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Astron. Astrophys. 320, 757-775 (1997)

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3. Results

Fig. 15 and Fig. 16 present our CMDs in different radial annuli, and clearly show how the different (CCD and photographic) sub-samples have been joined, as well as the main features of the individual branches. Since the lower part of the V, [FORMULA] colour-magnitude diagram (composed only by re-calibrated photographic data) was discussed at length in PH94, we will concentrate here exclusively on the bright part of these CMDs.

[FIGURE] Fig. 15. V, [FORMULA] CMD at different radial distances.
[FIGURE] Fig. 16. V, [FORMULA] CMD at different radial distances.

The main aspects worth of note are the following:

1. The main branches can easily be delineated in any radial bin, including the most internal region. In particular, the RGB and the AGB can be separated quite easily at the AGB base, located at [FORMULA]. The Giant Branch can easily be traced up to the tip, which is located at [FORMULA], [FORMULA] (star [FORMULA] 4191). The RGB-bump is also clearly detectable as a clump of stars at [FORMULA] (see below).

2. Despite the increased scatter in the CCD sample due to crowding in the inner regions (and to the bright plate limit in the B CFHT-exposures just above [FORMULA]), the matching of the different samples is adequately smooth. The bulk of stars located just above the TO-region within the colour range [FORMULA] are most probably the result of optical blending of two bright MS-stars of similar colour yielding a blend approximately 0.75 mag brighter than the individual components. This conjecture is further supported by their progressive disappearance with distance from the crowded central regions. The difficulty of properly separating these objects represents a crucial problem in the study of the Luminosity Function of the SGB. As already discussed for instance by Ferraro et al.  (1992a, b), some of these stars may also be blends of SGB objects and blue stragglers.

3. The HB is narrow and, over the considered region ([FORMULA]), it contains 186 variable stars, which have not been plotted in Fig. 15 and Fig. 16. The blue HB tail extends down to [FORMULA], about half a magnitude brighter than the TO-level, and there is little doubt that this extremely blue HB population is quite clearly detached from the bulk of the other HB stars by a discontinuity in the population at [FORMULA] 16.8-16.9 (see also Section 3.3 in PH94). There are also a few stars about half a magnitude brighter than the average luminosity of the HB, [FORMULA], and located within 2' from the cluster center. While the possibility of field interlopers seems quite improbable given the high galactic latitude of the cluster, their presence could be due to "optical blending" between HB and RGB components or to the existence of a more evolved ([FORMULA] HB) population.

4. Several candidate blue stragglers have been detected and discussed in F93. Their distribution is better seen in the V, [FORMULA] CMDs, where they trace, as expected, a continuation of the Main Sequence.

3.1. Mean ridge lines for M 3

Normal points for the main branches in the CMD of M 3 (MS, SGB, RGB, HB and AGB) are presented in Table 2. As usual, mean ridge lines for each evolutionary phase have been derived by plotting magnitude and colour histograms along each branch and by rejecting the most deviating objects via a k [FORMULA].


Table 2. Mean ridge lines

Specifically concerning the determination of [FORMULA], we have computed a running mean over a 0.2 mag box moving along the HB in colour; this procedure yields a value [FORMULA] [FORMULA] which represents the average magnitude level of the HB, thus including the effects due to evolution off the Zero Age HB (ZAHB) within the instability strip.

This value is the mean level of the HB obtained from the constant stars (at the edges of the instability strip). The mean magnitudes of the RR Lyrae variables within the strip will be discussed elsewhere. The associated uncertainty is the observed rms vertical scatter of the HB at that colour.

Although evolution off the ZAHB is short compared to the lifetime of the ZAHB-phase (i.e. that spent at almost constant luminosity, see f.i. Sweigart and Gross 1976, Sweigart et al.  1987, Lee et al.  1990), one should quite carefully distinguish between the average HB luminosity and the ZAHB luminosity. There are essentially two ways to take this difference into account: the first, by adding a small positive correction to [FORMULA] ([FORMULA] mag) to compensate for evolution; the second, by adopting as [FORMULA] the lower envelope of the HB distribution in luminosity within the instability strip (corresponding at Log [FORMULA]). Using our HB sample, we would get [FORMULA] = 15.70 in both approaches.

Since all these effects are actually partially smeared out by the photometric errors, the difference between the ZAHB and the average levels is only marginally significant. In conclusion, we will adopt [FORMULA] [FORMULA] and [FORMULA] [FORMULA].

