3. The color-magnitude diagrams
The CMDs derived from the photometry discussed in the previous section are presented in Figs. 1, 2, and 3. The upper part of the CMDs comes from the ground-based data, while the lower part is from the three WF cameras of the WFPC2. In the case of M22, the CMD for magnitudes fainter than V=19.8 comes from the WF2 only: the differential reddening of this cluster (Peterson & Cudworth 1994) makes the sequence much broader than expected from the photometric errors. The MS of M22 from the three WF cameras is shown in Fig. 4. In Table 2 the dispersion (defined as the sigma of the best fitting gaussian) of the MS (after the removal of the field star contamination as described in Sect. 4) is compared with the expected photometric error . The latter have been estimated from the artificial star tests (cf. Sect. 2.3), in one magnitude bins, in the interval . The resulting average differential reddening in the 3 WF fields is magnitudes. This value must be considered as an upper limit for the differential reddening in this region.
The ground-based and the HST fields are partially overlapping, with the ground-based images always covering a larger portion of the cluster. A detailed discussion of these CMDs will appear elsewhere. Here it suffice to note that we measured stars from the tip of the giant brach to a limiting magnitude . A white dwarf cooling sequence is clearly seen in all diagrams (but it will be discussed elsewhere). For the first time, we have a complete picture of a simple stellar population about 15 Gyr after its birth, from close to the hydrogen-burning limit to the final stages of its evolution along the white dwarf sequence. These diagrams can be used for a fine tuning of the stellar evolution and population synthesis models (Brocato et al. 1996).
Contamination by foreground/background stars is small for M10, as expected from its galactic latitute (), though a few background stars (likely from the outskirts of the Galactic bulge) are present. Despite the fact that M55 has the same latitude as M10, a significantly larger fraction of field stars is visible in the CMD of Fig. 3. Some of these stars are likely bulge members, but the prominent sequence blueward of the MS of M55 must be associated with the MS and TO of the stars in the Sagittarius dwarf spheroidal galaxy (Mateo et al. 1996, Fahlman et al. 1996). M22 is the most contaminated cluster. Both Galactic disk and Galactic bulge stars are clearly seen in the CMDs of Figs. 2 and 4.
Deep CMDs also contain information on the low-mass content of the clusters. This information can be extracted from our data only after we have a reliable transformation from luminosities to masses. Unfortunately, such a transformation remains uncertain for low-metallicity, low-mass stars. Almost nothing is known from the empirical point of view, and different calculations of stellar models yield different masses, particularly for the lowest-mass stars (King et al. 1998), and different overall trends (slopes) for the mass-luminosity relations (MLRs).
As already found for NGC 6397 (King et al. 1998) and the other three metal-poor clusters studied by PCK (cf. their Fig. 3), among the existing models we find that those by the group in Lyon (Baraffe et al. 1997) and by the group in Teramo (Cassisi et al. 1998, in preparation) best reproduce the observed sequences of M10, M22, and M55. [Note that Cassisi et al.'s (1998) models below () are the same models as in Alexander et al. (1997).] The level of agreement between the models and the observed data can be fully appreciated in Figs. 5, 6, and 7. In these figures the open circles represent the MS ridgeline, obtained by using a mode-finding algorithm and a kappa-sigma iteration in order to minimize the field star contamination. The dotted line represents the V magnitude limit of the LFs presented in the following Sect. 4; the data below this magnitude limit are not used in the present paper. The dashed line shows the isochrone corresponding to the metallicity which best matches the Zinn & West (1984) [Fe/H] (iron) content, scaled to the appropriate metallicity [M/H] assuming [O/Fe]=0.35 (Ryan & Norris 1991), and using the relation by Salaris et al. (1993). According to Table 3, we used the models for [M/H] for M22 and M55, and the models for [M/H] for M10. For comparison reasons, in Figs. 5, 6, and 7 we show also the isochrones which best match the Zinn & West (1984) metallicity assuming a solar ratio for the alpha elements (solid line). The distance modulus and reddening have been left as free parameters. The resulting values of are in very good agreement with the values in the literature (cf. Djorgovski 1993). This is also true for the resulting from the fit of the Lyon group models. The models from the Teramo group result systematically redder by about 0.06 magnitudes in than the isochrones from Baraffe et al. (1997), and the resulting reddening is marginally consistent with the reddening in the literature. In the LF comparison discussed in Sect. 4, we have adopted the distance moduli and reddenings used in the fit of the Baraffe et al. models and listed in Table 3.
Table 3. Adopted parameters
We want to briefly comment on the comparisons in Figs. 5, 6, and 7, leaving a more complete discussion to a future paper specific to the CMDs. There is an overall agreement between the models and the observed sequences. With the adopted distance moduli, both sets of models reproduce the characteristic bends of the MS, and at the correct magnitudes. The MSs of M22 and M55 seem to be better reproduced by the models, while the discrepancies seems to be more significant for M10. The deviations close to the TO might be due to the age of the adopted isochrones (the only ones available to us), which is 10 Gyr for the Lyon models and 14 Gyr for the Teramo ones. The isochrones seem to deviate more and more in color in the lowest part of the CMD. We can exclude that this is due to any internal errors in our photometry. The artificial-star experiments show that the average deviation in color due to photometric errors is less than 0.03 magnitudes at the faintest limit of the photometry. The residual differences might arise both from errors in the calibration from the HST to the standard system and to errors in the transformation from the theoretical to observational plane, very uncertain for these cool stars (Alexander et al. 1997).
© European Southern Observatory (ESO) 1999
Online publication: April 19, 1999