Correlations among the independently measured physical properties of globular
clusters (GCs) can provide powerful tests for theoretical models and new
insights into their dynamics, formation, and evolution. We review briefly some
of the previous work, and present preliminary results from a comparative study
of GC correlations in the Local Group galaxies. The results so far indicate
that these diverse GC systems follow the same fundamental correlations,
suggesting a commonality of formative and evolutionary processes which produce
them.Comment: An invited review, to appear in "New Horizons in Globular Cluster
  Astronomy", eds. G. Piotto, G. Meylan, S.G. Djorgovski, and M. Riello, ASPCS,
  in press (2003). Latex file, 8 pages, 5 eps figures, style files include

Cacciari, C.

Castro, S.

Cote, P.

Djorgovski, S. G.

Federici, L.

Jou, T.

Meylan, G.

Parmeggiani, G.

Pecci, F. Fusi

Rich, R. M.

English

arXiv

Correlations among the independently measured physical properties of globular clusters (GCs) can provide powerful tests for theoretical models and new insights into their dynamics, formation, and evolution. We review briefly some of the previous work, and present preliminary results from a comparative study of GC correlations in the Local Group galaxies. The results so far indicate that these diverse GC systems follow the same fundamental correlations, suggesting a commonality of formative and evolutionary processes which produce them

Côté, P.

Fusi Pecci, F.

