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

The impact of spin-orbit resonances on astrophysical black-hole populations U. Sperhake DAMTP , University of Cambridge Southampton Gravity Seminar 16 th May 2013 U. Sperhake (DAMTP, University of Cambridge) The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 1 / 59

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

1. Introduction U. Sperhake (DAMTP, University of Cambridge) The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 3 / 59

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

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

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

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

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

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

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

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

Parameters of a black-hole binary 10 intrinsic parameters for quasi-circular orbits 2 masses m 1 , m 2 6 for two spins S 1 , S 2 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

Evolution variables ⇒ Three variables: θ 1 , θ 2 , ∆ φ U. Sperhake (DAMTP, University of Cambridge) The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 13 / 59

Evolution equations 2.5 PN: precessional motion about ˆ L 3 PN: spin-orbit coupling U. Sperhake (DAMTP, University of Cambridge) The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 14 / 59

Schnittman’s resonances Schnittman ’04 For a given separation r of the binary, resonances are S 1 , S 2 , ˆ L N lie in a plane ⇒ ∆ φ = 0 ◦ , ± 180 ◦ Resonance condition: ¨ θ 12 = ˙ θ 12 = 0 Apostolatos ’96, Schnittman ’04 ∆ φ = 0 ◦ resonances: always θ 1 < θ 2 ∆ φ = ± 180 ◦ resonances: always θ 1 > θ 2 The resonance θ 1 , θ 2 vary with r or L N ⇒ Resonances sweep through parameter plane Time scales: t orb ≪ t pr ≪ t GW ⇒ “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

Evolution in θ 1 , θ 2 plane for q = 9 / 11 θ i := ∠ ( � S i ,� L N ) θ 1 = θ 2 S · L N = const S 0 · L N = const evolution ⇒ BHs approach θ 1 = θ 2 ⇒ S 1 , S 2 align if θ 1 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

Resonance capture: ∆ φ = 0 ◦ q = 9 / 11, χ i = 1, θ ( t 0 ) = 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

Resonance capture: ∆ φ = 180 ◦ q = 9 / 11, χ i = 1, θ ( t 0 ) = 170 ◦ , rest random Schnittman ’04 U. Sperhake (DAMTP, University of Cambridge) The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 18 / 59

Consequences of resonances EOB spin S 0 = M m 1 S 1 + M m 2 S 2 S 0 · L N = const evolution ⇒ S 0 ∼ conserved U. Sperhake (DAMTP, University of Cambridge) The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 19 / 59

Consequences of resonances Total spin S = S 1 + S 2 � S · � L N = const evolution blue steeper red ⇒ S , L N 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

Consequences of resonances r decreases ⇒ θ 1 , θ 2 → diagonal i.e. θ 1 = θ 2 ⇒ S 1 , S 2 become aligned; ∆ φ = 0 ◦ θ 12 = θ 1 + θ 2 ; ∆ φ = 180 ◦ U. Sperhake (DAMTP, University of Cambridge) The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 21 / 59

Summary: Resonances S 1 , S 2 , L N precess in plane 2 types: I) ∆ φ = 0 ◦ , II) ∆ φ = 180 ◦ Free binaries can get caught by symmetries Consequences for ∆ φ = 0 ◦ S 1 , S 2 aligned S , L N antialigned Consequences for ∆ φ = 180 ◦ S 1 , S 2 approach θ 12 = θ 1 + θ 2 S , L N aligned U. Sperhake (DAMTP, University of Cambridge) The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 22 / 59

3. Final spins U. Sperhake (DAMTP, University of Cambridge) The impact of spin-orbit resonances on astrophysical black-hole populations 05/16/2013 23 / 59

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 24 / 59

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

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

Final spin of merged BBH Numerical relativity ⇒ fitting formula ( q , S 1 , S 2 ) → S f Here: Barausse & Rezzolla ’09 , but similar results for others θ 1 ( t 0 ) , θ 2 ( t 0 ) , ∆ φ ( t 0 ) isotropic 10 × 10 × 10 large θ 1 , all 1000 binaries, small θ 1 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

Final spin of merged BBH Numerical relativity ⇒ fitting formula ( q , S 1 , S 2 ) → S f Here: Barausse & Rezzolla ’09 , but similar results for others θ 1 ( t 0 ) = 170 ◦ , 160 ◦ , 150 ◦ , 30 ◦ , 20 ◦ , 10 ◦ θ 2 ( t 0 ) , ∆ φ ( t 0 ) : 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

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 S 1 , S 2 ) ∆ 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

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