Numerical Simulations of Compact Binaries Lawrence E. Kidder Cornell University CSCAMM Workshop Matter and Electromagnetic Fields in Strong Gravity 26 August 2009, University of Maryland Cornell-Caltech Spectral Einstein Code (SpEC) Binary Black Hole Simulations Neutron Star - Black Hole Simulations Lawrence E. Kidder (Cornell) Numerical Simulations of Compact Binaries Maryland 26 August 2009 1 / 18
Binary Black Holes Collaborators: Cornell: Mike Boyle, Lawrence Kidder, Geoffrey Lovelace, Abdul Mroué, Rob Owen, Saul Teukolsky Caltech: Luisa Buchman, Tony Chu, Mike Cohen, Lee Linblom, Keith Matthews, Mark Scheel, Bela Szilagyi, Kip Thorne CITA: Harald Pfeiffer Motivation: Gravitational waves Properties of remnant BH Study strong-field region Numerical approaches: Generalized Harmonic with Excision [Pretorius; PRL 95, 121101 (2005)] Moving puncture [Campanelli, Lousto, Marronetti, Zlochower; PRL 96, 111101 (2006)] [Baker, Centrella, Choi, Koppitz, van Meter; PRL 96, 111102 (2006)] Lawrence E. Kidder (Cornell) Numerical Simulations of Compact Binaries Maryland 26 August 2009 2 / 18
Spectral Einstein Code (SpEC) [Kidder, Pfeiffer, Scheel] Generalized harmonic formulation of Einstein s equations [Friedrich; CMP 100, 525 (1985)] 10 coupled first-order wave equations (50 variables) [Lindblom, Scheel, Kidder, Owen, Rinne; CQG 23, S447 (2006)] Constraint damping [Gundlach, Calabrese, Hinder, Martin-Garcia; CQG 22, 3767 (2005)] Dual frame method with dynamic tracking of the black holes [Scheel, Pfeiffer, Lindblom, Kidder, Rinne, Teukolsky; PRD 74, 104006 (2006)] Time-dependent rotation and scaling Use control theory to adjust mapping to track holes Boundary conditions Excision boundary is pure outflow (no BC needed) Constraint preserving [Lindblom et al (2006)] No incoming physical radiation Minimize reflections of gauge modes [Rinne, Lindblom, Scheel; CQG 24, 4053 (2007)] Lawrence E. Kidder (Cornell) Numerical Simulations of Compact Binaries Maryland 26 August 2009 3 / 18
Multidomain pseudospectral method Exponential convergence for smooth solutions Highly efficient for high accuracy Lawrence E. Kidder (Cornell) Numerical Simulations of Compact Binaries Maryland 26 August 2009 4 / 18
BH-BH equal mass, non-spinning simulation r h 22 / m 16.5 orbit inspiral-meger-ringdown [Boyle, Brown, Kidder, Mroué, Pfeiffer, Scheel, Cook, Teukolsky; PRD 76, 124038 (2007)] [Scheel, Boyle, Chu, Kidder, Matthews, Pfeiffer; PRD 79, 024003 (2009)] Non-spinning S i /mi 2 < 10 5 Low eccentricity e 6 10 5 Numerical error: δφ 0.02 radians; δa/a 0.003 M f /M i = 0.95162(2) S f /Mf 2 = 0.68646(4) 0.4 0.2 0-0.2-0.4 0 1000 2000 3000 4000 t/m 4000 4100 t/m Lawrence E. Kidder (Cornell) Numerical Simulations of Compact Binaries Maryland 26 August 2009 5 / 18
BH-BH Getting from inspiral to ringdown Accurate, efficient inspirals up to an orbit before merger Choosing gauge source functions key to get common horizon [Lindblom, Szilagyi; arxiv:0904.4873 (2009)] Change grid decomposition, follow ringdown Lawrence E. Kidder (Cornell) Numerical Simulations of Compact Binaries Maryland 26 August 2009 6 / 18
