The Kicking of Black Holes Pablo Laguna Center for Relativistic - PowerPoint PPT Presentation

The Kicking of Black Holes Pablo Laguna Center for Relativistic Astrophysics School of Physics Georgia Tech, USA Stephen Hawking 75 th Birthday Conference, Cambridge, UK, July 4, 2017

GW150914 Credit: LIGO Scientific Collaboration

GW150914: Energy, Angular Momentum and Linear Momentum Linear Mom. / M (km/s) 140 km/s ~4% Energy / M (%) "I ✓Z t Z t Z t 0 ! # r 2 ◆ dJ i Ψ 4 dt 00 dt 0 ˆ Ψ 4 dt 0 d Ω dt = − lim 16 π Re J i r !1 Angular Mom. / M 2 �1 �1 �1 0.4 Z t 2 dP i r 2 � � I l i � Ψ 4 dt 0 � dt = lim d Ω � � 16 π r !1 � � �1 Time (M) KICK: Asymmetric beaming of gravitational radiation emission from un-equal masses and/or from spin asymmetries

The Making of a Kick: Fitchet 1983 dP i 63 h d 4 I iab d 3 I ab d 3 I ipa d 3 S qb dt = 2 dt 3 i + 16 45 h ✏ ipq dt 3 i dt 4 dt 3 • Newtonian Binary • Lowest order momentum flux • Kick is the result of a “beating” of the mass quadrupole moment against the mass octupole and current quadrupole moments Wiseman, PRD 46, 1517 (1992)] ⌘ 4 ⇣ ⌘ ⇣ f ( q ) 2( m 1 + m 2 ) V kick = 1 , 480 km/s m 1 > m 2 f max r term v 1 < v 2 f ( q ) = q 2 (1 − q ) q = m 1 m 2 (1+ q ) 5

The Making of a Black Hole Kick ⌘ 5 η 2 ⇣ m ˙ E ≈ r ⌘ 5 δ m ⌘ 1 / 2 η 2 ⇣ m ⇣ m ˙ P N ≈ r m r ⌘ 1 / 2 η 2 ⇣ m ⌘ 5 ⇣ m ˙ [ | ˆ r × ∆ | + | ˆ v · ∆ | ] P SO ≈ r r Kidder PRD 52, 621 (1995) m = m 1 + m 2 ˙ dP P ✓ δ m ◆ ⇣ m ⌘ 1 / 2 m 1 m 2 m , a ≈ ∼ ˙ dE r = E η m 2 ✓ dP ◆ ✓ ∆ E ◆ δ m = m 1 − m 2 V kick c ∼ dE m = ( a 2 m 2 − a 1 m 1 ) /m ∆ ✓ dP/dE ◆ ✓ ∆ E/m ◆ 180 km/s ∼ 0 . 02 0 . 03

The Role of Numerical Relativity Credit: LIGO

Generalized Harmonic Coordinates 2005 Gundlach: 2002 Garfinkle: 2005 Pretorius: Constraint Damping & HC HC for simulating BBH Inspiral & Merger 1992 Choptuik generic singularities AMR Pretorius, PRL 95, 121101 (2005) Constraint Damping Source Functions Principal Hyperbolic Part d + Γ bd c Γ ac d + κ [ n ( a C b ) − 1 1 2 g cd g ab , cd + g cd (, a g b ) d , c + H ( a , b ) − H d Γ ab 2 g ab n d C d ] = 0

BSSN Formulation ! ! ∂ t A = − E − ∇Φ ADM E = −∇ 2 ! ! ! ! ∂ t A + ∇∇⋅ A − 4 π j h ij K ij ! Γ = ∇⋅ A ! ! ∂ t A = − E − ∇Φ     φ Γ i h ij A ij K E = −∇ 2 ! ! ! ∂ t A + ∇Γ − 4 π j 1999 Baumgarte, Shapiro ∂ t Γ = −∇ 2 Φ − 4 π ρ 1995 Shibata, Nakamura

Moving Punctures Campanelli et al, PRL 96, 111101 (2006) Baker et al, PRL 96, 111102 (2006) Non-moving Moving ∂ t α = − 2 α K ∂ t α = β i ∂ i α − 2 α K 1+log Slicing [1995 Bona et al] ∂ t β i = 3 ∂ t β i = ξ B i − n B i 4 α Ψ 0 Γ i − η B i − ζ β j ∂ j  Γ i − η B i ∂ t B i = χ ∂ t  Γ i ∂ t B i = ∂ t  Gamma-driver shift [2003 Alcubierre et al]

Kicks from Un-equal Mass & Non-Spinning BHs What is going on! 300 250 h1 h2 200 h3 v (km/s) 150 100 50 0 0 100 200 300 t (M ADM ) 300 250 r 0 = 6.0 M 200 r 0 = 7.0 M v (km/s) 150 r 0 = 8.0 M 100 50 RIT 0 PN+CLA: Sopuerta et al PRD 74, 124010 (2006) 0 100 200 300 400 500 t (M ADM ) Num Rel:Gonzalez et al PRL 98, 091101 (2006) NASA-GSFC Penn State Damour & Gapakumar Hughes et al V = 750 km/s (4 η ) 2 p 1 − 4 η (1 − 0 . 93 η ) Event m 1 m 2 eta V kick (km/s) V max = 175 km/s at η = 0 . 195 GW150914 36 29 0.247 60.8 Final Spin: GW151226 14 8 0.231 137.5 GW170104 32 19 0.234 130.8 a f = 0 . 6 (4 η ) + 0 . 09

The Anti-Kick Rezzolla, Macedo, Jaramillo, PRL 104, 221101 (2010) Anisotropic curvature distribution on the horizon correlates with the direction and intensity of the recoil.

