Gravitational Recoil and Astrophysical impact U. Sperhake DAMTP , - - PowerPoint PPT Presentation

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Gravitational Recoil and Astrophysical impact U. Sperhake DAMTP , University of Cambridge 3 rd Sant Cugat Forum on Astrophysics 25 th April 2014 U. Sperhake (DAMTP, University of Cambridge) Gravitational Recoil and Astrophysical impact

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SLIDE 1

Gravitational Recoil and Astrophysical impact

  • U. Sperhake

DAMTP , University of Cambridge

3rd Sant Cugat Forum on Astrophysics 25th April 2014

  • U. Sperhake (DAMTP, University of Cambridge)

Gravitational Recoil and Astrophysical impact 25/04/2014 1 / 42

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Overview

Introduction and motivation Calculation of the recoil Suppression of superkicks Unknown Unknown Conclusions

  • U. Sperhake (DAMTP, University of Cambridge)

Gravitational Recoil and Astrophysical impact 25/04/2014 2 / 42

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  • 1. Introduction, motivation
  • U. Sperhake (DAMTP, University of Cambridge)

Gravitational Recoil and Astrophysical impact 25/04/2014 3 / 42

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Gravitational recoil

Recoil = move abruptly backward as a reaction on firing a bullet, shell, or other missile Anisotropic GW emission ⇒ Gravitational recoil Here: Black-hole binary kicks Also relevant for supernovae

  • U. Sperhake (DAMTP, University of Cambridge)

Gravitational Recoil and Astrophysical impact 25/04/2014 4 / 42

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Gravitational recoil

Anisotropic GW emission ⇒ recoil of remnant BH

Bonnor & Rotenburg 1961, Peres 1962, Bekenstein 1973

Escape velocities: Globular clusters 30 km/s dSph 20 − 100 km/s dE 100 − 300 km/s Giant galaxies ∼ 1000 km/s Ejection / displacement of BH

  • U. Sperhake (DAMTP, University of Cambridge)

Gravitational Recoil and Astrophysical impact 25/04/2014 5 / 42

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SLIDE 6

Motivation: Galaxies harbor BHs

Galaxies ubiquitously harbor BHs BH properties correlated with bulge properties

  • e. g. J.Magorrian et al., AJ 115, 2285 (1998)
  • U. Sperhake (DAMTP, University of Cambridge)

Gravitational Recoil and Astrophysical impact 25/04/2014 6 / 42

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SLIDE 7

Motivation: Formation history of SMBHs

Most widely accepted scenario for galaxy formation: hierarchical growth; “bottom-up” Galaxies undergo frequent mergers, especially elliptic ones large kicks ⇒ ejection of BHs ⇒ BH assembly possible? Higher accretion needed? E.g. Merrit et al 2004

  • U. Sperhake (DAMTP, University of Cambridge)

Gravitational Recoil and Astrophysical impact 25/04/2014 7 / 42

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Motivation: Ejection of SMBHs

recoil AGN (Blecha et al) double AGN Doppler shifts of BLR vs. NLR: 2 650 km/s ;

Komossa et al. 2008

Galaxy CID-42: Double AGN or recoiling AGN? Blecha et al. 2012 BH wandering from NGC 1275 to NGC 1277? Shields & Bonning 2013 Review: Komossa 2012

  • U. Sperhake (DAMTP, University of Cambridge)

Gravitational Recoil and Astrophysical impact 25/04/2014 8 / 42

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SLIDE 9

Motivation: BH ejection, BH populations

Hierarchical growth ⇒ BH mergers Most massive dark matter halos at z ≥ 11: BHs not retained if vkick 150 km/s ⇒ Even modest kicks suppress SMHB growth from seed BHs ⇒ >Eddington accretion needed to assemble SMBHs by z ≈ 6?

e.g. Merrit et al 2004 , Micic et al 2006

Ejection affects BH populations

e.g. Holley-Bockelmann et al 2008 , Miller & Lauburg 2009

BH depeleted globular clusters? e.g. Mandel et al 2008 Kicks impact event rates for GW observatories

  • U. Sperhake (DAMTP, University of Cambridge)

Gravitational Recoil and Astrophysical impact 25/04/2014 9 / 42

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SLIDE 10

Motivation: Displacement of SMBHs, Elm signature

Quasars kinemetically or spatially

  • ffset from host galaxy

E.g. COSMOSJ1000+0206: 2 optical nuclei, 2 kpc apart

Wrobel 2014

Moving BH ⇒ tidal disruption of star ⇒ X ray flares

Komossa & Bade 1999 , Bloom et al 2011 , Komossa & Merrit 2008a ,

BHs oscillating on scale of accretion torus ⇒ repeated flares

Komossa & Merrit 2008b

BH velocity relative to accreted gas

Lora-Calvijo & Guzman 2013

  • U. Sperhake (DAMTP, University of Cambridge)