3.2. The metallicity of M 3: a major change?

Based on the results presented in the previous Sections, we can now derive a new estimate of the metal abundance of M 3 using the so-called photometric indicators.

The main photometric parameters related to the cluster mean metallicity are [FORMULA] (Sandage and Smith 1966) and 1.4 (Sandage and Wallerstein 1960). Adopting [FORMULA] =15.70, [FORMULA] (see Table 10 of PH94), and the mean ridge line of the RGB listed in Table 2, we obtain [FORMULA] [FORMULA] and 1.4 [FORMULA]. Using then the relationships quoted in Table 3 we derive values for [Fe/H] ranging from -1.68 to -1.45 dex.


Table 3. Metallicity of M 3 from the RGB photometric parameters

Another photometric estimate of the metal abundance of M 3 can be obtained from the CMD in the ([FORMULA])-plane by exploiting the iterative method recently defined by Sarajedini (1994). From the mean ridge line listed in Table 2, we obtain [FORMULA], [FORMULA] 1.82 [FORMULA] 0.14, [FORMULA] 0.00 [FORMULA] 0.05, and, eventually, [Fe/H] [FORMULA] with a formal error of [FORMULA]  dex.

From Table 3, the lowest metallicity value is the same as the widely used figure from Zinn and West (1984; [Fe/H] [FORMULA]), and is based on their metallicity-scale calibration obtained via integrated cluster observations.

The higher value (-1.45) is based on direct spectroscopic determinations of [Fe/H] from individual stars, as opposed to the integrated indexes used by Zinn and collaborators. The latest high resolution spectroscopic investigations, namely Sneden et al. (1992; SKPL) and Carretta and Gratton (1996a; CG96), show that the problem of the reliable measure of the metal abundance of this template cluster is not trivial at all.

In fact, SKPL found [Fe/H]  [FORMULA] from the analysis of 7 stars (and a slight different value of -1.42 by adding 3 other stars, see Kraft et al.  1995), and CG96 derived [Fe/H]  [FORMULA] ([FORMULA]) from 10 stars. Both studies are based on high resolution, high signal-to-noise CCD echelle spectra of high quality. In particular CG96 have re-analysed the equivalent widths published by SKPL for M 3 and other clusters to obtain a new, homogeneous metallicity scale for 24 calibrating clusters.

The main differences between the two quoted studies (apart from minor changes in the adopted values for the microturbulent velocity) are in the set of adopted atomic parameters (in particular oscillator strengths gf for Fe I and Fe II) and in the choice of the model atmospheres used in the analysis. CG96 used the latest, updated models from the grid of Kurucz (1992), that allow an homogeneous comparison between solar and stellar abundances, alleviating a major drawback of any former analysis of abundances for globular cluster stars.

In fact, as discussed by CG96, all previous spectroscopic determinations of the [Fe/H] content of globular cluster stars were actually systematically uncertain because of the large differences ([FORMULA]  dex) still existing in the reference solar value adopted in the absolute analyses. In particular, a significant discrepancy persists in the solar Fe abundances as obtained using the Holweger and Müller (1974-HM) semi-empirical solar model (usually considered to be the best reproduction of the solar atmosphere) and the model atmospheres proposed by Bell et al.  (1976), generally adopted (also in the SKPL papers) in the analysis of cool cluster giants (see also Leep et al. 1987). The crucial problem thus is to find a firm answer to the question: what is the correct solar abundance to adopt as reference for Fe?

The recent analysis by CG96 has apparently settled the discrepancy as they have obtained a revised determination of the solar Fe abundance which is very similar to the value given by the HM model. This result has been obtained by using the set of gf values discussed in CG96 and a solar model extracted from the same grid of Kurucz (1992) models as used for the analysis of the cluster giants. Consequently, the study of CG96 yields a systematic difference, [FORMULA] [Fe/H]  [FORMULA] ([FORMULA] =0.08 over 162 stars analyzed; 0.08 in the case of M 3) with respect to previous analyses, which used the Bell et al.  (1976) models that are [FORMULA]  K cooler than HM in the line formation region. Therefore, even if the observational material ([FORMULA] the equivalent widths) is the same, the analysis of CG96 seems to be more self-consistent than that of SKPL.

Since the precise determination of the metallicity of M 3 has important implications on various items (f.i. on the long-standing problem of the so-called Sandage Period Shift Effect, see Sandage 1993), it may be useful to analyse further the discrepancy between the value [Fe/H]  [FORMULA] obtained via the Zinn and West (1984) calibration and the significantly higher [Fe/H]  [FORMULA] obtained from high-resolution spectroscopy.

