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Astron. Astrophys. 335, 929-942 (1998)

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3. The color-magnitude diagram

Table 3 presents the values adopted as fiducial points for the CMD of M 80 obtained as follows:


[TABLE]

Table 3. Fiducial points for M 80.


i) H-burning CMD sequences. In the range [FORMULA] mag we selected stars with [FORMULA] pix from the cluster center (to reduce the number of spurious blended objects), binned the data in magnitude (0.5, 0.2 mag bins, for the main sequence (MS) and the TO/subgiant branch, respectively) and, for each bin, calculated the mean V and the mode of the (B-V) histogram (0.02 mag bins); for [FORMULA] mag, we used the same method but dealing with data with [FORMULA] pix and V-bins of 0.4 mag. For the upper part of the RGB (V[FORMULA]14.2 mag) the 3 brighter fiducial points were determined by eye estimation.

ii) HB. We used data from the whole sample; in the range [FORMULA] mag we binned by 0.5 mag in V (0.1 mag in color), taking the mean V, B-V for each bin.

The TO appears rather well defined in shape, together with the subgiant (SG) and the initial portion of the red giant branch. The same figure shows that the expectation about the HB population is fully confirmed by the present observations: below the already known blue HB there is a well defined population of very hot HB stars stretching down to V-magnitudes fainter than those of TO stars. Recalling that the decrease in V-magnitude is mainly the consequence of bolometric correction, this is an evidence of the large temperatures reached by these HB stars. Quantitative evaluation based on theoretical models for hot HB stars (Castellani et al. 1995) and Kurucz (1992) atmosphere models indicates that the bottom of the cluster "blue tail" (hereafter BT) should be populated by stars as hot as [FORMULA], that is by stars where the He core is surrounded by a H rich envelope with mass of the order of just [FORMULA].

According to a well established scenario, the location of the RGB can be first used to derive and/or to test information about the cluster metallicity, since the RGB becomes bluer and steeper as the metallicity decreases. Several evaluations of the cluster metallicity are already available in the literature. Zinn (1985) gives for M 80 a value [Fe/H] [FORMULA]. Suntzeff et al. (1991) adopt a value of -1.64 based on the system of Zinn & West (1984). [Fe/H] [FORMULA] is derived by Bica & Pastoriza (1983) from DDO photometry, while Brodie & Hanes (1986) give [Fe/H] [FORMULA] from a low-resolution spectrophotometric study. The mean value from the above metallicity determinations is [Fe/H] [FORMULA] (rms error); taking into account the typical [FORMULA] dex uncertainty on the metallicity scales (Zinn and West 1984), we have [Fe/H]=[FORMULA].

"Photometric" estimates of the cluster metallicity can be derived from several RGB-based parameters calibrated in terms of [Fe/H]. In the following we will make use of the parameters [FORMULA] (Sandage & Smith 1966), [FORMULA] (Sandage & Wallerstein 1960) and S (Hartwick 1968). However, in order to evaluate a correct value for these parameters one needs information on both the interstellar reddening [FORMULA] and the zero age horizontal branch (ZAHB) luminosity level at the temperature of the RR Lyrae gap: [FORMULA]. These two quantities have been estimated as follows:

i) [FORMULA]. HR74 determined a color excess for M 80 of [FORMULA] from the comparison of their CMD with the mean lines of M 13. Racine (1973) found a value of 0.17 based on the cluster's integrated spectral type. More recently, using the same method, Reed et al. (1988) obtained a value of 0.18. In the following we will adopt [FORMULA] and comment on the possible effect of the uncertainties in the reddening on other derived quantities.

ii) [FORMULA]. Due to the reduced number of RR Lyrae variables (only six stars), the measurement of the ZAHB level is rather difficult in this cluster. Moreover, because of the blue HB morphology, these variables are probably evolved HB stars and do not represent the ZAHB level correctly. In order to derive [FORMULA], we have overplotted, on the horizontal branch of M 80, the HB of two other clusters: M 5 (Carney et al. 1991) and M 15 (Durrell & Harris 1993). These clusters have sufficiently populated HBs both in the blue side and in the instability strip; Fig. 2 shows the two superimpositions. Note that these clusters have either higher (M 5) or lower (M 15) metallicities than M 80, but this does not affect our determination of the HB luminosity. Following this procedure we got [FORMULA] in both cases. This value is slightly fainter than [FORMULA] and [FORMULA] given, respectively, by Wehlau et al. (1990) and HR74 from the mean magnitude of RR Lyrae stars in M 80, confirming the probable existence of evolutionary effects in these variables.

