Download Black Holes in Globular Clusters

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Black Holes in Globular Clusters
Douglas Heggie
University of Edinburgh
[email protected]
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Papers on black holes and globular clusters
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Spot the odd man out
 Cen
M15
www.jb.man.ac.uk
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The pioneer phase: 1970 - 1980+
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Discovery of variable X-ray sources
in globular clusters
Clark et al, 1975, ApJ, 199, L93-L96
NASA/CXC/MIT/D.Pooley et al
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An early theoretical model of
X-ray sources in globular clusters
1. Bahcall J.N., Ostriker J.P., 1975, Massive Black Holes in
Globular Clusters, Nature, 256, 23
2. Silk, J., Arons, J., 1975, On the nature of the globular cluster
X-ray sources, ApJ, 200, L131
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What effect would a black hole have
on the cluster?
1. Peebles P.J.E., 1972, Star Distribution near a Collapsed Object,
ApJ, 178, 371
2. Bahcall, J.N., Wolf, R.A., 1976, Star Distribution around
a Massive Black Hole in a Globular Cluster, ApJ, 209, 214
3. Bahcall, J.N., Wolf, R.A., 1977, Star Distribution around
a Massive Black Hole in a Globular Cluster. II. Unequal Star Masses,
ApJ, 209, 214
4. Shapiro, S.L., Lightman, A.P., 1976, The Distribution of Stars
around a massive black hole, Nature, 262, 743
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The distribution of stars around a black hole
Black Hole M
stars, mass m, density ,
velocity v
Inward flux of mass requires
outward flux of energy F
This is mediated by two-body relaxation, and so
F ~ r3v2/TR, where TR ~ v3/(G2m) and v2 ~ GM/r.
Hence F ~ G3/2m2r7/2/M1/2
In steady state F = const, and so  ∝ r-7/4
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An N-body model of the Bahcall-Wolf cusp
Preto et al, 2004, N-Body Growth
of a Bahcall-Wolf Cusp around a
Black Hole, ApJ, 613L, 109
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The surface brightness profiles of
globular clusters: M15
Newell et al, 1976, Evidence for
a Central Massive Object in the
X-Ray Cluster M15, ApJ, 208L, 55
King 1966
Note core radius
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Surface brightness profiles of
globular clusters
Djorgovski, S.; King, I. R.,
1984, “Surface photometry
in cores of globular
clusters”, ApJ, 277L, 49
~25% of all galactic
globular clusters have
a “collapsed core”
surface brightness
profile.
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How the case for black holes in globulars
was undermined. I
1. The X-ray sources are accreting neutron stars/white dwarfs
Grindlay et al, 1984, “Determination
of the mass of globular cluster X-ray
Guhathakurta et al, 1996, “Globular
sources”, ApJ, 282L, 13
Cluster Photometry With the Hubble
Space Telescope. V. WFPC Study of
AC211
M15's Central density Cusp”, AJ, 111,
cusp
267
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How the case for black holes in globulars was undermined. II
Alternative explanations of the cusp
1. A core of neutron stars
Illingworth, G.; King, I. R., 1977,
“Dynamical models for M15
without a black hole”,
ApJ, 218L, 109
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How the case for black holes in globulars was undermined. II
Alternative explanations of the cusp
2. The phenomenon of core collapse
Hénon, M., 1961, “Sur l'évolution dynamique des amas globulaires”,
AnAp, 24, 369
Lynden-Bell, D., Wood, R., 1968, “The gravo-thermal catastrophe
in isothermal spheres and the onset of red-giant structure
for stellar systems”, MNRAS, 138, 495
Lynden-Bell, D.; Eggleton, P. P., 1980, “On the consequences of
the gravothermal catastrophe”, MNRAS, 191, 483
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Core collapse: Two simulations
Entire system
13 seconds to t = 3.3
Central area
13 seconds to t = 330
The initial conditions
The quiet phase: 1980+ to 2000
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Growth of black holes during core collapse
Time
Black
Hole
Mass
Duncan, M. J., Shapiro, S. L., 1982,
“Star clusters containing massive,
central black holes.
IV - Galactic tidal fields”, ApJ, 253,
921-938.
but how was the process seeded?
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The Modern Phase: 2000 to the present day
Creation of seed black hole by runaway merger in young,
dense star clusters
Example: R136 in the LMC
Portegies Zwart et al, 1999, “Star cluster ecology. III. Runaway
collisions in young compact star clusters”, A&A, 348, 117
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Established the possibility of formation of massive star in
compact star forming regions
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Conditions for runaway coallescence
Concentration
Portegies Zwart et al, 2004,
“Formation of massive black holes
through runaway collisions in dense
young star clusters” Nature, 428, 724
Dynamical friction time scale
Another movie...
