Download Evolution of massive binary black holes

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
4 106 yr   c
 rc 


tdf 

-1 
log N  200 km s  100 pc 
2
 108 M sun 


 m 
increasing
1010yr
10-5pc
Dynamical
friction
decreasing a
10kpc
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
1010yr
3. Hard binary stage
increasing
three-body interactions with
low-J stars; -1
(E: BBH energy)
(Heggie 1975)
(Quinlan 1996)
 m2  200 km s -1 
Gm2


a
 2.8 pc  8
4 c2
10
M

sun 
c


2
10-5pc
Dynamical
friction
decreasing a
10kpc
Evolution of massive BBHs
4. Gravitational radiation stage
1010yr
(Peters 1964)
 a 

tgr (a)  5.8 10 yr 
0
.
01
pc


6
4
3
 108 M sun 
m12


m
1

 m2 (m1  m2 )
increasing
Gravitational
radiation
10-5pc
Dynamical
friction
decreasing a
10kpc
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
1010yr
Gravitational
radiation
increasing
•
10-5pc
Dynamical
friction
decreasing a
10kpc
Loss Region
•
Loss cone:
–
tidal disruption: J 2  J 2 (ε)  2r 2  (r ) ε 2GM r
lc
t
t
 t
ε
–
•
Hard BBH system:
GM  rt , ε: binding energy per unit mass 
rt  fa
f
1
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
1010yr
Gravitational
radiation
increasing
•
10-5pc
Dynamical
friction
decreasing a
10kpc
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 (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
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)
Estimated orbital properties of surviving BBHs
Semimajor axes
Orbital velocities
Orbital periods
(Yu 2002)
M * (rb )  M *interact
• The core mass versus the total mass of stars
interacting strongly with BHs during the hard
binary stage.
BBH Brownian motion:
8
 2
m*
m* 10 M  rc 
rran ~
~
rc  0.01 pc


G
M
M
M   100 pc 
•
•
(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 (~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
(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
……