Abstract
We investigate whether the stellar initial mass function (IMF) is universal,
or whether there are significant cluster-to-cluster variations of the IMF among
young stellar clusters in the Milky Way. We propose a method to uncover the
range of variation of the parameters that describe the IMF for the population
of young clusters in the Milky Way. The method relies exclusively on the high
mass content of the clusters, but is able to yield information on the
distributions of parameters of the IMF over the entire stellar mass range. This
is achieved by appropriately comparing the fractions of single and lonely
massive O stars in a recent catalog of the Milky Way clusters with a large
library of simulated clusters built with various distribution functions of the
IMF parameters. The masses of synthetic clusters are randomly drawn using a
power-law distributions function, while stellar masses in the clusters are
randomly drawn using a tapered power-law function. The synthetic clusters are
further corrected for the effects of binary population, stellar evolution,
sample incompleteness, and estimates are made for the effects of ejected O
stars. Our findings indicate that broad distributions of the IMF parameters are
required in order to reproduce the fractions of single and lonely O stars in
the Milky Way clusters and they do not lend support to the existence of a
cluster mass-maximum stellar mass relation. We propose a probabilistic
formulation of the IMF based on the distribution functions of its parameters.
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