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Observational evidence of black holes
in clusters in young compact
star forming regions
NOAO
M82
Galactic Centre cluster
Chandra
IR
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Another example of an
intermediate-mass black hole
in a young star cluster?
Maillard et al, 2004, “The nature of the Galactic Center source IRS 13
revealed by high spatial resolution in the infrared”, A&A, 423, 155
IR
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Did globular clusters start very compact?
Phinney, E.S., 1993, “Pulsars as Probes of Globular Cluster Dynamics”,
ASPC, 50, 141
Best initial model of M15 has M = 1.4x106, R = 1.5pc
⇒ Tdf ~ 50Myr, c ~ 1.8
⇒ well away from the domain where collision runaway occurs
Anyway....
...does a massive star give rise to an intermediate-mass black
hole?
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Globular clusters and the M●- relation
Gebhardt et al, 2002, “A 20,000 M⊙ Black Hole in the Stellar Cluster G1”,
ApJ, 578L, 41
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Observations of M15, models without
mass segregation
Gerssen et al, 2002, “Hubble Space Telescope Evidence for an
Intermediate-Mass Black Hole in the Globular Cluster M15. II. Kinematic
Analysis and Dynamical Modeling”, AJ, 124, 3270
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Models with mass segregation
Some responses to Gerssen et al
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1. Mass segregation was estimated from published models of M15 by
Dull et al, 1997, “The Dynamics of M15: Observations of the Velocity
Dispersion Profile and Fokker-Planck Models”, ApJ, 481, 267.
Old
New
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Some responses to Gerssen et al (1 cont)
In their Addendum (2003, ApJ, 585, 598)
Dull et al note
“On the basis of the original, incorrect
version of Figure 12, Gerssen et al.
(2002) concluded that the D97 models
can fit the new data
only with the addition of an
intermediate-mass black hole.
However, this is counter to our
previous finding, shown in Figure 6
of D97, that the Fokker-Planck models
predict the sort of moderately rising
velocity dispersion profile.....”
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Response 2: An N-body model of M15
Baumgardt et al, 2003,
“On the Central Structure of M15”,
ApJ, 582L, 21
Conclusions independent of
retention fraction of neutron stars
Note: scaling required
Evolutionary N-body models with a black hole
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Baumgardt et al, 2005, “Which Globular Clusters Contain
Intermediate-Mass Black Holes?”, ApJ, 620, 238
density profile
Cf M15: Guhathakurta et al,
1996, AJ, 111, 267
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What determines the core radius?
Recall
1. estimate for flux of energy in the cusp F ~ G3/2m2r7/2/M1/2
2. velocity dispersion in the cusp v2 ~ GM/r
Hence F ~ G5mM32/v7
At the edge of the cusp, ,v are values in the core, where Grc2 ~ v2.
Hence F ~ G5mM32/v7
~ G3mM3/(v3rc4)
Just as in a main sequence star, F is determined by conditions well outside
the core (Hénon). Hence rc∝ M3/4, i.e. a massive black hole requires a
large core. (H, Mineshige, Makino, Hut, Baumgardt, in preparation)
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Check of the relation between
black hole mass and core radius. I
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Check of the relation between
black hole mass and core radius. I
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The case of Omega Cen
Surface brightness profile
Noyola et al, 2006, “Evidence
for an Intermediate Mass
Black Hole in  Centauri”,
ASPC, 352, 269
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The case of Omega Cen. II
Inferred black hole mass 5x104M⊙
Velocity dispersion profile
M/L
Variation of stellar M/L is ignored,
because “mass segregation cannot be
an important effect”.
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A dynamic evolutionary model of  Cen
Mean mass
Giersz, M., H, 2003, MNRAS, 339, 486
Time (Myr)
There is mass segregation....
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A dynamic evolutionary model of  Cen
.... though this model does not produce a sufficient velocity dispersion at the
centre
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Summary
The early years:
X-ray sources in globular clusters as accreting black holes.
Do collapsed-core clusters harbour black holes?
The intermediate years:
Growing black holes from seeds, during core collapse
The modern era:
Creating the seeds in compact star forming reegions
Return to the globular clusters: do clusters with extended cores
harbour black holes? As of Prague (Aug 2006) K. Gebhardt
pins his case on  Cen and G1.