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Binary Black Holes, Gravitational Waves, & Numerical Relativity
Part 2Joan Centrella
Chief, Gravitational Astrophysics LaboratoryNASA/GSFC
Summer School on Nuclear and Particle Astrophysics:Connecting Quarks with the Cosmos
June 29 - July 10, 2009 University of Washington
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GWs from BBH mergers….
K. Thorne (Caltech) , T. Carnahan (NASA GSFC)
3GWs from final merger of BH binary...• Strong-field merger is “brightest” GW source, luminosity ~ 1023LSUN
• Requires numerical relativity to calculate dynamics & waveforms• Waveforms scale w/ masses, spins apply to ground-based & LISA
(graphic courtesy of Kip Thorne)
Must solve Einstein’s
equations on high
performance computers…
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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)
Computing black hole mergers…
• A very difficult problem –unsolved for > 40 years!
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It takes a team…. and a
community…
Groups & colleagues at:
• RIT (formerly UTB)• Jena• Penn State• AEI• UT Austin• Princeton• UMCP• LSU• Caltech• Cornell…
Goddard Numerical Relativity GroupGoddard Numerical Relativity GroupJC, Sean McWilliams, Bernard Kelly, JC, Sean McWilliams, Bernard Kelly,
Jim van Meter, Darian Boggs, Jim van Meter, Darian Boggs, John BakerJohn Baker
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A Brief History of BBH merger simulations….
• 1964: 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-DThis 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...”• 2000s: LIGO/GEO/VIRGO and LISA spur more development
– New groups arise: Caltech, UT-Brownsville, LSU, NASA/GSFC…• Since 2004....Breakthroughs & rapid progress throughout community
– late 2004: 1st complete orbit simulated…– 2005: 1st mergers + GWs; new methods accelerate progress…– 2006 onward: many new results….
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• 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…
• Units: set c = G = 11 M ~ 5 x 10-6 (M/MSun) sec ~ 1.5 (M/MSun) km
Numerical Relativity: Spacetime Engineering...
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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 βi
good choice of α & βi critical for successful evolution!
• 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?
9Major computational challenges...• Develop computational laboratory to simulate BBH mergers• Multiple scales:
– λGW ~ (10 – 100)Mneed adaptive computational grid w/ variable resolution
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Computing Computing BBH mergers: BBH mergers:
the resultsthe results
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The 1st complete binary black hole orbit…• Bruegmann, Tichy, & Jansen, PRL,
92, 211101 (2004), gr-qc/0312112*• equal mass, nonspinning BHs• Represent BHs as “punctures” that
are fixed in the computational grid• Use “comoving” coordinates
• “traditional” techniques• Runs for ~ (125 – 150)M
and BHs complete ~ 1 orbit• Crashes before BHs merge• Not accurate enough to be
able to extract GWs
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The 1st orbit, merger, & ringdown…
• Pretorius, PRL, 95, 121101 (2005) gr-qc/0507014
• Very different techniques
• Excised BHs move through grid
• Equal mass, nonspinning BHs
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A new idea: “moving puncture BHs”
• Allow puncture BHs to move across grid w/out excision
• Simultaneous, independentdiscovery by UTB & GSFC groups:– Campanelli, et al., PRL, 96,
111101 (2006), gr-qc/0511048– Baker, et al., PRL, 96, 111102
(2006), gr-qc/0511103• Uses traditional numerical
relativity techniques • Enables long duration, accurate
simulations
14A powerful new idea….that spread rapidly
• 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, 061501 (2006), gr-qc/06010901
15Revealing universal behavior…• Baker, al., PRD, 73, 104002 (2006), gr-qc/0602026 • 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
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Universal waveform…
• Robust, universal waveform, with a simple shape
Baker, al., PRD, 73, 104002 (2006), gr-qc/0602026
• Universal dynamics produces universal waveform....• All runs agree to within < 1% for final orbit, merger & ringdown• ~ 4% of mass emitted as GW Luminosity ~ 1023 LSun• Most energetic source by far: outputs more energy than all the
stars in observable universe combined!
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Binary Black Holes: The Movies
Re[ ψ4 ] ~ d2/dt2 h+ Im[ ψ4 ] ~ d2/dt2 hx
(Visualizations by Chris Henze, NASA/Ames)
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A gallery of BBH A gallery of BBH waveformswaveforms……..