Zinn and West (1984) based their estimates on integrated cluster features ultimately calibrated using old (and sometimes uncertain) [Fe/H]  abundances obtained from photographic high-dispersion spectra (Cohen 1983). However, from more than 160 giants homogeneously analyzed in 24 calibrating clusters, CG96 have demonstrated that the ZW metallicities differ significantly from these new results. In particular, they are about 0.10 dex higher for [Fe/H] [FORMULA], 0.23 dex lower for [FORMULA] [Fe/H] [FORMULA], and 0.11 dex too high for [Fe/H] [FORMULA]. This non-linearity of the ZW scale is significant at 3 [FORMULA] level and cannot be ignored when discussing astrophysical problems involving tiny metallicity differences among the clusters.

On the basis of the CG96 new scale, Carretta and Gratton (1996b) have also derived a new calibration of [FORMULA] in terms of [Fe/H] . Using the values of [FORMULA] from the compilation of Michel and Smith (1984) for 22 calibrating cluster on the new scale, they obtained a [FORMULA] order polynomial fit that closely resembles the theoretical calibration of Demarque et al.  (1982) from evolutionary red-giant models. Based on this new calibration, the metallicity of M 3 turns out to be [Fe/H]  [FORMULA], with a 1 [FORMULA] error bar of 0.18 dex, in good agreement with the spectroscopic determination reported by CG96.

In conclusion, from the detailed re-analysis discussed above, we are inclined to believe that the metallicity of M 3 is slightly larger than estimated so far and probably the best value to adopt at present is [Fe/H]  [FORMULA], where both the absolute figure and the size of the error are just the result of our global overview.

3.3. The bump on the Red Giant Branch

Theoretical evolutionary models predict the existence of a special feature along the RGB called the "RGB-bump" (see e.g. Thomas 1967, Iben 1968, RFP88). As discussed in detail among others by Rood and Crocker (1985), the practical detection of such a feature requires the availability of very populous RGB samples. Fusi Pecci et al.  (1990) detected the RGB-bump in 11 globular clusters, including M 3 (based on our early PH94 data; see also Ferraro 1992). The use of our new data-base allows us to confirm the detection of the RGB-bump (see Fig. 4, Fig. 17) located at [FORMULA] =15.45 [FORMULA] 0.05, i.e. exactly the same value as the previous measurement listed in Table 4 of Fusi Pecci et al.  (1990), and we thus refer to that paper for the discussion of this specific issue.

[FIGURE] Fig. 17. Integrated (a) and differential (b) luminosity functions of the RGB (Bright Complete Sample). The vertical line in b shows the location of the [FORMULA].

3.4. The HB population and morphology in M 3

Based on our bright sample, containing all the stars brighter than [FORMULA] and located within a square of about 7' [FORMULA] 7' (but with [FORMULA]), the HB of M 3 spans a very wide colour range ([FORMULA] mag), from the red end at [FORMULA] 0.7 to the bluest stars at [FORMULA]. Therefore the distribution in effective temperature is very wide, and, in turn, there is a wide spread in the HB mass distribution (Rood and Crocker 1985).

Recently, Fusi Pecci et al.  (1992, 1993) have discussed in detail the properties of the observed HB morphologies (and in particular the so-called "Second Parameter" problem) in relation to stellar mass loss, the effect of the environment on the evolution of the individual stars, and the presence of binary systems (primordial, collisional, merging, etc.). In particular, the HB of M 3 has been dissected into sub-groups having presumably different evolutionary histories. The basic idea is that both the blue and the red extremes of the observed HB might include peculiar objects which are intrinsically different from genuine HB stars and are rather the result of the stellar and dynamical evolution of binary systems (at least in part related to the blue stragglers), or are HB objects which keep track of interactions causing an "extra-mass loss" from the envelope during the previous evolutionary stages.

For the sake of brevity we refer to the quoted papers for a complete discussion and simply re-analyse the content of the boxes which have been defined in PH94 to describe the HB morphology.

As show in Fig. 18 we have "dissected" the HB into seven boxes and report below a few notes on each sub-group.

[FIGURE] Fig. 18. Enlargement of the colour-magnitude diagram of M 3 in the HB region, with boxes defining the areas we identified along the HB. All stars belonging to our BCS sample are plotted in this figure apart from the 186 known variables (see text).

