Astron. Astrophys. 343, L9-L14 (1999)

4. Discussion and conclusions

Stars brighter than have already evolved off the MS and, therefore, their LF provides no information on the underlying MF without uncertain corrections for evolution (Scalo 1998). Moreover, because of saturation at the bright end of our CMDs, the brightest portion of our LFs is uncertain. For cluster stars which are still on their MS, however, the LFs in Fig. 3 directly reflect the PDMF of the local population and immediately indicate a relative deficiency of low mass objects with respect to the stars with the TO mass ( M,), as we discuss below.

Indeed, the most important conclusion that one can draw from Fig. 3 is that the shape of the LFs completely deviates from that of any other GC for which relatively deep photometric data are available near the half-mass radius. Observations carried out with the WFPC 2 on board the HST over the past few years (Paresce, De Marchi & Romaniello 1995; Cool, Piotto, & King 1996; Elson et al. 1995; De Marchi & Paresce 1995a , 1995b , 1996a , 1997; Piotto, Cool, & King 1997; Pulone et al. 1998a; King et al. 1998; De Marchi 1998) have consistently revealed LFs that, near the cluster half-mass radius, increase with decreasing luminosity from the TO magnitude all the way down to about ( M,) where they flatten out and drop at fainter luminosities. Inverted LFs such as those shown in Fig. 3 have been observed right in the core of high density GCs (47 Tuc, NGC 6397, M 15) but in those cases a simple isothermal model of a cluster in equilibrium can easily explain this effect as being due to mass segregation (Paresce, De Marchi, & Jedrzejewski 1995; King, Sosin, & Cool 1995; De Marchi & Paresce 1996b). More complete multi-mass King-Michie models show, however, that thermal relaxation is much less efficient (if at all) at depleting low-mass stars near the half-mass radius (see Pulone, De Marchi, & Paresce 1998b), and we cannot therefore trace the origin of the LFs that we observe back to the effects of mass segregation alone.

To make it easier to compare the LF of NGC 6712 with that of other clusters, we display it in Fig. 4 as a function of the absolute R-band magnitude, assuming and or (Djorgovski 1993). Rather than showing the three individual LFs, we have combined them together into one single function by averaging their values in each magnitude bin, and have taken the standard deviation as a measure of the associated uncertainty (error bars). The dashed line shown in Fig. 4 corresponds to the LF of the low-metallicity cluster NGC 6397 as measured by King et al. (1998), while the dot-dashed line reproduces the LF of the metal rich cluster 47 Tuc from Hesser et al. (1987). Both LFs have been translated into the R-band by using the M-L relationship of Baraffe et al. (1997) for the appropriate metallicity, i.e. the magnitude corresponding to each observed point in the LF has been converted into a mass which has then been used to read the corresponding magnitude in the R band from the appropriate M-L relation. The size of each magnitude bin has also been rescaled to reflect the difference in the slopes of the M-L relationships for different bands. We have selected NGC 6397 and 47 Tuc as they both have accurate LF measurements at and below the TO luminosity, where we have normalized them to our observations, and because the metal content of these clusters nicely brackets that of NGC 6712 ([Fe/H]; Zinn & West 1984). It should, nevertheless, be clear that, due the uncertainties in the theoretical M-L relations and in the observed LFs, our comparison will only provide an indication of the true differences.

Fig. 4. Boxes: average of the three LFs shown in Fig. 3, converted to absolute magnitude (); dashed and dot-dashed lines: LFs of NGC 6397 and 47 Tuc translated to the R band and normalized to ours at the TO (); solid line: best fitting power-law MF ()

The difference between these two LFs and that of NGC 6712 is striking. While the LFs of NGC 6397, measured at , shows a steep increase starting from the TO, the LF of NGC 6712 sampled at slowly drops from the TO all the way to the detection limit at . We would like to point out that the discrepancy is so large that to bring the two LFs into agreement would require us to have underestimated the photometric incompleteness by a factor of . The same reasoning holds true for the LF of 47 Tuc, which has been measured at . This difference must thus be physical and reflect the properties of the local stellar population.

Under the simple assumption that the MF should be represented by an exponential distribution in the mass range 0.4-0.8 M, (a reasonable hypothesis given the narrow mass range), we have used the M-L relationship of Baraffe et al. (1997) appropriate for the metallicity of NGC 6712 to reproduce the observed LF. We obtain a fairly reasonable fit to the observations with a power-law distribution of the type (Salpeter's IMF would be ), in which the number of objects decreases with mass (solid line in Fig. 4).

Richer et al. (1991) and, more recently, De Marchi & Paresce (1997), Vesperini & Heggie (1997), and Pulone et al. (1998b) have convincingly shown that near the cluster half-mass radius the LF should closely reflect the IMF, as dynamical modifications should leave these regions almost untouched. In fact, the internal relaxation mechanism governed by energy equipartition through two- and three-body encounters mostly affects the region within a few core radii, while the interaction with the Galactic tidal field is expected to simply speed up the evaporation of light stars near the tidal boundary, but none of these processes should, in principle, significantly alter the properties of stars located close to the much safer half-mass radius area.

If this were true for NGC 6712 as well, one should conclude that this cluster is the only one so far to feature an inverse IMF (increasing with mass) that has not been observed in any other environment. While this hypothesis cannot be safely ruled out, there are far better reasons to believe that NGC 6712 might have experienced a much stronger interaction with the Galaxy than any other of the clusters studied so far. And indeed, with a perigalactic distance smaller than 300 pc this cluster ventures so frequently and so deeply into the Galactic bulge (Dauphole et al. 1996) that it is likely to have undergone severe tidal shocking during the numerous encounters with both the disk and the bulge during its lifetime. The latest Galactic plane crossing could have happened as recently as year ago (Cudworth 1988) which is much smaller than its half-mass relaxation time ( yr). Such an event might have imparted strong modifications on the mass distribution not only of the stars in the cluster periphery but also well into its innermost regions, perhaps even reaching the core where it could have triggered a premature collapse because of tidally induced relaxation (see Kundi & Ostriker 1997 and Gnedin & Ostriker 1997 for a detailed description of this mechanism).

As a result of such a catastrophe, it would be surprising if the present-day MF were still to bear any memory of its parent IMF anywhere in the cluster, including the half-mass radius region. Vesperini & Heggie (1997) have estimated that these effects would substantially decrease the slope of a simple power law MF, much in the same way as we are observing here. We, therefore, conclude that the VLT has revealed the consequences of the strong tidal stripping that the Galaxy (and particularly its bulge) exerts on GCs orbiting close to the center, and which might have contributed to the destruction of an initially much more numerous population of GCs (Aguilar, Hut, & Ostriker 1988; Vesperini 1997). Although Kanatas et al. (1994) and Piotto et al. (1997) had speculated that similar events could have happened respectively in M 4 and NGC 6397, the result that we show here is the first, clear, unambiguous detection of this mechanism. To characterize the strength and extent of these phenomena more accurately would require the investigation of the MS population outside the half-mass radius in many more clusters, and possibly at larger distance from the Galactic center, so as to probe the intensity of the stripping process as a function of the depth of the Galactic potential well. If the Z component of the space velocity of NGC 6712 is indeed appropriate for a halo cluster, as suggested by Cudworth (1988), then this violent stripping process might not be restricted only to objects orbiting the innermost Galactic regions.

© European Southern Observatory (ESO) 1999

Online publication: March 1, 1999
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