Astron. Astrophys. 324, 65-79 (1997)

2. Analysis

2.1. Method

The stellar population synthesis technique used for the HRD-GST is a powerful tool for the understanding of the complex distribution of stars in CMDs. The different stellar evolutionary phases are linked to each other through libraries with stellar evolutionary tracks. An interpolation is made between sets of evolutionary tracks with different metallicities to obtain a smooth metallicity coverage. With assumptions about the age, metallicity and the shape of the IMF (initial mass function), one obtains information about the star formation history (Bertelli et al. 1992) and the (synthetic) luminosity function.

The MS (main sequence) up to the AGB (asymptotic giant branch) stars from a synthetic population cover a specified age and metallicity range. The mass spectrum is specified with a power-law IMF and the number of stars with a specific age is determined by the SFR (star formation rate). The stars in a particular population all have the same scale height, because they are formed at the same period. High mass stars are only present in (very) young populations, while low mass stars are present in all populations under consideration.

The HRD-GST has thus far been used for the interpretation of the star counts from fields towards the galactic centre (Paper I, Bertelli et al. 1995 & 1996, the first reference is hereafter referred to as Paper II; Ng et al. 1996a, hereafter referred to as Paper III). In Paper I and Ng (1994) it is demonstrated that the age, the metallicity, the scale height of the disc stellar populations and the spatial distribution of the bulge/halo populations (flattening parameter) are the most sensitive parameters. They do not depend critically on the exact choice of the remaining input parameters for which we adopt reasonable values; see Table 1 for the scale length, IMF and SFR. The latter parameters have not been changed throughout the analysis. In this way, the study is simplified and one can focus on the exploration of a limited, but fundamental fraction, of the HRD-GST parameter space. The parameters are determined through an iterative approach: first the most sensitive parameter then the next sensitive and so forth.

Table 1. The stellar populations in the HRD-GST determined from the analysis of the star counts towards the North Galactic Pole. It is emphasized that the shapes for the IMF and SFR have been assumed and have not been determined from the star counts data. For all populations a power-law IMF has been adopted with an index . For the disc populations a scale length of 4.5 kpc is assumed. Better constraints on this value cannot be obtained from this study.

The combined data sets from the selected NGP fields span a range of 12 magnitudes in V. We determine the scale heights and age-metallicity for the various stellar populations along the line of sight and apply them to fields towards the SGP and to intermediate latitude fields towards the GAC. It is not possible to obtain stronger constraints for the scale heights and age-metallicity from the latter fields, because they cover a smaller magnitude range. Those fields provide a consistency test and an independent verification of the input parameters from the HRD-GST for an overall galactic model. In all fields the same local normalization is applied (see Sect. 2.3), as determined from the NGP star counts (see Sect. 3.1). Any difference between model and observations is either an imperfection of the model or is due to a local difference in the galactic structure.

2.2. Limits

We adopted in the MC (Monte-Carlo) simulations for all fields the following limiting magnitudes: , and . Differences in the definition of zero-points of the photometric passbands and their transformations result in small colour shifts between the simulated and observed data. Shifts are also induced by differences in age, metallicity or extinction and are considered when a general shift due to a zero-point difference did not remove the observed discrepancy.

The parameters for the HRD-GST determined in this paper are not unique. This makes any test as valid as the most simple test: the MC-simulations goes through all the data points. It has been assumed that young disc populations ought to have higher metallicities and lower scale heights than older ones.

The present mass limit is 0.6 M/ and work is in progress to extend it to lower masses. (Girardi et al. 1996a, b). The absence of synthetic main sequence stars with even lower masses is not a major disadvantage. The missing stars do not contribute to the evolved stars, because they remain on the main sequence for at least a Hubble time. At bright magnitudes, say , the contribution of low mass stars is negligible. At faint magnitudes, say , the colour distribution splits up around B-V 1 0 in two parts: a blue and a red distribution (see Fig. 1.3). We have tied our calibration to the blue section, where the low mass stars do not contribute. The presence of low mass stars is not necessary for the determination of the scale heights and the age-metallicities of the disc populations. For the latter a calibration to the blue section is essential.

2.3. Normalization

The total mass of the stars within 0.5 kpc along the line of sight is determined for each population. The various populations are then scaled relative to the intermediate disc population (see Table 1). A normalization based on the local mass density in the solar neighbourhood for each population is used here, because it is independent of the assumed passband and detection limit of the simulations. It can eventually be tested against the mass density in the solar neighbourhood. The contribution for each population is obtained by matching through trial and error the observed and the simulated distribution. The following local normalization is inferred for the various stellar populations: , , , , and . This normalization has also been applied in the other fields shown in Sect. 3. The normalization above is governed by the local mass density and is not the same as the normalization to the local stellar density from other star counts models.

© European Southern Observatory (ESO) 1997

Online publication: May 26, 1998

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