Caltech Authors - Main

ar
X
iv
:a
str
o-
ph
/0
30
21
29
v3
  2
1 
Fe
b 
20
03
To appear in: New Horizons in Globular Cluster Astronomy
ASP Conference Series, Vol. ???, 2003
Eds. G. Piotto, G. Meylan, S.G. Djorgovski & M. Riello
Correlations of Globular Cluster Properties:
Their Interpretations and Uses
S. G. Djorgovski
California Institute of Technology, Pasadena, CA 91125, USA
P. Coˆte´
Dept. Phys. & Astronomy, Rutgers U., New Brunswick, NJ 08854, USA
G. Meylan
Space Telescope Science Institute, Baltimore, MD 21218, USA
S. Castro
IPAC/SSC, Caltech, Pasadena, CA 91125, USA
L. Federici, G. Parmeggiani, C. Cacciari, F. Fusi Pecci
INAF – Osservatorio Astronomico di Bologna, Bologna, I-40127, Italy
R.M. Rich
Dept. of Physics & Astronomy, UCLA, Los Angeles, CA 90095, USA
T. Jou
California Institute of Technology, Pasadena, CA 91125, USA
Abstract. Correlations among the independently measured physical
properties of globular clusters (GCs) can provide powerful tests for the-
oretical models and new insights into their dynamics, formation, and
evolution. We review briefly some of the previous work, and present pre-
liminary results from a comparative study of GC correlations in the Local
Group galaxies. The results so far indicate that these diverse GC systems
follow the same fundamental correlations, suggesting a commonality of
formative and evolutionary processes which produce them.
1. Introduction
Understanding of the physics, formation, and evolution of any type of astro-
nomical objects or systems, including globular clusters (GCs) as a family, must
rest on a solid, quantitative empirical foundation. In the order of an increas-
ing information content, the first step is a definition of characteristic values,
e.g., a typical mass or luminosity or half-light radius, etc. The next step is a
1
2 S.G. Djorgovski et al.
determination of distribution functions for various physical quantities, e.g., the
luminosity function. Finally, most information can be obtained from non-trivial
correlations of independently measured or derived quantities. Such correlations
are products of some physical or evolutionary processes, and as such contain
valuable clues towards the understanding of the objects in question.
In the context of globular clusters, previous studies include, e.g., Chernoff &
Djorgovski (1989), Djorgovski (1991, 1995, 1996), Djorgovski & Meylan (1994),
Bellazzini et al. (1996), Bellazzini (1998), McLaughlin (2000), and numerous
papers by Sidney van den Bergh, e.g, van den Bergh (1996). For a comparison
of GCs with other old stellar systems, see, e.g., Kormendy (1985) or Djorgovski
(1993). On-line compilations of Galactic GC data useful for such studies include
Harris (1996), 1 which is an updated superset of the data 2 presented in the
First Ivan King Festschrift (eds. Djorgovski & Meylan 1993). Both are now well
overdue for a major revision and updates, including Hipparcos-based distances,
uniform IR photometry and reddenings derived from the 2MASS data, better
core parameters from the HST-based surface photometry, etc.
Additional insights can be gained by comparing correlations of GC prop-
erties in GC systems of different galaxies. Currently, we are in practice limited
to the galaxies of the Local Group. Previous studies include, e.g., Fusi Pecci
et al. (1994), Djorgovski et al. (1997), Dubath & Grillmair (1997), Dubath et
al. (1997), Meylan et al. (2001), Barmby et al. (2002), etc. In this paper we
present preliminary results from a new study of dynamical correlations for GC
systems in several Local Group galaxies.
2. Correlations for Galactic GCs: A Brief Overview
A generic expectation from the differences in corresponding dynamical time
scales is that the evolution at the core radius scales would be much faster than
at the half-light radius scales. The former then reflects mainly the evolution
towards the core collapse (and any self-similar behavior before and after the core
collapse), whereas the latter reflects more the initial conditions and a long-term
evolution. Position of a GC in the Galactic potential modulates the evolutionary
effect through the effect of dynamical shocks due to the disk and bulge passages,
in the sense that clusters exposed to more frequent and stronger shocks evolve
faster. This introduces a secondary dependence on the distance to the Galactic
center and plane in many of the observed trends and correlations. All this
was well documented in the references cited above, and at least the qualitative
agreement between the observations and theory is striking.
In a simple core collapse picture, as t→ tc (time of the maximum collapse),
the core radius rc → 0, the concentration parameter c→∞, the central density
ρ0 →∞, and the central surface brightness I0 →∞, in a self-similar manner; see,
e.g., Meylan & Heggie (1997) for a review and references. The observed cluster
properties at the core scale are thus driven towards a (nearly) 1-parameter se-
quence corresponding to the relative dynamical time away from the core collapse
1http://physun.physics.mcmaster.ca/Globular.html
2http://www.astro.caltech.edu/∼george/glob/data.html
Correlations of Globular Cluster Properties 3
Figure 1. Examples of core parameter correlations, driven by the
evolution towards the core collapse. Left : Correlation between two
observables, the King concentration parameter c, and the core radius
rc. Clusters with an unresolved (from the ground) post-core-collapse
(PCC) morphology have been assigned c = 2.5. Right : An illustra-
tive correlation between two derived quantities, the central luminosity
density, ρ0, and the central relaxation time, trc.
