 0.01 19/25 16/25 at ω 22, ref (aligned) early inspiral 0.1 Inspiral Premerger Δ A/A 0.01 0.001 Finite radius Finite resolution Δφ (radians) 1 0.1 0.01 7 1 2 3 4 5 6 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 RIT JCP FAU GATech Lean AEI PC SXS UIUC 9
Cross-validation • Di ff erent codes (“A” = AEI and “U” = UIUC): same waveform for cross-check • Di ff erence between results comparable with error estimate 10 1 A A - A U Amplitude difference f A -f U 10 - 1 Phase difference 2 + Df U 2 + D A U 2 2 D A A Df A 10 0 10 - 2 10 - 1 10 - 3 10 - 2 0 500 1000 1500 2000 0 500 1000 1500 H t - r * Lê M H t - r * Lê M 10
Analytic Models • E ff ective-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 11
Criteria • Ine ff ectualness Z ∞ h 1 ( f )˜ ˜ h ∗ 2 ( f ) h h NR , h AR i ¯ • h h 1 , h 2 i ⌘ 4 Re d f , E ⌘ 1 � max , S h ( f ) p h h NR , h NR ih h AR , h AR i 0 t c , � c , ~ � • Detection Z ∞ h k ( t ) e − 2 ⇡ i ft dt ˜ h k ( f ) = ( k = 1 , 2) • Very expensive to compute due to need −∞ S h : ZERO_DET_HIGH_P to minimise over parameters • Unfaithfulness h h NR , h AR i • ¯ F ⌘ 1 � max p h h NR , h NR ih h AR , h AR i t c , � c • Parameter estimation • An upper bound on ine ff ectualness • In this work, usually compute unfaithfulness 12
Unfaithfulness: Effective One Body model • Non-precessing SEOBNRv1 model with non-precessing NR waveforms: SEOBNRv1 6: G2+15-60 2: J2-15+60 7: G2+30+00 4: F3+60+40 10: L4 * 5: G1+60+60 12: A1+30+00 8: G2+60+60 1% 13: A1+60+00 14: P1+80-40 16: S1+44+44 * (Calibrated) 15: P1+80+40 20: S3+30+30 17: S1-44-44 * (Calibrated) 30% 25: U1+30+00 18: S1+30+30 0.8% 19: S2+30+30 24: S3-60+00 10% 0.6% _ F 3% 0.4% 1% 0.2% 0.3% 0.1% 0 0 40 80 120 160 200 40 80 120 160 200 M ( M sun ) M ( M sun ) Figure 7. Unfaithfulness ¯ F of the SEOBNRv1 waveform model compared to the • NB: SEOBNRv1 calibrated with previous simulations (*) • Few % unfaithfulness also for mildly-precessing NR waveforms 13
Unfaithfulness: Phenomenological model • Non-precessing IMRPhenomB model with non-precessing NR waveforms: IMRPhenomB 4: F3+60+40 2: J2-15+60 5: G1+60+60 6: G2+15-60 13: A1+60+00 7: G2+30+00 14: P1+80-40 8: G2+60+60 3% 10% 15: P1+80+40 10: L4 16: S1+44+44 12: A1+30+00 18: S1+30+30 17: S1-44-44 19: S2+30+30 25: U1+30+00 20: S3+30+30 24: S3-60+00 3% 2% _ F 1% 1% 0.3% 0 0 40 80 120 160 200 0 40 80 120 160 200 M ( M sun ) M ( M sun ) • Good agreement for high mass • Higher unfaithfulness at low masses (expected: templates designed to be e ff ectual rather than faithful) 14
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 15
Conclusions 2 • First time to compare previously-calibrated models to new NR data • E ff ective One Body model: • Good towards both low and high total masses • Ine ff ectualness < 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 ine ff ectualness < 1% for non-precessing NR waveforms for 100-200 M ☉ • Waveforms have larger unfaithfulness towards low masses 16
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