Gravitational Recoil and Astrophysical impact 25/04/2014 10 / 42

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  • 2. Calculation of kicks
  • U. Sperhake (DAMTP, University of Cambridge)

Gravitational Recoil and Astrophysical impact 25/04/2014 11 / 42

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Influential work pre NR

Non-spinning, equal-mass BH binaries ⇒ no kick by symmetry ⇒ Symmetry breaking through mass ratio or spins Quasi-Newtonian calculation for unequal masses (no spins)

Fitchett 1983

vkick = Aη2√1 − 4η(1 + Bη) , η =

q (1+q)2 ,

q = m2

m1

But: Amplitude unclear. PN calculations including spin-orbit coupling

Kidder 1995

dP dt = dPF dt + dPSO dt

,

dPF dt = Fitchett , dPSO dt

= spin-orbit contr.

  • U. Sperhake (DAMTP, University of Cambridge)

Gravitational Recoil and Astrophysical impact 25/04/2014 12 / 42

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SLIDE 13

Kicks from non-spinning BHs

NR simulations for BH binaries with q ∈ [0.1, 1] ⇒ Max. kick: ∼ 175 km/s for q = 0.36

González et al 2007a, 2009

  • U. Sperhake (DAMTP, University of Cambridge)

Gravitational Recoil and Astrophysical impact 25/04/2014 13 / 42

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SLIDE 14

Kicks from spinning BHs

Spins S||L but S1 = S2 ⇒ kicks up to vkick 500 km/s

Herrmann et al 2007 , Koppitz et al 2007 Kidder 1995, Campanelli et al 2007a: maximum kick expected for

“Superkicks”: S1 = −S2 in orbital plane

  • U. Sperhake (DAMTP, University of Cambridge)

Gravitational Recoil and Astrophysical impact 25/04/2014 14 / 42

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Superkicks

Measured: vkick ≈ 2 500 km/s Extrapolated maximum: ∼ 4 000 km/s

González et al 2007b , Campanelli et al 2007b

Sinusoidal dependency on spin orientation α

  • U. Sperhake (DAMTP, University of Cambridge)

Gravitational Recoil and Astrophysical impact 25/04/2014 15 / 42

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Even larger kicks: superkick and hang-up

Lousto & Zlochower, PRL 107 231102

Superkicks Moderate GW generation Large kicks Hangup Strong GW generation No kicks

  • U. Sperhake (DAMTP, University of Cambridge)

Gravitational Recoil and Astrophysical impact 25/04/2014 16 / 42

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Superkicks and orbital hang-up

Maximum kick about 25 % larger: vmax ≈ 5 000 km/s Distribution asymmetric in θ; vmax for partial alignment Higher order corrections to hang-up kick ⇒ Further 10 % increase “Cross-kick”

Lousto & Zlochower 2013

  • U. Sperhake (DAMTP, University of Cambridge)

Gravitational Recoil and Astrophysical impact 25/04/2014 17 / 42

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Fitting formulae for the kick

Goal: Machine, in: BH parameters, out: vkick

Campanelli 2007b

  • Vkick(q,

αi) = vme1 + v⊥ [cos ξ e1 + sin ξ e2] + v||e|| , vm = A q2(1−q)

(1+q)5

  • 1 + B

q (1+q)2

  • ,

v⊥ = H

q2 (1+q)5

  • α||

2 − qα|| 1

  • ,

v|| = K cos(Θ − Θ0)

q2 (1+q)5 |

α⊥

2 − q

α⊥

1 |

A = 1.2 × 104 km/s , B = −0.93 , H = 7.3 × 103 km/s , ξ ∼ 145◦

  • αi = Si/m2

i , Θ = infall angle

  • U. Sperhake (DAMTP, University of Cambridge)

Gravitational Recoil and Astrophysical impact 25/04/2014 18 / 42

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SLIDE 19

Fitting formulae for the kick

Extensions of the fitting formula Systematic spin expansion, exploit symmetry conditions to reduce terms Boyle, Kesden &

Nissanke 2007, 2007a

Calibration of higher-order spin terms, ∼ 100 NR simulations (q = 1) Lousto & Zlochower 2013 Ongoing work; more simulations required

  • U. Sperhake (DAMTP, University of Cambridge)

Gravitational Recoil and Astrophysical impact 25/04/2014 19 / 42

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  • 3. Open questions
  • U. Sperhake (DAMTP, University of Cambridge)

Gravitational Recoil and Astrophysical impact 25/04/2014 20 / 42

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Open problems with current kick predictions

Mass ratio q

Current calibration through q = 1 runs Predictions for q < 1 uncertain; too large? Solution: More runs

BH parameters

Fitting formulae apply to parameters shortly before merger Astrophysical BH parameters apply to large separations What happens to the statistical spin distribution during inspiral?

