After these corrections it is possible to review the mass limits of the sample. To facilitate this investigation, a number of subsamples are defined in Table 3.
A comparison of the metallicity distribution of all stars left in the sample and the conservative () sample is shown in Fig. 10a. Fig. 10b shows the conservative sample compared with the sample. There is little difference between the conservative sample and the sample, and it is thus possible to extend the sample down to . As seen in Fig. 11a the sample is affected if the range is extended all the way down to the lowest mass, the main peak is lower and wider, which is not the expected result. The main peak shows no influence from the lack of high-metallicity low-mass stars predicted from the color limit. This can be explained in two ways: The first explanation is that the interpolation program forms a natural lower mass limit, e.g. if very few stars below a certain mass, say 0.7 , are accepted because of the location of the tracks in the HR diagram. The second explanation is that the conservative sample is also affected. In that case the low metallicity tail would be over-represented in this study. This should be taken into consideration when evaluating the results from this study. The next step is to examine the upper limit. The first thing to notice here is that the low metallicity tails in Fig. 10b are comparable. This indicates that the upper mass limit is beyond . Fig. 11b shows the effect of extending the sample upward to . There is little change, although the low metallicity tail is slightly less prominent. This indicates that the upper mass limit can safely be set to .
In Fig. 12a the upper mass limit is removed. This has an effect on the low metallicity tail, which is nearly halved. The main bulge is also slightly broader, and it is thus not prudent to extend the sample to higher masses. This is obvious in Fig. 12b where only the stars above is shown. This is caused by the short mainsequence lifetimes of high mass - low metallicity stars. In conclusion it is possible to use the interval from to . The distribution of the stars in this interval is shown in Fig. 13. This distribution is also tabulated in Table 4. The weighted column indicates the normalized weight of the bin after scaleheight correction.
5.1. Scatter estimation
It is of great interest to have an estimate of the error associated with this distribution. Such an estimate is obtained in two steps. First a smoothed distribution is found, and then a Monte Carlo simulation of the error in [Fe/H] is made using this smoothed distribution. This ignores errors arising from the mass limits, the model uncertainies etc., but will give an estimate of the scatter that is present.
The observational scatter is taken to be 0.15 dex, although for stars above [Fe/H] =-0.6, 0.13 dex is more appropriate. The intrinsic scatter is taken to be the intrinsic scatter in the age-metallicity relation for stars at solar age and galactocentric distance. This is 0.15 dex from Edvardsson et al. (1993). Deconvolving the final distribution with a normal distribution with a standard deviation of dex, and using the optimum noise filter, results in a filtered distribution. From the filtered distribution a reconstructed sample is made by a convolution of the filtered distribution and a normal distribution ().
The [Fe/H] of all stars in the sample was shifted with a normally-distributed random function with a standard deviation of 0.15 dex. The mass was shifted with a standard deviation of . Error bars were constructed so that 67% of all distributions fall inside them. The result of this simulation is shown in Fig. 14. The error bars in this figure do match the extended sample and the reconstructed distribution very well, with the only problems located near the "edges" of the main peak. It should also be noted that while there are large uncertainties in the distribution, the low metallicity tail can not be explained away, as the error bars are established based on the presence of stars in the low metallicity tail, and do not in any way touch on the possibility that they should not be in the sample e.g. mis-identified subdwarfs or RS CVn stars. It is however highly unlikely that this is the case, as the tail consists of several stars neatly distributed into the bins between [Fe/H]=-1.0 and [Fe/H]=-0.5. However, a more detailed observational investigation of these stars might be interesting.
© European Southern Observatory (ESO) 2000
Online publication: December 5, 2000