gravitational recoil in the coalescence of astrophysical ... · black holes black holes in...
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Ulrich Sperhake
California Institute of Technology
Gravitational recoil in the coalescenceof astrophysical black-hole binaries
Ole’Miss Colloquium Oxford, 24th Mar 2009
Projects with B.Brügmann, J.A.González, M.D.Hannam,S.Husa E.Berti, V.Cardoso
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Overview
Black holes
Black holes in astrophysics
Results on gravitational recoil
MBH formation history BH populations Structure of galaxies
Discussion…
The recoil effect
Analytic predictions Numerical results: non-spinning binaries Numerical results: spins
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1. Black Holes
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What are black holes?
General Relativity
Regions of extreme curvature black hole
⇒ Gravitation via spacetime curvature, no force!
⇒
Mathematical: Event horizon, apparent horizon
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Black hole solutions
Mathematical solutions of Einstein’s equations
Just a mathematical curiosity or physically real?
( )222221
22 sin2121 φθθ ddrdrrMdt
rMds ++#
$
%&'
( −+#$
%&'
( −−=−
Schwarzschild 1916
With charge and/or spin
Reissner & Nordström 1916 Kerr 1963 Kerr-Newman 1965
Renaissance in the last 20-30 years!
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What about black-hole binaries?
Pioneers: Hahn, Lindquist ’60s, Eppley, Smarr et.al. ‘70s
Expected problem to be solved with bigger computers
Instabilities for several decades
Problems not common in other computational physics
(gauge, formulation of equations,…)
Breakthrough Pretorius ‘05, Brownsville ‘05, Goddard ‘05
BBH inspiral now routinely performed by about 10 groups Pretorius, RIT, Goddard, Penn State, U.S. (Lean), Jena (BAM), Potsdam-Louisiana, Caltech-Cornell, Urbana-Champaign
Numerical Relativity necessary to simulate BBHs!!
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Black-hole binaries
Black holes orbiting each other emit GWs
Indirect proof of GR via Neutron Star inspiral⇒ The orbit shrinks
Hulse & TaylorNobel Prize 1993
Requires solution of Einstein equations
Most complex system of Eqs. In physics Numerics!⇒
Caltech-Cornell
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The anatomy of a BBH inspiral Two black holes from a bound system
⇒
Orbit shrinks due to three-body-interactions, gas,… Eventually, GW emission dominates energy loss Still many orbits (thousands, millions) circularization Merger into one hole
Ringdown
Three stages of a BBH inspiral
PN
NR
RD
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Gravitational Wave (GW) Physics Einstein GWs; Analog of electromagn. waves Strongest sources merging black holes
Latest laser technology: Geo600, LIGO, TAMA, VIRGO
⇒
GWs Change of distances⇒
Atomic nucleus in < km 1
Space mission: LISA
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The big picture
Model GR (NR) PN Perturbation theory Alternative Theories?
External Physics Astrophysics Fundamental Physics Cosmology
Detectors Physical system
describes
observe
test
Provide info
Help de
tectio
n
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2. The recoil effect
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Gravitational recoil
Anisotropic emission of GW carries away linear momentum recoil of remaining system
Lowest order: overlap of mass-quadrupole with mass octupole and/or flow quadrupole Bonnor & Rotenburg ’61, Peres ’62, Bekenstein ‘73
⇒
Observations: QSO Komossa et al. ‘08 BH kicked out of galaxy?
Blueshift of Narrow Line Region Relative to Broad Line Region
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Black hole recoil
Initial COM frame is not the final COM frame!!!
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BBH-inspiral
Efficiency depends on
Early stages: three-body interaction Boylan-Kolchin et al.’04
⇒
SMBH inspiral: Galaxies merge BHs merge?
Final parsec problem: Does inspiral stop? Probably not!
Late stages: GW kick
Possible ejection/displacement from host
Magnitude of kick
Depth of potential well
⇒
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BBH-inspiral
Escape velocities: globular clusters dSph dE large galaxies Merritt et al.’04
km/s 30km/s 10020−km/s 300100−km/s 1000≈
Higher redshift DM halos smaller smaller escv⇒ ⇒
Consequences BH growth via mergers stops Population of intergalactic BHs Event rates for LISA Structure of galactic cores
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3. Black Holes in Astrophysics
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Black holes in astrophysics End product of stellar evolution
Gamma-ray bursts?
Structure formation Massive black holes in centres of (almost) all galaxies
Structure of galaxies
AGNs
σ−BHM Relation
BH-formation, populations
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MBH formation history
Seed BHs form in low mass DM halos10≥z6...10≈z0...6≈z
Problem: Large kicks eject BHs in DM halo mergers at high
⇒
Evolution into bright QSOs via halo merger,Growth into SMBH remnants we observe today
(e.g. Madau & Quataert ’04)
z
Not enough time for MBHs to grow hierarchicallyKicks constrain growth models for MBHs; gas accretion?Merrit et al. ’04, Haiman ‘04
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MBH formation history Sloan Digital Sky Survey
⇒sol
910 M> 6≈zQuasars with MBHs exist at
Questions
When does hierarchical BH-formation start?
What is the mass of seed BHs?
Do all progenitor halos have seed BHs?
Alternative BH growth processes (gas accretion)?
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BH populations
Kicks might deplete globular clusters, galaxies of their BHs
Population of interstellar and intergalactic BHs
Larger kicks allow for larger masses of wandering BHs
Kicks also affect population of BHs in the galaxies
Kick leads to deviations from this relationBHM BulgeM
⇒Libeskind et al.’06
e.g. Madau & Quataert ’04, Merritt et al.’04
⇒
and are related linearly
BHs get ejected but regrow IMBHs?
