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

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4. The luminosity function

Making reference to this (m-M)0 value and bearing in mind the above evaluation of the cluster distance modulus one can further compare the observed sample of RGB stars with the theoretical prescriptions.

In the upper panel of Fig. 3 the RGB luminosity function (LF) is compared with the theoretical LF for the two labeled choices of the metallicity and for a cluster age t=14 Gyr (t=16 Gyr in the lower panel). The observed LF is obtained selecting stars with [FORMULA] pix, not belonging to the NE field (because of the lower exposure time of the NE V-frame) and lying within [FORMULA] from the cluster ridge line. The LF is also corrected for the field stars contamination by using the CMD obtained in the external region, located [FORMULA] arcmin from the cluster center. Theoretical LFs (Degl'Innocenti et al. 1997) are normalized to the total number of stars on the RGB ([FORMULA] mag). The last two points ([FORMULA] mag) of the observed LF in Fig. 3 are clearly below the theoretical LF, this could be due to the assumed IMF but it is very likely due to the incompleteness of the sample at these fainter magnitudes (cf. Sect. 2 ).

[FIGURE] Fig. 3. Observed luminosity function (filled circles) for the stars with [FORMULA] pix not belonging to the NE field and lying within [FORMULA] from the cluster ridge line, decontaminated for the field stars contribution. The vertical error bars represent the Poisson standard deviation, the horizontal ones account of the uncertainty in the [FORMULA] determination ([FORMULA] mag). Theoretical LF, from Degl'Innocenti et al. (1996), are computed for the specified ages and metallicities, shifted by the labeled DM.

The overall morphology would suggest that the upper limit of the adopted metallicity range should be preferred to account for the star distribution around the subgiant branch (i.e. around [FORMULA]). Comparison between the upper and lower panel of the figure shows that, under the above quoted assumptions, models for an age of 14 Gyr better reproduce the observed LF. As shown in Fig. 4, the LF also allows to locate the position of the RGB luminosity bump marking the encounter of the H burning shell with the interior chemical discontinuity. As shown by Fusi Pecci et al. (1990), the bump is better revealed by the changing slope of the cumulative luminosity function produced by the variation in the core mass-luminosity relation for the RGB structures. The bottom panel of Fig. 4 shows that the bump can be recognized in the usual differential luminosity function too. We find [FORMULA]. The position of the bump in M 80 can now be compared with the results obtained for the other globular clusters: Fusi Pecci et al. (1990) defined the parameter [FORMULA] and studied its dependence on the cluster metallicity. The authors replaced [Fe/H] with the parameter [FORMULA] (cf. their definition), which was useful in order to make the comparison with the theoretical models. From the previous discussion, for M 80 we have [FORMULA]. M 80 shares the general trend of the present sample of clusters (cf. Saviane et al. 1998 for an updated discussion on this subject).

[FIGURE] Fig. 4. Cumulative (a ) and differential (b ) luminosity function for all the stars detected brighter than 17.5 mag.

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© European Southern Observatory (ESO) 1998

Online publication: June 26, 1998