Astron. Astrophys. 319, 487-497 (1997)

5. Discussion and conclusions

The prime intention of this paper has been to independently investigate whether there indeed exists a systematic and significant discrepancy between observed and theoretical luminosity functions of Globular Clusters as claimed by Faulkner & Swenson (1993) and Bolte (1994). We have demonstrated in Sect. 3 that for the clusters used in their papers and for additional data by Piotto & Saviane (in prep.) the agreement between our standard luminosity functions and the observations is good for reasonable assumptions about cluster composition, distance and age. Actually, we have used values from the literature for these parameters, but exploited the range of uncertainties to find the best fit. All data points can be fitted within of the statistical errors, except for the main sequences. To illustrate the influence of pure number statistics we have performed the following test: we took one of our standard LFs (16 Gyr; , ) and constructed a synthesized LF by the rejection method to construct random deviates. Fig. 12 shows the comparison between the synthetic and the theoretical LF for a total number of stars and a number of brightness bins comparable to the cases discussed in this paper. The similarity, for example with Fig. 1, demonstrates that our fits are perfect within the statistical errors, and that deviations like those at or 3.8 are to expected. In fact, some of our cases show a better agreement than would be consistent with the statistics. In these cases, the fit parameters might be overdetermined. Of course, the systematic deviations on the main sequences are a clear indication of non-statistical errors. Since all clusters by Piotto & Saviane (in prep.) are more deficient with respect to the main-sequence parts of the theoretical LFs, while those used by FS are to a smaller extend, we ascribe this to an underestimate in the completeness correction applied by the observers. This is consistent with the fact that Bolte (1994) used the most sophisticated completeness correction for M30 and this cluster shows the smallest deviation. Clearly, there is a need for a further improvement both in the data and in the completeness corrections of the main sequence LF. Bolte (1994) for M30 and Brocato et al. (1996) for M80 have already demonstrated that such an improvement is achievable.

Fig. 12. Theoretical and synthetic luminosity functions for standard parameters (16 Gyr; , ). 26000 random points in the N- plane were chosen, out of which 6873 fell below the theoretical probability function and were accepted. The number of brightness bins is 30. errors are indicated

Alternatively, one could speculate that the IMF for these clusters is flatter than assumed. This uncertainty - and the additional one of the helium content - prevented us from using the main sequence for the normalization of the LFs, in spite of the much smaller statistical errors. Instead, we used the RGB for normalization, whose LF-slope is an extremely stable quantity independent of all input variables. In the case of M80 we demonstrated that the use of the main sequence would lead to a "discrepancy" in the standard LF and its resolution by an isothermal core, just as was the case in the papers triggering the present work.

The main sequence being inadequate for a detailed comparison and the red giant branch being robust against model changes, the subgiant branch is left to reflect model differences, parameter influences and potential problems. However, the present observations do not resolve the LF in this region sufficiently well and with adequate accuracy. We propose that in the future observations aiming at obtaining the LFs of GCs should concentrate exactly on this region.

We found one cluster (NGC6352), which withstands all attempts to fit a theoretical LF. The shape of the observed one is in fact very strange and looks like that of a very low-metallicity system in terms of the missing subgiant break, and like one of high helium content with respect to the slope at the TO (Ratcliff 1987). However, within the parameter range investigated by us, we could not obtain any good fit. We rather suspect that the subgiant break was not resolved properly, and this should be checked by further observations.

Of all quantities we have tested for their influence on the LFs, we found that metallicity and distance (see the example of M80; Figs. 6 and 7) have the largest influence. Age variations of up to 2 Gyr can be compensated by a luminosity shift smaller than the quoted distance uncertainty (because old clusters change their TO-luminosity hardly with age). Discrepancies in the LF should therefore first raise the question of correct distance or metallicity determinations. In this context information about -element enrichment is important, too.

In Sect. 4 we repeated the LF-calculations, but with a very efficient energy transport in the innermost 10% of our models (following again FS and Bolte 1995). Our results show that the fits are not improved significantly. Since we found no evidence for a LF-discrepancy when using standard physics, it is not necessary to discuss properties of hypothetical WIMPs for additional energy transport in the core of main-sequence stars.

To summarize, we have shown that the agreement between observed and theoretical luminosity functions appears to be very good, with problems only arising on the lower main sequence (corrections for completeness might have to be improved) and for the exact shape of the subgiant bump and break (resolution in brightness), which have the potential to yield information about metallicity, age and distance of the cluster. However, to exploit this potential diagnostic value, a definite improvement in the observation of both branches is required.

© European Southern Observatory (ESO) 1997

Online publication: July 3, 1998
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