3 Clusters and target selection

The aim of our observations was to understand the correlation between the mass of the stars evolving along the AGB and the lithium abundance. This cannot be done on field giants, because their masses are unknown, while the age of clusters (and therefore the masses of the stars evolving along the AGB) can be derived from the turnoff and/or from the location of the helium core burning (clump) stars. We mainly used for this purpose the recent models by Ventura et al., in preparation, described in Kalirai et al. (2001). For the same models, the evolution is completed through the HBB phases as described in Ventura et al. (2000).

Unfortunately there are not many AGB stars in the young LMC open clusters and it is not well known which ones, among the few M type giants in the clusters, are in the TP phase. Our sample of targets was assembled including the candidates from the list of FMB90 adding a few objects in the clusters NGC 1866 and NGC 2031 that, from our own near IR photometry (Testa, unpublished), come out to be "early AGB'' candidates (see Fig. 2).

Figure 2: De-reddened CM diagram of NGC 1866 (squares) and NGC 2031 (triangles). The target stars are identified according to the numbering of  Table 1. An isochrone is also shown (from Ventura et al., in prep.) corresponding to a mass in AGB of $\sim$4.3 $M_\odot$, together with the TP AGB evolution of a 4 $M_\odot$ star (the difference in mass with respect to the isochrone is of no relevance here). The transformation from the theoretical to the observational diagram was performed by means of the relations of BCP98.

3.1 Cluster selection

3.1.1 NGC 1866

This cluster, one of the most populous of the LMC, has been very much debated in the literature, as it turns out to be a good test of the possible occurrence of core overshooting during hydrogen burning (see the latest discussion by Barmina et al. 2002). Testa et al. (1999) carefully compared the optical data with models, deriving ages which vary according to the input evolutionary tracks. The authors used either "standard'' models, or models with an "extended core'' during the hydrogen burning stage, that is, an artificially enlarged convective core (without a physical reason for this extension). This simplified treatment provides limits for the evolving masses which range from 4.4-5 $M_\odot$ for the standard case, to 3.9 $M_\odot$ for the extended core computations (A. Chieffi, private communication). We can compare these results with the models by Ventura et al., in preparation. These include a more physical description of core overshooting, by considering non-instantaneous mixing in the whole core, and extending it beyond the formal convective region. The mixing velocities of these models are taken from the convective model of Canuto et al. (1996). In the overshooting region, the velocities are extrapolated by assuming an exponential decay (consistent with large eddy numerical simulations of convection). The decay scale length is calibrated by means of several observational parameters (first of all, the main sequence observational width), through a parameter (the larger the value of $\zeta$, the slower the decay). Models with reproduce the observations (Ventura et al. 1998). The same overshooting is also used for the helium-core burning phases. These new models roughly confirm the Testa et al. (1999) computations. The turnoff location and the luminosity level of the red clump stars lead us to date the cluster at ages : the smaller value refers to models without overshooting (), the larger one to those with the largest overshooting ( ), and to a composition Y=0.26 and . The corresponding evolving mass in the AGB ranges from 4.3 ( ) to 5 $M_\odot$ ().

It has to be stressed that the great difference in the evolving masses between scenarios with and without overshooting does not correspond to a large difference in the AGB evolution, as the carbon oxygen core mass, that mainly determines the AGB evolution, is about the same in both cases. Both the 4.3 $M_\odot$ ( $\zeta =0.03$) and the 5 $M_\odot$ ($\zeta =0$) models with Z=0.01 will evolve through a HBB phase and produce lithium, at least if the Full Spectrum of Turbulence (FST) efficient convection model Ventura et al. (2000) is adopted.

3.1.2 NGC 2031

The CMD of this cluster looks very much similar to that of NGC 1866, although it is much less populated. Because of its location, in a highly populated region of the LMC, the analysis of the photometric data is rather difficult. This, together with the absence of dynamical studies, leaves open the question of the cluster membership of some of its stars. Mould et al. (1993) estimated ages of $140~\pm~20$ Myr by means of an isochrone fitting to the optical CMD, and stressed the similarity with NGC 1866.

  

Table 1: Photometric and spectroscopic observations.

^aThe magnitude of NGC~2214 and NGC~2107 are not reddened.

NGC 2214 and NGC 2107: Two comparison clusters

These two clusters have been selected for comparison with the NGC 1866 and NGC 2031, the two main clusters analyzed in this paper. The first one is definitely younger as can be seen by looking at the CMD published by Banks et al. (1995) or at the one previously available from Robertson (1974). The age estimate for NGC 2214 ranges from 32 Myr (Elson 1991) to 100 Myr (Girardi et al. 1995). We have re-calibrated the cluster age by using synthetic CMDs built with a grid of models from Ventura et al. (2000), obtaining  Myr. NGC 2107 is, on the other hand, older than NGC 1866 and NGC 2031, as found by Corsi et al. (1994) with a (V, B-V) CMD. Girardi et al. (1995) suggest an age of 250 Myr for this cluster. Our re-calibration, by using the same method applied for NGC 2214, is in agreement with the above value.

3.2 Target selection

The final sample of target stars is listed in Table 1. Each star is identified with the cluster name and is labeled in order of increasing K magnitude. Table 1 lists the magnitudes in various bands. The B, V photometry of NGC 1866 is from Testa et al. (1999); the R photometry for all clusters but NGC 2107 was obtained from calibration shots taken in November 1999 with SUSI2 - NTT; the J, H, K magnitudes of NGC 1866 and 2031 were obtained in 1995 at ESO 2.2 m - IRAC2. However, for the three brightest stars of NGC 1866 we had to adopt the J, H, K magnitudes by FMB90. This choice was preferred because these bright objects fall in the non-linear regime of the infrared IRAC2 detector. The B and V magnitudes of NGC 2214 are from the original work of Robertson (1974).

In order to de-redden the magnitudes of NGC 1866 we adopted A_J=0.09, A_H=0.06, A_K=0.03 and A_V=0.25. The absorption in the R and B bands were derived by means of the Rieke & Lebofsky (1985) relations for absorption in different bands. The reddening of NGC 2031 is more uncertain: Mould et al. (1993) gives E(B-V) spanning from 0.06 to 0.18. On the basis of the good match of the red clump of the two clusters we decided to adopt the same reddening values for both of them.

Figure 2 shows the near IR color magnitude diagram for NGC 1866 and NGC 2031 (Testa, unpublished), from which most of the targets have been selected, and a superposed isochrone by Ventura et al., in preparation, describing the clump stars and the early AGB evolution. An age of $\log t=8.2$ was chosen on the basis of the fit of the whole CM diagram (V versus B-V from Testa et al. 1999), including the turnoff.

The TP AGB phase is sketched on the same plot, by adopting an evolutionary mass of 4 $M_\odot$, (Y=0.26, Z=0.01) from Ventura et al. (2000). The track includes mass loss according to Blöcker (1995) formulation, with the Reimer's parameter $\eta$ fixed at 0.01.

Only one star per cluster could be selected in NGC 2214 and NGC 2107 from the sample of FMB90, namely star B69 of NGC 2214 (the notation refers to the work of Robertson 1974), and star No. 6 of NGC 2107.