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Random fragmentation of turbulent molecular clouds lying in the central region of giant galaxies

A stochastic model of fragmentation of molecular clouds has been developed for studying the resulting Initial Mass Function (IMF) where the number of fragments, inter-occurrence time of fragmentation, masses and velocities of the fragments are random variables. Here two turbulent patterns of the velocities of the fragments have been considered, namely, Gaussian and Gamma distributions. It is found that for Gaussian distribution of the turbulent velocity, the IMFs are shallower in general compared to Salpeter mass function. On the contrary, a skewed distribution for turbulent velocity leads to an IMF which is much closer to Salpeter mass function. The above result might be due to the fact that strong driving mechanisms e.g. shocks, arising out of a big explosion occurring at the centre of the galaxy or due to big number of supernova explosions occurring simultaneously in massive parent clouds during the evolution of star clusters embedded into them are responsible for stripping out most of the gas from the clouds. This inhibits formation of massive stars in large numbers making the mass function a steeper one.