5. The mass functions
The LFs can be transformed into MFs using a MLR. As emphasized in Sect. 3, such transformations are still uncertain for low-mass, low-metallicity stars, and we must rely on the models almost entirely. It is somehow reassuring that not only at least two of the existing models are able to reproduce the observed diagrams, but also the distance moduli and reddenings that result from the fit are in agreement, within the errors, with the values in the literature. This does not mean that the models by the Lyon and the Teramo groups used in Sect. 3 are the correct ones. They are simply the best ones presently available, and we will use both of them to gather some information on the general shape of the MFs of M10, M15, and M22. The cautionary remarks on the absence of empirical MLR data should still be heeded. For the sake of comparison, and in order to give an idea of the possible range of uncertainty, we will also use the MLR of the Roma group (D'Antona & Mazzitelli 1995).
In Fig. 13 we compare the MFs derived from the I LFs of M10, M22, and M55 from the TO down to . An arbitrary vertical shift is applied for reasons of clarity. The adopted distance moduli, reddenings, and metallicities for the MFs obtained using the Lyon and Teramo models are in Table 3. For the Roma model we adopted the values in Djorgovski (1993) and used the isochrone corresponding to 10 Gyr.
The MFs obtained using the Lyon and Teramo models track one other closely for . The small differences for higher masses might be due, at least in part, to the difference in the adopted ages. The MFs from the Roma models are systematically steeper, as already noted in PCK. Fig. 14 compares the MFs obtained from the V and I LFs, using the Teramo models. In all cases, the two MFs are very similar, despite the fact that the two LFs have been independently obtained. This result is also reassuring on the theoretical side, showing the internal consistency of the models.
In all cases, there is a hint of flattening at the low-mass end, but no sign of a drop-off.
As the transformation from the LF to the MF is the weakest part of the present analysis, we prefer not to comment further on the detailed structure of the MF. We note only that the slopes of the MFs below , using any existing MLRs, are shallower than the slope ( for the Salpeter MF in this notation) for which the integration of the total mass down to would diverge.
© European Southern Observatory (ESO) 1999
Online publication: April 19, 1999