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Astron. Astrophys. 363, 947-957 (2000)

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6. Comparisons

It is interesting to compare the distribution of the extended sample with distributions obtained by other authors. In Fig. 15 the distributions from Pagel (1989) and Rocha-Pinto & Maciel (1996) are compared with the distribution of the extended sample.

[FIGURE] Fig. 15. Comparison with the Pagel (1989) (dashed) and the Rocha-Pinto & Maciel (1996) (dotted) distributions. The solid line is the extended sample (H).

The Pagel (1989) distribution (containing 132 stars) does not compare well with the extended sample distribution. It is much broader, and the low metallicity tail begins at a much lower [Fe/H] ([FORMULA]). This suggests that the discrepancy might be caused by the different metallicity estimators (Strömgren [FORMULA] vs Johnson UV excess [FORMULA]) and callibrations, i.e. [Fe/H] vs the [O/H] used in Pagel (1989). This makes it hard to compare these distributions.

The Rocha-Pinto & Maciel distribution displayed in Fig. 15 contains 287 stars, and is corrected with the Sommer-Larsen f method (mentioned in Sect. 4). It has the same pronounced peak at [Fe/H] [FORMULA] as the extended sample distribution, but the tail is not as small. While these two distributions are af samples having comparable size (287 vs. 253 stars), the more thorough methods used in obtaining the extended sample implies that more weight should be placed on the extended sample.

6.1. Comparison with theoretical models

When comparing with theoretical models it is practical to use the recontructed sample, as that removes some effects from observational scatter. However, the observational and intrinsic scatter are still present. To compensate for this the theoretical models are convolved with a normal distribution with [FORMULA]. A variation of [FORMULA] for the normal distribution has the greatest effect on steep distributions. A high [FORMULA] will make any steep distribution considerably wider.

The extended sample was compared with the simple model (e.g. Pagel 1997), the Prompt Initial Enrichment model (Truran & Cameron 1971) and Larson's model (Larson 1972). None of these models fits the data in any acceptable way.

In Fig. 16 the extended sample is compared with Pagel & Tautvaisiene (1995). Their model fits reasonably well. The adopted parameters were: [FORMULA], [FORMULA] and [FORMULA]. Considering the scatter inherent in the distribution this is a good fit. While the convolution does degrade the fit, it is still not unreasonable.

[FIGURE] Fig. 16. Comparison with the Pagel & Tautvaisiene (1995) model. The solid line is the reconstructed sample. The dashed line is the Pagel & Tautvaisiene (1995) model, while the dotted line is including the convolution.

The Lynden-Bell model is also a good fit (see Fig. 17). The Lynden-Bell model has [FORMULA] and a yield of [FORMULA]. This value of [FORMULA] is not in any way unreasonable (in Pagel 1989 a value twice this is used). The reconstructed sample lies more or less directly between the convolved and the unconvolved models. This indicates that if the intrinsic and observational scatter are less than anticipated an even better fit can be made. In any case, the infall models fits the distribution rather well, and are perfectly capable of explaining the G dwarf problem considering the scatter in the observed distribution. The only problem with these models is around [Fe/H] =-0.6. Here the models are a little too broad, although this disappears if the scatter is overestimated. This indicates that models should perhaps try to relax the perfect mixing assumption, which could counter the intrinsic scatter making models more directly comparable to observational data.

[FIGURE] Fig. 17. Comparison with the Lynden-Bell (1975) model. The solid line is the reconstructed sample. The dashed line is the Lynden-Bell (1975) model with [FORMULA], while the dotted line is including the convolution.

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© European Southern Observatory (ESO) 2000

Online publication: December 5, 2000