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

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3. Colour-magnitude diagrams and isochrone fits

3.1. The Colour-Magnitude Diagrams

3.1.1. The case of SL 666

We constructed the R vs [FORMULA] colour-magnitude diagram (CMD). Fig. 5a shows the overall CMD (regions A and B, Fig. 1), as well as a series of CMDs in rings at radial distances from the centre of the cluster 0 - 0.5, 0.5 - 1.0, 1.0 - 1.5, 1.5 - 2.0, 2.0 - 2.5 and 2.5 - 4 arcmins (Fig. 5b-5g). The innermost CMD (Fig. 5b) is the least contaminated by field stars, and shows clearly the locus of the main-sequence stars of SL 666, reaching in these central areas [FORMULA]. Inspection of the rest of the radial CMDs reveals a gradual increase of the field contamination, as expected, with the field stars dominating almost entirely beyond 2.5 arcmin. As will be shown by the star-counts described in Sect. 4, we can practically treat this last CMD as representative of the field component.

[FIGURE] Fig. 5a-f. CMDs for the cluster SL 666 a for regions A & B; At rings with radial distance from the centre b 0 to 0.5 arcmin c 0.5 to 1.0 arcmin d 1.0 to 1.5 arcmin e 1.5 to 2.0 arcmin and f 2.0 to 2.5 arcmin, with isochrone models superimposed for the inner ring. The isochrones are shifted for reddening [FORMULA].

[FIGURE] Fig. 5. (continued) g CMD for the cluster SL 666 at ring with radial distance from the centre 2.5 to 4 arcmin (field), with isochrone models superimposed. The isochrones are shifted for reddening [FORMULA].

Although the star counts show a parametric (King model) tidal radius at [FORMULA] arcmin, the density profile shows that beyond [FORMULA] arcmin the cluster star members are very few. Up to 2 arcmins the main sequence reaches approximately [FORMULA] mag, while in the last CMD the brightest main sequence stars are fainter than [FORMULA] mag and may well correspond to the youngest component of the field population in this region. The bulk of faint main sequence, subgiant, red giant branch and red horizontal branch/clump stars represent the older field populations in the field as it is shown from the CMD of region F (Fig. 6f) inspite its lower quality. The ratio of red giants/clump stars takes a value of [FORMULA] for all regions apart from the very central one, where this ratio is [FORMULA]. We took under consideration red giants brighter than [FORMULA] mag. The differences between the two rations do not show any significance considering the crowding of the innermost region.

[FIGURE] Fig. 6a-f. CMDs for the cluster NGC 2098 a for regions A & B, and at rings with radial distance from the centre b 0 to 1.0 arcmin c 1.0 to 2.0 arcmin d 2.0 to 3.0 arcmin and e 3 to 4 arcmin (field). f shows the CMD of frame F (see Fig. 1). Isochrone models are superimposed for the inner ring and Frame F. The isochrones are shifted for reddening [FORMULA].

The differential Luminosity Function Histogram for various radial distances (Fig. 7) is illustrating that the bright stars are concentrated in the innermost region and that the cluster contains fainter stars down to the adopted detection limit (R=22.00 mag) to a distance [FORMULA] 2.4 arcmin.

[FIGURE] Fig. 7. The differential Luminosity Function Histogram of SL 666 for various radial distances. See Sect. 3.1.1.

3.1.2. The case of NGC 2098

Fig. 6 shows the CMDs for NGC 2098. Fig. 6a shows the overall CMD (from regions A and B), while in Figs. 6b-6e, we present a series of radial CMDs. The grid is coarser than in the case of SL 666, due to the poorer quality of the data. The brightest main sequence stars are again concentrated in the central region, and reach [FORMULA]. Beyond a radius of [FORMULA]3 arcmin (Fig. 6e), the field population is dominating. This last CMD is essentially identical to the CMD of region F (Fig. 6f), and similar (taking into account the different limiting magnitude) to that of the adopted field CMD (Fig. 5e) in SL 666.

As in the case of SL 666, the red giants and red horizontal branch/clump stars belong to field population. This can be easily verified by comparing the numbers of stars in the clump and red giant branch in the regions of the cluster and field (Fig. 1). This ratio takes a value of [FORMULA] except the very central region with [FORMULA] arcmin, where the ratio is [FORMULA].

3.2. Isochrone fitting and the ages of the clusters

Determination of the ages of clusters with the isochrone fitting method requires knowledge of their distance modulus, reddening and metal abundance.

