On the Similarity between Cluster and Galactic Stellar Initial Mass Functions

The stellar initial mass functions (IMFs) for the Galactic bulge, the MilkyWay, other galaxies, clusters of galaxies, and the integrated stars in theUniverse are composites from countless individual IMFs in star clusters andassociations where stars form. These galaxy-scale IMFs, reviewed in detailhere, are not steeper than the cluster IMFs except in rare cases. This is trueeven though low mass clusters generally outnumber high mass clusters and theaverage maximum stellar mass in a cluster scales with the cluster mass. Theimplication is that the mass distribution function for clusters andassociations is a power law with a slope of -2 or shallower. Steeper slopes,even by a few tenths, upset the observed equality between large and small scaleIMFs. Such a cluster function is expected from the hierarchical nature of starformation, which also provides independent evidence for the IMF equality whenit is applied on sub-cluster scales. We explain these results with analyticalexpressions and Monte Carlo simulations. Star clusters appear to be the relaxedinner parts of a widespread hierarchy of star formation and cloud structure.They are defined by their own dynamics rather than pre-existing cloudboundaries.Comment: 22 pages, 2 figures, ApJ, 648, in press, September 1, 200