Binary Black Holes, Gravitational Waves, & Numerical Relativity Part 2

Transcription

1 1 Binary Black Holes, Gravitational Waves, & Numerical Relativity Part 2 Joan Centrella Chief, Gravitational Astrophysics Laboratory NASA/GSFC Summer School on Nuclear and Particle Astrophysics: Connecting Quarks with the Cosmos June 29 - July 10, 2009 University of Washington

2 GWs from BBH mergers. 2 K. Thorne (Caltech), T. Carnahan (NASA GSFC)

3 GWs from final merger of BH binary... 3 Strong-field merger is brightest GW source, luminosity ~ L SUN Requires numerical relativity to calculate dynamics & waveforms Waveforms scale w/ masses, spins apply to ground-based & LISA Must solve Einstein s equations on high performance computers (graphic courtesy of Kip Thorne)

4 Computing black hole mergers 4 Nearly as difficult as building these (gravitational wave) observatories, however, is the task of computing the gravitational waveforms that are expected when two black holes merge. This is a major challenge in computational general relativity and one that will stretch computational hardware and software to the limits. However, a bonus is that the waveforms will be quite unique to general relativity, and if they are reproduced observationally, scientists will have performed a highly sensitive test of gravity in the strong-field regime. -- Connecting Quarks with the Cosmos: Eleven Science Questions for the New Century (National Academies, 2003) A very difficult problem unsolved for > 40 years!

5 It takes a team. and a community 5 Groups & colleagues at: Goddard Numerical Relativity Group JC, Sean McWilliams, Bernard Kelly, Jim van Meter, Darian Boggs, John Baker RIT (formerly UTB) Jena Penn State AEI UT Austin Princeton UMCP LSU Caltech Cornell

6 A Brief History of BBH merger simulations : Hahn & Lindquist: try to evolve collision of 2 wormholes 1970s: Smarr and Eppley: head-on collision of 2 BHs, extract GWs Pioneering efforts on supercomputers at Livermore Natl Lab 1990s: LIGO moves ahead & work on BBH problem starts up again.. NSF Grand Challenge: multi-institution, multi-year effort in 3-D This is really difficult! Instabilities, issues in formalisms, etc Multiple efforts (AEI, UT-Austin, PSU, Cornell ) While progress is made, though incrementally Difficulties still proliferate, instabilities arise, codes crash... Numerical relativity is impossible s: LIGO/GEO/VIRGO and LISA spur more development New groups arise: Caltech, UT-Brownsville, LSU, NASA/GSFC Since Breakthroughs & rapid progress throughout community late 2004: 1 st complete orbit simulated 2005: 1 st mergers + GWs; new methods accelerate progress 2006 onward: many new results.

7 Numerical Relativity: Spacetime Engineering... Construct spacetime by solving Einstein eqns on a computer Slice 4-D spacetime into a set of 3-D t= constant hypersurfaces Set (constrained) initial data on a slice at t = 0 Evolve data forward in time, from one slice to the next Need to solve 17 eqns Partial differential eqs Nonlinear Coupled Codes must be stable & accurate for binary to evolve for several orbits or more 7 Units: set c = G = 1 1 M ~ 5 x 10-6 (M/M Sun ) sec ~ 1.5 (M/M Sun ) km

8 Building a spacetime, slice by slice... General relativity gives freedom to choose how coordinates will evolve in time Relationships between coords on neighboring slices lapse function α shift vector β i good choice of α & β i critical for successful evolution! 8 How to represent the black holes on a computational grid? Excise the singular regions inside horizon? Puncture method. Do the black holes move through the grid?

9 Major computational challenges... 9 Develop computational laboratory to simulate BBH mergers Multiple scales: λ GW ~ (10 100)M need adaptive computational grid w/ variable resolution

10 10 Computing BBH mergers: the results

11 The 1 st complete binary black hole orbit 11 Bruegmann, Tichy, & Jansen, PRL, 92, (2004), gr-qc/ * equal mass, nonspinning BHs Represent BHs as punctures that are fixed in the computational grid Use comoving coordinates traditional techniques Runs for ~ ( )M and BHs complete ~ 1 orbit Crashes before BHs merge Not accurate enough to be able to extract GWs

12 The 1 st orbit, merger, & ringdown 12 Pretorius, PRL, 95, (2005) gr-qc/ Very different techniques Excised BHs move through grid Equal mass, nonspinning BHs

13 A new idea: moving puncture BHs 13 Allow puncture BHs to move across grid w/out excision Simultaneous, independent discovery by UTB & GSFC groups: Campanelli, et al., PRL, 96, (2006), gr-qc/ Baker, et al., PRL, 96, (2006), gr-qc/ Uses traditional numerical relativity techniques Enables long duration, accurate simulations

