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Astron. Astrophys. 336, 503-517 (1998)

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6. Discussion

We have presented observational evidence that there is a mass segregation effect in the two young LMC globular clusters SL 666 and NGC 2098. The CMDs and LFs, the distribution of spectral types (Kontizas et al., 1988) and star counts from the various observations (AAT, 1.2m UK Schmidt, ESO astrograph GPO - Kontizas et al., 1988) show that the most massive stars are located in the center and that these happen to be early type stars.

In some very young open clusters in our Galaxy, the most massive stars are located in the outer regions of the cluster. This is most probably due to the fact that the Jeans mass during star formation decreases as the density increases (Burki, 1978; Larson, 1973) and this may be true for the loose galactic open clusters as well. On the other hand, Larson (1982) and Sagar et al. (1988) found young open clusters showing mass segregation with the most massive stars concentrated in the inner regions of the clusters. This effect is attributed either to the initial location of the stars during their formation, or to redistribution of stars in the clusters via dynamical processes. However the open clusters of our Galaxy are often under disruption. This doesn't seem to be the case for the LMC young clusters such as SL 666, which had no time to relax dynamically. As it is known so far violent relaxation does not produce mass segregation (Spitzer, 1969; Lightman & Shapiro, 1978). The two body relaxation mechanism does, but it is slow and it needs at least one mean relaxation time to give mass stratification.

However the same authors have developed a test showing that if the massive stars in a cluster are sufficiently numerous and there is a certain wide mass range then equipartition and therefore mass stratification can occur in time scale shorter than the mean relaxation one as given by the formula:


where [FORMULA], [FORMULA] are the two mass groups in the cluster with [FORMULA] with accepted lower limit of this ratio equal to 4. If the total mass of the stars with mass [FORMULA] is [FORMULA] whereas [FORMULA] the mass of all stars with mass [FORMULA] then the heavy stars contract to the core of the cluster by conductive losses under the following requirement:


where [FORMULA]. Under these requirements the heavy stars in equipartition are confined to the core region, whereas the density of the light stars is nearly equal all along the cluster region (Spitzer, 1987). In our case this is illustrated in the Fig. 8a where the density profile of the faintest stars shows a narrow gradient, whereas in Fig. 8f it is a lot steeper. Considering that we found the radius, where the bright stars are segregated (Spitzer radius [FORMULA] 0.5 arcmin for stars with magnitude [FORMULA] 18 mag - Table 2), within the half-mass radius, we have an additional indication of the existence of a heavy star core. Despite several recent theoretical evolutionary models, referring to idealised systems, it appears that "the conditions for the achievement of approximate equipartition resemble those derived on the basis of simple theory by Spitzer (1969)" as emphasized by Meylan & Heggie (1997).

From the CMDs and the adopted isochrones, we assume the mass range, whereas the LFs provide us an estimate of the total number of stars at this mass range independent of the dynamical mass. We can accept the detection limit as the low mass limit and calculate the total mass of the faint stars. The LFs are normalised to a defined area so if we multiply the numbers by the total cluster area we can calculate the total number of mass at the faint limit.

Extrapolating below our accepted completeness to [FORMULA] mag for the cluster SL 666, this limit corresponds to [FORMULA] giving a total mass for these stars [FORMULA]. This mass corresponds to the lower limit found for the parametric dynamical mass. If we accept that the observational limit is accurate down to [FORMULA] mag then the observed low mass limit ([FORMULA] in Eq. 4) leads to an equipartition time [FORMULA] yr, since the upper limit is [FORMULA] (for [FORMULA] mag).

For R down to 23.00 mag this equipartition time becomes [FORMULA] yr. Even if the lowest mass limit is that of the adopted isochrones (i.e. 0.72 [FORMULA]) the equipartition time is still [FORMULA] yr. To achieve an equipartition time equal to the evolutionary time we need a mass function range which is of the order of [FORMULA]. One upper mass limit is [FORMULA], so the low limit should reach [FORMULA]. But if we accept that stars as faint as [FORMULA] are also cluster members, then the number of stars must be much higher and the relaxation time will increase dramatically. Therefore all indications support the conclusion that the mass segregation is due to the star formation process.

The star formation and early-evolution of globular like clusters in the LMC have been discussed by Elson et al. (1987). They suggested that a large spread between the slope [FORMULA] of outer and inner regions would mean that the relative amount of gas lost in the inner and outer regions may vary. Therefore [FORMULA] must be different in the two regions. For SL 666, in the innermost regions for [FORMULA] arcmin the slope [FORMULA] changes (see Fig. 8b). This is systematically observed in all data sets (Fig. 8). It is not easy to decide whether this is an indication supporting the above remark, but it might be a point for further investigation. If this is the case then SL 666 appears to indicate slow star formation and low efficiency, where much gas is lost during the cluster formation, but the cluster remains bound. A further investigation towards this is given below.

Chernoff & Weinberg (1990) discuss the steepening of the IMF at larger radii indicating mass segregation. They also emphasized that although the complexity of dynamical effects and the mass spectrum is large it is very important that the rate of relaxation and collapse is mainly related to the initial central concentration of the cluster. Assuming that the Spitzer radius and the [FORMULA] characterise the innermost density when the cluster is just formed (Murray & Lin, 1993), then the value of [FORMULA] (Table 2) can give a minimum disruption time [FORMULA] yr (Spitzer, 1958). If we adopt the King model's core radius then this time is much longer. Therefore the cluster is bound and not near to disruption.

Unbound halos observed by Elson et al. (1987) are also to be expected to form in young clusters due to expansion after violent relaxation or mass loss. In our case the profiles from the photographic plates (where all fluctuations are smoothed all over the measured rings) do not show such "halos", whereas the CCD data may indicate a spread which is apparently due to the fact that the CCD frames are only indicative of a fraction of the outer cluster region. Tidal stripping of low mass stars is related to the orbital period of clusters and this happens at a time scale (Elson et al., 1987) much larger than the age of the clusters, so it is not expected to affect these clusters.

Larson (1982) has studied the mass spectra of young stars and the correlation with the properties of the associated molecular clouds to explain the spatial distribution of stars. He suggested the more massive stars form by accumulation processes in the dense core regions of protoclusters. Murray & Lin (1993) also emphasize the importance of mass spectra and their spatial distribution during the cluster's lifetime. So the above observations are a good indication of this effect. If this is more prominent in NGC 2098 which is the youngest of the two, we do not know because of the poor observations. Further observations with better resolution (i.e. HST) will reveal the low mass end and the radial distribution of stars at the earliest stages of their formation.

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Online publication: July 20, 1998