More Clues to Galaxy Formation:
Massive Globular Clusters,
Stochastic Self-Enrichment, and
Mass/Metallicity Correlations
NGC 4696
HST/ACS
Harris && 2006
Young massive star
clusters (YMCs)
forming at ~105 M0 in
starburst dwarfs today
Pregalactic dwarf
Starburst dwarf NGC 5253 (ESO/HST)
M GC  10
2
Proto-GCs
M GMC
Bimodal or not?
Harris && 2008
Harris && 2006
Bimodal or not?
Harris && 2008
Harris && 2006
Disagreements ahead --
Serious questions persist!
Is this effect caused by --(1) A gradual shift of the blue sequence to
redder color at higher luminosity?
(Mass/Metallicity relation)
(2) The disappearance of bimodality
altogether at the highest masses?
(Threshold enrichment effect)
(3) An artifact of photometric
measurement procedures? (i.e. not real)
If it’s a true, physical MMR then Z ~ M1/2 at high mass, and it may
smoothly connect upward to the UCD regime.
Does it continue to low mass?
Is it present in all galaxies?
Why no red-sequence MMR?
What is its astrophysical origin?
The systematic properties of globular clusters begin to
change for M > 2 x 106 M0 …
w Cen (Villanova && 2007)
- Appearance of the MMR
- Multiple populations within a
single GC
- Different scaling of size vs. mass
Evstigneeva et al. 2008
The basic feature of bimodality is a first-order and (probably)
universal effect. The MMR is a second-order effect and
harder to trace. Though new, much confusion already exists:
Category 1: MMR is present and measurable
M87, NGC 1399, several other BCGs and gE’s
Category 2: MMR is not present
M49; any others?
Category 3: presence of MMR not decidable; GC sample too small or
does not extend to high enough luminosity
Milky Way; M31; dwarf galaxies; most spirals; GC-poor E’s
Can be helped (partially) by constructing composite
samples; e.g grouping Virgo Cluster Survey galaxies into 4
luminosity groups (Mieske && 2006) or combining several
supergiants (Harris && 2006)
But if amplitude of MMR differs from one galaxy to another,
net effect will be diluted in composite samples
Most galaxies do not have clusters
in the 106 – 107 M0 range
1: strong MMR
2: no MMR
3: Not decidable
Milky Way GCs
MV
[Fe/H]
First, let’s get the measurements straightened out.
NGC 5128: d=3.8 Mpc
Globular clusters are easily
resolved at <1’’ seeing
Photometry must account for
individually different scale
sizes
GC profile as seen on image =
PSF
Intrinsic GC profile
rh ~ 1 – 5 parsecs; averages 3
pc  0.3” width
NGC 3311/3309 (A1060)
d = 50 Mpc
2 rh ~ 6 pc  0.025”
fwhm(PSF) = 0.5”
 starlike! psf-fitting
photometry is fine
Gemini-S + GMOS, Wehner & Harris
Several regimes
determined by distance; no
single photometric method
is suitable for all regimes
4 distinguishable regimes: compare fwhm of stellar PSF
with intrinsic cluster size D (= 2 rh), half-light diameter
Well resolved:
D >> fwhm(PSF)
Partially resolved:
D ~ fwhm
Marginally resolved:
D ~ 0.1 – 0.3 fwhm
Unresolved (starlike):
D < 0.1 fwhm
Aperture photometry
r(ap) adjusted for D
PSF-fitting photometry
All this is subject to S/N considerations …
HST/ACS imaging of GCs around 6 central supergiants in
Abell-type clusters (Harris et al. 2006, 2008)
(B,I) bandpasses  metallicity-sensitive
Thousands of GCs per galaxy, thus good statistical samples
and big luminosity (mass) range
HST/ACS Imaging program for BCGs
NGC 1407
Eridanus
NGC 3258
Antlia
41 Mpc
-21.87
NGC 3268
Antlia
41 Mpc
-21.96
NGC 3348
CfA69
41 Mpc
-22.13
NGC 4696
Centaurus
42 Mpc
-23.31
NGC 7626
Pegasus I
49 Mpc
-22.58
Virgo
16 Mpc
-22.4)
(M87
D = 6 pc
at
d=23 Mpc MV = -22.35
d ~ 40 Mpc 
compare PSF fwhm = 0.1” 
(Partial list –
biggest GCSs out
of 12 studied)
half-light profile width ~ 0.03”
marginally resolved
Photometric technique:
- Uniform catalog of detected objects with DAOPHOT
- Construct PSF from average of many bright starlike objects
- For each individual source, convolve PSF with “King30”
model GC profile and vary D(model) to obtain best match
(ISHAPE; Larsen 1999)
- finally, use fixed-aperture photometry corrected for profile
width to obtain final magnitude in each band
ISHAPE
sample fits
1 px = 0.05”
HST/ACS
S/N=441
S/N=24
S/N=108
fwhm a=1.3 px
fwhm a=0.82 px
starlike
b/a = 0.91
b/a = 0.50
Growth curves for simulated GC
profiles convolved with PSF
ISHAPE  solve for best-fit D
Measure magnitude through 2.5-px
aperture, corrected back to the
growth curve for a starlike profile
Simulations show that the
systematically correct intrinsic D
(FWHM of GC profile) is returned for
D > 0.1 (PSF) (transition boundary
from unresolved to marginally
resolved)
Our regime
More tests …
Measured size a not affected
by modestly elliptical shape
S/N > 50 !!
