Mass segregation in diverse environments

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 $m=0.40\pm0.03$, $c=-1.86\pm0.27$ and $m=0.01\pm0.001$, $c=-0.85\pm0.02$, 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.