Luminosity functions and initial mass function variations from large samples of H

Large high-quality samples of H<ns0:sc>II</ns0:sc> regions and their parent giant molecular clouds (GMCs) are now available for local galaxies. It is therefore possible to investigate the links between the CO and Hα luminosity functions and whether massive stars form in GMCs of all masses. The CO luminosity functions, representing the distribution of GMC masses, are consistently steeper than the Hα luminosity functions. The CO luminosity function invariably steepens in the outer disk, where fewer massive GMCs are present beyond the median cloud galactocentric distance. The Hα luminosity function also steepens in the outer disk for most of the galaxies examined. Using Salpeter, Kroupa, and Chabrier initial mass functions (IMFs) along with stellar mass-luminosity-radius relations, we calculate the bolometric luminosity and Hα emission from young star clusters. The cluster masses are linked to the GMC mass by assuming that the cluster mass is a constant fraction (3%) of the parent cloud mass. In particular, results for a fully stochastic IMF are compared to suggestions that very massive stars only form in massive clusters or clouds. Within the limits of the observations - no small molecular clouds or low-luminosity H<ns0:sc>II</ns0:sc> regions can be detected at the typical ∼10 Mpc distance of the sample galaxies - we find no evidence for a maximum stellar mass that varies with cloud or cluster mass.