(Fig. 1). This is indeed consistent with the observations: the predicted trend
in simple single-component, Fokker-Planck core collapse models is ρ0 ∼ r
−2.23
c ,
whereas the observed trends are I0 ∼ r
−1.8±0.2
c and ρ0,lum ∼ r
−2.6±0.2
c . This
implies for the core mass mcore ∼ r
0.3±0.2
c (M/L), i.e., a nearly constant core
mass, possibly slightly diminishing due to the evaporation of high-energy stars,
and/or becoming slightly darker due to the mass segregation of heavy stellar
remnants.
No such trends are seen at the half-light radius scale, where the dynamical
range of the relaxation time scales relative to the Galactic age are is much smaller
(trh ∼ 10
8
− 1010 yr, whereas for the core relaxation time scales trc ∼ 10
5
− 1010
yr), so that the internal spread of GC properties dominates over the dynamical
evolution effects.
Likewise, there are only a few noisy trends with the cluster luminosity
(∼ mass), which are apparent only when the data are binned: more luminous
clusters tend to be more concentrated, rc ∼ L
−0.5±0.25, ρ0 ∼ L
2±1.
One can also estimate the rough tidal radii rt from the observed surface
brightness profiles, and the mean cluster densities ρt within the rt. One finds
a mean trend with the present Galactocentric radius RGC of rt ∼ R
0.37±0.05
GC ,
as intuitively expected, and also ρt ∼ R
−1.6±0.2
GC , close to the mean density law
for the dark halo. Using a simple theory (Innanen et al. 1983) and an assumed
Galactic rotation curve, it is then possible to estimate the perigalactic radii,
Rperi (see Djorgovski 1996 for more details). Intriguingly, the ratio RGC/Rperi
peaks near the unity, with a long tail, suggesting that most GCs today are on
4 S.G. Djorgovski et al.
Figure 2. The Fundamental Plane (FP) bivariate correlations for
GCs: an optimal combination of the central velocity dispersion (σ)
and core radius (rc) is correlated with the central surface brightness
in the V band (left panel), and a different combination of σ and the
half-light radius rh with the mean surface brightness within rh (right
panel). Pearson (r) and Spearman (s) correlation coefficients are indi-
cated in each panel. The residual scatter is completely accounted by
the measurement errors.
nearly circular orbits. This could be a survival selection effect, or a reflection of
the initial conditions, or a combination of the two.
Possibly the most interesting monovariate correlations are those including
core velocity dispersions, σ: σ ∼ L0.6±0.15 (or equivalently, L ∼ σ5/3), σ ∼
I 0.5±0.1
0
, and σ ∼ I 0.45±0.05h , where Ih is the mean surface brightness within
the half-light radius (see Figs. 3–4). The origin of these correlations is still not
understood, but several possibilities exist; see, e.g., Djorgovski & Meylan (1994)
for a discussion. These correlations may be reflecting the formative mechanisms
of GCs, and they should be reproduced by any successful model of GC formation
and long-term evolution. They are also very different from the corresponding
correlations for elliptical and dwarf (dE, DSph) galaxies (Djorgovski 1993).
It is notable that GC metallicities do not seem to correlate with anything,
in contrast to other old stellar systems. This strongly suggests that GCs were
not self-enriched.
Another interesting question is how many independent physical parameters
control the observable properties of GCs? Following the pioneering study by
Brosche & Lentes (1984), more modern data sets suggest that there are at most
6 significant parameters among 9 or 10 independently measured observables
(Djorgovski 1991, Djorgovski & Meylan 1994). If one considers just the observed
photometric, structural, and dynamical parameters at both core and half-light
scales, the statistical dimensionality of the data is 3, or 4 if the (M/L) ratios
are included. This is exactly as expected for a manifold of King (1966) models.
Correlations of Globular Cluster Properties 5
Figure 3. Luminosity – velocity dispersion correlations in the V (top)
and K (bottom) bands for GCs in 4 Local Group galaxies, encoded
with different symbols as indicated in the figure. The clusters in N205
appear to be slightly underluminous for their velocity dispersions, but
this may be due to a systematic error. Otherwise, all of these GC
systems appear to follow the same dynamical correlations.
6 S.G. Djorgovski et al.
Figure 4. Correlations between the velocity dispersion σ and the
mean surface brightness within the half-light radius in the V band
(µhV , left panel) and in the K band (µhK , right panel) for the Galactic
GCs (open circles) and M31 GCs (solid squares). The M31 extends
to higher luminosities and masses, and is selection-limited at the low
end, but in the overlap region the two GC systems follow the same
correlations.
Constraining the input parameter set to either core or half-light ones, brings
the statistical dimension of the data set to 2, i.e., the triplets of observables are
connected by bivariate correlations (Djorgovski 1995; see Fig. 2). This is the
equivalent of the Fundamental Plane (FP) of elliptical galaxies. For the core
parameters, the scaling relation is: rc ∼ σ
2.0±0.2I −1.1±0.1
0
. If we assume a
structural homology (probably a good assumption for the GC cores), the virial
theorem implies: r ∼ σ2I−1(M/L)−1. Thus, the FP of GC cores implies that
their (M/L) ratios are (nearly?) constant; this is the sharpest observational
constraint on the constancy of GC (M/L) ratios to date. In contrast, for the
half-light parameters, the scaling relation is: rh ∼ σ
1.45±0.2I −0.85±0.1h . This is
remarkably similar to the FP of E-galaxies, and is almost certainly a consequence
of the non-homology of GC structures.
An alternative look at the FP of GCs was provided by McLaughlin (2000).
