Possible density dependent local variations in the IMF

A robust feature of turbulent fragmentation theories is a universal Salpeter like slope (2.2 -2.4), for the mass spectrum of the fragments, at the high mass end. This is so due to the scale-free nature of turbulence and gravity. There are reports of top heavy / flatter Initial Mass Functions (IMF), inferred for many regions where we expect star formation to take place in gas clouds with comparatively higher gas density. Also, a higher Star Formation Efficiency (SFE) for regions of higher gas density has been proposed, to understand the formation of bound stellar systems in which dark matter is not a significant factor affecting the internal dynamics. In turbulent fragmentation models for star formation, we do not expect the mass of the stellar cluster to influence the maximum stellar mass directly and thereby imply a relation between the maximum stellar mass and the cluster mass. However, such a relation may be expected from statistical considerations. In this context, we explore the density dependence of the IMF, that would arise due to denser clouds producing more massive clusters due to the density dependence of the SFE.