BH-BH Current status M 2 /M 1 S1 /M1 2 S 2 /M2 2 N orbits Status Reference 1 0 0 16 Ringdown [Scheel et al (2009)] 2 0 0 15 Ringdown [Buchman et al (in prep)] 3 0 0 15 Inspiral [Buchman et al (in prep)] 4 0 0 15 Inspiral [Buchman et al (in prep)] 6 0 0 8 Inspiral [Buchman et al (in prep)] 1 0 0.5ẑ 4.5 Inspiral [unpublished] 3 0 0.5ẑ 6 Inspiral [unpublished] 1 0.4ẑ 0.4ẑ 11 Ringdown [Chu et al (in prep)] 1 0.4ẑ 0.4ẑ 15 Merged [Chu et al (in prep)] 1 0.5ˆx 0.5ẑ 6.5 Inspiral [unpublished] 2 0.2 2 (ẑ ˆx) 0.4 2 (ẑ + ŷ) 1.5 Ringdown [unpublished] 2 0.2 2 (ẑ ˆx) 0.4 2 (ẑ + ŷ) 8.25 Ringdown [unpublished] Inspiral -> Merger -> Ringdown First case: 1.5 years (not robust) Latest case: worked within days Lawrence E. Kidder (Cornell) Numerical Simulations of Compact Binaries Maryland 26 August 2009 7 / 18
NR vs PN: Waveforms Matched at mω 0.04 (about 24 cycles before merger) mω = 0.063(0.1) is about 10(5) cycles before merger [Boyle, Buonanno, Kidder, Mroué, Pan, Pfeiffer, Scheel; PRD 78, 104020 (2008)] φ PN - φ NR (radians) 2.5 0-2.5-5 t=t 0.063 t=t 0.1 E-approximant P-approximant TaylorT1 TaylorT2 TaylorT3 TaylorT4 0 1 2 3 PN order 0 1 2 3 PN order Lawrence E. Kidder (Cornell) Numerical Simulations of Compact Binaries Maryland 26 August 2009 8 / 18
BH-BH calibrating EOB with NR 0.004 0 EOB Re(ḣ. 22) RM NR Re(Ψ 4 ) RM 0.05 0 [Buonanno, Pan, Pfeiffer, Scheel, Buchman, Kidder; PRD 79, 124028 (2009)] Numerical error: δφ 0.02 radians δa/a 0.003 Similar results using same NR data found by [Damour, Nagar; PRD 79, 081503 (2009)] -0.004 0.01 EOB Re(ḣ. 22) RM NR Re(Ψ 4 ) RM 0.001 0.0001 0.01 φ (rad) A/A 0-0.01 0 1000 2000 3000 t/m -0.05 10-1 10-2 10-3 10-4 10-5 0.16 0.08 0-0.08 3900 3950 4000 4050 t/m Lawrence E. Kidder (Cornell) Numerical Simulations of Compact Binaries Maryland 26 August 2009 9 / 18
BH-BH Future work Comparison among codes [Hannam et al;prd 79, 084025 (2009)] Looked at (2,2) mode from equal mass, non-spinning BBH Compared results from 5 codes Results agreed within numerical accuracies of codes Improve robustness of gauge conditions, domain decomposition, constraint damping parameters Generate as many long simulations as reasonable to calibrate analytic waveforms and test data analysis pipelines Higher spins and more extreme mass ratios Improved extraction of gravitational waves Lawrence E. Kidder (Cornell) Numerical Simulations of Compact Binaries Maryland 26 August 2009 10 / 18
BH-NS binaries Collaborators: Cornell: Matthew Duez, Francois Foucart, Lawrence Kidder, Saul Teukolsky Caltech: Christian Ott Motivation: Gravitational waves Formation of post-merger disk (short GRB engine?) First crude efforts [Shibata, Uryu; PRD 74, 121503(R) (2006)] [Shibata, Uryu; CQG 24, S125 (2007)] [Shibata, Taniguchi; PRD 77, 084015 (2008)] [Etienne, Faber, Liu, Shapiro, Taniguchi, Baumgarte; PRD 77, 084002 (2008)] [Duez, Foucart, Kidder, Pfeiffer, Scheel, Teukolsky; PRD 78, 104015 (2008)] Lawrence E. Kidder (Cornell) Numerical Simulations of Compact Binaries Maryland 26 August 2009 11 / 18
