Binary Black Holes and Binary Black Holes and Gravitational WavesGravitational Waves

Joan CentrellaJoan CentrellaChief, Gravitational Astrophysics LabChief, Gravitational Astrophysics LabNASA Goddard Space Flight CenterNASA Goddard Space Flight Center

National Capitol Astronomers MeetingNational Capitol Astronomers MeetingUniversity of Maryland ObservatoryUniversity of Maryland Observatory

November 10, 2007November 10, 2007

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Gravitational Waves . . .

• New prediction of Einstein’s General Relativity (GR)• Ripples in spacetime curvature• Travel at velocity v = c• Generated by moving masses -- such as binaries

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Gravitational Waves (GWs). . .

• First indirect detection: observe the effects of GWs in the Hulse-Taylor binary pulsar PSR 1913+16– binary system of 2 neutron

stars, one a pulsar– GWs carry away energy– Orbital period decays – agrees with GR to w/in the

observational errors of less than 1%

– Nobel Prize 1993

The The direct direct detection of detection of gravitational waves will gravitational waves will

open a fundamental new open a fundamental new window on the universe...window on the universe...

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Detecting gravitational waves directly. . .• The detector has some length L• A passing GW distorts detector by amount ΔL• Measure strain amplitude h(t) = ΔL/L ~ 10-21 or smaller!

(graphic courtesy of B. Barish, LIGO-Caltech)

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Ground-based GW detectors . . . • Laser interferometers with kilometer-scale arms

– LIGO: Hanford, WA, and Livingston, LA; L = 4 km

– GEO600: Hannover L = 600 m

– VIRGO: PISA, L = 3 km

• Detect high frequency GWs in the band 10 Hz - 104 Hz• Typical sources: NS/NS, NS/BH, BH/BH, stellar collapse...

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LISA: Laser Interferometric Space Antenna

• 3 spacecraft in equilateral triangle

– arm length L = 5 million km

– orbits Sun following 20o (50 million km) behind Earth

• Detect low frequency GWs in the band 10-4 Hz - 1 Hz

• typical sources: MBH/MBH, compact binaries, captures…

• ESA/NASA partnership

• In formulation...

Black hole binaries are Black hole binaries are strongstrong sources of sources of

gravitational waves....gravitational waves....

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Massive Black Holes (MBHs)... are found at centers of galaxies

• Most galaxies believed to have central MBH

• Masses M ≥ 105 Msun

• First found in active galaxies• Jets emanate from centers of active

galaxies

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Merging galaxies….

Most galaxies have merged with another at least once....

John Dubinski (CITA)

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...produce Massive Black Hole binaries

0402+379 Separation ~ 24ly NGC 6244

Separation ~ 3000ly

(X-ray: NASA/CXC/AIfA/D.Hudson & T.Reiprich et all;Radio:NRAO/VLA/NRL)

(NASA/CXC/MPE/S.Komossa et al. )

Abell 400 Separation ~ 25,000ly

(Rodriguez, et al. ApJ, astro-ph/0604042)

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Intermediate mass & Stellar BH binaries…• IMBHs M ~ few x(102–103)MSun

• IMBHs and stellar BHs are also expected to form binary systems....

• Stellar BHs M ~ (5 – few x 10)MSUN

If we know these signals If we know these signals – the waveforms – – the waveforms –

we can compare them with the we can compare them with the predictions of Einstein’s General predictions of Einstein’s General

Relativity and test it in the regime of Relativity and test it in the regime of very strong gravity....very strong gravity....

GW detectors will measure GW detectors will measure signals from BH binaries.....signals from BH binaries.....

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Gravitational waveforms are a map of the binary motion…

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GWs from the final merger of a BH binary...• Strong-field merger is brightest GW source

• Luminosity ~ 1023LSUN outputs more energy than all the stars in observable universe combined!

(graphic courtesy of Kip Thorne)

can only be calculated

on a computer!

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A numerical relativity primer....• Solve Einstein’s equations numerically• Slice 4-D spacetime into a stack of 3-D slices• Start the binary in its initial state on a slice at some time• Evolve forward in time, from one slice to the next• Typically solve 17 or more nonlinear, coupled partial

differential equations

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Some subtleties....crucial for success• How do you slice the spacetime when near a BH?• How do you set up a grid of coordinates on each slice?• And…how do prevent that grid from being swallowed up

by the strong gravity of the BHs?• How do you represent a BH on a computer?• The GWs emitted have wavelengths much larger than the

size of the binary orbit. How do you get enough detail in your grid near the BHs, and near the waves?

