Modelling the gravitational radiation emitted by merging black holes - PowerPoint PPT Presentation

Modelling the gravitational radiation emitted by merging black holes Harald Pfeiffer CITA, University of Toronto AEI, Potsdam Stephen Hawking 75th Birthday Conference July 4, 2017 LIGO-G1701238

Waveform-knowledge essential to GW astronomy Detection by matched filtering Parameter estimation “GW150914” Abbott+ PRL 116, 061102 (2016) “GW151226” Abbott+ PRL 116, 241203 (2016) Testing GR Modelling ⇒ physics & astronomy ➔ Pablo Laguna ➔ Gaby Gonzalez ➔ Bruce Allen ➔ Frans Pretorius “GW170104” Abbott+ PRL 118, 221101 (2017) 2 Harald Pfeiffer Hawking 75 Jul 4, 2017

https://youtu.be/Zt8Z_uzG71o Waveforms! Accurately & comprehensively 3 Harald Pfeiffer Hawking 75 Jul 4, 2017

https://youtu.be/Zt8Z_uzG71o Waveforms! Accurately & comprehensively 3 Harald Pfeiffer Hawking 75 Jul 4, 2017

Tools to model BBH Inspiral Merger Ringdown 4 Harald Pfeiffer Hawking 75 Jul 4, 2017

Tools to model BBH Inspiral Merger Ringdown Perturbative expansion in v/c Blanchet, Living Reviews 5 Harald Pfeiffer Hawking 75 Jul 4, 2017

Blanchet, Living Reviews 6 Harald Pfeiffer Hawking 75 Jul 4, 2017

Tools to model BBH Inspiral Merger Ringdown 0 mass-ratio 1 Berti+ 06 7 Harald Pfeiffer Hawking 75 Jul 4, 2017

Tools to model BBH Inspiral Merger Ringdown 8 Harald Pfeiffer Hawking 75 Jul 4, 2017

Tools to model BBH Inspiral Merger Ringdown 0 mass-ratio 1 9 Harald Pfeiffer Hawking 75 Jul 4, 2017

Tools to model BBH Inspiral Merger Ringdown 0 mass-ratio 1 e , S 10 Harald Pfeiffer Hawking 75 Jul 4, 2017

Tools to model BBH Inspiral Merger Ringdown 0 mass-ratio 1 LIGO/Caltech/MIT/Sonoma State (Aurore Simonnet) e , S 11 Harald Pfeiffer Hawking 75 Jul 4, 2017

Tools to model BBH Inspiral Merger Ringdown 0 mass-ratio 1 NS-BH (stellar mass) LIGO/Caltech/MIT/Sonoma State (Aurore Simonnet) e , S 12 Harald Pfeiffer Hawking 75 Jul 4, 2017

Tools to model BBH Inspiral Merger Ringdown 0 mass-ratio 1 NS-NS SMBH mergers NS-BH (stellar mass) Congrats to the approved mission! Extreme-mass-ratio inspirals e , S 13 Harald Pfeiffer Hawking 75 Jul 4, 2017

