Theoretical considerations lead to the expectation that stars should not havemasses larger than about m_{max*}=60-120Msun, while the observational evidencehas been ambiguous. Only very recently has a physical stellar mass limit near150Msun emerged thanks to modern high-resolution observations of localstar-burst clusters. But this limit does not appear to depend on metallicity,in contradiction to theory. Important uncertainties remain though. It is nowalso emerging that star-clusters limit the masses of their constituent stars,such that a well-defined relation between the mass of the most massive star ina cluster and the cluster mass, m_{max}=F(M_ecl) \le m_{max*}\approx 150Msun,exists. One rather startling finding is that the observational data stronglyfavour clusters being built-up by consecutively forming more-massive starsuntil the most massive stars terminate further star-formation. The relationalso implies that composite populations, which consist of many star clusters,most of which may be dissolved, must have steeper composite IMFs than simplestellar populations such as are found in individual clusters. Thus, forexample, 10^5 Taurus--Auriga star-forming groups, each with 20 stars, will everonly sample the IMF below about 1Msun. This IMF will therefore not be identicalto the IMF of one cluster with 2 times 10^6 stars. The implication is that thestar-formation history of a galaxy critically determines its integratedgalaxial IMF and thus the total number of supernovae per star and its chemicalenrichment history. Galaxy formation and evolution models that rely on aninvariant IMF would be wrong.
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