• We’ll use some special units:

Setting c = G = 1 allows us to measure distances and times in “mass” units

1 M ~ 5 x 10-6 (M/MSun) sec ~ 1.5 (M/MSun) km

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A Brief History of BBH simulations….

• 1964: Hahn & Lindquist: try to evolve collision of 2 “wormholes” • 1970s: Smarr & 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 (Potsdam), UT-Austin, PSU, Cornell…)– Difficulties 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, Jena, FAU…• Since 2004.....

– Breakthroughs & rapid progress throughout community– Orbits, waveforms, and astrophysical applications....

A look at some of the A look at some of the exciting results....exciting 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

• *For gr-qc and astro-ph papers, see http://arxiv.org/

• “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

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A new idea: “moving puncture BHs”

• Allow puncture BHs to move across grid w/out excision

• Simultaneous, independent discovery 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

23A powerful new idea….that spread rapidly

• Developed w/in “traditional” numerical relativity

• Represent BHs as punctures and allow them to move• Requires novel – yet simple – slicing and coordinates• UTB, GSFC moved ahead rapidly, do multiple orbits• Moving punctures quickly adopted by many other

groups:– PSU, Jena, AEI/LSU, FAU…– At April 2006 APS meeting,

held a full session devoted to results of BBH mergers w/ moving punctures!

– Summer 2006: method widely adopted

– Winter 2007: many new results coming out quickly!

Campanelli, et al., PRD, 73, 061501 (2006), gr-qc/06010901

24Revealing universal behavior…

• Baker, al., PRD, 73, 104002 (2006), gr-qc/0602026 • Equal mass, nonspinning BHs• Run several cases, start from successively wider sep’ns• 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….• Universal dynamics produces universal waveform....• All runs agree to within < 1% for final orbit, merger &

ringdown

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Comparison of results…• Baker, Campanelli, Pretorius, Zlochower, gr-qc/0701016 • Compare GWs from equal mass, nonspinning case• 3 different , independently-written codes

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Binary Black Holes: The Movies

+ polarization x polarization

(Visualizations by Chris Henze, NASA/Ames)

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Recoil kicks from BBH mergers...

• When the masses are not equal:– 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!

• Need numerical relativity simulations for accurate results…

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Recoil kicks from nonspinning BBH mergers...

• Nonspinning BHs with m2 ≠ m1

– Baker et al. ApJL, 653, (2006) L93 (astro-ph/0603204)

•m1 = .67 m2 Vkick ~ 90 km/s

– Gonzalez, et al. PRL. 98 (2007) 091101 (gr-qc/0610154)

• found maximum Vkick ~ 176 km/s for m1 ~ .36 m2

• Interesting, but not terribly “dangerous” – However…..

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Recoil kicks from BH mergers w/spin…

• Anti/aligned spins: spins are perpendicular to the orbit of the BHs

• For equal masses: – Herrmann, et al., gr-qc/0701143

vkick up to ~ 400 km/s

– Koppitz, et al., gr-qc/0701163 vkick up to ~ 250 km/s

• For unequal masses, the kick velocities are generally smaller

But…

31If the BH spins are not perpendicular to the orbital plan…

• Such mergers can produce much larger kick velocities

• Gonzalez et al. (gr-qc/0702052), Tichy & Marronetti (gr-qc/0703075): show vkick ~2000 km/s!

• Campanelli et al. (gr-qc/0701164): predict possible max kicks up to vkick ~ 4000 km/s!

32Spinning Black Holes: The Movies

• m1 = m2

• each BH has a/m ~ 0.9

• Final BH has:– a/m ~ 0.67– vkick ~ 1500 km/s

in +z direction

(Visualizations by Chris Henze, NASA/Ames)

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Status of BBH merger simulations...

• Impressive recent progress on a broad front: many research groups, different codes, methods…

• Equal mass, nonspinning BBHs: several groups are now evolving for several orbits, followed by the plunge, merger, and ringdown

• There is general agreement on the simple waveform shape and that – total GW energy emitted in last few cycles

ΔE ~ (0.035 – 0.04)M (depends on # of orbits)– final BH has spin a ~ 0.7M

• Long runs now possible…~ 7 orbits before merger• Applications to GW data analysis are beginning• Explosion of work on nonequal mass and spinning BH

mergers and the resulting kicks– Very interesting results coming out – Important astrophysical applications…

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The emerging picture….

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Stay Tuned!Stay Tuned!