Black Hole Mergers at Galactic. The Final Parsec: Supermassive. Centers. Milos Milosavljevic. California Institute of Technology
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1 The Final Parsec: Supermassive Black Hole Mergers at Galactic Centers Milos Milosavljevic California Institute of Technology
2 MBH Binaries Form in Galaxy Mergers Borne et al 2000 by transferring binding energy and angular momentum to the ambient medium
3 GALAXY MERGER hard binary a hard G ( M = 8 + σ 1 2 M 2 ) black hole mass (solar mass) binary s semi-major axis (parsec)
4 ) 10 G Gyr ( M 1 + a hard = 8 σ 2 M c a t gr ~ 3 64 G M M ( M M ) 1 2 F ( e ) COALESCENCE black hole mass (solar mass) binary s semi-major axis (parsec)
5 The Final Parsec Problem GALAXY MERGER Can the binaries cover this? binary s semi-major axis (parsec) COALESCENCE black hole mass (solar mass)
6 Interaction of MBHB with Environment Stellar dynamics Dynamical friction Gravitational slingshot interaction Response of the stellar system Gas dynamics Economy of a QSO / AGN / star forming nucleus Accretion disks Multiple MBH / IMBH Gravitational slingshot interaction Resonances (Kozai, etc.)
7 Stellar Dynamics Initial Conditions: Phase Space Structure ρ ~ r 2 power-law core Gebhardt et al 1996 luminosity density luminosity density radius radius and Merger Dynamics Wechsler et al 2002
8 Major Mergers Proceed on a Dynamical Time Scale σ 1 σ 2 The merger time scale at a given separation depends on the stellar mass bound to the black holes >> M bh
9 The Minor Mergers are a Bottleneck t DF ~ (σ 1 /σ 2 ) 3 t dyn In shallow cusps, the smaller MBH is stripped bare of its stars
10 Gravitational Slingshot Mechanism The velocity of ejection scales as, but need not equal, the binary s orbital velocity v eject ~ v bin ~ (GM bin /a) 1/2 The velocity can increase or decrease, but preferentially increases Re-ejection and the potential well depth
11 Merger Finish Marks Start of Long Term Evolution orbital mass ~ 10 binary masses Simulations show that the binary rapidly shrinks by the factor of x10 from after v bin exceeds σ
12 The Loss Cone circular orbit Definition: Domain in phase space consisting of orbits strongly perturbed by individual components of a MBH binary Analogy with the loss cone for the tidal disruption of stars & the capture of compact objects energy However: The binary loss cone is much more extensive and does not destroy stars angular momentum
13 Diffusion into The Loss Cone E = const energy Equilibrium diffusion: Lightman & Shapiro 1977 Cohn & Kulsrud 1978, etc. Magorrian & Tremaine 1999 Yu 2002 GC Galaxies It can take more than a Hubble time to reach the state of equilibrium, particularly in intermediate and massive galaxies angular momentum
14 The Loss Cone: An Initial Value Problem Energy R L / L c ( E N t = µ 2 R ) N Heat equation in cylindrical coordinates The loss cone boundary Angular Momentum
15 Loss Cone Out of Equilibrium 1 Myr 10 Myr 100 Myr 1 Gyr 10 Gyr number of stars angular momentum actual loss cone profile profile in collisional equilibrium
16 Episodic Refilling? E.g. Zhao, Haehnelt, & Rees 2002 log(l) loss cone refilled loss cone refilled N(L) separation Satellite/star cluster infall Star formation episode log(l) time N(L)
17 Spherical Galaxy: Evolution of the Semi-Major Axis Loss cone always full 1 a t Loss cone partially full a 1 N α t α, 1 3 (Makino 1997) Loss cone almost empty a 1 1 N t Large-N limit Re-ejection only a 1 constant 1 a ln ( 1 + β t ) + γ Stalling? (MM & Merritt 2002)
18 Details The binary formation must be simulated. N-body simulations provide: Orbital parameters of the binary (a, e) Initial damage to the stellar cusp Geometry & kinematics of the new cusp Convergence is difficult With N<10 7-8, the simulations lack sufficient resolution due to the spurious relaxation and the spurious Brownian motion (to date, N<10 6 ) Latest, successful effort: Makino & Funato 2003 w/grape
19 Details (Cont d) Non-spherical loss cones add complexity, enhance the flux of stars entering Axisymmetry (e.g., Magorrian & Tremaine 1999, Yu 2002) Triaxiality (Merritt & Poon 2003 Time-dependent potentials (real galaxies!) (fig. J. Barnes)
20 Details (Cont d) Semi-analytic modeling of the binary decay requires detailed scattering data Basic elements studied via 3-body scattering (Hills 1980s, Quinlan 1996, etc.) The special case with equal black holes and a spherical loss cone is fairly well understood Eccentricity remains small Ejected mass ~ few times M bin Dynamics of unequal mass binaries & their effect on the galaxy structure have not been adequately studied
21 Observed Galaxies When photometric data are available, the distribution of stars near the loss cone cannot be determined without knowing the binary s age & the history of the stellar environment. Inferences about the binary separation based on the present-day luminosity profiles potentially underestimate the past decay rate, when the stellar cusp could have been denser.
22 The Mass Deficit γ min = 2.0 γ min =1.75 Definition: Mass that had to be removed to produce the observed profile from the fiducial pure power-law. γ min =1.5 MM, Merritt, Rest & van den Bosch 2001
23 Gas Dynamics Additional physics: dissipation, magnetic fields and star formation γ
24 The First Simulation! Escala, Larson, Coppi & Mardones 2003
25
26 Migration (A protoplanetary disk!) Ivanov, Papaloizou & Polnarev 1999 Armitage & Natarajan 2002 Goodman & Tan 2003 Levin 2003 Armitage & Natarajan 2002
27 Conclusions Idealized stellar dynamical models suggest that long-lived massive black hole binaries are generically produced in the mergers of intermediate and massive galaxies. Massive black hole binaries that form in mergers of low-mass galaxies coalesce in a Hubble time due to stellar dynamical processes. All established physical mechanisms aid an efficient coalescence of the black holes. Physical conditions in the nuclei of perturbed (merging, gas rich) galaxies are not well known, but progress is expected soon!
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