Almost all galaxies harbor BHs

Superkicks easily eject BHs from giant hosts Why are BHs still there?

  • U. Sperhake (DAMTP, University of Cambridge)

Gravitational Recoil and Astrophysical impact 25/04/2014 21 / 42

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Superkicks easily eject BHs from their host galaxies But: Almost all observed galaxies host BHs How probable are superkicks?

EOB study of q ∈ [0.1, 1], αi = 0.9 ⇒ ∼ 3 % with vkick > 500 km/s, ∼ 12 % with vkick > 1 000 km/s

Schnittman & Buonanno 2007

Gas-rich mergers tend to align S1,2 with L 10 (30)◦ residual misalignment for cold (hot) gas ⇒ superkick suppression

Bogdanovi´ c et al 2010, Dotti et al 2009

PN inspiral of isotropic BH ensemble remains isotropic

Bogdanovi´ c et al 2010

But: How about non-isotropic ensembles?

  • U. Sperhake (DAMTP, University of Cambridge)

Gravitational Recoil and Astrophysical impact 25/04/2014 22 / 42

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SLIDE 23
  • 4. Spin orbit resonances
  • U. Sperhake (DAMTP, University of Cambridge)

Gravitational Recoil and Astrophysical impact 25/04/2014 23 / 42

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Parameters of a black-hole binary

10 intrinsic parameters for quasi-circular orbits 2 masses m1, m2 6 for two spins S1, S2 2 for the direction of the orbital ang. mom. ˆ L. Elimination of parameters in PN inspiral 1 mass; scale invariance 2 for ˆ L; fix z axis 2 spin magnitudes, 1 mass ratio q; conserved 1 spin direction; fix x axis

  • U. Sperhake (DAMTP, University of Cambridge)

Gravitational Recoil and Astrophysical impact 25/04/2014 24 / 42

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Evolution variables

⇒ Three variables: θ1, θ2, ∆φ

  • U. Sperhake (DAMTP, University of Cambridge)

Gravitational Recoil and Astrophysical impact 25/04/2014 25 / 42

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Evolution equations

2.5 PN: precessional motion about ˆ L 3 PN: spin-orbit coupling

  • U. Sperhake (DAMTP, University of Cambridge)

Gravitational Recoil and Astrophysical impact 25/04/2014 26 / 42

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SLIDE 27

Schnittman’s resonances

Schnittman ’04

For a given separation r of the binary, resonances are S1, S2, ˆ LN lie in a plane ⇒ ∆φ = 0◦, ±180◦ Resonance condition: ¨ θ12 = ˙ θ12 = 0

Apostolatos ’96, Schnittman ’04

∆φ = 0◦ resonances: always θ1 < θ2 ∆φ = ±180◦ resonances: always θ1 > θ2 The resonance θ1, θ2 vary with r or LN ⇒ Resonances sweep through parameter plane Time scales: torb ≪ tpr ≪ tGW ⇒ “Free” binaries can get caught by resonance

  • U. Sperhake (DAMTP, University of Cambridge)

Gravitational Recoil and Astrophysical impact 25/04/2014 27 / 42

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SLIDE 28

Evolution in θ1, θ2 plane for q = 9/11

θi := ∠( Si, LN) θ1 = θ2 S · LN = const S0 · LN = const

evolution

⇒ BHs approach θ1 = θ2 ⇒ S1, S2 align if θ1 small

Kesden, US & Berti ’10

  • U. Sperhake (DAMTP, University of Cambridge)

Gravitational Recoil and Astrophysical impact 25/04/2014 28 / 42

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Resonance capture: ∆φ = 0◦

q = 9/11, χi = 1, θ1(t0) = 10◦, rest random

Schnittman ’04

  • U. Sperhake (DAMTP, University of Cambridge)

Gravitational Recoil and Astrophysical impact 25/04/2014 29 / 42

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SLIDE 30

Resonance capture: ∆φ = 180◦

q = 9/11, χi = 1, θ1(t0) = 170◦, rest random

Schnittman ’04

  • U. Sperhake (DAMTP, University of Cambridge)

