[PPT] - The impact of spin-orbit resonances on astrophysical black-hole PowerPoint Presentation

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The impact of spin-orbit resonances on astrophysical black-hole populations

U. Sperhake

DAMTP , University of Cambridge

Southampton Gravity Seminar 16th May 2013

U. Sperhake (DAMTP, University of Cambridge)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 1 / 59

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Overview

Introduction Spin orbit resonances Final BH spins Suppression of superkicks Stellar-mass BH binary formation

Kesden, Sperhake & Berti, PRD 81 (2010) 084054 Kesden, Sperhake & Berti, ApJ 715 (2010) 1006-1011 Berti, Kesden & Sperhake, PRD 85 (2012) 124049 Gerosa, Kesden, Berti, O’Shaughnessy & Sperhake, arXiv:1302.4442 [gr-qc] Schnittman, PRD 70 (2004) 124020

U. Sperhake (DAMTP, University of Cambridge)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 2 / 59

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

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 3 / 59

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Introduction: Kicks

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)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 4 / 59

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Introduction

Most widely accepted scenario for galaxy formation: hierarchical growth; “bottom-up” Galaxies undergo frequent mergers, especially elliptic ones

U. Sperhake (DAMTP, University of Cambridge)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 5 / 59

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Superkicks

Numerical relativity breakthroughs in 2005

Pretorius ’05, Goddard, RIT ’06

NR now able to accurately calculate kicks Superkicks: up to several 1000 km/s

González et al. ’07, Campanelli et al. ’07

> escape velocities from giant galaxies!

U. Sperhake (DAMTP, University of Cambridge)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 6 / 59

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Introduction: BH binary formation

Evolution of single stars

U. Sperhake (DAMTP, University of Cambridge)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 7 / 59

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Introduction: BH binary formation

Stellar binaries Tides Roche lobe ⇒ mass transfer

U. Sperhake (DAMTP, University of Cambridge)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 8 / 59

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Gravitational wave detectors

LIGO, VIRGO upgraded; ET design studies

U. Sperhake (DAMTP, University of Cambridge)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 9 / 59

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Gravitational wave detectors

GW sources What can we learn from GW observations about BH binary formation?

U. Sperhake (DAMTP, University of Cambridge)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 10 / 59

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2. Spin orbit resonances
U. Sperhake (DAMTP, University of Cambridge)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 11 / 59

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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)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 12 / 59

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Evolution variables

⇒ Three variables: θ1, θ2, ∆φ

U. Sperhake (DAMTP, University of Cambridge)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 13 / 59

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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)

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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)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 15 / 59

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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, Berti & US ’10

U. Sperhake (DAMTP, University of Cambridge)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 16 / 59

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Resonance capture: ∆φ = 0◦

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

Schnittman ’04

U. Sperhake (DAMTP, University of Cambridge)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 17 / 59

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Resonance capture: ∆φ = 180◦

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

Schnittman ’04

U. Sperhake (DAMTP, University of Cambridge)

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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)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 19 / 59

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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)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 20 / 59

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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)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 21 / 59

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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 symmetries 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)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 22 / 59

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3. Final spins
U. Sperhake (DAMTP, University of Cambridge)

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Resonance capturing in practice: q = 9/11

Isotropic 10 × 10 × 10 grid of configurations At R = 1000 M + ǫ, 1000 M, 100 M, 10 M

U. Sperhake (DAMTP, University of Cambridge)

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Resonance capturing in practice: q = 1/3

Isotropic 10 × 10 × 10 grid of configurations At R = 1000 M + ǫ, 1000 M, 100 M, 10 M

U. Sperhake (DAMTP, University of Cambridge)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 25 / 59

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Resonance capturing in practice: q = 9/11

Isotropic 10 × 10 × 10 grid of configurations At R = 1000 M + ǫ, 1000 M, 100 M, 10 M

