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

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5. Evolution of a stellar complex

As defined by Efremov (1988), Stellar Complexes (SC) are "groupings of stars hundreds of parsecs in size and up to 108 yr in age, apparently uniting stars born in the same gaseous complex". Associations and open clusters are the brighter and denser parts of these huge gaseous complexes. In other words, and according to Elmegreen & Elmegreen (1983), the fundamental unit of star formation is an HI-supercloud of [FORMULA] [FORMULA] which, during fragmentation into [FORMULA]-[FORMULA] [FORMULA] giant molecular clouds, gives birth to a SC. From these giant molecular clouds clusters and associations are formed. Examples of SCs are the Gould Belt in our Galaxy, 30 Doradus in the LMC, and NGC 206 in Andromeda.

In this section we explore the possibility that such objects are the progenitors of MGs. Since both galactic differential rotation and disc heating effect tend to disrupt any unbound system of stars on a short timescale, the large number of stars born inside a SC - and therefore roughly sharing the same kinematics and ages - may ensure a high spatial concentration for a longer time, especially at the focusing points.

In order to analyse the possible link between SCs and MGs, we have generated a SC as a set of different unbound systems born at different epochs. Its main characteristics are taken from the literature and are described in what follows. Although there are no preferences on the galactic plane region where SCs are formed (they can even be found in the interarm region, as suggested by the observations of OB Associations in Andromeda, e.g. Magnier et al. 1993), we select the position and velocity of the B4 nucleus at birth ([FORMULA] yr), since in this way we can compare the results here obtained with observations on this real group. According to several authors' estimations (Efremov, 1988; Elmegreen, 1985; Efremov & Chernin, 1994), SCs are several hundreds of parsecs in size. The original shape of our simulated complex has been designed as an ellipsoid whose equatorial plane is 250 pc in radius and lies on the galactic plane, and its vertical semi-axis is 70 pc. Six associations are born inside it at different epochs, randomly distributed inside this volume. Since the dispersion in age can be large when considering the SC as a whole (Efremov, 1988), we impose the condition that one associations borns every 107 yr. Hence, the first one is born at [FORMULA] yr, the second one at [FORMULA] yr, and so on. The mean velocities of these associations at birth follow a gaussian distribution around the B4 nucleus velocity, with an (isotropic) dispersion similar to the velocity dispersion inside a molecular cloud, i.e. [FORMULA] km s-1 in each component (Stark & Brand, 1989). Each of these associations is defined as follows: they contain 500 stars, which are randomly distributed inside a sphere of 15 pc in diameter, an intermediate value between the smallest associations (e.g. the Trapezium cluster) and the largest ones (Blaauw, 1991; Brown, 1996); and their internal velocity dispersion is 2 km s-1 in each velocity component, as observed in most of the closer OB Associations (Blaauw, 1991) and in molecular clouds (Scoville, 1990); their internal dispersion in ages is 10 7 yr (Efremov, 1988). We also assume that all the simulated stars survive up to the time (t) when we study the system.

The orbit of each simulated star from the moment it was born up to the present ([FORMULA]) is determined considering the galactic gravitational potential ([FORMULA]), without taking into account the disc heating effect. Their current spatial distribution is shown in Fig. 9, where different symbols are used for the stellar "groups" coming from each simulated association. According to our simulation, these groups are still concentrated in space, although their distribution is, at present, far from being isotropic due to the differential rotation. Each of them occupies an ellipsoidal volume [FORMULA] 150-250 pc wide, 500 pc long, and 70 pc height, and are perfectly separated in space (four of them can be observed at different positions inside a 300 pc radius sphere around the Sun). The dispersion in each velocity component of any of the groups is still [FORMULA] 2 km s-1, as expected from Eqs. A2. Although the mean velocity of these stars is very similar to that of B4, the dispersions in both velocity and space are too small when compared to dispersions in detected MGs that are a few 108 yr old (Table 1). Thus, the spiral arms and central bar perturbations to the galactic gravitational potential cannot account for the observational MGs' velocity dispersions.

[FIGURE] Fig. 9a and b. Position on the galactic a and meridional b planes of the simulated stellar complex at [FORMULA] (see text) when no disc heating effect is considered. Three square regions (600 pc/side) on the galactic plane have been enlarged to better distinguish the details. A different symbol is used for each group of stars coming from the same association. GC: galactic center; NP: north galactic pole; GR: galactic rotation

Results drastically change when considering the effect of constant heating on each individual star's trajectory, as described in Sect. 3.2. To determine these trajectories we use only the axisymmetric part of the galactic potential, since the asymmetric perturbations to this potential are already included in the treatment of the heating. The distribution of the simulated stars at present is shown in Fig. 10. The members of the different groups are now completely mixed with each other. The total SC forms a long structure [FORMULA] 3 kpc long and [FORMULA] 1 kpc wide. Since in this simulation the Sun has been considered to be in the very center of the SC at [FORMULA], the members of this complex can be found up to some 500 pc from us in the radial direction, and much further in the tangential direction. By enlarging a square region (600 pc/side) around the Sun we observe in Fig. 10 that, although the members of two groups dominate in the solar neighbourhood, all the other evolved associations are also represented. Again, the mean velocity components of B4 are recovered when considering only the (636) stars closer than 300 pc from the Sun. However, as expected, the dispersions in velocities are now higher than in the former simulation - the total velocity dispersion is [FORMULA] 8-10 km s-1, depending on the region of the evolved SC. Hence, a constant diffusion of the stellar velocities can perfectly account for B4 velocity dispersions.

[FIGURE] Fig. 10a and b. Same as Fig. 9 but considering now the effect of the disc heating on the trajectory of the stars

In order to study the properties of younger MGs, we analyse the general properties of the complex at its earlier stages, only [FORMULA] yr after the first association was born. At that moment ([FORMULA] yr) some stars in the youngest simulated groups are not yet born, while some others are as young as B1 and B2 members. The associations are still very concentrated in the phase space, though some merging can be observed, as happens with B2 group. Velocity dispersions inside each association clearly depend upon their ages, as expected. Thus, in the U-component the velocity dispersion varies from [FORMULA] 2.7 km s-1 for youngest groups to [FORMULA] 4.1 km s-1 for the oldest (in the other components the dispersions are smaller).

Finally, it is interesting to take a look to the general properties of a simulated SC at a larger t. The mean properties of the simulated SC are now taken from the B3 nucleus at birth ([FORMULA] yr). At present ([FORMULA] yr), assuming a constant heating of [FORMULA] km s-1 every [FORMULA] yr, the 3000 simulated stars occupy a huge curved region, about 2 kpc wide and almost 10 kpc long. In the most dense parts of this region, [FORMULA] 200 stars can be found in a 300 pc radius sphere, whose total velocity dispersions are very high (12-14 km s-1). Stars with such large dispersions would be completely merged with field stars, so they could not be detected as MG members. A much smaller diffusion coefficient is needed to recover the B3's velocity dispersions ([FORMULA] km s-1).

Thus, the disgregation of SCs by means of a constant heating mechanism is not able to account for the whole set of Pleiades MG substructures. A diffusion coefficient that depends on the stellar peculiar velocity and/or on the time (e.g. episodic diffusion) probably might explain the observed properties of these groups. Moreover, the presence of some open clusters in the original SC could keep the stars together in phase space during longer periods. Some young open clusters, i.e. IC 2391, [FORMULA] Persei, Pleiades, etc, share roughly the same kinematics as the groups in Table 1, which favours this hypothesis.

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© European Southern Observatory (ESO) 1999

Online publication: October 4, 1999