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 75th Birthday Conference, Cambridge, UK, July 4, 2017

Credit: LIGO Scientific Collaboration

GW150914

GW150914: Energy, Angular Momentum and Linear Momentum

Linear Mom. / M (km/s) Energy / M (%) Angular Mom. / M2

140 km/s ~4% 0.4

Time (M)

dP i dt = lim

r!1

r2 16π I li

• Z t

1

Ψ4 dt0

• 2

dΩ

dJi dt = − lim

r!1

r2 16π Re "I ✓Z t

1

Ψ4 dt0 ◆ ˆ Ji Z t

1

Z t0

1

Ψ4 dt00 dt0 ! dΩ #

KICK: Asymmetric beaming of gravitational radiation emission from un-equal masses and/or from spin asymmetries

The Making of a Kick: Fitchet 1983

• Newtonian Binary
• Lowest order momentum flux
• Kick is the result of a “beating” of the mass

quadrupole moment against the mass

• ctupole and current quadrupole moments

Vkick = 1, 480 km/s ⇣

f(q) fmax

⌘ ⇣

2(m1+m2) rterm

⌘4

f(q) = q2(1−q)

(1+q)5

q = m1

m2

dP i dt = 2 63hd4Iiab dt4 d3Iab dt3 i + 16 45h✏ipq d3Iipa dt3 d3Sqb dt3 i

Wiseman, PRD 46, 1517 (1992)]

m1 > m2 v1 < v2

The Making of a Black Hole Kick

˙ E ≈ η2 ⇣m r ⌘5 ˙ PN ≈ η2 ⇣m r ⌘5 δm m ⇣m r ⌘1/2 ˙ PSO ≈ η2 ⇣m r ⌘5 [|ˆ r × ∆| + |ˆ v · ∆|] ⇣m r ⌘1/2

m = m1 + m2 η = m1 m2 m2 δm = m1 − m2 ∆ = (a2m2 − a1m1)/m

dP dE ≈ ˙ P ˙ E ∼ ✓δm m , a ◆ ⇣m r ⌘1/2 Vkick ∼ c ✓dP dE ◆ ✓∆E m ◆ ∼ 180 km/s ✓dP/dE 0.02 ◆ ✓∆E/m 0.03 ◆

Kidder PRD 52, 621 (1995)

The Role of Numerical Relativity

Credit: LIGO

Generalized Harmonic Coordinates

1 2 gcdgab,cd + gcd

(,agb)d,c + H(a,b) − HdΓab d + Γbd c Γac d +κ[n(aCb) − 1

2 gabndCd] = 0

Principal Hyperbolic Part Constraint Damping Source Functions Pretorius, PRL 95, 121101 (2005)

2002 Garfinkle: HC for simulating generic singularities 2005 Gundlach: Constraint Damping & HC 2005 Pretorius: BBH Inspiral & Merger 1992 Choptuik AMR

BSSN Formulation

hij Kij

 hij φ  Aij  K  Γi

1999 Baumgarte, Shapiro 1995 Shibata, Nakamura

ADM

∂t ! A = − ! E − ∇Φ ∂t ! E = −∇2 ! A + ∇Γ − 4π ! j ∂t Γ = −∇2Φ − 4π ρ

Γ = ∇⋅ ! A

∂t ! A = − ! E − ∇Φ ∂t ! E = −∇2 ! A + ∇∇⋅ ! A − 4π ! j

Moving Punctures

∂tα = β i ∂iα − 2αK ∂t β i = ξ Bi ∂t Bi = χ ∂t  Γi −η Bi −ζ β j ∂ j  Γi

1+log Slicing [1995 Bona et al] Gamma-driver shift [2003 Alcubierre et al]

∂tα = −2αK ∂t β i = 3 4 α Ψ0

−n Bi

∂t Bi = ∂t  Γi −η Bi Non-moving Moving

Campanelli et al, PRL 96, 111101 (2006) Baker et al, PRL 96, 111102 (2006)

Kicks from Un-equal Mass & Non-Spinning BHs

PN+CLA: Sopuerta et al PRD 74, 124010 (2006) Num Rel:Gonzalez et al PRL 98, 091101 (2006)

RIT NASA-GSFC Penn State Damour & Gapakumar Hughes et al

V = 750 km/s (4 η)2p 1 − 4η (1 − 0.93η)

Vmax = 175 km/s at η = 0.195 af = 0.6 (4 η) + 0.09

Final Spin:

100 200 300 t (MADM) 50 100 150 200 250 300 v (km/s)

h1 h2 h3

100 200 300 400 500 t (MADM) 50 100 150 200 250 300 v (km/s)

r0 = 6.0 M r0 = 7.0 M r0 = 8.0 M

What is going on!

Event m1 m2 eta Vkick(km/s) GW150914 36 29 0.247 60.8 GW151226 14 8 0.231 137.5 GW170104 32 19 0.234 130.8

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) 0.2 0.3 0.4 0.5 0.6 0.7 0.8 100 200 300 400 spin parameter a V (km/s)

h=1/40 h=1/35 h=1/32

Vx (km/s) 1e−2 1e−1 1e0 1e1 1e2

<2,−2|2,−1> <2,2|2,1> <3,−3|3,−2> <3,3|3,2> <2,2|3,3> <2,−1|3,−2> <2,1|3,2> <2,−2|3,−1> <2,2|3,1>

Vy (km/s) 1e−2 1e−1 1e0 1e1 1e2 10 20 30 40

<2,−2|2,−1> <2,2|2,1> <2,−2|3,−3> <2,2|3,3> <3,3|4,4> <2,1|3,2> <2,−1|3,−2>

sorted contributing mode overlaps Vx (km/s) 20 40 60 80 100 all modes <2,−2|2,−1> top 2 Vy (km/s) 50 100 150 200 100 150 200 all modes <2,−2|2,−1> top 2 time (M)

Generic BH Spins

vx (km/s) 25 50 75 vy (km/s) 100 200 300 vz (km/s) 15 30 45 60 75 90 300 600 900 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) Campanelli, et al, PRL, 98, 231102 (2007) Healy, et al PRL, 102, 041101 (2009)

Hyperbolic Encounters

Anatomy of a Superkick

Brugmann et al, PRD 77, 124047 (2008)

Ψ4 = κ F(t) Y −2

22 (θ, φ) + λ ¯

F(t) Y −2

2−2(θ, φ)

dE dt = r2 16π (κ2 + λ2)

• Z t

1

F(t0)dt0

• 2

dP dt = 2 3 r2 16π (κ2 − λ2)

• Z t

1

F(t0)dt0

• 2

Vkick ≈ c ˙ P ˙ E ! ✓∆E m ◆ ≈ c(κ2 − λ2) (κ2 + λ2) ✓∆E m ◆ Vkick ≈ 2, 160 km/s ✓(κ2 − λ2)/(κ2 + λ2) 0.4 ◆ ✓∆E/m 0.03 ◆

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

Unequal mass, non-spinning Spins || ang. mom. Superkicks

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 105-6 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
• f 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)

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 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.

Black Holes Kicks as New Gravitational Wave Observations

• D. Gerosa, C.J. Moore, PRL 117, 011101 (2016)

−2 −1 1 2 h+

vk · ˆ n = 0.5c vk · ˆ n = 0

50 100 150 200 250 t/M −2 −1 1 2 h×

vk · ˆ n = −0.5c vk · ˆ n = 0

50 100 150 200 250 t/M

M → M(1 + ~ vk · ~ n)

∆Mr Mr ≈ 0.322 ρr

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