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Astron. Astrophys. 331, 934-948 (1998)

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5. Results and discussion

Results of the preceding analyses are summarized in Tables 3 and 4, for both the individual fields and the combined survey of seven fields. In the following subsections, the optimized structural parameters found for the density models of all four Galactic components and the metallicity structures of the thin disk and halo are discussed in turn, before we finally present our preliminary conclusions on the metallicity structure of the thick disk component.


Table 3. Optimized parameter values


Table 4. Mean metallicity and gradient of thick disk

5.1. Optimized values and constraints: primary parameters

The determination of optimized parameter values and constraints is based on the analysis of the [FORMULA] -selection from a large range of models, as described in Sect. 4.2. Due to the systematic coverage of high latitudes, we expect the survey data to be particularly suitable for measuring the scale heights of the old thin and thick disks, and for providing reliable extrapolations of the thick-disk and halo densities to the local volume near the sun. For all the individual fields as well as for the combined survey of seven fields, the [FORMULA] -curves for these parameters do indeed show the most pronounced minima, with growth rates increasing to several times [FORMULA], fully vindicating the above expectations. Thus, the most important conclusion to be drawn from the results given in the bottom lines of Table 3 is that, apart from its thin disk with canonical scale height [FORMULA], the Milky Way Galaxy has a thick disk with a local density of [FORMULA] relative to the thin disk and scale height [FORMULA], and only a weak halo with local density [FORMULA] relative to the thin disk. The thick disk portrayed by the above results appears to be a more substantial component than originally suggested by Gilmore and Reid (1983) and by Fenkart (1989a-d), but fits well with the picture emerging from the more recent studies discussed by Majewski (1993).

On the other hand, the present survey data are rather less sensitive to the two remaining primary parameters, the scale length of the old thin disk, [FORMULA], and the scale height of the young thin-disk dwarfs, [FORMULA]. Over the full variation ranges explored for these parameters, the [FORMULA] -curves have amplitudes which are of order [FORMULA] or less only above their [FORMULA], and the corresponding frequency distributions for the good models are rather flat. Therefore, although optimized mean values could be derived with surprisingly little scatter from field to field, the actual constraints imposed on these values from the combined survey data are not very strong.

5.2. Consistency with external data: secondary parameters

A gratifying result of the present analysis is that, upon determination of optimized values and constraints for the primary parameters, the secondary parameter values - which are left to freely float for final adjustment only after the primary parameters -, come out in close agreement with external data and constraints. For example, although the local density of the thin-disk dwarfs has been left to float in the range between 0.07 and 0.10 [FORMULA], the final optimized result turns out to be [FORMULA] [FORMULA], which is almost identical to the [FORMULA] [FORMULA] derived from the Gliese-Wielen luminosity function, if due account is taken of the frequency of binary and multiple stars that remain unresolved at the typical distances and the low-angular resolution of the Basel Palomar-Schmidt field survey (Buser & Kaeser 1985).

On the other hand, due to the relatively limited survey range of the thin disk and the steep decline of the luminosity function toward bright stars, the present survey data are rather insensitive to the density parameters of the brighter dwarfs of the young thin disk and the giants of the old thin disk. Therefore, the mean values for these parameters (e.g., [FORMULA]) are not, in general, strongly constrained by the [FORMULA] -curves and their associated frequency distributions. However, since the systematic coverage of many Galactic directions also provides adequate coverage of the different sensitivity ranges for all such low-sensitivity parameters - which also include the scale length of the thick disk, [FORMULA], and the halo parameters [FORMULA] and [FORMULA] -, the mean values derived from the data aggregate in seven fields are evidently derived consistent with independent investigations (Majewski 1993).

