Binding Energy and the Fundamental Plane of Globular Clusters

By D. McLaughlin. 2000

133 citations recorded by the source corpus.

This paper develops a physical description of the fundamental plane of Galactic globular clusters that explains all empirical trends and correlations in a large number of cluster observables and provides a small but complete set of truly independent constraints on theories of cluster formation and evolution in the Milky Way. In a very good first approximation, the internal structures and dynamics of Galactic globulars are described by single-mass, isotropic King models and are thus characterized by four nominally independent physical parameters. Within this theoretical framework, it is shown that (1) 39 regular (non-core-collapsed) globulars with measured central velocity dispersions all share a common core mass-to-light ratio, ϒV,0 = 1.45 M☉ L, and (2) 109 regular globulars both with and without direct observations of ϒV,0 show a very strong correlation between global binding energy and total luminosity, regulated by Galactocentric position: Eb = 7.2 × 1039 ergs(L/L☉)2.05(rgc/8 kpc)-0.4. The observational scatter about either of these two constraints can be attributed fully to random measurement errors, making them the defining equations of a fundamental plane (FP) to which real clusters are confined in the larger, four-dimensional parameter space of general King models. They are shown to underlie a pair of bivariate correlations first found, and used to argue for the existence of a globular cluster FP, by Djorgovski. A third, weaker correlation, between clusters' total luminosities and King-model concentration parameters, is related to the (nonrandom) distribution of globulars on the FP. With L, ϒV,0, Eb, and the central concentration c thus chosen as the four physical quantities that define any single globular cluster, the FP equations for ϒV,0 and Eb(L,rgc) are used to derive expressions for any other observable in terms of only L, rgc, and c. Results are obtained for generic King models and applied specifically to the globular cluster system of the Milky Way.

Subfields: Astronomy and Astrophysics, Instrumentation

View Paper: https://www.semanticscholar.org/paper/06a5bc9daea16cd513c456c5ba90ec9cf92a9203

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Citations in the corpus

A CATALOG OF GLOBULAR CLUSTER SYSTEMS: WHAT DETERMINES THE SIZE OF A GALAXY'S GLOBULAR CLUSTER POPULATION? (2013, background): “In addition to Mdyn ∼ Reσ 2 e , another quantity used occasionally in the literature especially for pressuresupported systems such as star clusters, molecular clouds, or E galaxies, is the system’s binding energy Eb ∼ Mσ2 ∼ Reσ 4 e (e.g. McLaughlin 2000; Hopkins et al. 2007; Snyder et al. 2011).”
The ACS Virgo Cluster Survey. XII. The Luminosity Function of Globular Clusters in Early-Type Galaxies (2007, background): “In fact, this idea was recently invoked by Waters et al. (2006) as a potential explanation for the fact that theI-band GCLF of M87 is broader than that of the Milky Way; and by Strader et al. (2006) as a possible reason for the narrower composite GCLF of a subsample of ACSVCS dwarfs versus the GCLFs”
The ACS Virgo Cluster Survey. X. Half-Light Radii of Globular Clusters in Early-Type Galaxies: Environmental Dependencies and a Standard Ruler for Distance Estimation (2005, background): “4, which could be the reflection of an original “fundamental line” (McLaughlin 2000).”
The ACS Virgo Cluster Survey. VII. Resolving the Connection between Globular Clusters and Ultracompact Dwarf Galaxies (2005, methodology): “This term seems appropriate since these objects have luminosities that place them simultaneously among the brightest known globular clusters and the faintest dwarf elliptical galaxies.”
Young Massive Star Clusters (2010, background): “Old globular clusters of low mass tend to be less concentrated than high-mass clusters (McLaughlin 2000).”
Globular Cluster Systems in Brightest Cluster Galaxies: Bimodal Metallicity Distributions and the Nature of the High-Luminosity Clusters (2005, background): “The ratio (M/L) is difficult to measure accurately and is likely to differ somewhat between clusters (e.g. Meylan et al. 1995; McLaughlin 2000; Baumgardt et al. 2003; Pasquali et al. 2004; Martini & Ho 2004) but we assume it to be roughly invariant with luminosity.”
From star clusters to dwarf galaxies: the properties of dynamically hot stellar systems (2008, background): “Some well established observations can be identified easily in this plot: The strong correlation between M and re for elliptical galaxies (Bender et al. 1992) in the high mass range and the absence of a dependency of re on M for GCs (McLaughlin 2000; Jordán et al. 2005) at the lowest masses.”
Resolved Massive Star Clusters in the Milky Way and Its Satellites: Brightness Profiles and a Catalog of Fundamental Parameters (2005, methodology): “Note the strong concentration of clusters atΥpopV ≃ 1.9M⊙ L−1⊙,V , which is to be compared to the averagedynamically determined〈ΥdynV 〉 = 1.45M⊙L−1⊙,V for a much smaller sample of clusters (McLaughlin 2000).”
THE RELATIONSHIPS AMONG COMPACT STELLAR SYSTEMS: A FRESH VIEW OF ULTRACOMPACT DWARFS (2011, methodology): “This tidal model may explain the observed sizedistance relation of Milky Way halo clusters, with β ∼ 0.4–0.5 (van den Bergh et al. 1991; McLaughlin 2000; Larsen & Brodie 2003; Mackey & van den Bergh 2005; Baumgardt et al. 2010; cf Gieles et al. 2011).”
A Hubble Space Telescope Census of Nuclear Star Clusters in Late-Type Spiral Galaxies. II. Cluster Sizes and Structural Parameter Correlations (2003, background): “…the old GCs in the Milky Way, which constitute the best-studied family of stellar clusters, are remarkably free of any such trend; the effective radii of Galactic GCs are independent of cluster luminosity or mass (van den Bergh, Morbey, & Pazder 1991; Djorgovski & Meylan 1994; McLaughlin 2000).”
The life cycle of star clusters in a tidal field (2011, background): “McLaughlin (2000) showed that, if a correction is made for the galacto-centric radius, the cluster half-mass radius is approximately constant, i.e. independent of mass:rh/R0.”
Masses of Star Clusters in the Nuclei of Bulgeless Spiral Galaxies (2004, methodology): “These population-synthesis M/L values generally compare quite well with the dynamical M/LV derived by McLaughlin (2000) for a subsample of 40 globulars with measured velocity dispersions; see McLaughlin & van der Marel (2004, in prep) for more details.”