Astron. Astrophys. 324, 505-522 (1997)

1. Introduction

The fate of globular clusters is characterized by their dynamical evolution towards core collapse, a state of very high central stellar density. Most dynamical-evolution models predict that globular clusters may then experience a succession of expansion and contraction phases, the so-called gravothermal oscillations. The dynamical state of a cluster may be unveiled by the presence of cusps in both its surface-brightness and velocity-dispersion profiles. On the one hand, star counts from HST provide excellent insight into the innermost parts of a few high-concentration globular clusters, revealing, e.g., in the case of M15 (Guhathakurta et al. 1996, Sosin & King 1996, King et al. 1996) an unresolved core. On the other hand, spectroscopic observations of the same high-concentration clusters currently have lower spatial resolution.

At the center of globular clusters, radial velocities can be measured only for a limited number of individual stars because of the small number of bright stars, and also because of the crowding in the case of high-concentration clusters. Therefore, reliable velocity dispersions derived from radial velocities of individual stars can only be obtained over relatively large central areas: in general, larger than ten seconds of arc in radius. Over smaller areas, uncertainties due to small number statistic become important. An alternative is to obtain integrated-light spectra over small central apertures and to derive the velocity dispersion by measuring the Doppler line broadening due to the random spatial motions of the stars along the line of sight. However, even in this case, statistical uncertainty is a limitation because the contributions from a small number of bright stars can dominate the integrated light over small central areas. These observational difficulties are clearly illustrated in the case of M15 (see Peterson et al. 1989, and Dubath & Meylan 1994). Even by combining integrated-light measurements and radial velocities of individual stars, the statistical uncertainties are too large to allow the observations to constrain the shape of the velocity-dispersion profile in the inner few seconds of arc, i.e., in the area where the luminosity cusp is observed.

In contrast with the relatively large number of clusters for which radial-velocities are available from the literature, integrated-light measurements have only been carried out for a handful of Galactic and Magellanic globular clusters (e.g. Dubath et al. 1990, Mateo et al. 1991, Zaggia et al. 1992). In many Galactic high-concentration clusters, however, the integrated-light approach provides reliable velocity dispersions over small central areas, where crowding prevents the radial-velocity measurements of a large enough number of individual stars.

In the case of the Magellanic clusters, HST images show how difficult are the measurements of radial velocity of individual stars. Most of the time, several stars overlap on a typical seeing disk of , and the measurement of a bright star velocity can be biased by one, or several, close companions. For these clusters, the integrated-light measurements are carried out over areas physically larger, for practical reasons, than those used for Galactic clusters. These measurements therefore provide velocity dispersions averaged over larger areas, which are much less affected by statistical uncertainties, since the number of bright stars within those areas is large. For the above two reasons, the integrated-light approach can provide better results for any remote globular cluster, such as Magellanic clusters.

In this paper, we present integrated-light measurements of the velocity dispersions of relatively large numbers of high-concentration Galactic globular clusters, and of old Magellanic globular clusters. The uncertainties on these measurements due to small number statistic is carefully established by means of detailed numerical simulations. We give here some details on the data reduction and analysis techniques, as well as on the analysis of standard star results, which were not published in previous papers based on the same observational approach.

This new set of data is complementary to the radial velocity measurements, and often provides, for the Galactic clusters, the innermost data point of the velocity dispersion profile. These kinematical data are used to constrain and discriminate King-Michie (e.g., Meylan et al. 1995) and Fokker-Plank (e.g., Grabhorn et al. 1992) dynamical models. For example, our Galactic cluster data set is used in Pryor and Meylan (1993) to derive cluster masses and mass-to-light ratios.

This paper is structured as follows: Sect. 2 presents our observations, Sect. 3 describes our data reduction procedure, Sect. 4 provides precise results from the standard star measurements, Sect. 5 presents the results about the cluster radial velocities and core velocity dispersions, Sect. 6 presents a careful discussion of our estimates of the statistical errors on the measurements due to the small samples of stars contributing most of the luminosity, Sect. 7 compares our results with previous measurements, Sect. 8 compares our results with previous measurements, Sect. 9 elaborates on the fundamental plane of the observed globular clusters, i.e., on the relation between the velocity dispersion, the luminosity, and a physical scale. Sect. 10 discusses the present results and summarizes this paper.

© European Southern Observatory (ESO) 1997

Online publication: May 26, 1998

helpdesk.link@springer.de