14 A powerful new idea.that spread rapidly 14 Developed w/in traditional numerical relativity approach Represent BHs as punctures and allow them to move Requires novel yet simple slicing and coordinates UTB, GSFC moved ahead rapidly, quickly do multiple orbits Moving punctures quickly adopted by many other groups: PSU, AEI/LSU, FAU/Jena At April 2006 APS meeting, a full session devoted to BBH mergers w/ moving punctures! Summer 2006: method adopted by most of community Winter 2007: many new results coming out quickly! Campanelli, et al., PRD, 73, (2006), gr-qc/

15 Revealing universal behavior 15 Baker, al., PRD, 73, (2006), gr-qc/ Equal mass, nonspinning BHs Run several cases, starting from successively wider separations BH orbits lock on to universal trajectory ~ one orbit before merger BH trajectories (only 1 BH shown) BH separation vs. time

16 Universal waveform 16 Robust, universal waveform, with a simple shape Baker, al., PRD, 73, (2006), gr-qc/ Universal dynamics produces universal waveform... All runs agree to within < 1% for final orbit, merger & ringdown ~ 4% of mass emitted as GW Luminosity ~ L Sun Most energetic source by far: outputs more energy than all the stars in observable universe combined!

17 Binary Black Holes: The Movies 17 Re[ ψ 4 ] ~ d 2 /dt 2 h + Im[ ψ 4 ] ~ d 2 /dt 2 h x (Visualizations by Chris Henze, NASA/Ames)

18 18 A gallery of BBH waveforms.

19 Comparing gravitational waveforms Compare GWs from equal mass, nonspinning case 3 different, independently-written codes Baker, Campanelli, Pretorius, Zlochower, Class. Quantum Grav. 24 (2007) S25-S31 (gr-qc/ )

20 Comparing gravitational waveforms Compare GWs from equal mass, nonspinning case 5 different, independently-written codes Hannam, et al. (arixiv: [gr-qc])

21 21 GWs from unequal mass, nonspinning BHs Sum over modes up to l = 3 at θ=0, φ = 0 Scale by η = (m 1 + m 2 )/(m 1 + m 2 ) 2 Baker, et al., Phys. Rev. D 78 (2008) (arxiv: ) Mass ratio 10:1 Ψ lm (t) for l = m modes Gonzales, Sperhake, & Bruegmann, (arxiv:0811:3952 [gr-qc])

22 GWs from equal mass BHs with spin 22 Equal up-up and down-down spins Equal masses, each BH has a = 0.75 m Initially MΩ = 0.05 T orbital ~ 125M Campanelli, et al., Phys.Rev. D74 (2006) (gr-qc/ ) Anti/aligned attractive/repulsive Final spins: - a=0.9m (aligned) - a=0.44m (anti)

23 GWs from precessing unequal mass BHs 23 m 1 /m 2 ~ 0.8, a 1 /m 1 ~ 0.6, a 2 /m 2 ~ 0.4 Spins initially at arbitrary orientations Completes ~ 9 orbits before merger Campanelli, et al. (arxiv: [gr-qc]) Trajectory difference r = x 1 x 2

24 24 Applications: Astrophysics

25 Recoil kicks from BBH mergers... For binaries with asymmetric spins and/or unequal masses: the GW emission is asymmetric the GWs are beamed in some direction 25 Since the GWs carry momentum, the final BH that forms suffers a recoil kick in the opposite direction If this kick velocity is large enough, the final BH that forms could be ejected from its host structure For reasonably rich globular clusters, escape speed is ~ 50 km/s For galaxies with central MBHs in LISA s range, need kick of ~ ( ) km/s to escape completely, and ~ ( )km/s to dislodge merged BH from center Note escape speeds from mergers at earlier times (higher z) will be smaller Since most of the effect occurs in the regime of strong gravity, need numerical relativity simulations for accurate results

26 Recoil kicks from BBH mergers Nonspinning, unequal mass BHs: max kick velocity ~ 175 km/s Spins perpendicular to orbital plane: kicks up to ~ 400 km/s for spins parallel to orbital angular momentum relevant for wet mergers, in which torques from gas disks around BHs align the spins kicks < 200 km/s merged BH is retained by galaxy Spins in the orbital plane: can give very large kicks up to max of ~ 4000 km/s! Campanelli, et al., Phys. Rev. D 75 (2007) gr-qc/

27 Spinning Black Holes: The Movie 27 m 1 = m 2 each BH has a/m ~ 0.9 spins oppositely directed in orbital plane Final BH has: a/m ~ 0.67 v kick ~ 1500 km/s in +z direction (Visualizations by Chris Henze, NASA/Ames)

28 28 Applications: Observing BBH mergers using GWs

29 Detecting BH mergers: from the ground 29 Equal mass, nonspinning black holes Make composite waveform by matching to PN Contours of SNR for detection using LIGO sensitivity curve) Advanced LIGO Baker, et al., PRD 75 (2007) (gr-qc/ )

30 Observing MBH mergers from space 30 Equal mass, nonspinning black holes Contours of SNR for detection using LISA sensitivity curve Baker, et al., PRD 75 (2007) (gr-qc/ ) LISA

