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

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3. The color-magnitude diagram

Fig. 3 shows the CMDs for the stars located inside (left panel ) and outside (right panel ) the known tidal radius ([FORMULA], Trager et al. 1995). The main features of the CMD can be clearly identified also in the outer region, implying either that the tidal radius must be larger than previous estimates (cf. Sect. 5 for a detailed discussion), or that Pal 12 is surrounded by a remarkable halo of extra-tidal radius cluster stars (Grillmair et al. 1995, Zaggia et al. 1997).

[FIGURE] Fig. 3. Color-magnitude diagram for the inner ([FORMULA], left panel), and the outer region (right panel) of Palomar 12. The adopted fiducial points are shown, together with the BSS region. The HB level is identified by a horizontal dotted line. The stars used for the computation of the cluster's profile are marked by filled circles. The [FORMULA] completeness level is represented by the dashed line. The four bright stars in the diagram, marked by squares, are those for which spectroscopy has been done (DA91, B97).

Stars from [FORMULA] mag below the turnoff (TO) up to the red giant branch (RGB) tip have been measured. Eleven blue straggler stars (BSS) are clearly identified in the region [FORMULA], [FORMULA]. Nine of them were already known, while two BSS are located outside the limits of the previously studied fields of the cluster. The BSS are marked with open triangles in Fig. 1. As shown in Fig 4, the BSS are more concentrated than the sub giant branch (SGB) stars with similar magnitude. This is consistent with what found in other GGCs, though the small number of BSS does not allow to assess the statistical significance of this result.

[FIGURE] Fig. 4. Cumulative distribution of the BSS and the SGB stars with similar V magnitude in Pal 12. Though the BSS seem to be more concentrated than the SGB stars, their small number does not allow to assess the significance of this result. There is a probability of 49% for the null hypothesis that the two samples share the same radial distribution.

In the region [FORMULA] and [FORMULA] of the inner CMD a number of stars are present just above the TO. We have compared these stars with the corresponding objects in the S89 photometry. From this analysis we found that 45% of our objects are blends of 2 S89 stars, 20% are blends of 3 S89 stars and 35% of them are single stars in the S89 photometry (where the pixel size is just [FORMULA], i.e. half of ours). Notice that almost no such stars are present in the outer, less crowded, region. It is likely that all stars with [FORMULA] in Fig. 2 being significantly brighter in our photometry are photometric blends.

The horizontal branch (HB) is formed by 5 stars (already identified in the literature), and it is located in a very small region around the point [FORMULA], on the red side of the instability strip, as expected on the basis of the cluster metallicity. A dashed horizontal line marks the level of the HB in Fig. 3. The TO can be identified at [FORMULA] and [FORMULA].

The foreground/background star contamination is low, as expected from the high galactic latitude of the cluster ([FORMULA]). This is clearly seen by comparing the right and left panels of Fig. 3; the right panel shows the typical pattern of the halo background, superposed to the cluster CMD. The field contamination is redder than the Pal 12 MS, and decreases from fainter to brighter magnitudes. Notice also that the central CMD area is 5 times smaller than the external one, so that the cluster/background ratio clearly favors Pal 12 stars.

In order to determine the cluster profile, we defined a sample of stars with higher membership probability, by selecting all the objects within [FORMULA] from the MS-SGB-RGB line (where [FORMULA] represents the mean error in color as a function of magnitude, as calculated from the artificial star experiments, and the fiducial line has been drawn by hand). BSS, HB and photometric blends (see previous discussion) were added to this sample.

Artificial star tests have been performed in order to investigate the completeness of our sample. A total of [FORMULA] stars have been added in 40 separate runs. The results of these experiments show that the [FORMULA] completeness level is located at [FORMULA] and [FORMULA]. Only the stars above these limits (marked by a dashed line in Fig. 3) have been selected for the following analysis. In order to get a meaningful profile it is also critical that no radial dependence of the completeness exists. We checked that the completeness profile is constant in the range [FORMULA] arcsec from the cluster center, while a slight rise in magnitude of the [FORMULA] level is observed in the inner region.

The star subsample defined with the previous criteria is identified by filled circles in Fig. 3, whereas open circles mark probable halo field stars. The same convention is used in the maps presented in Fig. 1.

In order to compare the Pal 12 CMD with other clusters and theoretical isochrones, a discussion of its relevant parameters is now given.

3.1. Metallicity

A summary of early studies on Pal 12 metallicity is presented in S89. Although a large uncertainty in the metal content determinations for Pal 12 existed at the time, a combination of several metallicity indices yielded a value comprised between the ones of M5 and 47 Tuc (i.e. [FORMULA]).

Since then, three new metallicity determinations have been obtained: besides new CCD photometry, low and high resolution spectra have been analyzed for a few giant stars. These stars are marked with open squares both in the cluster's map (Fig. 1, right panel) and in the CMD (Fig. 3, left panel).

Da Costa & Armandroff (1990) derived [FORMULA] from V, I photometry of 20 Pal 12 giant branch stars, by comparing the position of the RGB with other calibration clusters. Applying the same method to our data, we obtain a value [FORMULA], where the small difference, well within the uncertainties, is mainly due to our 0.06 mag redder colors (see Sect. 2).

Armandroff & Da Costa (1991, DA91) obtained the metallicity from the Ca II triplet strenghs, and found [FORMULA] for Pal 12, later confirmed by Da Costa & Armandroff (1995; [FORMULA]).

