Astron. Astrophys. 333, 897-909 (1998)

4. Discussion

Our main goal, as stated in the Introduction, is to use these new results to test the usual explanation of mass segregation in term of dynamical relaxation over a large age interval. We then need to compare the radial structure of the three open clusters (NGC 6231, Pleiades and Praesepe) and the observed mass segregation. We shall also consider published results for a few other clusters (MonR2, Orion, M11, M67).

4.1. Relaxed clusters: Pleiades and Praesepe

Both clusters, respectively and 8 10⁸ yr old, should be well relaxed (the typical relaxation times for these open clusters are estimated at around yr). As a consequence of equipartition of kinetic energy between stars of different mass, both clusters should exhibit similar mass segregation. We observe that this effect is alike for the most massive stars, but appears less pronounced in Praesepe than in the Pleiades for the intermediate mass stars, although M44 is about 8 times older than the Pleiades (Fig. 14a-c).

Mathieu (1984) has examined the structure and mass segregation in NGC 6705 (M11) on the basis of extensive proper motions and photometry. This cluster has an age intermediate between that of the Pleiades and Praesepe ( 2.3 yr), with the mass of the most massive stars around 3.5 . His Fig. 9 offers a clear evidence for a fine mass segregation and is very similar to our Fig. 14b (Pleiades).

The old open cluster M67 behaves quite differently: the radial distribution of the member stars (Fig. 13) contrasts dramatically with those presented for our three clusters. It presents a small amount of mass segregation for single stars with M 1.5 . Only red giants, blue stragglers and binaries are somewhat concentrated towards the cluster center (Mathieu 1985). Fig. 13 also reveals the incompleteness of the membership list in the outer part resulting either from the lower completeness of measurements of fainter stars at large distance from the cluster center or from the membership estimates.

Fig. 13. Apparent magnitudes of the stars as a function of their radial distances to the center of M67. The HEP (Hydrogen Exhaustion Phase) gap is apparent at 13. This radial distribution of stars contrasts dramatically with those presented for NGC 6231 and Praesepe (figs. 9 and 2).

Fig. 14. Cumulative distributions for stars in identical relative intervals of mass, for the three clusters. These intervals are computed relatively to the maximum stellar mass of the considered cluster. Triangles: M 0.36 ; crosses: 0.23 M 0.36 ; open squares: 0.14 M 0.23 ; filled squares: M 0.14 . The 9 bright stars of the corona of NGC 6231 are not included in the figure.

We will now consider two possible explanations for the less pronounced mass segregation observed in Praesepe.

4.1.1. The dominant mass component

The first one follows the results of numerical simulations by Spitzer & Shull (1975). From them we infer that if stars belonging to a small range of mass constitute almost all the cluster mass, the spatial distribution of that component will be unaffected by interactions with stars of other mass groups. Accordingly one should observe little, if any, mass segregation among this dominant group. The other stars will be either more or less concentrated, on whether they are heavier or lighter than the dominant group. This kind of mass segregation will be only slightly dependent on the exact individual stellar masses.

In the case of Praesepe, we note that the total cluster mass effectively observed (derived by summing up all the stellar masses) is contained within the interval of the theoretically estimated masses (Table 7). It was not the case for the Pleiades (RM98)). We then observe a large part of the total mass of Praesepe. If we consider that stars with masses between 0.9 and 2.3 constitute the dominant mass group of the cluster, we should observe little, or no, mass segregation among this group. Furthermore, all heavier stars (M 2.3 ) should be identically more concentrated. This description would explain correctly our results.

4.1.2. The potential well

The second explanation could be related to the smaller total mass of Praesepe (Sect. 3.1.6), compared to that of the Pleiades (RM98)). Praesepe has then a shallower potential well than the Pleiades and the velocity distribution of the stars of Praesepe are more severely truncated by the galactic tidal field (the two clusters have similar galactic locations). This will result in a lesser degree of mass segregation among Praesepe stars (Mathieu 1985).

