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Astron. Astrophys. 321, 379-388 (1997)

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1. Introduction

Valuable information about globular clusters and galaxy formation can be obtained by investigating the extent to which the properties of globular clusters belonging to different galaxies are similar. For example, differences in initial mass function during cluster formation and/or in susbsequent cluster dynamical evolution, which may both depend on galactic environment, would translate into differences in present-day stellar content. The globular cluster stellar content can be characterized by the mass-to-light ([FORMULA]) ratio, which can now be determined for relatively remote globular clusters.

Collecting all the available data from the literature, Pryor & Meylan (1993) derive [FORMULA] ratios for 56 Galactic globular clusters using King-Michie dynamical models. They obtain global [FORMULA] ratios ranging from about 1 to 5 with a mean of 2.3 (in solar units), and found no significant correlations (apart from a possible weak one between [FORMULA] and cluster mass) between the global [FORMULA] ratios and other parameters such as metallicity, concentration, half-mass relaxation time, or distance from either the Galactic center or the Galactic plane. [FORMULA] ratios similar to those obtained for Galactic clusters have been obtained in studies of globular clusters belonging to the Magellanic clouds (Dubath et al. 1996b) and to the Fornax dwarf spheroidal galaxy (Dubath et al. 1992).

Another way of investigating globular cluster similarities, in terms of structure and [FORMULA] ratio, is to look at the correlations between velocity dispersion, luminosity and a physical size scale. These correlations, which are analogous to the fundamental plane correlations for elliptical galaxies, have already been discussed for Galactic clusters by several authors (e.g., Meylan & Mayor 1986, Paturel & Garnier 1992, Djorgovski & Meylan 1994, Djorgovski 1995). The tight correlation between the velocity dispersion, the core radius and the central surface brightness obtained for Galactic clusters (Djorgovski 1995) is consistent with expectations from the Virial theorem assuming that Galactic globular cluster cores have a universal and constant [FORMULA] ratio to within the measurement errors.

Because of its relative proximity and large size, the M 31 globular cluster system is an obvious target for the study of extragalactic clusters. Previous studies of various aspects of the M 31 globular cluster system have been reviewed by Fusi Pecci et al. (1993), Huchra (1993), Tripicco (1993), and Cohen (1993). The only velocity-dispersion determinations of M 31 clusters published so far are by Peterson (1988). Corresponding [FORMULA] ratio estimates are given for two clusters and are found to be similar to those typically obtained for Galactic clusters. A limitation in this work, however, arises from the difficulty of measuring M 31 cluster structural parameters from the ground. In M 31 the angular sizes of core and half-light radii are typically [FORMULA] [FORMULA] 2 and [FORMULA], respectively.

In this work, we present new velocity dispersion and [FORMULA] ratio determinations for a sample of M 31 globular clusters, for which structural parameters derived from HST observations are available in the literature. The [FORMULA] ratio estimates are based on simple relations derived from the Virial theorem and from King models. Our velocity dispersion estimates are also key observational constraints for more detailed dynamical analyses, e.g., based on Fokker-Plank or King-Michie multi-mass models, which are beyond the scope of this paper.

The spectroscopic observations and the data reduction are presented in Sect. 2. Numerical simulations used for deriving velocity dispersions from the integrated-light spectra and the corresponding results are described in Sect. 3. Sect. 4 discusses the structural parameters, and [FORMULA] estimates are given in Sect. 5. The relations between velocity dispersion, luminosity and different physical scales are discussed in Sect. 6 for our M 31 cluster sample together with samples of clusters belonging to the Galaxy, the Magellanic clouds, the Fornax dwarf spheroidal galaxy, and Centarus A. We summarize our findings in Sect.  7.

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© European Southern Observatory (ESO) 1997

Online publication: June 30, 1998