The most recent result has been obtained by Brown et al. (1997). They present high-resolution spectra of the two brightest stars of AD91, obtaining a [FORMULA]. They also analyzed the [FORMULA] abundances, obtaining a zero value.

In view of the larger uncertainties related to indirect metallicity determinations with respect to high resolution spectroscopy, in the following we will adopt [FORMULA] for Pal 12, and assume a null [FORMULA] element enhancement.

3.2. Reddening

The interstellar reddening towards Pal 12 is expected to be low, given the high galactic latitude of the cluster. Although no accurate estimates exist, two independent values have been suggested; HC80 adopted a value of [FORMULA] from the cosecant law (Harris & Racine 1979), and noted that this value is consistent with that estimated from the color-color diagram of stars in their photoelectric sequence, [FORMULA]. A small reddening is also indicated by the maps by Burstein and Heiles (1982): [FORMULA]. Adopting [FORMULA] (Dean et al. 1978), we obtain the value [FORMULA], which will be the assumed reddening throughout this paper.

3.3. Distance

Distance moduli of the Palomar class clusters have been often overestimated in the past. Kinman & Rosino (1962) searched Palomar 12 for variables. They found three variables, one of them previously discovered by Zwicky (1957). Based on the mean apparent magnitude of these RR Lyrae, Pal 12 was initially located farther than 50 kpc from the Galactic center (Harris 1976). It is only after HC80 photometric study that a more precise distance modulus has been given (about 14 kpc), on the basis of the V magnitude of the poorly populated HB.

We derive the distance to Pal 12 by comparing its HB with that of NGC 6362, which is the only GC at [FORMULA] with measured [FORMULA]-elements abundance (cf. Table 2 in Carney, 1996). Piotto et al. (1998) give [FORMULA] for NGC 6362; this value is not representative of the Pal 12 HB luminosity, since we must correct for the age (cf. Sect. 4) and [FORMULA] abundance offsets between both clusters.

A decrease in age implies an increase in the HB stars mass and luminosity, the exact dependency being a function of Z. Although no [FORMULA] (the Pal 12 metallicity) models are available, an interpolation from the [FORMULA] and [FORMULA], Bertelli et al. (1994, hereafter B94) model isochrones leads to estimate a change [FORMULA]  mag, which reduces the age by [FORMULA] (cf. Sect. 4).

Spectroscopy of 2 NGC 6362 giants has been obtained by Gratton (1987), who measured [FORMULA]. In view of the results by Brown et al. (1997) presented in Sec. 3.1, a comparison of the Pal 12 CMD with NGC 6362 must take into account the "[FORMULA]-enhancement" of the latter.

As discussed in more detail in Sect. 4, an increase of 0.3 dex in [FORMULA] mimics an increase of 0.2 dex in the equivalent [Fe/H], and implies a decrease in the HB brightness. The exact value depends on the slope of the luminosity-metallicity relation for the HB. Although this is still controversial, a typical value [FORMULA] can be used (Carney et al. 1992), which therefore means [FORMULA] mag in our case.

We should also take into account possible differences in the mass loss rates along the RGB between the two clusters. These would affect the ZAHB mass, and hence its luminosity. In order to constrain such an effect, we can compare the colors of the red HB of Pal 12 and NGC 6362. Indeed, using again the B94 isochrones we find that, in the red HB region, a change in the ZAHB mass of +0.1[FORMULA] will change the HB location of a star by [FORMULA] mag in [FORMULA] and -0.07 mag in V. The effect is therefore three times larger in the [FORMULA] color than in the V magnitude.

The actual dereddened colors of the red HBs of the two clusters are [FORMULA] for Pal 12 (Stetson et al. 1989), and [FORMULA] for NGC 6362 (Piotto et al. 1998). Hence, a color difference of [FORMULA] mag in [FORMULA] exists between Pal 12 and NGC 6362, which corresponds to a [FORMULA] mass loss difference.

However, this higher HB mass for Pal 12 is consistent with its lower age. According to B94, the turnoff mass of a cluster will change by [FORMULA] if its age is changed by [FORMULA] Gyr. Since, in the B94 scale, the typical GC age would be [FORMULA] Gyr (Saviane et al. 1998), the higher mass of the Pal 12 HB is easily explained by its [FORMULA] lower age (cf. Sect. 4). A mass loss differential correction is therefore not needed.

In summary, we expect that the Pal 12 HB should be 0.07 mag brighter than that of NGC 6362 in view of its younger age and 0.04 mag brighter due to its lower [FORMULA] element content, i.e. [FORMULA].

As the apparent magnitude of the Pal 12 HB is [FORMULA] (where the error has been computed taking into account the calibration uncertainties), the apparent distance modulus becomes [FORMULA]. Given the assumed reddening [FORMULA], the absolute distance modulus is [FORMULA]. The estimate of the error includes the uncertainties on the calibration zero-point, on the magnitude of the NGC 6362 HB, and on the absorption. Our value of the distance to Pal 12 is perfectly compatible with previous estimates: HC80 give [FORMULA], GO88 [FORMULA], S89 16.3, and DA90 16.46 for the absolute distance modulus.

The adopted distance modulus corresponds to a distance from the Sun [FORMULA] Kpc, a distance from the Galactic center [FORMULA] kpc, and a height [FORMULA] below the Galactic plane (we adopted a distance from the Sun to the Galactic center [FORMULA] kpc; Reid 1993).

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© European Southern Observatory (ESO) 1998

Online publication: September 30, 1998
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