1. Evolution of massive binary black holes (BBHs)
Qingjuan Yu
Canadian Institute for Theoretical Astrophysics
November 19, 2002

2. Outline Introduction Evolution of massive BBHs (stellar dynamics)
Four evolution stages
Main uncertainty
Results: BBH evolution in realistic galaxy models
Gas dynamics around BBHs
Summary

3. Introduction
Each galaxy has a central BH+galaxy mergers  BBHs (Begelman, Blandford & Rees 1980)
Study of the evolution of BBHs
Studying/testing BH physics and gravitation theory
BBH mergers  gravitational waves (detected by LISA? BBH merger rates?)
Physical processes in the vicinity of surviving BBHs  dynamics in strong gravitation fields (BBH surviving rates?)
Understanding galaxy formation
The M• – and M• –L correlations  a close link between the formation and evolution of galaxies and their central BHs.
Probe of the hierarchical model

4. Hierarchical galaxy formation (Cole et al. 2000)
Evolution of BBHs
Stellar dynamics
Gas dynamics
Input:
BH masses
Velocity dispersions
Shapes of bulges
Amount of gas in galactic nuclei
Output:
BBH evolution timescales as a function of BBH semi-major axes
BH growth
(Kauffmann &
Haehnelt, 2000)

5. Evolution of massive BBHs

6. Evolution of massive BBHs
Dynamical friction stage
decreasing a
10-5pc
increasing
1010yr
10kpc
Dynamical friction

7. Evolution of massive BBHs
2. Non-hard binary stage
bound
decreasing a
10-5pc
increasing
1010yr
10kpc
Dynamical friction
dynamical friction (two-body interactions) and three-body interactions with stars passing in their vicinity
3. Hard binary stage
three-body interactions with low-J stars; -1 (E: BBH energy)
(Heggie 1975)
(Quinlan 1996)

8. Evolution of massive BBHs
4. Gravitational radiation stage
decreasing a
10-5pc
increasing
1010yr
10kpc
Dynamical friction
Gravitational radiation
(Peters 1964)

9. Evolution of massive BBHs
Main uncertainty is in the non-hard binary stage and the hard binary stage..
Are low-J stars depleted before the gravitational radiation stage?
Analogy: stellar tidal disruption rates around massive BHs (e.g. Magorrian & Tremaine 1999)
decreasing a
10-5pc
increasing
1010yr
10kpc
Dynamical friction
Gravitational radiation
bottleneck

10. Loss Region
Loss cone:
tidal disruption:
Hard BBH system:
BBH energy loss rate: determined by the rate of removal of stars from the loss cone.
Depletion of the initial population of stars in the loss cone;
New stars are scattered into the loss cone by two-body relaxation;
Steady state: controlled by the balance between the loss rate and the rate at which stars refill the loss cone,
Rate of refilling the loss cone caused by two-body relaxation: solving the steady-state Fokker-Planck equation.

11. `Diffusion’ regime: `Pinhole’ regime:
at small radii, the loss cone is nearly empty.
`Pinhole’ regime:
at large radii, the loss cone is full.
Lightman & Shapiro
(1977)

12. Transition radii rlc the `diffusion’ regime (r<rlc)
the `pinhole’ regime (r>rlc).
Hard BBH system
(Yu 2002)

13. Effects of galaxy shapes
Spherical system (loss cone J<Jlc);
Axisymmetric (flattened) system (loss wedge |Jz|<Jlc):
Js: characteristic angular momentum marking the transition from centrophilic to centrophobic orbits
J<~Js: centrophilic orbits
J>~Js: centrophobic orbits
Stars on centrophilic orbits with |Jz|<Jlc can precess into the loss cone
Triaxiality (loss region J<Js).