However, we should keep in mind that the comparison between Praesepe and the Pleiades has a limited validity, because the two clusters could have experienced different external constraints. For instance, we could not exclude that the lesser degree of mass segregation observed in Praesepe may be due to the effects of external forces acting on the cluster.

4.2. Non-relaxed cluster: NGC 6231

The analysis of the structure of NGC 6231, the youngest open cluster that we considered, clearly shows some mass segregation (Sect. 3.2.2).

The estimation of the cluster relaxation time gives a value of about 10⁷ yr (Raboud 1997), larger than the cluster age (3-4 10⁶ yr, Raboud et al. 1997). Therefore the cluster dynamical evolution did not have enough time to produce energy equipartition among the cluster members and no mass segregation should be present. Thus we are tempted to consider that the observed mass segregation in NGC 6231 is initial and to identify it as a signature of the stellar formation processes. Within this picture, the most massive stars form near the cluster center.

However, as discussed in Raboud (1997), the computed relaxation is an upper limit. This relaxation time, calculated with the standard equations from Chandrasekhar (1942) and Spitzer & Hart (1971), refers to stars of average mass. As real clusters present a wide mass spectrum, this implies that the systems evolve on a timescale shorter than that estimated by this mean relaxation time. Furthemore, the relaxation time depends upon the location in the cluster: it significantly increases from the center to the outer regions (Mathieu 1983). Finally, N -body calculations that treat close gravitational encounters and binary formation predict more rapid dynamical evolutions than that indicated by the mean relaxation time (Sagar et al. 1988 and references therein).

We therefore cannot exclude a dynamical evolution on shorter timescales, typically one order of magnitude, particularly in the innermost part of the cluster or for the most massive stars.

Nevertheless, the mean relaxation time is also a lower limit because we observe only the brightest stars of the cluster and therefore we underestimate the total number of stars and the characteristic radius of the cluster while we overestimate its mean stellar mass.

Numerical modelling are then truly needed to clearly quantify the amount of mass segregation due to dynamical evolution and due to the initial conditions.

Such a modelling had been done by Bonnell & Davies (1997) for the Orion Nebula Cluster (ONC), based on the data of Hillenbrand (1997a). The authors show that the position of massive stars in the center of rich young clusters cannot be due to dynamical mass segregation. In particular, they claim that for producing a Trapezium-like system within just a few crossing times, the massive stars most likely formed within the inner 10% of the cluster.

Other indications for an initial mass segregation, i.e. an imprint of the stellar formation processes and not a consequence of the cluster dynamical evolution, have been obtained from the observations of other very young open clusters like: NGC 3293 (Herbst & Miller 1982), NGC 6530 (McNamara & Sekiguchi 1986), IC 1805 (Sagar et al. 1988), NGC 2264, NGC 6913, NGC 654, NGC 581, Tr 1 and h and Per (Pandey et al. 1991). But, as these indications of initial mass segregation are mainly based on the comparison between the ages of the clusters and their mean relaxation times, these studies suffer drawbacks similar to those described above.

Clusters still embedded within their parent molecular clouds and already displaying mass segregation may be more convincing. Examples are, among others, NGC 2024 and NGC 2071 (Lada & Lada 1991). Such clusters have ages of the order of their crossing time ( yr) or below. Relaxation processes are then negligible for them and the observed locations of their stars are close to their birthplace. Consequently, the presence of mass segregation in these extremely young open clusters should not result from their dynamical evolution.

All the preceding constatations favour the hypothesis that some of the mass segregation observed in a cluster as young as NGC 6231 is likely to be primordial.

Inspection of Fig. 12 also reveals that only the most massive stars are concentrated toward the cluster center. On the contrary, stars with masses between 20 and 5 are spatially well mixed. Similar results are obtained for a cluster embedded in the MonR2 molecular cloud (Carpenter et al. 1997). The authors pointed out that mass segregation may be limited to the OB stars forming in this region. Moreover, in the case of the ONC, Fig. 6 from Hillenbrand (1997b) shows very different spatial distributions for stars more massive or less massive than 5 . For masses smaller than 5 the distributions are rather similar. We then conclude that, in very young clusters, mass segregation likely concerns only the most massive stars.

