A study of the young cluster NGC 330 in the Small Magellanic Cloud

In this study we analyze the Colour-Magnitude Diagram (CMD) and the Luminosity Function (LF) of the SMC cluster NGC 330 on the basis of the new BV CCD photometry obtained by Vallenari et al. (1994) and the effective temperatures and bolometric magnitudes of a few supergiant stars taken from Caloi et al. (1993) and Stothers and Chin (1992a,b). The main goal of this study is to infer the kind of mixing taking place in stellar interiors. To this aim we make use of three grids of stellar tracks calculated with different schemes of mixing, namely classical semiconvection (Bressan et al. 1993), full overshoot (Bressan et al. 1993; Fagotto et al. 1994), and diffusive overshoot (Deng 1994; Deng et al. 1994). All the models are fairly homogeneous as far as the remaining input physics is concerned (opacity, nuclear reactions, mass loss rates), and are calculated with the new radiative opacities of Iglesias et al. (1992). We adopt the colour excess E(B-V) = 0.06 and the true distance modulus (m - M)(o) = 18.85. The metallicity of the cluster is highly uncertain: the observational determinations in fact go from Z = 0.0003 to Z = 0.006. The analysis of the CMD and LF is made by means of isochrones and synthetic CMDs. These latter allow us to match the CMD and the LF and to get an estimate of the slope x of the initial mass function (IMF) at the same time. With the assumed colour excess and distance modulus, NGC 330 turns out to possess a metallicity slightly lower than Z = 0.008 and an age a few 10(7) yr. However, we find that a significant spread in the age is present. The CMD is compatible with ages in the range 1 to 2.5 x 10(7) yr for semiconvective models, and 1 to 4.8 x 10(7) yr for full and diffusive overshoot models. Contrary to what claimed by Caloi et al. (1993) and Stothers and Chin (1992a,b), no clear indication arises about the mixing scheme. Indeed, neither the analysis of the integrated LF nor the location of the blue supergiant stars in the theoretical HRD are able to cast light on this point, even though there is some marginal indication that full and/or diffusive overshoot models ought to be preferred. The study of the integrated LF suggests that the slope of the IMF is about x = 2.35 for semiconvective models, about x = 2.35 for full overshoot models, and x = 2.00 for those with diffusive overshoot.