14. Jz=0
(Magorrian & Tremaine 1999)

15. Evolution of massive BBHs
Main uncertainty is in the non-hard binary stage and the hard binary stage..
Are low-J stars depleted before the gravitational radiation stage?
Analogy: stellar tidal disruption rates around massive BHs (e.g. Magorrian & Tremaine 1999)
decreasing a
10-5pc
increasing
1010yr
10kpc
Dynamical friction
Gravitational radiation
decreasing a
10-5pc
increasing
1010yr
10kpc
Dynamical friction
Gravitational radiation
bottleneck

16. Role of the BBH orbital eccentricity
(Artymowicz 2000)

17. BBH orbital eccentricity
Scattering experiments in the restricted three-body approximation (Quinlan 1996):
Hardening timescale is independent of its orbital eccentricity (Quinlan 1996).
If the initial eccentricity is small (say, <~0.3), the BBH eccentricity hardly grows as the BBH hardens (Quinlan 1996).
Gravitational radiation stage: the eccentricity decays exponentially.

18. (Quinlan 1996)

19. BBH evolution in realistic galaxy models
Sample: nearby early-type galaxies observed by HST (Faber et al. 1997)
(Yu 2002)

20. BBH evolution in realistic galaxy models (Yu 2002):
increasing triaxiality
increasing velocity dispersion
increasing flattening
merged BBHs
surviving BBHs
Depends on BH masses, and velocity dispersions and shapes of host galaxies
small BHs (m2/m1<10-3) do not decay into galactic centers;
BBHs are more likely to have merged in low-dispersion galaxies and survive in high-dispersion galaxies;
BBHs are more likely to have merged in highly flattened or triaxial galaxies and survive in spherical and nearly spherical galaxies
Estimated orbital properties of surviving BBHs:
separation: 10-3 –10 pc

21. Estimated orbital properties of surviving BBHs
Semimajor axes
Orbital velocities
Orbital periods
(Yu 2002)

22. Estimated orbital properties of surviving BBHs
Semimajor axes
Orbital velocities
Orbital periods
(Yu 2002)

23. The core mass versus the total mass of stars interacting strongly with BHs during the hard binary stage.

24. BBH Brownian motion: generally not important;
might decrease the lifetime of BBHs in some flattened or triaxial galaxies with low velocity dispersion.
(Bahcall & Wolf 1976)

25. Gas dynamics around BBHs
Begelman, Blandford & Rees (1980)
flung out of the system
accrete onto the larger BH (causing orbital contraction as the product of Mr is adiabatically invariant).
Ivanov, Papaloizou & Polnarev 1999; Gould & Rix 2000; Armitage & Natarajan 2002
Planet-like migration

26. Possible observational characteristics of surviving BBHs
double nuclei (upper limit ~ HST resolution)
bending or wiggling of jets (e.g. Blandford, Begelman, Rees 1980)
double-peaked emission lines from broad line regions associated with BBHs in active galactic nuclei (AGNs) (Gaskell 1996)
periodic behavior in the radio, optical, X-ray or -ray light curves (e.g. Valtaoja et al. 2000, Rieger & Mannheim 2000)
broad asymmetric Iron K emission line shape from a two-accretion-disc system associated with a BBH (Yu & Lu 2001)

27. Fe K lines: a tool to probe BBHs in AGNs?
Strongest lines of evidence for the existence of massive BHs
Broad and asymmetric (Doppler and gravitational broadening)
Short-term variability (~104s)
Emitted from inner disc region
Profiles are affected by the inclination between the observer and the disc.
Fe K line profile
Two-accretion-disc system associated with a BBH with different spin axis directions
(Yu & Lu 2001)

28. Summary
The orbital evolution of BBHs depends on the velocity dispersion and shape of the host galaxy, and the masses of BHs.
BBHs are most likely to survive in spherical or nearly spherical and high-velocity dispersion galaxies.
The upper limit of the separations of surviving BBHs is close to the HST resolution for the typical nearby galaxies (at Virgo).
The absence of double nuclei in the centers of nearby galaxies does not necessarily mean that they have no BBHs.
If all galaxies are highly triaxial, there will be no surviving BBHs.
Abundant gas in galactic nuclei may decrease BBH evolution timescales.

29. Hierarchical galaxy formation (Cole et al. 2000)
Evolution of BBHs
Stellar dynamics
Gas dynamics
Input:
BH masses
Velocity dispersions
Shapes of spheroids
Amount of gas in galactic nuclei
Output:
BBH evolution timescales as a function of BBH semi-major axes
BH growth
(Kauffmann &
Haehnelt, 2000)
Three or more BHs

30. BBH merger rates
BBH surviving rates
Relations between BBHs and QSOs/AGNs ……