Similarly, even though the present survey was not specifically designed for determining the chemical structure of the thin disk, the data provide strong enough samplings of this component for a significant measurement of its vertical metallicity gradient - and "mean" metallicity. This is due to the fact that first, there is a large enough number (5 out of 7) of directions where the thin disk dominates the star counts down to the limiting magnitudes of the survey (cf. Figs. 18 and 19), and second because the colors are sufficiently metallicity sensitive to warrant significant mapping of the metallicity effect (Figs. 14 and 15).

[FIGURE] Fig. 18. Star counts N(G) in the Praesepe field, comparing the observed histogram with the predicted total built up by the contributions from the individual components. The thin disk dominates down to the magnitude limit at [FORMULA]. Compare with Fig. 11.

[FIGURE] Fig. 19. Star counts N(G) in the field SA 57, comparing the observed histogram with the predicted total built up by the contributions from the individual components. The thin disk dominates down to [FORMULA] but is overtaken by the thick disk and the halo at fainter magnitudes.

Thus, the "mean" metallicity suggested by the minimum of the global [FORMULA] -curve in Fig. 20 is fully consistent with the thin disk having mean metallicity [FORMULA] dex in the very local volume, but which, due to a gradient [FORMULA] dex/kpc, decreases by a factor of [FORMULA] in the more distant thin-disk volumes sampled by the present survey. These results are in good agreement with those obtained from photoelectric photometry and spectroscopy for smaller samples of G-K giants and F-G dwarfs by Yoss et al. (1987) and by Trefzger et al. (1995).

[FIGURE] Fig. 20. [FORMULA] -curve for the thin-disk mean metallicity derived from the all-survey data in seven fields. Although only weakly pronounced, the minimum near [FORMULA] dex goes along with a vertical metallicity gradient [FORMULA] dex/kpc, which demonstrates that the present data and results are consistent with the canonical knowledge of this component.

On the other hand, because the present survey does not penetrate to very faint magnitudes, the field halo is not well sampled out to its farthest reaches. Therefore, while a metallicity gradient for the halo could not be derived reliably, the mean metallicity, [FORMULA] dex, indicated by the global [FORMULA] -curve in Fig. 21, is again consistent with canonical values.

[FIGURE] Fig. 21. [FORMULA] -curve for the halo mean metallicity derived from the all-survey data in seven fields. The curve suggests that the minimum occurs near [FORMULA] dex, which is clearly different from the value (-1.75 dex) adopted initially.

5.3. Preliminary constraints: metallicity structure of thick disk

Table 4 summarizes the metallicity structure of the thick disk component that we find from the present (preliminary) analysis. As anticipated in 4.2.6, these results are derived assuming two different basic models: (1) for the chemically homogeneous model, we calculate a mean metallicity [FORMULA] dex with dispersion [FORMULA] dex, where [FORMULA] dex is the dispersion intrinsic to the adopted color-magnitude and color-color relations and [FORMULA] dex is the dispersion derived from the [FORMULA] -curves and frequency distributions of the good models; (2) for the model including chemical gradients, the mean metallicities in each field are calculated from the best-fitting gradient solution and averaging all the individual stellar metallicities summed over the successive volumes. Interestingly, this model gives a marginally higher "mean" metallicity, [FORMULA] dex, but with a somewhat larger dispersion [FORMULA] dex which is slightly skewed toward lower metallicities. Clearly, the stronger derived gradients in fields 1, 3, and 6 of Table 4 predict lower metallicities for larger distances and, hence, for the implied larger count contributions, leading to lower "mean" metallicities for these fields as well.

Even though the results of Table 4 do not yet provide a definitive answer to the question of whether or not (a) gradient(s) exist(s) in the thick disk - because the numerical data are still consistent with either of the above model assumptions on the two-sigma level -, what they seem to indicate however is that chemical inhomogeneities are likely present in this component which give rise to a rather larger metallicity spread than anticipated initially. We expect that a more refined and comprehensive analysis of the full-survey data in 14 fields will allow us to considerably sharpen the present picture.

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© European Southern Observatory (ESO) 1998

Online publication: March 3, 1998