While recognizing the equivalence of his FP with the one described above,
his preferred scaling relation is the expression of the binding energy, Eb ∼
L2.05R −0.4GC , where the 2nd term effectively corrects for the known dependences
of the GC parameters on their position in the Galaxy. However, we note that
the binding energy can be written as: Eb = L
2(M/L)2r −1h f(c), where f(c) is
a slow function of the cluster concentration. If the (M/L) ratios are indeed
constant, and knowing that rh does not correlate much with anything, it is then
not surprising that the observed RGC -corrected scaling is Eb ∼ L
2.05.
Correlations of Globular Cluster Properties 7
Figure 5. Dependence of the derived (M/L) ratios (in Solar V band
units) on the metallicity, for the Galactic GCs (open circles) and M31
GCs (solid squares), in the V (left) and K (right) bands. The larger
observed scatter for the Galactic GCs may be caused in part by the
distance errors, whereas all M31 GCs are effectively at the same dis-
tance. While no trend is seen in the V band (as implied by the FP; see
above), there is a trend in the K band in the sense of more metal-rich
clusters having more luminous stellar populations at a given mass.
3. A Comparison of Dynamical Correlations for GCs in Five Local
Group Galaxies: Some Preliminary Results
Correlations between the velocity dispersion and other parameters (L, I0, Ih, and
the FP) may probe directly the physics and formative processes of GCs, their
homogeneity (or lack thereof) in different galaxies, and can be also used as new
distance indicator relations for their parent galaxies, providing an independent
check of other distance scales. Fusi Pecci et al. (1994) and Barmby et al. (2002)
established that the structural and photometric parameters of GCs in M31 as
observed with the HST occupy the same portion of the parameter space as the
Milky Way GCs. Following on the initial studies by Dubath & Grillmair (1997)
and Djorgovski et al. (1997), we set to explore in more detail the dynamical
correlations for GCs in 5 Local Group galaxies: the Milky Way, M31, M33,
N185, and N205.
The extra-Galactic sample consists of HST imaging of GCs in M31, M33,
N185, and N205 available as of the early 2002, for which we have done sur-
face photometry (Federici, Parmeggiani, et al., in prep.). Velocity dispersions
have been measured using Echelle spectra obtained at the Keck-I telescope with
the HIRES instrument, as described, e.g., in Djorgovski et al. (1997); these
measurements will be presented in detail elsewhere (Coˆte´ et al., in prep.).
Figures 3–5 illustrate some of our preliminary results. Our first conclusion
is that GCs in these different galaxies follow essentially the same dynamical
correlations. This suggests a common set of physical mechanisms affecting their
8 S.G. Djorgovski et al.
formation and evolution, despite a broad range of their host galaxy properties.
The observed dependence of the (M/L) ratios on the metallicity, especially in
the K-band (Fig. 5), represents a useful observational constraint on the models
of old stellar populations. In a future paper (Djorgovski et al., in prep.) we will
present a more complete and detailed analysis, including the FP correlations for
these GC systems.
Even with the resolution of the HST, such studies cannot be pushed much
beyond the Local Group. For example, Harris et al. (2002) present an excellent
study of GCs in Cen A = N5128.
Acknowledgments. We wish to thank our collaborators, and the staff of
W.M. Keck Observatory for their expert help during our observing runs. This
work was supported by grants from the NSF, NASA/STScI (GO-6671 and AR-
8735), and private donors in the U.S., and ASI and MURST in Italy. PC was
supported in part by a Fairchild Fellowship, and TJ by a SURF Fellowship at
Caltech.
References
Barmby, P., Holland, S., & Huchra, J. 2002, AJ, 123, 1937
Bellazzini, M., Vesperini, E., Ferraro, F., & Fusi Pecci, F. 1996, MNRAS, 279,
337
Bellazzini, M. 1998, NewAst, 3, 219
Brosche, P., & Lentes, F. 1984, A&A, 139, 474
Chernoff, D., & Djorgovski, S. 1989, ApJ, 339, 904
Djorgovski, S. 1991, in: The Formation and Evolution of Star Clusters, ed. K.
Janes, ASPCS, 13, 112
Djorgovski, S. 1993, in: The Globular Cluster – Galaxy Connection, eds. G.
Smith & J. Brodie, ASPCS, 48, 496
Djorgovski, S.G., & Meylan, G. (editors) 1993, Structure and Dynamics of Glob-
ular Clusters, ASPCS, 50, pp. 325-382
Djorgovski, S.G., & Meylan, G. 1994, AJ, 108, 1292
Djorgovski, S.G. 1995, ApJ, 438, L29
Djorgovski, S.G. 1996, in: Dynamical Evolution of Star Clusters, IAU Symp.
174, eds. P. Hut & J. Makino, Dordrecht: Kluwer, p. 9
Djorgovski, S.G., et al. 1997, ApJ, 474, L19
Dubath, P., & Grillmair, C. 1997, A&A, 321, 379
Dubath, P., Meylan, G., & Mayor, M. 1997, A&A, 324, 505
Fusi Pecci, F., et al. 1994, A&A, 284, 349
Harris, W. 1996, AJ, 112, 1487
Harris, W., Harris, G., Holland, S., & McLaughlin, D. 2002, AJ, 124, 1435
Innanen, K., Harris, W., & Webbink, R. 1983, AJ, 88, 338
King, I.R. 1966, AJ, 71, 64
Kormendy, J. 1985, ApJ, 295, 73
Meylan, G., & Heggie, D. 1997, A&ARv, 8, 1
Meylan, G., Sarajedini, A., Jablonka, P., Djorgovski, S.G., Bridges, T., & Rich,
R.M. 2001, AJ, 122, 830
McLaughlin, D. 2000, ApJ, 539, 618
van den Bergh, S. 1996, AJ, 112, 2634


Correlations of Globular Cluster Properties: Their Interpretations and Uses

http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.317.7038

Correlations of Globular Cluster Properties: Their Interpretations and
  Uses

Correlations of Globular Cluster Properties: Their Interpretations and Uses

Abstract

Similar works

Full text

Available Versions

Caltech Authors - Main