U. Sperhake (DAMTP, University of Cambridge)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 26 / 59

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Final spin of merged BBH

Numerical relativity ⇒ fitting formula (q, S1, S2) → Sf Here: Barausse & Rezzolla ’09, but similar results for others θ1(t0), θ2(t0), ∆φ(t0) isotropic 10 × 10 × 10 large θ1, all 1000 binaries, small θ1 Initially isotropic stays isotropic

cf. Bogdanovi´

c, Reynolds & Miller ’07

U. Sperhake (DAMTP, University of Cambridge)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 27 / 59

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Final spin of merged BBH

Numerical relativity ⇒ fitting formula (q, S1, S2) → Sf Here: Barausse & Rezzolla ’09, but similar results for others θ1(t0) = 170◦, 160◦, 150◦, 30◦, 20◦, 10◦ θ2(t0), ∆φ(t0): 30 × 30 isotropic dotted: switching off precession solid: with precession

U. Sperhake (DAMTP, University of Cambridge)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 28 / 59

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Summary: Final spins

Resonances act as attractor for random binaries This is a statistical effect! Initially isotropic ensembles stay isotropic; cancelation ∆φ = 0◦ resonances increase final spin (alignment of S1, S2) ∆φ = 180◦ resonances mildly decrease final spin

U. Sperhake (DAMTP, University of Cambridge)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 29 / 59

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4. Suppression of superkicks
U. Sperhake (DAMTP, University of Cambridge)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 30 / 59

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Superkicks

θ1 = θ2 = 90◦, ∆φ = 180◦ Superkicks: up to several 1000 km/s

González, Hannam, Sperhake, Brügmann & Husa, PRL 98, 231101 (2007) Campanelli, Lousto, Zlochower & Merritt, ApJ 659, L5 (2007)

> escape velocities from giant galaxies!

U. Sperhake (DAMTP, University of Cambridge)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 31 / 59

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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)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 32 / 59

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Kick distributions with and without PN inspiral q = 9

11

U. Sperhake (DAMTP, University of Cambridge)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 33 / 59

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Kick distributions with and without PN inspiral q = 1

3

U. Sperhake (DAMTP, University of Cambridge)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 34 / 59

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Even larger kicks: superkick and hang-up

Lousto & Zlochower, arXiv:1108.2009 [gr-qc]

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

U. Sperhake (DAMTP, University of Cambridge)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 35 / 59

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Superkicks and orbital hang-up

Maximum kick about 25 % larger: vmax ≈ 5 000 km/s Distribution asymmetric in θ Largest recoil for partial alignment

U. Sperhake (DAMTP, University of Cambridge)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 36 / 59

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Kick distributions with and without PN inspiral q = 9

11

U. Sperhake (DAMTP, University of Cambridge)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 37 / 59

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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)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 38 / 59

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5. Stellar-mass BH binary

formation

U. Sperhake (DAMTP, University of Cambridge)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 39 / 59

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A simplified scenario for stellar-mass BBH formation

Stellar binary: M

′

Si, M

′′

Si = 35, 16.75 M⊙ or 30, 24 M⊙

Primary expands to fill Roche lobe 50% M transfer to Secondary until core remant M

′

C = 8.5 or 8M⊙

Primary explodes as SN → BH with M

′

BH = 7.5 or 6M⊙

SN kick tilts L Tides may align S

′′ and circularize orbit

Secondary expands to fill Roche lobe ⇒ Common envelope Secondary becomes helium core with M

′′

C = 8 or 8.5M⊙

Secondary explodes as SN → BH with M

′

BH = 6 or 7.5M⊙

SN kick again tilts orbital plane

U. Sperhake (DAMTP, University of Cambridge)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 40 / 59

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Comments: Initial separation

a0 drawn from logarithmic distribution [amin, amax] amax: Primary fills Roche lobe amin: Secondary does not fill Roche lobe at transfer a0 > amax ⇒ binary unbound by SN kick a0 < amin ⇒ merger in CE phase

U. Sperhake (DAMTP, University of Cambridge)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 41 / 59

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Comments: Mass transfer

Star fills Roche lobe ⇒ stable transfer or CE Our q ⇒ SN1 → stable transfer, SN2 → CE

Clausen, Wade, Kopparapu & O’Shaughnessy ’12

Accretion by secondary: M

′′

Sf = M

′′

Si + fa(M

′

Si − M

′

C)

We choose semi-conservative: fa = 0.5 fa tied to fraction of RMR vs. SMR ⇒ potentially measurable via GWs