Numerical Relativity 14 Harald Pfeiffer Hawking 75 Jul 4, 2017

50 Years of numerical relativity for BBH 
 2007- 
 2005 Pretorius 
 2000-04 
 1962 ADM 
 1992,3 
 Ajith, AEI, Jena 
 inspiral-merger- 
 AEI / UTB-NASA 
 3+1 formulation Choptuik; 2011 
 1999-00 
 ringdown (IMR) 
 phenom GW models revive crashing Abrahams+Evans 
 w/ harmonic AEI/PSU 
 Lousto ea 
 codes ( Lazarus) 2009- 
 critical phenomena q=100 grazing collisions 2005-06 
 1964 
 UMD, SXS 
 2014- 
 Campanelli+; Baker+ 
 1997 
 ~2000 Choptuik; 
 EOB GW models Hahn-Lindquist 
 IMR w/ BSSN & 
 precessing 
 Brandt- Schnetter;Brügmann 
 moving punctures 2 wormholes 2011 
 GW models Brügmann 
 mesh refinement Schmidt ea; 2015 
 2006-08 
 1984 
 puncture data 2005 
 Boyle ea 
 Szilagyi ea 
 Scheel+ ( SXS) 
 Unruh 
 1994-98 
 Gundlach ea 
 Radiation aligned 175 orbits IMR w/ spectral excision BBH Grand Challenge frame constraint damping 2015 1964 ~1999 ~2005 1975-77 
 2006,07 
 1999 
 2011 
 2000-02 
 2008 
 1994 Cook 
 Smarr-Eppley 
 BSSN 
 Baker ea; 
 Alcubierre 
 Lovelace ea 
 all of NR 
 Bowen-York 
 head-on evolution 
 Gonzalez ea 
 S/M 2 =0.97 gauge conditions NINJA initial data collision 
 system 2004 
 non-spinning BBH 2011- 
 1994-95 
 1979 York 
 Brügmann ea 
 kicks 1999 Y ork 
 Le Tiec ea NCSA-WashU 
 2009-11 
 kinematics and one orbit 2007 SXS 
 conformal thin self-force studies dynamics of GR improved 
 Bishop, ... 
 sandwich ID 2003-08 
 PN-NR 
 head-on collision 2013 
 1989-95 
 Cauchy 
 comparison Cook, Pfeiffer ea 
 GaTech; SXS characteristic Bona-Masso 
 improved ID extraction 2007-11 
 Precessing modified ADM, 1999-2005 JW York, parameter 2000 Ashtekar 
 (hyperbolicity) 2010 
 RIT; Jena; AEI;… 
 Cornell, Caltech, LSU 
 studies isolated horizons Courtesy Carlos Lousto, BBH superkicks Bernuzzi ea 
 hyperbolic formulations updated by HP C4z 15 Harald Pfeiffer Hawking 75 Jul 4, 2017

First simulations Baker+06 Campanelli+06 Pretorius 05 Baker+07 Important early result: Simplicity of merger Continuous transition 
 inspiral → ringdown 16 Harald Pfeiffer Hawking 75 Jul 4, 2017


 The two main approaches to BBH Puncture initial-data Quasi-equilibrium (Brandt&Brügmann 97) excision initial-data BSSN or C4z 
 (Cook&HP 04, 
 w/ moving punctures Lovelace..HP+ 08) Generalized Harmonic 
 (Campanelli ea 06, Baker ea 06, 
 Bernuzzi, Hildtich 10, Alic ea 12) w/ constraint damping (Gundlach+ 05, Pretorius 05) Damped harmonic gauge 
 1+log, Gamma-driver gauge Constraint preserving and Sommerfeld outer BC minimally reflective outer BC Multi-domain spectral methods Finite differences w/ AMR Pretorius SpEC/SXS collaboration 
 RIT, GATech, Goddard, Jena, 
 FD, AMR, GH 17 Harald Pfeiffer Hawking 75 Jul 4, 2017 Palma, Cardiff, Perimeter Cornell/Caltech/CITA/WSU/Fullerton/AEI

Einstein constraints … ˜ r 2 ψ R + (tr K ) 2 � K 2 = 0 = . . . ˜ σ ˜ r · ( 1 L V ) = . . . r · ( K � g tr K ) = 0 ˜ g = ψ 4 ˜ Lichnerowicz 44 g K = 1 3 tr K g + A conformal scaling A ˜ A A = ψ − 10 ˜ A conformal 
 TT TT decomp. decomp. conformal scaling A TT + 1 A = A TT + 1 A = ˜ ˜ σ (˜ York(+) 72;74;99 L V ) σ ( L V ) A TT = ψ − 10 ˜ ˜ A TT HP,York 03 σ = ψ 6 ˜ σ Hamiltonian picture ≡ Lagrangian picture 18 Harald Pfeiffer Hawking 75 Jul 4, 2017