4.2.1. Double origin for the mass segregation ?

The evolutive picture emerging from the analysis of the considered clusters (MonR2, Orion, NGC 6231, Pleiades, NGC 6705, Praesepe and M67) do not agree with the usual description of the mass segregation, as a pure consequence of dynamical evolution. We observe that the younger clusters (MonR2, Orion and NGC 6231), likely still not relaxed, already present a mass segregation and that the older ones (Praesepe, M67) present the lesser degree of mass segregation (Fig. 14a-c). Possible explanations for the last observation have been discussed in Sect. 4.1., but the presence of some mass segregation within clusters likely still not relaxed implies a reconsideration of the physical origin of this effect.

The above results allow us to propose a qualitative scenario for the evolution of mass segregation with age in open clusters:

(I) The most massive stars ( for NGC 6231) form near the center of clusters.

Several hypotheses could be made to explain the presence of massive stars near the center of clusters at the early beginning of their life. Either the massive protostars sink towards the center of clusters or physical conditions in the center of protostellar clouds favour the formation of massive stars. These various hypothesis are: the dynamical friction between protostellar clouds and inter-protostellar medium (Larson 1991, Gorti & Bhatt 1995, 1996); the collision and coalescence of protostellar clouds (Murray & Lin 1996); the accretion of matter, during stellar formation phases. This accretion could be faster in regions of higher temperature and turbulence (Maeder 1997), i.e. in the center of protocluster clouds, thus leading to the formation of more massive stars in these regions. This last hypothesis implies that the IMF is dependent on the local physical conditions. It is flatter in the central part of the cluster and steeper in the outer part. Therefore open clusters could be the first physical environments, observed with a sufficient spatial resolution, in which we note a non-universality of the IMF.

In the context of massive star formation in the center of clusters, it is worth noting that we observe numerous examples of multiple systems of O-stars in the center of very young open clusters. In the case of NGC 6231, 8 stars among the 10 brightest are spectroscopic binaries with periods shorter than 6 days. Moreover, we observe trapezium systems of O-stars in the ONC, NGC 6823 and Tr 37. Four-component and triple systems have also been found in NGC 2362 (van Leeuwen & van Genderen 1997) and Collinder 228 (Leung et al. 1979).

(II) In less than yr these spatially concentrated massive stars will disappear due to stellar evolution. As they may represent a non-negligible percentage of the total mass of the cluster (between 10 and 30 % in the case of NGC 6231), the disappearance of these massive stars could lead to a violent relaxation phase. If a mass segregation was previously established in the cluster it could be more or less erased during this phase, depending on the importance of the initial population of massive stars.

We are then possibly left with a cluster presenting no mass segregation at all. NGC 6531 (Forbes 1996) provides an example of such a cluster: it is 8 10⁶ yr old and does not contain any stars with masses greater than 20 (which make up the concentrated population in NGC 6231). Forbes shows convincingly that NGC 6531 does not exhibit any mass segregation, and he explains this result by the young age of the cluster. According to him, NGC 6531 is too young for dynamical evolution to have left any significant impression. But this hypothesis was based on an estimation of the relaxation time and suffers drawbacks described in the Sect. 4.2.

Another interesting point related to the disappearance of the massive stars is the stability of the cluster. It is possible that a bound cluster becomes unbound after this violent phase. Numerical simulations by Terlevich (1987) show that clusters with flat initial mass functions have to be rich enough to survive the initial violent period of mass loss.

(III) The last point of our scenario is that all mass segregation observed in older clusters (like the Pleiades or Praesepe) is merely the consequence of the cluster's dynamical evolution. However, this conclusion does not imply that NGC 6231 is a representative precursor of older clusters.

To better quantify this hypothesis of a possible double origin (initial and dynamical) of the mass segregation we need to analyse the structure of open clusters just old enough (around 10⁷ yr) to have lost their most massive stars. Thus, one consequence of our hypothesis is that some of these clusters, those which initially contained an important population of massive stars, should not present any mass segregation.

© European Southern Observatory (ESO) 1998

Online publication: April 28, 1998

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