b/a, q returned correctly for
a > 0.1 PSF
Full, profile-corrected aperture
photometry for 6 supergiant ellipticals
Previous PSF-fitting data
(Harris && 2006)
Trend lines:
- blue and red?
- linear slope? or top
end only?
- how steep?
N=12000 brighter
than MI = -8.
Largest sample in
existence!
Red sequence: no trend
Blue sequence: gradual
changeover to MMR toward
higher mass
Z ~ M0.3+-0.1
RMIX fits of bimodal gaussians
within selected magnitude intervals:
forces two modes into the solution,
but (a) less affected by field
contamination, (b) avoids the strong
assumption imposed by a ‘linear fit’
The top end: uni- or bi-modal?
A detour: the measured cluster sizes
Trends (?) versus galactocentric distance and
metallicity: projection effects, or intrinsic?
Low-metallicity GCs average larger
size at any galactocentric zone
The MMR is not due to an
unaccounted-for size-mass
relation.
What is responsible for the metallicity
distribution function (MDF)?
Bailin & Harris 2008
Is a proto-GC
- PRE-enriched from the
surrounding GMC gas?
- internally SELF-enriched by its
own SNe within the first few Myr?
- stochastic? (can self-enrichment
be responsible for the internal
dispersion of the MDF?)
Input assumptions to self-enrichment model:
SNe from >8 M0 stars enrich lower-mass stars while still in formation
Salpeter IMF 0.3  100 M0
SF efficiency f* ~ 0.3
Woosley/Weaver SN yields, and fraction fZ of heavy elements retained in GMC
 Zc 
fZ M Z
Mc
and
and thus
[m / H ]  0.38  log ( f f Z )
NSN ~ 1 per 100 M0
Pre-enrichment
level for fZ = 0.08
Internal dispersion of MDF due
to statistical variation in NSN
Z
1/ 2
M 
 0.059  GC
5 
Zc
10


Stochastic self-enrichment fails to explain the MDF
dispersion at any cluster mass higher than 104 M0
Two additional, major factors to add:
- reff ~ M1/2 at high mass
- fZ is a strong function of M(init) and thus reff as well
Proto-GC = truncated isothermal sphere 
logarithmic potential F(R). All SNe go off while
PGC is still highly gaseous; all ejected energy
absorbed and thermalized.
Gas will leave if outside an “escape radius”
defined by total energy > potential energy at
edge of cloud.
Ejecta become efficiently retained at a
characteristic mass (after star formation)
M GC (retain) 
ESN f*2 reff
100 GM 
 107 M 
Combined effects of preenrichment, self-enrichment,
and mass/radius relation
Match to BCG data for 6 galaxies
-pre-enrichment of each “mode”
(blue, red) tuned to match mean
color
-self-enrichment drives shape of
mean MDF at high mass
Basic features of the model:
- No MMR for cluster masses < ~106 M0 (i.e., sequences vertical)
- Very metal-poor, very massive GCs should be rare (anywhere)
- blue and red sequence converge at high-mass end
- Similar red-sequence MMR should exist at top end, but smaller amplitude
- Internal dispersion and mean metallicity of each mode driven by pre-enrichment
Wehner
&& 2008