In this paper , using 2MASS photometry , we study the mass functions \phi ( M ) = dN / dM \propto M ^ { - \alpha } of a sample of nine clusters of ages varying from 4 Myr–1.2 Gyr and Galactocentric distances from 6–12 kpc .
We look for evidence of mass segregation in these clusters by tracing the variation in the value of \alpha in different regions of the cluster as a function of the parameter \tau = t _ { age } / t _ { relax } ( where t _ { age } is the age of the cluster and t _ { relax } is the relaxation time of the cluster ) , Galactocentric distance , age and size of the cluster .
The value of \alpha value increases with age and \tau and fits straight lines with slopes m and y-intercepts c given by m = 0.40 \pm 0.03 , c = -1.86 \pm 0.27 and m = 0.01 \pm 0.001 , c = -0.85 \pm 0.02 , respectively and is a clear indicator of the dynamical processes involved .
The confidence level of the Pearson ’ s product-moment correlation of \alpha with age is 0.76 with p=0.002 and with \tau is 0.71 with p=0.007 .
The value of \alpha also increases with Galactocentric distance , indicating the presence of a larger relative number of low mass stars in clusters at larger Galactocentric distances .
We find two clusters , viz .
IC 1805 and NGC 1893 , with evidence of primordial or early dynamical mass segregation .
Implications of primordial mass segregation on the formation of massive stars and recent results supporting early dynamical mass segregation are discussed .