We show that we can obtain a good fit to the present day stellar mass functions ( MFs ) of a large sample of young and old Galactic clusters in the range 0.1 - 10 M { { } _ { \odot } } with a tapered power law distribution function with an exponential truncation of the form dN / dm \propto m ^ { \alpha } [ 1 - e ^ { - ( m / m _ { c } ) ^ { \beta } } ] .
The average value of the power-law index \alpha is \sim - 2 , that of \beta is \sim 2.5 , whereas the characteristic mass m _ { c } is in the range 0.1 - 0.8 M _ { \odot } and does not seem to vary in any systematic way with the present cluster parameters such as metal abundance , total cluster mass or central concentration .
However , m _ { c } shows a remarkable correlation with the dynamical age of the cluster , namely m _ { c } / M _ { \odot } \simeq 0.15 + 0.5 \times \tau _ { dyn } ^ { 3 / 4 } , where \tau _ { dyn } is the dynamical age taken as the ratio of cluster age and dissolution time .
The small scatter seen around this correlation is consistent with the uncertainties on the estimated value of \tau _ { dyn } .
We attribute the observed trend to the onset of mass segregation via two-body relaxation in a tidal environment , causing the preferential loss of low-mass stars from the cluster and hence a drift of the characteristic mass m _ { c } towards higher values .
If dynamical evolution is indeed at the origin of the observed trend , it would seem plausible that high-concentration globular clusters , now with median m _ { c } \simeq 0.33 M _ { \odot } , were born with a stellar MF very similar to that measured today in the youngest Galactic clusters and with a value of m _ { c } \simeq 0.15 M _ { \odot } .
This hypothesis is consistent with the absence of a turn-over in the MF of the Galactic bulge down to the observational limit at \sim 0.2 M _ { \odot } and , if correct , it would carry the implication that the characteristic mass is not set by the thermal Jeans mass of the cloud .