(i) Distance modulus: For the purpose of the present study we shall adopt the distance modulus of 18.55[FORMULA]0.10 for the LMC as a whole (Feast, 1992), based on revised Cepheid data. This value is in good agreement with the one of 18.50[FORMULA]0.13 derived by Panagia et al. (1991) from the geometry of the ring around the supernova SN1987A. The value derived by Layden et al. (1996) is somewhat lower at [FORMULA] mag, but still compatible with the former values, within the combined errors. They based their estimate on new statistical parallax solutions for the absolute magnitude and kinematics of RR-Lyrae stars.

Caputo (1997) has found an [FORMULA] from RR-Lyrae stars, whereas from the Cepheid period-luminosity zero point from Hipparchos trigonometric parallaxes Feast & Catchpole (1997) give [FORMULA]. Alcock et al. (1996) find for the bar of the LMC [FORMULA]. So we finally think that a mean [FORMULA] is quite realistic.

(ii) Reddening: There are no direct measurements of the reddening towards SL 666 and NGC 2098. From Schwering & Israel (1991), the foreground extinction in the area of interest is [FORMULA] mag.

This value constitutes a lower limit of the actual reddening, since it does not include interstellar absorption within the LMC. The average reddening within the LMC is probably about 0.06 mag, but there are regions with reddenings as high as 0.3 mag, making the adoption of an average reddening inadvisable (Bessell, 1991). Hill et al. (1993) give [FORMULA] for the association LH111, which lies in the same general area but closer to the Bar than our clusters. The same authors give a value of [FORMULA] for the reddening (intrinsic and galactic) towards the association LH58, which lies geographically further away from our clusters, being on the other side of the Bar, but at similar projected distance from it as our clusters. Garmany et al. (1994) also find very low reddening towards LH58, comparable to the galactic foreground reddening. The loci of the zero-age main sequences of our clusters place an upper limit to the possible reddening at [FORMULA] 0.09 mag, in agreement with the reddening towards LH58. The value we adopt, [FORMULA], according to the isochrone fitting does not seem to contradict with the above indications. Of course for NGC 2098 this isochrone fitting is only indicative.

(iii) Metal abundance: There are no independent measurements of the metal abundances of SL 666 and NGC 2098, spectroscopic or otherwise. Note that the red giant branch method often used to estimate the metallicity of older clusters from their CMDs is inapplicable in this case, due to the young age of the clusters. Olszewski et al. (1991) measured the metallicities for a selection of star clusters in the LMC. The youngest objects in their sample (five in number) have ages between [FORMULA]yr, and metal abundances between [FORMULA]dex and 0.0. Kontizas & Kontizas (1996) have estimated that both NGC 2098 and SL 666 have metal abundances of the order of [FORMULA] (based on an empirical correlation between the ratio of late to early-type stars in clusters and their metallicity, proposed by Xiradaki, 1990), well within the above limits. We shall therefore adopt the value of [Fe/H][FORMULA] for the purposes of this study.

(iv) Ages of the clusters: In Figs. 5b and 6b we have superimposed on the observed CMDs of SL 666 and NGC 2098 correspondingly a set of appropriate isochrones taken from Alongi et al. (1993). We selected this set of isochrones as the best available that are appropriate for young populations of relatively low metallicity. We used Z=0.008, which corresponds better to the value [FORMULA] (or Z=0.01), a distance modulus of 18.55, and a reddening of [FORMULA]. For both clusters we have used the innermost CMDs, which are the least affected by back/foreground contamination. Comparison with the isochrones gives an age of 1-1.25 [FORMULA]yr for SL 666 and a somewhat younger age of [FORMULA]yr for NGC 2098. These age ranges do not include the uncertainties in the adopted values of distance modulus, reddening and metallicity, which can alter significantly the resulting ages. Use of different isochrones (e.g. with no convective overshooting) would also alter the results. The ages given above are only indicative. As mentioned in Sect. 3.1, the brightest main sequence stars are concentrated in the innermost regions of the clusters. If we had used the region next to the innermost, we would have derived larger ages by a factor of about 1.5-2.0, with this method. This difference is within the uncertainties arising from the ambiguity on the membership of the brightest stars.

(v) Ages of the field: The ratios RG/Clump stars have shown that these populations belong to the field. Therefore the CMDs best fit isochrones correspond to ages between [FORMULA] yr (Fig. 5g and 6f).

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© European Southern Observatory (ESO) 1998

Online publication: July 20, 1998