Astron. Astrophys. 333, L27-L30 (1998)

2. Properties of the residual component

The observational data provided by the database for stars in open clusters (BDA, http://obswww.unige.ch/bda/) have been used in this study. This database has been developed since 1987 at the Institute of Astronomy (University of Lausanne) by Mermilliod (Mermilliod 1996, and references therein). For the present purpose, several data are required, namely distance and angular diameter in order to compute the real diameter, age, and earliest spectral type observed. Only 418 clusters with both distances and angular diameters known have been found. The vast majority of the diameters have been taken from Lynga's catalogue (Lyngå 1987) and correspond more or less to the central part of the cluster. The distribution of the clusters used in this work as a function of the cluster radius is shown in Fig. (1a). This sample is strongly biased; Fig. (1b) shows that only young clusters with massive and bright stars are observed at large distances.

Fig. 1a and b. a (Left panel) Apparent distribution of open clusters as a function of cluster radius. All clusters with radius greater than 7 pc have ages smaller than 0.1 Gyr. Almost 90% of clusters in the sample have radius smaller than 4 pc. b  (Right panel) Dependence of cluster distance with age. For large distances only young clusters are found because of the high luminosity of massive stars. This shows that the sample utilized has a selection effect, so the possible existence of a large number of old and faint clusters at large distances ( kpc) should be considered.

These observational data will be compared with results from a large set of simulations performed with the standard N -body code NBODY5 (Aarseth 1985) in the last five years (de la Fuente Marcos 1997b) for clusters situated in the solar neighbourhood. These computations include the effects of stellar evolution, the galactic tidal field and realistic initial mass functions. The change in the distribution of cluster properties (number of stars, half-mass radius, fraction of binaries) with time for the computed models is analyzed in de la Fuente Marcos (1997a) and references therein.

2.1. Stellar density and remnant radius

Detecting OCRs requires a certain contrast of the candidate object against the stellar background. In order to be observed, a cluster must have a stellar density larger than the local Galactic value. When considering the solar neighbourhood, the stellar density of the system should be greater than 0.044 pc^-3. Moreover, the density of a star cluster in the solar neighbourhood must be greater than about 0.08 pc^-3 in order to be stable against tidal disruption. On the other hand, the smallest mean mass density for detected open clusters is about 0.5 pc^-3 (Lohmann 1977, and references therein) so probably a loose cluster should be about ten times denser than the surrounding star field in order to be detected. Although extended stellar associations have typical values of 0.1 pc^-3, they have very bright and massive stars which facilitate their observation. Fig. (2) shows superimposed the evolution of the cluster (half-mass and core) radius for three selected models with a fraction of primordial binaries (hereafter PBs) in the sample of clusters considered. For N = 100, the model reaches a stellar density approximately equal to that of the solar neighbourhood when its half-mass radius is about 4.6 pc, and for N = 750 this value is reached for a half-mass radius of about 5.5 pc. It is clear from the figure that only a very small fraction of the observed clusters seems to match the properties of such an OCR. However, for N = 10, 500 the OCR has a stellar density larger than the solar neighbourhood (about 12 pc^-3) even when the population is as low as 30. It is possible that some of the oldest known open clusters are in fact remnants of densely populated () clusters.

Fig. 2a-c. Variation of cluster radius with age for the open cluster sample used (see the text). Left panel shows the evolution of the half-mass and the core radius for a model with N = 100; the middle panel shows a model with N = 750; and the right panel is for a model with N = 10, 500. The latter model has 500 PBs, the others a binary fraction of 1/3.

Table (1) shows the half-mass radius, population and age for a selected group of models with binary fractions equal to 0 and 1/3 respectively. These values are for the instant at which the half-mass stellar density (density inside the half-mass radius) is about the reference value. OCRs from rich clusters with a certain binary fraction have higher populations than similar models with no PBs. OCRs from poor clusters () should contain about 40% of their initial population in order to have a stellar density larger than the field. For N in the range 750-1,000, it should keep about 7% of its initial population. OCRs from clusters in the range 200-500 have 10-20% of their initial members. Densely populated clusters (N = 10, 000) generate OCRs containing about 0.1% of the initial population, but with stellar densities in the range 0.3-15 pc^-3.

Table 1. Main properties of the OCRs

2.2. Differential stellar content

Since the initial membership of a star cluster is the main parameter as regards cluster life-time for a given galactocentric distance, it is expected that there is some kind of differential behaviour depending on N. Neglecting the possible effect of binary stellar evolution, it should be easy to distinguish between OCRs from poor and rich clusters considering their stellar content. OCRs from poorly populated clusters should have massive stars because they reach the local mass density before dominant mass loss, and those from densely populated clusters should not have massive stars at all. Moreover, the characteristics of the remnant depend on the initial binary fraction of the model. The percentage of binaries in OCRs for models without PBs is about 20% and up to 80% for models with PBs. The exact stellar composition of an OCR depends also on the initial mass function. For models with PBs and a few hundred stars, the cluster disintegration occurs before intermediate mass stars have left the main sequence, so most of the binaries have not yet been destroyed due to mass loss. Binaries in an OCR have the same probability of being massive because most of the former have not been disrupted or ejected from the cluster. If the initial population of the cluster increases, then the disintegration time scale is similar to that needed for stars with masses greater than 4 to leave the main sequence. For clusters with 500, it is sometimes possible to find a white dwarf in the OCR as a primary or even a secondary. Neutron stars are ejected from the cluster due to a large velocity kick after the supernova. For clusters with about 1,000 stars most binaries in the OCR have masses of about 1.2 which corresponds to both components typically in the range K5-M5, although sometimes a sub-giant or even a giant is observed. For densely populated clusters, the probability of finding white dwarfs increases significantly. Fig. (3) shows the synthetic Hertzsprung-Russell diagram for one of these objects. For models without PBs, the OCR usually contains one binary but a differential behaviour as regards the stellar content is also observed, depending on the initial cluster richness. In any case, it is clear that simulations can help to study the original properties of an observed cluster remnant. For example, our calculations suggest that some of the oldest open clusters known could be remnants of very rich open clusters. However, we see young clusters today, which do not necessarily contain stars so this fact could point to different physical conditions at early stages of the formation of the galactic disk. A single, but striking, example of this possibility are the Magellanic Clouds which show very populous and young star clusters.

Fig. 3. H-R diagram for a simulated OCR with an age of 5.387 Gyr. It contains 32 stars with several white dwarfs. The core radius is 0.77 pc, the half-mass radius is 1.95 pc and the tidal radius is 4.48 pc. The initial population of the model was 10,010 stars with 10 PBs. There is only one binary in the OCR. The half-mass stellar density is about 0.44 pc-3.

© European Southern Observatory (ESO) 1998

Online publication: April 20, 1998
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