Evolution of massive binary black holes (BBHs)

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) BH growth (Kauffmann & Haehnelt, 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

5. Evolution of massive BBHs

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

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

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

9. Gravitational radiation Dynamical friction 1010yr increasing 10kpc 10-5pc decreasing a 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) 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: • 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. (Magorrian & Tremaine 1999) Jz=0

15. Gravitational radiation Gravitational radiation Dynamical friction 1010yr 1010yr increasing 10kpc 10-5pc decreasing a Dynamical friction increasing 10kpc 10-5pc decreasing a 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) 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. surviving BBHs merged BBHs increasing velocity dispersion increasing flattening surviving BBHs increasing triaxiality merged BBHs BBH evolution in realistic galaxy models (Yu 2002): • 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. 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) Possible observational characteristics of surviving BBHs

27. 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. Two-accretion-disc system associated with a BBH with different spin axis directions Fe K lines: a tool to probe BBHs in AGNs? Fe K line profile (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. Three or more BHs Hierarchical galaxy formation (Cole et al. 2000) BH growth (Kauffmann & Haehnelt, 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

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