1. Group HEB: 10 stars (2 in PH94), the faintest one reaching [FORMULA] and with [FORMULA], but a few other bluer and/or fainter objects might deserve a further check. Their location in the CMD could well be due to large photometric errors or they could be non-members. Most of them are confined within the inner 2 arcmin from the cluster center. If their photometry and membership are confirmed, they could represent good candidates to search for the possible descendants of late collisional mergers (Bailyn and Iben 1989, Fusi Pecci et al.  1992) or they could be post-HB stars (such as AGB-manquè, see e.g. Greggio and Renzini 1990, Cacciari et al.  1995, D'Cruz et al.  1996).

2. Group EB: 10 stars (4 in PH94). Together with the 10 HEB stars, this group constitutes a subset of 20 stars clearly segregated from the bulk of the HB stellar population. Their total number and location seems sufficient to exclude the possibility that all of them are interlopers. Hence, we are inclined to conclude that there is now clear-cut observational evidence for the existence of a very extended (though sparsely populated) blue HB tail in M 3, possibly separated by a gap from the bulk of the normal HB objects. The HST UV data currently being analyzed, coupled with spectroscopy, could be very helpful in understanding their true origin.

3. Group B: 205 objects, (70 in PH94). The population of this box includes presumably normal HB stars located above a small (apparent?) gap at [FORMULA] and bluer than the blue edge of the instability strip. The scatter of the points around the mean ridge line is compatible with the size of the observational errors (note that the B exposures are short), but it could also partially reflect the effects due to evolution off the ZAHB for some stars.

4. Group V: 185 stars (85 in PH94). This group contains only RR Lyrae variables. In Fig. 18 variables are not reported as appropriate mean values are still lacking. At present, mean V and [FORMULA] values are listed for the 85 HB variables of the photographic sample in Table 10 of PH94. For the other 100 HB variables mean magnitudes and colours are not available from the present photometric data. Consequently, their presence in the plotted CMD would introduce a "confusing" scatter of the points both in magnitude and in colour mostly due to a random-phase effect of the available measurements, which are insufficient to cover completely the light curve.

A few of these stars could however also be evolved HB stars brighter than the ZAHB. Finally, there are 17 constant stars which are located within the box because of photometric errors or due to the existence of some overlapping in colour of the variable and non-variable strips. This specific item will be dealt with in more details in a forthcoming paper. However, we have included them in the total number of HB stars.

5. Group R: 116 stars (51 in PH94). They lie to the red of the instability strip and reach up to about half a magnitude brighther and redder than the ZAHB level within the instability strip.

6. Group ER: 16 stars (7 in PH94). This group overlaps in colour with the previous one, but it is composed of stars brighter than [FORMULA] and still well separated from the AGB base. As mentioned in PH94, at least some of them could be the "progeny" of BSS (see Fusi Pecci et al.  1992) and they are thus worth of further study.

7. Group SHB: 7 stars. They are located well above the HB and could represent highly evolved HB objects which are travelling from their original ZAHB location towards the AGB. Alternatively, they could be blends of HB+RGB stars.

3.5. Star counts and population ratios: mixing and He abundance

A complete sample of stars with accurate photometry offers a major tool for an observational verification of the predictions of the stellar evolution theory. In particular, star counts in a given evolutionary phase yield a direct test of the duration of that specific phase (Renzini and Buzzoni 1986). In turn, this allows one to get a deeper insight on unsolved problems like for instance the extent of the mixing phenomena, or to measure important basic quantities like the primordial helium abundance Y (see RFP88).

The approach to the problem is well established (see e.g. RFP88, PH94): from the CMD one can measure a set of parameters to be used along with the appropriate calibrations based on theoretical models. The most frequently used are:

  • [FORMULA], the ratio of the numbers of stars on the HB and on the RGB brighter than ZAHB luminosity at Log [FORMULA] ;
  • [FORMULA], which includes also the number of stars in the AGB phase;
  • [FORMULA] ;
  • [FORMULA].

To preserve full homogeneity with the study of Buzzoni et al.  (1983, BFBC) which is still the standard reference for this subject, we have adopted their prescriptions. In particular, we fixed the separation between HB and AGB at [FORMULA], about 0.8 mag above the mean magnitude of the HB, and counted RGB stars brighter than [FORMULA], adopting a differential bolometric correction [FORMULA] B.C.=0.11 mag (O. Straniero, private communication) between HB and RGB stars. The results for the star counts along the various branches and the derived parameters are listed in Table 4.


