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Astron. Astrophys. 339, 61-69 (1998)

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4. Age

The first evidence of a relatively young age for Pal 12 was given by GO88, who estimated that Pal 12 must be 30% younger than 47 Tuc on the basis of an atypically small value of the magnitude difference between the HB and the TO. Indeed, this was the first clear identification of a young GGC.

Almost at the same time, S89 presented an independent BV CCD study. They compared the Pal 12 fiducial RGB to those of 47 Tuc and M5, which bracket Pal 12 metallicity, concluding that no match could be found. The simplest explanation was that Pal 12 is younger than the other two clusters by some 25%-30%.

In both studies, the 47 Tuc fiducial lines were taken from Hesser et al. (1987, hereafter H87). These fiducials were constructed by merging B and V CCD photometry for 8800 stars below the MS turnoff to the evolved part of the CMD coming from earlier photographic work (Hesser & Hatwick 1977, Lee 1977). Also the HB and MS fiducial lines of M5 come from two different studies (cf. S89 for more details). Possible photometric calibration discrepancies between the different datasets contribute to the age uncertainty in these early estimates.

The heterogeneity of the data base for the comparison clusters and the high uncertainty in the metal content do not allow us to quantify the error associated to the results by GO88 and S89. In the following we will attempt a new, independent determination of the Pal 12 relative age by comparison with suitable template clusters.

Since no GGCs with metallicity [FORMULA] have been observed to date in the V, I bands, as done by the previous authors, we will use 47 Tuc (NGC 104) and M5 (NGC 5904), whose metallicities bracket that of Pal 12. These are the nearest metallicity clusters for which (a) published homogeneous V, I photometry exists, from the RGB tip down to the MS; (b) both [FORMULA] and [FORMULA]-elements abundance have been obtained from high-resolution spectroscopy; (c) do not show any age anomaly either in published or in our preliminary analysis of GGC relative ages.

The best VI, photometric sample for 47 Tuc is that of Kaluzny et al. (1998, see Paper I for a discussion of the other available VI CMDs for 47 Tuc). Two photometric catalogs can be used for M5, namely Sandquist et al. (1996) and Johnson & Bolte (1998). Since Johnson & Bolte discuss possible problems in their earlier calibrations of the M5 photometry, we will use the most recent sample. In any case, the stellar [FORMULA] colors are the same in the two studies.

The metallicities and [FORMULA] abundance ratios have been taken from Table 2 of Carney (1996): [FORMULA] and [FORMULA] for 47 Tuc, and [FORMULA] and [FORMULA] for M5.

Fig. 5 shows the fiducial points of M5, 47 Tuc and Pal 12 registered to a common TO point. It is clear that, while the RGBs of 47 Tuc and M5 are almost overlapping, the RGB of Pal 12 is significantly redder. The modest color shift between the RGB of M5 and that of 47 Tuc shows that metallicity differences have small influence on the RGB-TO color-difference, in the V vs. [FORMULA] plane. A change of 0.5 dex in metallicity implies a color offset as small as 0.01 mag. This fact is confirmed by the theoretical models, and has been pointed out by Saviane et al. (1997). Assuming an age of 14 Gyr, the models of Vandenberg 1998 (hereafter V98) predict a change of 0.011 mag in [FORMULA] increasing the metallicity from [FORMULA] to [FORMULA] (the color difference between the RGB and the TO has been measured at 2.2 mag above the TO).

[FIGURE] Fig. 5. The fiducial points for M5, 47 Tuc and Pal 12 are presented, after that the TOs have been shifted in magnitude and colors to a common value. A large difference in color exists between the RGBs of the two template clusters and the Pal 12 RGB. The small color difference between the RGB of M5 and the one of 47 Tuc (whose metallicities encompass that of Pal 12) demonstrates that a 0.5 dex difference in metallicity has small influence on the [FORMULA] color-difference between the RGB and the TO. Pal 12 must therefore be younger than the two template clusters.