Gravitational Recoil and Astrophysical impact 25/04/2014 30 / 42

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Consequences of resonances

EOB spin S0 = M

m1 S1 + M m2 S2

S0 · LN = const

evolution

⇒ S0 ∼conserved

  • U. Sperhake (DAMTP, University of Cambridge)

Gravitational Recoil and Astrophysical impact 25/04/2014 31 / 42

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SLIDE 32

Consequences of resonances

Total spin S = S1 + S2

  • S ·

LN = const

evolution

blue steeper red ⇒ S, LN become antialigned; ∆φ = 0◦ aligned;

∆φ = 180◦

  • U. Sperhake (DAMTP, University of Cambridge)

Gravitational Recoil and Astrophysical impact 25/04/2014 32 / 42

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SLIDE 33

Consequences of resonances

r decreases ⇒ θ1, θ2 → diagonal i.e. θ1 = θ2 ⇒ S1, S2 become aligned;

∆φ = 0◦ θ12 = θ1 +θ2; ∆φ = 180◦

  • U. Sperhake (DAMTP, University of Cambridge)

Gravitational Recoil and Astrophysical impact 25/04/2014 33 / 42

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Summary: Resonances

S1, S2, LN precess in plane 2 types: I) ∆φ = 0◦, II) ∆φ = 180◦ Free binaries can get caught by resonances Consequences for ∆φ = 0◦

S1, S2 aligned S, LN antialigned

Consequences for ∆φ = 180◦

S1, S2 approach θ12 = θ1 + θ2 S, LN aligned

  • U. Sperhake (DAMTP, University of Cambridge)

Gravitational Recoil and Astrophysical impact 25/04/2014 34 / 42

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SLIDE 35
  • 5. Suppression of superkicks
  • U. Sperhake (DAMTP, University of Cambridge)

Gravitational Recoil and Astrophysical impact 25/04/2014 35 / 42

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Setup

BBHs inspiral from 1000 M to 10 M Ensemble 1: 10 × 10 × 10 isotropic Ensemble 2: 30 × 30 isotropic in θ2, ∆φ fix θ1(t0) = 170◦, 160◦, 150◦, 30◦, 20◦, 10◦ Map S1, S2, q to vkick

  • v(q, χ1, χ2) = vmˆ

e1 + v⊥(cos ξˆ e1 + sin ξˆ e2) + v||ˆ ez v|| ∼ |∆⊥|, ∆ = qχ2−χ1

1+q

Campanelli, Lousto, Zlochower & Merritt ’07

  • U. Sperhake (DAMTP, University of Cambridge)

Gravitational Recoil and Astrophysical impact 25/04/2014 36 / 42

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SLIDE 37

Kick distributions with and without PN inspiral q = 9

11

Kesden, US & Berti 2010

  • U. Sperhake (DAMTP, University of Cambridge)

Gravitational Recoil and Astrophysical impact 25/04/2014 37 / 42

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SLIDE 38

Same game for hang-up kicks: q = 9

11

Berti, Kesden & US 2012

  • U. Sperhake (DAMTP, University of Cambridge)

Gravitational Recoil and Astrophysical impact 25/04/2014 38 / 42

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SLIDE 39

Summary: Kick suppression

Resonances attract aligned (anti aligned) configurations towards ∆φ = 0◦ (180◦) Superkicks suppressed (enhanced) for ∆φ = 0◦ (∆φ = 180◦) resonances If accretion torque partially aligns S1 with LN ⇒ ∆φ = 0◦ resonances dominate and suppress kicks Kick suppression still effective for hang-up kicks Why? Because the key angle is ∆φ

  • U. Sperhake (DAMTP, University of Cambridge)

Gravitational Recoil and Astrophysical impact 25/04/2014 39 / 42

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SLIDE 40
  • 6. Conclusions
  • U. Sperhake (DAMTP, University of Cambridge)

Gravitational Recoil and Astrophysical impact 25/04/2014 40 / 42

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SLIDE 41

Conlcusions

Kicks important for many astrophysical scenarios BH ejection, BH populations, SMBH assembly, galaxy struxture Kicks generate through asymmetry: mass ratio, spins Superkicks: vkick up to 4 000 km/s , Hangup kicks: 5 000 km/s Kick formulae: apply to late inspiral Gas disks ⇒ spin alignment Spin-orbit resonances ⇒ change spin distribution ⇒ can suppress superkicks Open questions: q dependence, spin distribution

  • U. Sperhake (DAMTP, University of Cambridge)

Gravitational Recoil and Astrophysical impact 25/04/2014 41 / 42