Evolution of massive binary black holes BBHs Qingjuan

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

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

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

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

Evolution of massive BBHs

Evolution of massive BBHs 1. Dynamical friction stage increasing 1010 yr 10 -5 pc Dynamical friction decreasing a 10 kpc

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

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

Evolution of massive BBHs • Main uncertainty is in the nonhard 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 1010 yr Gravitational radiation increasing • 10 -5 pc Dynamical friction decreasing a 10 kpc

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.

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

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

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).

Jz=0 (Magorrian & Tremaine 1999)

Evolution of massive BBHs • Main uncertainty is in the nonhard 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 1010 yr Gravitational radiation increasing • 10 -5 pc Dynamical friction decreasing a 10 kpc

Role of the BBH orbital eccentricity (Artymowicz 2000)

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.

(Quinlan 1996)

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

BBH evolution in realistic galaxy models (Yu 2002): • Depends on BH masses, and velocity dispersions and shapes of host galaxies – small BHs (m 2/m 1<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 surviving BBHs merged BBHs increasing velocity dispersion increasing flattening surviving BBHs • Estimated orbital properties of surviving BBHs: – separation: 10 -3 – 10 pc merged BBHs increasing triaxiality

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

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

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

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

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 twoaccretion-disc system associated with a BBH (Yu & Lu 2001)

Fe K lines: a tool to probe BBHs in AGNs? • Strongest lines of evidence for the existence of massive BHs Fe K line profile – Broad and asymmetric (Doppler and gravitational broadening) – Short-term variability (~104 s) – 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 (Yu & Lu 2001)

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.

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 Three or more BHs

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