Merger event rates, GW detector design?
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Structure of galaxies
Recoil has impact on structure of host stellar bulges
Density profile of the bulge steep (powerlaw)
Recoil makes density profile evolve: flattening near centre Effect strongest for kicks just below escv
BHs get displaced but fall back Stars follow BH, heating via dynamic friction
Kicks may cause cores in bright ell. galaxies km/s 500100−
How can galaxies with steep profiles exist? No BHs in small galaxies?
Density profiles of early type galaxies show 2 categories: steep profiles and cores
Boylan-Kolchin et al.’04
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4. Calculation of recoil
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4.1. Analytic results
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(Semi-)Analytic predictions
First efforts: perturbation theoryMoncrief ’79, Nakamura & Haugan ‘82
First study of binary inspiral Fitchett ’83
Ensuing studies: Particle approximation Post-Newtonian Close-limit
Newtonian analysis of 2 particles using quadrupole formula
Focus on non-spinning binaries with 12
1 ≠≡MMq
Emerging picture: Kicks unlikely to exceed a few km/s 100 Impact of spins???
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4.2. Numerical results: no spin, unequal masses
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Radiated linear momentum Typical extracted at large radiusradP
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Recoil I: Unequal masses
621 10 ... 1/ =MM
3/ 21 ≈MMkm/s 178 Maximal kick
Expected mass ratios
( )6-
221
21 10 ... 25.0: =+
=MMMM
η
Numerical study: González, US, Brügmann, Hannam & Husa ‘07
)93.01(41102.1 24 ηηη −−×=v
Fit: Fitchett ’83
für
4 ... 1/ 21 =MM
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Recoil I: Unequal masses
What about more extreme mass ratios?
González, US & Brügmann ‘08 10/ 21 =MM
What about eccentricity? Close limit:Sopuerta et al. ’06a, b
vkick / (1 + e)
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Comparison with Post-Newtonian results
Excellent agreement between velocity maximum and Blanchet et al.’05
Ring-down omitted in PN calculations⇒Ring-down breaking?
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4.3. Numerical results II: Spins
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Recoil of spinning holes
Kidder ’95: PN study with Spins
= “unequal mass” + “spin(-orbit)”
Penn State ‘07: SO-term larger
extrapolated:
8.0,...,2.0=ma
km/s 475=v AEI ’07: One spinning hole, extrapolated: km/s 440=v
UTB-Rochester:
km/s 454=v
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Super Kicks
Side result RIT ‘07, Kidder ’95: maximal kick predicted for
Test hypothesisGonzález, Hannam, US, Brügmann & Husa ‘07
Use two codes: Lean, BAM
km/s 1300≈v
Generates kick for spinkm/s 2500=v 0.75≈a
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Super Kicks
Side result RIT ‘07, Kidder ’95: maximal kick predicted for
Test hypothesisGonzález, Hannam, US, Brügmann & Husa ‘07
Use two codes: Lean, BAM
km/s 1300≈v
Generates kick for spinkm/s 2500=v
Extrapolated to maximal spin RIT ‘07
0.75≈a
km/s 4000=v
Highly eccentric orbits PSU ‘08
km/s 10000=v
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Convergence
Discretization error: km/s 43=Δv
Confirmed by various studies PSU, RIT, FAU
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What’s happening physically?
Black holes “move up and down”
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A closer look at super kicks Physical explanation:
“Frame dragging”
Recall: rotating BH drags objects along with its rotation
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A closer look at super kicks Physical explanation:
“Frame dragging”
Recall: rotating BH drags objects along with its rotation
Thanks to F. Pretorius
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A closer look at super kicks
Final kick depends on angle between and
UTB-Rochester ‘07, Jena ‘07
~S ~P
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How realistic are superkicks?
Observations BHs are not generically ejected!
Are superkicks real?
Gas accretion may align spins with orbit Bogdanovic et al.
Kick distribution function:
Analytic models and fits: Boyle, Kesden & Nissanke,AEI, RIT, Tichy & Marronetti,…
EOB study only 12% of all mergers have km/s 500>v⇒
Use numerical results to determine free parameters
⇒
7-dim. Parameter space: Messy! Not yet conclusive…
Schnittman & Buonanno ‘08
vkick = vkick(~S1, ~S2, M1/M2)
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Conclusions
BHs important in many areas of astrophysics
Numerical relativity has solved the BBH problem
Maximum kick from non-spinning binarieskm/s 178 for 3/ 21 ≈MM
Spins generate much larger kicks
Superkicks ; maybe observedkm/s 2500
Observations superkicks most likely not generic⇒
Kick distribution function? Not yet clear…
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Astrophysical implications
larger than escape velocities from giant elliptic galaxieskm/s 2500=v
Giant elliptic galaxies do harbor SMBHs Magorrian et al.’98 constraints kicks; massive kicks not realized?
Important note: is possible. We do not know whether it is generic or even likely!!
km/s 2500=v
⇒
Further astrophysical constraints
Libeskind et al.’06: Deviations of relation
Merritt et al.’06: Narrow emission lines in quasar spectra
km/s 500≤⇒ v
km/s 500≤⇒ v
It appears unlikely, kicks as large as thousands of are generic km/s
Why? Eccentricity?, Spin alignment? Parameter study needed!!!
mBH / mbulge
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Black holes in astrophysics
Many galaxies have MBHs at their centers
CDM cosmogony:
Galaxy mergers imply
Structure forms via hierarchical growth of small objects Galaxies form from mergers of smaller progenitors Dark matter resides as DM halos in galaxies, progenitors These DM halos undergo frequent merger!
BH merger
if BHs are present!