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Comparing gravitational waveforms…2006• 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/0701016)
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Comparing gravitational waveforms…2008• Compare GWs from equal mass, nonspinning case• 5 different , independently-written codes
Hannam, et al. (ariXiv:0901.2437[gr-qc])
21GWs from unequal mass, nonspinning BHs…
• Sum over modes up to l = 3 at θ=0, φ = 0• Scale by η = (m1 + m2)/(m1 + m2)2 Baker, et al., Phys. Rev. D 78 (2008)
044046 (arXiv:0805.1428)
• Mass ratio 10:1Ψlm(t) for l = m modes
• Gonzales, Sperhake, & Bruegmann, (arXiv:0811:3952 [gr-qc])
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GWs from equal mass BHs with spin…• Equal up-up and down-down spins• Equal masses, each BH has a = 0.75 m• Initially MΩ = 0.05 Torbital ~ 125M
Campanelli, et al., Phys.Rev. D74(2006) 041501 (gr-qc/0604012)
•• Anti/aligned attractive/repulsive
• Final spins:- a=0.9M (aligned) - a=0.44M (anti)
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GWs from precessing unequal mass BHs…
• m1/m2 ~ 0.8, a1/m1 ~ 0.6, a2/m2 ~ 0.4• Spins initially at arbitrary orientations• Completes ~ 9 orbits before merger
Campanelli, et al. (arXiv: 0808.0713 [gr-qc])
Trajectory difference r = x1 – x2
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Applications: Applications: AstrophysicsAstrophysics
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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…
• 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
~ (500 – 1000) km/s to escape completely, and ~ (250 - 500)km/s to dislodge merged BH from center
– Note escape speeds from mergers at earlier times (higher z) willbe smaller
• Since most of the effect occurs in the regime of strong gravity, need numerical relativity simulations for accurate results…
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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 Campanelli, et al., Phys. Rev. D 75 (2007) 064030 gr(2007) 064030 gr--qc/0612076qc/0612076
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Spinning Black Holes: The Movie
• m1 = m2– each BH has
a/m ~ 0.9– spins oppositely
directed in orbital plane
• Final BH has:– a/m ~ 0.67– vkick ~ 1500 km/s
in +z direction
(Visualizations by Chris Henze, NASA/Ames)
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Applications: Applications: Observing BBH mergers Observing BBH mergers
using GWsusing GWs……
29Detecting BH mergers: from the ground
Advanced LIGO
• Equal mass, nonspinning black holes• Make composite waveform by matching to PN• Contours of SNR for detection using LIGO sensitivity curve)
Baker, et al., PRD 75 (2007) 124024 (gr-qc/0612117)
30Observing MBH mergers…from space
• Equal mass, nonspinning black holes• Contours of SNR for detection using LISA sensitivity curve
Baker, et al., PRD 75 (2007) 124024 (gr-qc/0612117)
LISA
31Observing MBH mergers with LISA….• MBH binary with total mass M=105MSUN 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)
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Observing MBH mergers with LISA…Binary Black Holes: strong signals
Sign
al S
tren
gth
Frequency
105 + 105 M at z=20
day hour104 M @z=5
107 M @z=1
High SNR needed for mass, spin, distance
LISA Sensitivity
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LISA: Precision Measurements of BH 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.
High SNR waveforms carry precision information about the emitting systems
34Absolute Distances: Cosmological parameters
H0 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 wouldrevolutionize cosmography by determining the distance scale of the universe in a precise, calibration-free measurement.”(NRC BEPAC)
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Can we “see” what LISA will “hear”?• 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….
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Modeling flows around MBH mergers• 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 < rcrit “collision”– Collision energies insensitive to the chosen value
of rcrit in the range 0.01M < rcrit < 1 M
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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 = 11 M ~ 5 x 10-6 (M/MSun) sec ~ 1.5 (M/MSun) km
38Merger of nonrotating BHs, m1=m2
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
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Particles move at relatively high radial velocities
Outer regions show high radial outflow velocities
Merger of nonrotating BHs, m1=m2
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Van Meter, et al. 2009
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Van Meter, et al. 2009
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• 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
Will We See EM Signals from BH mergers?
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.
43Summary 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
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The emerging picture….
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Stay Tuned!Stay Tuned!