… for binary black holes ˜ r 2 ψ = . . . • Asymptotics/boundary conditions Brandt,Brügmann 97; Cook,HP 04 ˜ N ˜ r · ( 1 L β )= . . . ˜ • Elliptic solver r 2 ˜ ˜ N = . . . HP+ 02, Ansorg 04 • High spin • Control eccentricity Lovelace..HP+ 08 1 E rot / E rot, max 0.8 0.6 w/ conformal flatness 0.4 0.9995 0.2 0 0 0.25 0.5 0.75 1 2 S/M HP+ 05; Buonanno..HP+ 08 19 Harald Pfeiffer Hawking 75 Jul 4, 2017

Einstein Evolution Equations 20 Harald Pfeiffer Hawking 75 Jul 4, 2017


 
 
 
 
 
 
 Spectral Einstein Code (SpEC) • Expand in basis-functions 
 N � u ( x, t ) = u ( t ) k Φ k ( x ) ˜ k =1 • Compute derivatives 
 analytically 
 N X u 0 ( x, t ) = u ( t ) k Φ 0 ˜ k ( x ) Simulations of Extreme Spacetimes (SXS) collaboration k =1 http://www.black-holes.org/SpEC.html 21 Harald Pfeiffer Hawking 75 Jul 4, 2017


 
 
 
 
 
 
 Spectral Einstein Code (SpEC) • Expand in basis-functions 
 N � u ( x, t ) = u ( t ) k Φ k ( x ) ˜ k =1 • Compute derivatives 
 analytically 
 N X u 0 ( x, t ) = u ( t ) k Φ 0 ˜ k ( x ) Simulations of Extreme Spacetimes (SXS) collaboration k =1 http://www.black-holes.org/SpEC.html 21 Harald Pfeiffer Hawking 75 Jul 4, 2017


 
 
 
 
 
 
 Spectral Einstein Code (SpEC) • Expand in basis-functions 
 N � u ( x, t ) = u ( t ) k Φ k ( x ) ˜ k =1 • Compute derivatives 
 analytically 
 N X u 0 ( x, t ) = u ( t ) k Φ 0 ˜ k ( x ) Simulations of Extreme Spacetimes (SXS) collaboration k =1 http://www.black-holes.org/SpEC.html 21 Harald Pfeiffer Hawking 75 Jul 4, 2017


 
 
 
 
 
 
 Spectral Einstein Code (SpEC) • Expand in basis-functions 
 N � u ( x, t ) = u ( t ) k Φ k ( x ) ˜ k =1 • Compute derivatives 
 analytically 
 N X u 0 ( x, t ) = u ( t ) k Φ 0 ˜ k ( x ) Simulations of Extreme Spacetimes (SXS) collaboration k =1 http://www.black-holes.org/SpEC.html 21 Harald Pfeiffer Hawking 75 Jul 4, 2017

BH boundaries • Excise inside BH horizons • Grid rotates with BHs, 
 and conforms to shape of AH • Outer boundary - constraint preserving - minimally reflective Lindblom, Rinne+ 06 Scheel, HP+ 06, 08; Szilagyi+08; Hemberger+ 13 22 Harald Pfeiffer Hawking 75 Jul 4, 2017

https://youtu.be/p647WrQd684 23 Harald Pfeiffer Hawking 75 Jul 4, 2017

https://youtu.be/p647WrQd684 23 Harald Pfeiffer Hawking 75 Jul 4, 2017

24 Harald Pfeiffer Hawking 75 Jul 4, 2017

Equal mass, zero spin 25 Harald Pfeiffer Hawking 75 Jul 4, 2017 Scheel,HP+ 09

Equal mass, zero spin • Rapid convergence due to spectral methods • Small errors due to moving grid 25 Harald Pfeiffer Hawking 75 Jul 4, 2017 Scheel,HP+ 09

post-Newtonian vs. NR GW-cycles to merger 26 18 10 2 PN order 2.0 0.3 PN order 2.5 PN order 3.0 φ PN - φ NR (radians) PN order 3.5 0 -0.3 TaylorT1 TaylorT2 TaylorT3 TaylorT4 -0.6 2400 1200 3600 PN approximants t/m Equally justified approaches to derive inspiral rate from dE Boyle..HP+ 07 energy balance dt = − F GW 26 Harald Pfeiffer Hawking 75 Jul 4, 2017