WHAT DETERMINES THE STELLAR MASS FUNCTIONS IN GLOBULAR-CLUSTERS

We analyze the dependence of stellar mass function slopes for a sample of 17 globular clusters on a variety of cluster parameters. The princ ipal novelty of our approach is the use of appropriate multivariate st atistical methods to disentangle the complex situation which is presen t in this problem: the slopes depend simultaneously on more than one v ariable, and many cluster parameters are mutually (albeit weakly) corr elated. We find that the mass function slopes in the range 0.5 less-th an-or-equal-to M/M. less-than-or-equal-to 0.8 are largely determined b y at least two or three quantities: mainly the position in the Galaxy (distance to the Galactic center, R(GC), and to the Galactic plane, Z( GP)), and also, to a lesser extent, by the cluster metallicity. Other cluster parameters have little effect, at least in the present sample. Clusters closer to the Galactic center or plane have shallower mass f unction slopes. At a given distance to the Galactic center, clusters c loser to the Galactic plane have shallower mass function slopes. At a given R(GC) and/or Z(GP), more metal-rich clusters have shallower mass function slopes. Thus, the monovariate correlations with the position or metallicity (as found by previous studies) are both correct, but o nly partial, and in terms of slopes, biased descriptions of the situat ion. We present trivariate least-squares solutions where the mass func tion slopes can be predicted within the measurement accuracy (DELTAx a pproximately 0.4) from a combination of R(GC), Z(GP), and [Fe/H]. This relation can serve as a powerful observational constraint for theorie s of globular cluster formation and evolution, and it is one of the ti ghtest correlations between globular cluster properties now known. We briefly discuss some possible explanations for the observed correlatio ns.