Kicks from Equal Mass & Aligned Spinning BHs Herrmann, Hinder, Shoemaker, PL, Matzner, ApJ 661, 430 (2007) 400 h=1/40 h=1/35 h=1/32 V (km/s) 300 200 100 0.2 0.3 0.4 0.5 0.6 0.7 0.8 spin parameter a 100 all modes <2, − 2|2, − 1> 1e2 <2,2|2,1> V x (km/s) V x (km/s) 80 <2, − 2|2, − 1> <3, − 3|3, − 2> <3,3|3,2> 1e1 60 top 2 <2,2|3,3> 1e0 40 1e − 1 <2, − 1|3, − 2> 20 <2,1|3,2> <2, − 2|3, − 1> 0 1e − 2 <2,2|3,1> 200 <2, − 2|2, − 1> all modes 1e2 <2,2|2,1> V y (km/s) V y (km/s) 150 <2, − 2|3, − 3> <2, − 2|2, − 1> 1e1 <2,2|3,3> <3,3|4,4> 100 top 2 1e0 50 1e − 1 <2,1|3,2> <2, − 1|3, − 2> 0 1e − 2 0 10 20 30 40 100 150 200 sorted contributing mode overlaps time (M)

Generic BH Spins v x (km/s) 75 50 25 0 v y (km/s) 300 200 100 0 v z (km/s) 900 600 300 0 0 15 30 45 60 75 90 θ (degrees) Herrmann, et al PRD 76, 084032 (2007) Campanelli, et al ApJL, 659, 5 (2007) Koppitz, et al PRL, 99, 041102 (2007)

Super-Kicks Gonzalez, et al, PRL, 98, 231101 (2007) Hyperbolic Encounters Campanelli, et al, PRL, 98, 231102 (2007) Healy, et al PRL, 102, 041101 (2009)

Anatomy of a Superkick 22 ( θ , φ ) + λ ¯ Ψ 4 = κ F ( t ) Y − 2 F ( t ) Y − 2 2 − 2 ( θ , φ ) Z t 2 dt = r 2 � � dE 16 π ( κ 2 + λ 2 ) � � F ( t 0 ) dt 0 � � � � �1 Z t 2 r 2 � � dP dt = 2 16 π ( κ 2 − λ 2 ) � � F ( t 0 ) dt 0 � � 3 � � �1 ˙ ! ✓ ∆ E ◆ ≈ c ( κ 2 − λ 2 ) ✓ ∆ E ◆ P V kick c ≈ ( κ 2 + λ 2 ) ˙ m m E ✓ ( κ 2 − λ 2 ) / ( κ 2 + λ 2 ) ◆ ✓ ∆ E/m ◆ V kick 2 , 160 km/s ≈ 0 . 4 0 . 03 Brugmann et al, PRD 77, 124047 (2008)

The Role of Numerical Relativity • Phenomenological and EOB waveform models • Fitting Formulas for Final • Spin • Mass • Kick Lousto et al, CQG 27, 114006 (2010)

The Escape Velocity Kick Problem Superkicks Spins || ang. mom. Unequal mass, non-spinning Merritt et al APJ (2004)

Implications of Spin Alignment Spins aligned with orbital ang. mom. if inspiral • driven by torques from a circumbinary disc. Spin orientations closer to random if inspiral • driven by stellar interactions or chaotic accretion. Blecha et al, MNRAS 456, 961 (2016)

Detecting Recoiling Black Holes Recoiling supermassive BH: Carries with it the inner parts of the accretion disk. • Accretes gas for 10 5-6 years, appearing quasar-like. • Travels away from the center of the host galaxy. • Potentially capturing more gas along the way. • Observational Signatures: A quasar spatially offset from the center of its host galaxy • Broad emission lines in a quasar spectrum with different velocity from that • of the host galaxy. Caveats: The quasar could be in a disturbed/interacting/post-merger galaxy with the BH • not settled down yet. Broad emission lines of quasars are notoriously asymmetric, thus difficult to • define and measure their velocity shift.

QSO 3C 186: A gravitational wave recoiling black hole? M. Chiaberge, et al, A&A 600, A57 (2017) HST imaging shows that the AGN is offset by 1.3 ± 0.1 arcsec (i.e. 11 kpc) • from to the center of the host galaxy. Spectroscopic data show that the broad emission lines are offset by - • 2,140 ± 390 km/s with respect to the narrow lines. Host galaxy displays a distorted morphology with possible tidal features • that are typical of the late stages of a galaxy merger.

QSO J0927+2943: Recoiling or binary black hole candidate? R. Decarli, et al, MNRAS 445, 1558 (2014) Komossa (2008): • Two sets of optical emission lines One set very narrow and a second set of broad • Balmer and broad high-ionization forbidden. The second are blueshifted by 2,650 km/s • relative to the narrow emission lines. The recoiling/binary black hole scenarios are ruled out by the clear detection of a galactic–scale molecular gas reservoir at the same redshift of the QSO broad lines

Black Holes Kicks as New Gravitational Wave Observations D. Gerosa, C.J. Moore, PRL 117, 011101 (2016) 2 n = 0 . 5 c n = − 0 . 5 c M → M (1 + ~ n ) v k · ˆ v k · ˆ v k · ~ v k · ˆ n = 0 v k · ˆ n = 0 1 h + 0 − 1 − 2 2 1 h × 0 − 1 − 2 0 50 100 150 200 250 0 50 100 150 200 250 t/M t/M ∆ M r M r ≈ 0 . 322 ρ r

Conclusions: Gravitational Wave Astronomy is here • Numerical Relativity is a tool for astronomical • discoveries BH holes kicks are an excellent candidate for • multi-messenger astrophysics