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Astron. Astrophys. 350, 434-446 (1999)

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1. Introduction

A "supercluster" can be defined as a group of stars gravitationally unbound that share the same kinematics and may occupy extended regions of the Galaxy. A "moving group" (MG hereafter) or "moving cluster", however, is the part of the supercluster that can be observed from the Earth (see, for instance, Eggen 1994).

Independent of the physical process that leads to the formation of superclusters, there are basically two factors acting against their persistence in the general stellar background. First, when a group of unbound stars concentrated in the phase space has a certain velocity dispersion, the galactic differential rotation tends to spread them out very quickly in the direction of the galactic rotation (e.g., Woolley 1960). Secondly observations show that the velocity dispersion of disc stars is increased with their age, which is usually interpreted as the result of a continuous process of gravitational acceleration that may be produced by different agents (e.g., Lacey 1991). This second factor, generally referred to as disc heating , also disperses stars very efficiently. It is therefore striking to verify that some of the classical MGs are several [FORMULA] yr old. Some authors have overcome part of this problem by assuming that the velocity dispersion of these stellar groups must be very small - e.g. Eggen (1989), Yuan & Waxman (1977), Soderblom & Mayor (1993). Nevertheless, some recent studies (Chen et al., 1997; Sabas, 1997; Figueras et al., 1997; Chereul et al., 1998; Asiain et al., 1999) do not support such a small dispersions.

There have been several attempts to explain the origin of superclusters. Perhaps one of the most widely accepted explanation is the "evaporation" of the outermost stellar component (or corona) of open clusters (e.g. Efremov 1988). Over time, open clusters are disrupted by the gravitational interaction with massive objects in the Galaxy (such as giant molecular clouds), and as a result the open cluster members fill a long tube in space. The part of this tube that we can observe should have a small velocity dispersion - e.g. Weidemann et al. (1992), Eggen (1994). Although based in old stellar evolutionary models by Iben (1967), Wielen (1971) found that about 50% of the open clusters disintegrate in less than 2[FORMULA]108 years, a result supported by posterior studies (Terlevich, 1987; Theuns, 1992). If superclusters come from the evaporation of open clusters's coronae, then Wielen's (1971) results indicate that most superclusters should be young or the last tracers of former clusters.

MGs may also be produced by the dissolution of larger stellar agglomerations, such as stellar complexes or fragments of old spiral arms (Woolley, 1960; Wielen, 1971; Yuan, 1977; Elmegreen, 1985; Efremov, 1988; Comeron et al., 1997). Thus, a MG could be a mixture of stars coming from different open clusters' coronae and disrupted associations that share the same origin (and motion). This process of MG formation includes the first hypothesis mentioned here. Alternatively, Casertano et al. (1993) proposed that MGs are open clusters that evolved under the gravitational influence of a large local mass that surrounds and traps them. However, it seems difficult to specify the nature of such a large mass. Finally, it has been proposed that superclusters could actually be made of stars trapped around stable periodic orbits (e.g. Müllari et al. 1994; Raboud et al. 1998).

In this paper we assume that superclusters occupied a small volume in the phase space in their first stages, when they became gravitationally unbound. From that point on, they evolved under the influence of the gravitational potential of the Galaxy, as it would be the case in the classical picture of stellar evaporation from open clusters' coronae. We then analyse different aspects related to the evolution of MGs.

First, in Sect. 2 we use epicycle approximation to study the ability of the "focusing phenomenon" (Yuan, 1977) to periodically group MG stars when no disc heating is considered. In Sect. 3 we show how to determine the stellar trajectories from an analytic expression of the galactic potential. The disc heating effect on moving groups' properties can be considered by introducing random perturbations to the velocity components of stars. These trajectories allow us to study the evolution of unbound stellar systems independent of the local galactic properties (in contrast with epicycle approximation).

We focus our study on the origin and evolution of the Pleiades moving group, since it is the youngest moving group in the solar neighbourhood and, therefore, we may find it easier to recover its past properties with certain confidence (Sect. 4). We consider the different Pleiades substructures found in Asiain et al. (1999, Paper I), and estimate their kinematic age and galactic position at birth. Finally, in Sect. 5 we simulate a stellar complex and determine the trajectory of its stars to study its disruption over time. The disc heating effect on the evolution of the stellar complex is evaluated.

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© European Southern Observatory (ESO) 1999

Online publication: October 4, 1999