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Cluster Density and the IMF

Observed variations in the IMF are reviewed with an emphasis on environmental density. The remote field IMF studied in the LMC by several authors is clearly steeper than most cluster IMFs, which have slopes close to the Salpeter value. Local field regions of star formation, like Taurus, may have relatively steep IMFs too. Very dense and massive clusters, like super star clusters, could have flatter IMFs, or inner-truncated IMFs. We propose that these variations are the result of three distinct processes during star formation that affect the mass function in different ways depending on mass range. At solar to intermediate stellar masses, gas processes involving thermal pressure and supersonic turbulence determine the basic scale for stellar mass, starting with the observed pre-stellar condensations, and they define the mass function from several tenths to several solar masses. Brown dwarfs require extraordinarily high pressures for fragmentation from the gas, and presumably form inside the pre-stellar condensations during mutual collisions, secondary fragmentations, or in disks. High mass stars form in excess of the numbers expected from pure turbulent fragmentation as pre-stellar condensations coalesce and accrete with an enhanced gravitational cross section. Variations in the interaction rate, interaction strength, and accretion rate among the primary fragments formed by turbulence lead to variations in the relative proportions of brown dwarfs, solar to intermediate mass stars, and high mass stars.