U. Sperhake (DAMTP, University of Cambridge)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 42 / 59

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Comments: SN kicks

Calibrate kick using observed motion of young pulsars vpNS ∈ Maxwellian with σ = 265 km/s Fallback ⇒ vBH = (1 − ffb)vpNS For our q, simulations suggest ffb = 0.8

Fryer ’99, Fryer & Kalogera ’01

Kicks ∈ cone with θb about S We consider: isotropic θb = 90◦, polar θb = 10◦

U. Sperhake (DAMTP, University of Cambridge)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 43 / 59

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Comments: Kick effect on orbit

SN ⇒ mass reduction, tilt of orbit SN equally likely anywhere in orbit ⇒ true anomaly At SN1: assume S1,2 aligned with L af, ef from conservation of energy, ang. mom. ef > 1 ⇒ Binary unbound Overall: isotropic kicks less likely to unbind binary ⇒ wider ranges of tilt angles

U. Sperhake (DAMTP, University of Cambridge)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 44 / 59

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Comments: Tidal alignment

Tidal dissipation ⇒ circularize orbit; align S2 with L We consider two extremes: i) fully efficient tides, ii) no tidal effects Tidal effects on BH can be safely ignored Tidal effects operate when secondary fills Roche lobe Change in separation due to tides negligible compared with CE phase

U. Sperhake (DAMTP, University of Cambridge)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 45 / 59

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Comments: Common envelope phase

If a1 after SN1 too large ⇒ no CE phase; game over Otherwise: CE has Eb = −

GM

′′ Sf (M ′′ Sf −M ′′ C )

λRL

We use λ from analytic fit of Dominik et al. ’12 Energy, momentum conservation ⇒ a1CE a1CE too small ⇒ helium core fills Roche lobe, prompt merger; game over We neglect accretion onto BH

U. Sperhake (DAMTP, University of Cambridge)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 46 / 59

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Summary: Evolution sequence

U. Sperhake (DAMTP, University of Cambridge)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 47 / 59

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Spin evolution θ1, θ2, tides, iso-kick: SMR, RMR

U. Sperhake (DAMTP, University of Cambridge)

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Spin evolution ∆φ, θ12, tides, iso-kick: SMR, RMR

U. Sperhake (DAMTP, University of Cambridge)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 49 / 59

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Spin evolution θ1, θ2, tides, pol-kick: SMR, RMR

U. Sperhake (DAMTP, University of Cambridge)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 50 / 59

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Spin evolution ∆φ, θ12, tides, pol-kick: SMR, RMR

U. Sperhake (DAMTP, University of Cambridge)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 51 / 59

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Spin evolution θ1, θ2, no tides, iso-kick: SMR, RMR

U. Sperhake (DAMTP, University of Cambridge)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 52 / 59

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Spin evolution ∆φ, θ12, no tides, iso-kick: SMR, RMR

U. Sperhake (DAMTP, University of Cambridge)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 53 / 59

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Spin evolution θ1, θ2, no tides, pol-kick: SMR, RMR

U. Sperhake (DAMTP, University of Cambridge)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 54 / 59

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Spin evolution ∆φ, θ12, no tides, pol-kick: SMR, RMR

U. Sperhake (DAMTP, University of Cambridge)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 55 / 59

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Spin distribution at GW frequencies: ∆φ

U. Sperhake (DAMTP, University of Cambridge)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 56 / 59

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Spin distribution at GW frequencies: θ12

U. Sperhake (DAMTP, University of Cambridge)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 57 / 59

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Summary: BH binary formation

Simplified model for stellar mass BHB formation Key ingredients: mass reversal, tides

U. Sperhake (DAMTP, University of Cambridge)

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Conclusions

Spin orbit resonances attract inspiraling binaries 2 classes of resonances: ∆φ = 0◦, 180◦ Isotropic ensembles remain isotropic Non-isotropic ensembles can be drastically affected Superkicks suppressed if heavy BH’s S more aligned with L Stellar-mass BH binary formation affected by resonances depending on mass transfer, tides

U. Sperhake (DAMTP, University of Cambridge)

The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 59 / 59