Recent results [Shibata, Kyutoku, Yamamoto, Taniguchi; PRD 79, 044030 (2009)] [Etienne, Liu, Shapiro, Baumgarte; PRD 79, 044024 (2009)] Effects of mass ratio q = M BH /M NS For higher q, expect disruption closer to plunge smaller disk, more BBH-like GWs Studied for 1 q 5 Effects of BH spin s = S BH /M 2 BH For higher aligned s, expect smaller ISCO leads to larger disk longer inspiral Studied by [Etienne et al (2009)] for s = -0.5, 0, 0.75 (aligned) High s led to big disk Effects of compactness C = M NS /R NS Studied by [Shibata et al (2009)] for 0.145 C 0.178 More compact star leads to smaller disk, stronger GW signal Lawrence E. Kidder (Cornell) Numerical Simulations of Compact Binaries Maryland 26 August 2009 12 / 18
BH-NS numerical methods [Duez, Foucart, Kidder, Pfeiffer, Scheel, Teukolsky; PRD 78, 104015 (2008)] [Duez, Foucart, Kidder, Ott, Teukolsky; unpublished] GR handled as with BBH Use shock-capturing finite volume for hydro 2 grids, interpolation, automated remapping fluid grid limited to where the fluid is Lawrence E. Kidder (Cornell) Numerical Simulations of Compact Binaries Maryland 26 August 2009 13 / 18
BH-NS initial data [Duez, Foucart, Kidder, Ott, Teukolsky; unpublished] M BH = 3M NS Initial separation 7.5M (at least two orbits of inspiral) Eccentricity reduced Vary spin Γ = 2 polytrope, C = M NS /R NS = 0.15 Vary s = S BH /MBH 2 = 0, 0.5, 0.9 Vary Equation of State s = 0.5 1 Γ = 2, C = 0.15 2 Γ = 2.75, C = 0.15, 0.18 3 Shen EoS, C = 0.15; advect Y e or impose β-equilibrium Lawrence E. Kidder (Cornell) Numerical Simulations of Compact Binaries Maryland 26 August 2009 14 / 18
BH-NS gravitational waves [Duez, Foucart, Kidder, Ott, Teukolsky; unpublished] Spin orbital hangup smear radius 10-21 10-22 h 10-23 eff 10-24 a/m=0 a/m=0.5 a/m=0.9 10-25 1 2 3 4 f(khz) 10-21 10-22 EoS large compaction effect smaller Γ effect 10-23 h eff 10-24 10-25 10-26 Γ=2, C=0.15 Γ=2.75, C=0.15 Γ=2.75, C=0.18 Shen-β, C=0.15 Shen-Adv, C=0.15 0.5 1 2 4 f(khz) Lawrence E. Kidder (Cornell) Numerical Simulations of Compact Binaries Maryland 26 August 2009 15 / 18
BH-NS post-merger disks [Duez, Foucart, Kidder, Ott, Teukolsky; unpublished] 1 0.8 0.6 M 0 /M 0i 0.4 0.2 a/m=0 a/m=0.5 a/m=0.9 0 0 200 400 600 800 1000 t/m 1 0.8 M 0.6 0 /M 0i 0.4 0.2 0 Γ=2, C=0.15 Γ=2.75, C=0.15 Γ=2.75, C=0.18 Shen-β, C=0.15 Shen-Adv, C=0.15 300 400 500 600 700 t/m Lawrence E. Kidder (Cornell) Numerical Simulations of Compact Binaries Maryland 26 August 2009 16 / 18
BH-NS Future Work Improved resolution and fluid grid Try out multipatch FD for GR to reduce interpolation cost [Pazos, Tiglio, Duez, Kidder, Teukolsky; PRD 80, 024027 (2009)] Generic spins, masses, EoS MHD (MRI turbulence), ν-transport, nuclear reactions Longer inspirals, follow disk longer Lawrence E. Kidder (Cornell) Numerical Simulations of Compact Binaries Maryland 26 August 2009 17 / 18
Conclusions Binary black holes: Can produce long accurate waveforms sufficient for building analytic templates and testing data analysis pipelines Black hole - neutron star binaries Preliminary results suggest large disks can be formed (also seen by [Etienne, Liu, Shapiro, Baumgarte; PRD 79, 044024 (2009)]) Starting to explore effect of NS equation of state Lawrence E. Kidder (Cornell) Numerical Simulations of Compact Binaries Maryland 26 August 2009 18 / 18