Transcript Intermediate Mass Black Holes in Globular Clusters

A Recipe for Making
Intermediate Mass Black Holes
Doug Hamilton
U. Maryland
Review
In collaboration with Cole Miller,
Kayhan Gultekin, and Vanessa Lauberg
Pathways to Intermediate Mass
Black Holes
Low Metallicity
Normal Stars
Colliding Stars
Very Massive Stars
Stellar
Reviewmass BH
BH mergers
stellar mergers
100 Msun BH
BH mergers
300 -1000 Msun BH
Numerical Simulations
1. Start with an (X:10)Msun binary black hole
2. Wait until another 10Msun BH approaches
3. Resolve the encounter
4. Encounter Time > Merger Time?
Yes
No
Merge Masses,
Repeat
History of 3 Body Encounters
100:10:10
Semimajor Axis
Pericenter Distance
History of 3 Body Encounters
1000:10:10
Semimajor Axis
Pericenter Distance
Semimajor Axis Distribution
Just after the Last Encounter
Eccentricity Distribution
Just after the Last Encounter
Eccentricity Distribution
in the LISA Band
Porb = 1000 s
Gravitational Waves from IMBHs
Lisa Sensitivity Curve
Local
Globular
Virgo
Cluster
IMBH Mergers from
Single-Binary Encounters
In a cluster with vesc = 50km/s, 10Msun interlopers
Number of Encounters
Number of Ejections
Merger Time
100+10
93
20
15Myr
1000+10
483
87
4.4Myr
Binary Ejections:
Probability of building up from 100 to 300: 16%
Probability of building up from 50 to 300: 1%
Process is very inefficient!
Additional Effects
that decrease efficiency ...
Near Ejections
that increase efficiency ...
Mass Distribution of Black Holes
Direct 2 -Body Capture (M > 500 Msun)
Secular Effects in Triple Systems
Halo
Core
Why Do Large Masses Exchange In?
M3
M1
M2
1. Larger masses move more slowly & are more focused
2. Large mass M3 gives larger impulse to M2
Binary -Binary Interactions
Any of the Mj can
be tight binaries
M3
M1
M2
A tight binary will often swap into a wide binary
to form a hierarchal triple.
Evolution of these triples by subsequent encounters
is common and important!
Secular Evolution of Triples
Individual orbital energies are conserved.
Angular momentum is exchanged.
Oscillations in eccentricity and inclination.
Timescale set by the tidal acceleration
imposed by the distant object on the binary.
Can be very rapid compared to encounter times.
Kozai Resonance (Restricted Problem)
Kozai (1962) considered a test particle in a binary
influenced by a distant third companion.
The test particle's pericenter and node librate with large
correlated oscillations in eccentricity and inclination.
The quantity Lz = sqrt(1-e^2)cos i is conserved.
The Critical Inclination is 90o.
Planetary Applications:
Asteroids
Oort Cloud comets
Extrasolar Planets
Distant Planetary Satellites
What if the Moon had an
i=90 Orbit?
General Kozai Resonance
Assume: No constraint on the masses, Hierarchal triple,
Quadrupole order
Then: Outer planet's eccentricity e2 is constant.
Cyclic oscillations (often extreme) in e1 & i1 & i2.
Critical Inclination 90o < i < 180o.
Curiosity:
start
with
counter-rotating
coplanar orbits
then
outer orbit reverses
and inner merges
Kozai Critical Inclination
Newtonian Gravity, m0=m1
The Loss Cone
GR included
Equal masses
The Effect of Triples
Much more rapid merger rates.
Mergers without three-body recoil.
Significantly fewer ejections.
Bottom Line
IMBH production efficiency greatly enhanced by triples.
What do We Learn from a Detection
of one or more IMBHs?
If formed from collapse of a massive star:
maximally spinning IMBH, J/M^2 ~ 0.7-0.8
If formed from merger of multiple black holes:
low spin IMBH, J/M^2 ~ 0.1-0.3
Secular Exchange of Angular
Momentum
Outer eccentric orbit,
Inner circular orbit
Review
Outer less eccentric
Inner more eccentric
Chandra ULX Sources
M82