31 Observing MBH mergers with LISA. MBH binary with total mass M=10 5 M SUN at redshift z = 15 Create mock LISA data: inject numerical waveform into simulated LISA data stream with instrumental noise and WD-WD stochastic background Michelson observable X on system s equatorial plane (min signal) 31

32 Observing MBH mergers with LISA Binary Black Holes: strong signals M at z=20 Signal Strength day hour 10 4 LISA Sensitivity High SNR needed for mass, spin, distance Frequency

33 LISA: Precision Measurements of BH Systems 33 High SNR waveforms carry precision information about the emitting systems High-precision black hole properties from LISA measurements: Massive black hole mergers: Masses, spins to <0.1%, distances to 3% or less (z=1; an order of magnitude worse at z=20) Extreme mass ratio inspirals: Spins to 0.01%, distances to 1-2% (z<1) Masses,spins, and numbers as a function of redshift: How did black holes (BHs) initially form and what were their masses? How did accretion spin-up the BHs? How do the spins evolve over time? What happened to BHs as the initial galaxies merged to make modern galaxies.

34 Absolute Distances: Cosmological parameters 34 H 0 potentially measured to <1% Luminosity distances to ~1-10% LISA also has the potential to measure the dark energy equation of state, along with the Hubble constant and other cosmological parameters. Through gravitational wave form measurements LISA can determine the luminosity distance of sources directly. If any of these sources can be detected and identified as infrared, optical or x-ray transients and if their redshift can be measured, this would revolutionize cosmography by determining the distance scale of the universe in a precise, calibration-free measurement. (NRC BEPAC)

35 Can we see what LISA will hear? 35 Does the merger produce an EM signal? Merging MBHs could be surrounded by gas, accretion disk, magnetic fields Will there be any effects of the merger that produce EM radiation? Effects of ejected or dislodged central MBHs? Many possibilities active area of research: Inspiraling binary may cause pulses in the disk ~ 4% of mass emitted in GWs disk may react to this change in the gravitational potential Gas flows and accretion onto the merging BHs themselves.

36 Modeling flows around MBH mergers 36 Model the behavior of gas and magnetic fields in the dynamical spacetime around the merging BHs First step: map flow of test particles as BHs merge Set up initial distribution of particles around BH binary Evolve the BH binary using numerical relativity Trace the motion of the particles along the geodesics as the binary evolves Estimate energetics of the flow from collisions For each particle, look at nearest 8 neighbors and calculate minimum distance between these two particles If this minimum distance is < r crit collision Collision energies insensitive to the chosen value of r crit in the range 0.01M < r crit < 1 M

37 37 Modeling flows around MBH mergers Initial setup: thermal thick disk Up to 75,000 particles, uniformly distributed extent: 8M < r < 25M, -5M < z < +5M Particles have thermal velocities sampled from a Gaussian Consider these cases Nonrotating BHs, with 2 or 5 orbits before merger Rotating BHs, with equal and aligned spins a/m = 0.8, and 5 orbits before merger Nonrotating BH (25,000 particles) Units: set c = G = 1 1 M ~ 5 x 10-6 (M/M Sun ) sec ~ 1.5 (M/M Sun ) km

38 Merger of nonrotating BHs, m 1 =m 2 38 Initial state: 25,000 particles, uniformly distributed - extent: 8M < r < 25M, -5M < z < +5M - thermal velocities with random directions BHs complete ~ 2 orbits & form common horizon at ~ 126 M

39 Merger of nonrotating BHs, m 1 =m 2 39 Particles move at relatively high radial velocities Outer regions show high radial outflow velocities

40 Van Meter, et al

41 Van Meter, et al

42 Will We See EM Signals from BH mergers? Not guaranteed, but if detected yields exciting scientific return Host galaxy identification provides unique information on galaxy-bh co-evolution Host galaxy identification allows accurate determination of distance-redshift relation LISA will provide few-degree error boxes and time of merger months before event Error boxes shrink to degree or sub-degree size as signal-to-noise increases and merger approaches 42 The first LISA detections of massive Black Hole mergers will mobilize global astronomical resources and be an astronomical event of enormous excitement. These are the most energetic events in the universe since the Big Bang.

43 Summary and outlook... Impressive progress on a broad front: many research groups, different codes, different methods Equal mass, nonspinning BBHs: Excellent agreement on simple waveform shape total GW energy emitted in last few cycles ΔE ~ 0.04M final BH has spin a ~ 0.7M Run for many orbits long wavetrains Comparisons with post-newtonian analysis. Applications to GW data analysis are beginning Explosion of work on nonequal mass and spinning BH mergers and the resulting kicks Higher mass ratios, more generic precessing spins Important astrophysical applications Triggering new work on EM counterparts. Modeling flows around MBH mergers Preliminary results show high velocity flows may produce high energy emissions 43

44 The emerging picture. 44

45 Stay Tuned! 45