[FIGURE] Fig. 2. The HBs of M 5 (upper panel) and of M 15 (lower panel) are superimposed on M 80 CMD. M 5 and M 15 CMDs have been shifted, respectively, by [FORMULA], [FORMULA] and [FORMULA], [FORMULA]. The dotted line represents the ZAHB level.

The color of the RGB at [FORMULA] is [FORMULA], where the error includes the uncertainty on the HB level, to which we have to add an uncertainty of [FORMULA] mag due to the photometric error (cf. Sect. 2 ). The true RGB color is then [FORMULA] where the uncertainty includes also the error on [FORMULA].

Inserting this value in the relations listed in Table 4 we obtain the corresponding values for [Fe/H] showed in column 3 of the same Table: a weighted mean gives [Fe/H] = [FORMULA].


[TABLE]

Table 4. Metallicity from RGB parameters: relations and derived values for M 80.


The V magnitude of the RGB at [FORMULA] is [FORMULA] = 13.3 [FORMULA]; the error due to the uncertainty in the reddening has a negligible effect, compared to the [FORMULA] mag uncertainty in defining the RGB ridge line. Therefore, [FORMULA]: the relations in Table 4 lead to the metallicity values listed in column 3, and a weighted mean gives [Fe/H] = [FORMULA].

Finally, we can use the parameter [FORMULA], where [FORMULA] is the difference between [FORMULA] and the color of the RGB point which is 2.5 V mag brighter than the HB. Therefore, [FORMULA], where the errors include both the uncertainty in locating the two points on the ridge lines, and the photometric errors. A weighted mean of the values listed in Table 4 finally gives [Fe/H] = [FORMULA].

In summary, we have now three additional determinations of [Fe/H]. We must point out that the first two photometric methods rely on the assumed reddening and that increasing the reddening would increase the estimated metallicity. In this respect, it might be of some interest to note that the [Fe/H] value derived from the S index, which does not depend on the cluster reddening, is very close to the mean value derived from the literature. In any case, a weighted mean of the three metallicity determinations gives [Fe/H] = [FORMULA].

However, even regarding the quoted error as at [FORMULA] level, one has to notice that the quoted metallicity determination is far from being very satisfactory, since it leaves room for the cluster being regarded either as a very metal poor (Z=0.0002) or a moderately metal rich (Z=0.0006) object.

By relying on the above estimates one can proceed to a comparison with current evolutionary theories. According to Caputo (1997), theoretical results from Castellani et al. (1991: CCP) can be combined with Kurucz (1992) atmosphere models to derive the ZAHB luminosity

[EQUATION]

which gives, for the assumed metallicity, [FORMULA]. However, recent improvements in the input physics (see Salaris, Degl'Innocenti & Weiss 1997) already disclosed that CCP probably underestimated the HB luminosity by [FORMULA]. With such a correction, from the observed magnitude of the HB, one finally derives a cluster apparent distance modulus [FORMULA]

Apart from the theoretical route, we could obtain a distance modulus estimate using other empirical or semi-empirical calibrations of the [FORMULA] vs. [Fe/H] relation. Column 1 of Table 5 summarizes the different values of the absolute magnitude of the ZAHB using the most recent calibrations of the relation. The corresponding distance modulus (and uncertainties) are in column 3 (and 4, respectively) of Table 5. A mean of the different distance moduli in Table 5 gives: [FORMULA], very similar to the value obtained above from the theoretical HB magnitude. Assuming E(B-V)=0.17, and AV=3E(B-V) we get an absolute distance modulus: (m-M)0=15.07[FORMULA]0.16


[TABLE]

Table 5. Distance from different calibrations of the magnitude of the ZAHB.


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© European Southern Observatory (ESO) 1998

Online publication: June 26, 1998
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