Table 4. Star counts on HB, AGB, and RGB of M 3

The parameters [FORMULA] and [FORMULA] essentially indicate the relative ratios of the lifetimes of the AGB, RGB, and HB. Since these lifetimes are basically driven by nuclear burning and mixing phenomena (which may alter the "local" fuel quantity), different ratios are predicted from the models with varying mechanisms and extension of mixing for fixed properties of the nuclear burning. Within the framework discussed by RFP88, the values here obtained for [FORMULA] and [FORMULA] are fully compatible with the predictions of "standard and canonical" models.

The values for R and [FORMULA] can be used along with eqs. 11 and 13 of BFBC to obtain an estimate of the primordial He abundance based on their calibrations of these parameters in terms of Y. From the values listed in Table 4 (the errors are just from count statistics), we obtain [FORMULA] and [FORMULA], in excellent agreement with the mean value found by BFBC as well as with other estimates (see e.g. Boesgaard and Steigman 1985, Olive and Steigman 1995 and ref. therein). In the computation we have considered for the HB all the stars included in the samples ER+R+V+B+EB+HEB. This may not be fully correct if at least some of them are non-genuine HB stars (in the sense that they are not evolving "directly" from the RGB). However, since their number (including the few SHB stars) is so small, the result is practically unaffected taking into account the size of the errors. For instance, by deleting from the HB all the stars in the samples ER+EB+HEB, the computed ratios would become [FORMULA], [FORMULA], [FORMULA], [FORMULA], which would leave the conclusions on Y unchanged.

3.6. The Blue Stragglers population of M 3: toward the definition of a complete and reliable sample

A comprehensive discussion on the BSS population of M 3 has already been presented in F93. Therefore, here we shall only extend to the BSS region the same kind of comparisons with the data-sets of other previous studies in order to verify the quality of the different samples in terms of completeness and selection bias. We anticipate that the problem of identifying a truly pure sample of BSS candidates is far from being solved, in particular in the inner regions of the clusters where crowding undermines photometry and for the faint BSS, whose separation from normal TO stars is always difficult and somewhat subjective.

We report below identifications and comparisons made with respect to BHS for the region in common with our newly re-calibrated CFHT CCD data. The comparison will be based on V and I colours only, because of the poor response of the chip used for the observations in the B filter.

Fig. 19 shows the result of the comparison with the sample obtained by BHS for [FORMULA]. Panel (a) shows the data from BHS (kindly made available to us by Dr. M. Bolte) with their instrumental magnitudes shifted to our system. The box reproduces the polygonal region used by BHS (their Fig. 3) for selecting their BSS candidates. Open squares are the stars in the BHS sample that are the counterparts of our BSS candidates on the BHS field. Panel (b) displays our CCD-sample, restricted to the BHS field. The box is the same as we used to delimitate the region occupied by our (F93) BSS candidates and is identical to that in Fig. 3 of F93. Open squares are the stars of our sample which are counterparts of the BSS candidates selected by BHS and falling outside our adopted limits. In both panels, black squares represent stars that are considered BSS by both surveys.

[FIGURE] Fig. 19. Comparison of the BSS found in our sample and in BHS study. In a are plotted the data from BHS, with instrumental magnitudes shifted to our system. The box reproduces the polygonal region used by BHS (their Fig. 3) for selecting their BSS candidates. Open squares are the stars in BHS sample that are the counterparts of our BSS candidates on the BHS field. b shows our CCD sample, restricted to the BHS field; the box is the same we used to encircle the region occupied by our BSS candidates (Fig. 3 of F93). Open squares are the stars of our sample which are counterparts of BHS BSS candidates. In both panels, black squares represent stars that are considered BSS by both surveys.

As can be seen, there are only 15 BSS candidates in common (the black squares), while there are 50 stars labeled as BSS candidates in only one of the two surveys. Could all of them be mis-selected; could they actually be normal stars? The answer is difficult to find, but some additional considerations may be useful.

Our 25 BSS candidates not identified as such by BHS mostly fall between their BSS box and their SGB. Judging on the basis of the scatter in the TO region, our photometry seems to display smaller internal errors. This may indicate that we can better separate the two populations because of the different quality of the photometry. Another obvious explanation is, of course, that we reached too close to the MS in defining our BSS box. On the other hand, the 10 stars identified as BSS candidates only by BHS fall in panel (b) of Fig. 19 at somewhat brighter magnitudes than the TO region. Since the quality of the CCD frames available to BHS seems to be better as far as seeing conditions are concerned, this might imply that we were unable to separate the optical blends formed by a BSS-candidate and a SGB star. HST -data should be suitable to settle the issue.

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© European Southern Observatory (ESO) 1997

Online publication: June 30, 1998