The position of the Pal 12 RGB cannot therefore be explained by a simple metallicity effect. The observed difference in the location of the RGB of Pal 12 with respect to 47 Tuc and M5 must be due either to a different [FORMULA] element abundance or to an age effect.

We begin by examining the first possibility. According to Salaris et al. (1993), an enhancement by a factor f in the ratio [FORMULA] is equivalent to an increase of a factor [FORMULA] in the metallicity Z. As discussed in Sec. 3.1, the current measurements give [FORMULA], 0.2 and 0.3 for Pal 12, 47 Tuc and M5, respectively. This means that, in order to compare the Pal 12 fiducials with the reference clusters, we must take into account these differences in [FORMULA] element abundances, which correspond to increasing the Pal 12 metallicity by [FORMULA] dex. The [FORMULA]-enhancement effect makes the [m/H] of Pal 12 close to that of 47 Tuc. Therefore, Fig. 5 shows that the [FORMULA] element abundance differences cannot justify the large observed RGB color differences.

An age difference is the only remaining explanation. In order to make an estimate of the Pal 12 relative age, we have measured [FORMULA] between the TO and the RGB for different (fixed) [FORMULA] values in the models of B94, Straniero et al. (1997, hereafter S97), and V98). The first two sets of models are [FORMULA], while the third one is. Fig. 6 displays the [FORMULA] for [FORMULA] mag as a function of the logarithm of age. With a good approximation, [FORMULA] linearly depends on the logarithm of age. The -2.2 mag level has been chosen after an analysis of the behavior of the TO-RGB color difference with respect to the age. We have repeated our measurements at the RGB levels marked by dotted lines in Fig. 5 and found that, if a value [FORMULA] is taken, the SGB plays an important role, making relative measurements difficult to interpret. The same occurs for [FORMULA], where the slope of the RGB becomes very sensitive to the clusters metallicity. Conversely, for [FORMULA] in the range [FORMULA] and age older than 8 Gyrs, the [FORMULA] seems to be almost independent of metallicity. We simply chose a mean value -2.2. The linear relations in Fig. 5 have the same slopes for [FORMULA], while for [FORMULA] the B94 and V98 models give the same slope, which is slightly different from that obtained from S97. The zero points are different, but this does not affect the relative age determination. We will therefore obtain the same relative ages when using either the B94, V98 or S97 models at [FORMULA], while the S97 isochrones give age differences larger by [FORMULA] than B94 or V98 at Z=0.003.

[FIGURE] Fig. 6. RGB-TO ([FORMULA]) color-differences at 2.2 mag above the TO have been computed using B94, V98, and S97 isochrones, for different ages and for the two labeled metallicities. Keeping the metallicity fixed, a linear relation with the same slope (within [FORMULA]) is found between the RGB-TO color width and the logarithm of age, regardless of the model used. The discrepant zero-points are partly due to different assumptions on the [FORMULA]-element content of the three theoretical sets. The similarity in the slope shows that the three sets of models give consistent relative ages, at least in the small metallicity interval considered here.

From Fig. 5 we have [FORMULA]=0.280 for M5, [FORMULA]=0.265 for 47 Tuc, and [FORMULA]=0.330 for Pal 12. Assuming Z=0.003, from Fig. 6, we obtain that Pal 12 is 34%, 34%, or 30% younger than 47 Tuc on the basis of V98, B94 and S97 models, respectively. As discussed above, adopting Z=0.001 we have quite similar results: formally, Pal 12 is 33%, 32%, or 32% younger than M5. Taking into account the errors in measuring the [FORMULA] parameter (estimated assuming an uncertainty of [FORMULA] mag and [FORMULA] mag in the magnitude and color of the TO) for both Pal 12 and the reference clusters, the uncertainties in the relative ages is of the order of 10%. We conclude that Pal 12 has an age [FORMULA] that of a typical GGC, assuming that 47 Tuc and M5 age are representative of the ages of the bulk of the GGC population (Buonanno et al 1998).

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© European Southern Observatory (ESO) 1998

Online publication: September 30, 1998
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