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The ages of young star clusters, massive blue stragglers and the upper mass limit of stars: analysing age dependent stellar mass functions

Massive stars rapidly change their masses through strong stellar winds and mass transfer in binary systems. We show that such mass changes leave characteristic signatures in stellar mass functions of young star clusters which can be used to infer their ages and to identify products of binary evolution. We model the observed present day mass functions of the young Galactic Arches and Quintuplet star clusters using our rapid binary evolution code. We find that shaping of the mass function by stellar wind mass loss allows us to determine the cluster ages to 3.5$\pm$0.7 Myr and 4.8$\pm$1.1 Myr, respectively. Exploiting the effects of binary mass exchange on the cluster mass function, we find that the most massive stars in both clusters are rejuvenated products of binary mass transfer, i.e. the massive counterpart of classical blue straggler stars. This resolves the problem of an apparent age spread among the most luminous stars exceeding the expected duration of star formation in these clusters. We perform Monte Carlo simulations to probe stochastic sampling, which support the idea of the most massive stars being rejuvenated binary products. We find that the most massive star is expected to be a binary product after 1.0$\pm$0.7 Myr in Arches and after 1.7$\pm$1.0 Myr in Quintuplet. Today, the most massive 9$\pm$3 stars in Arches and 8$\pm$3 in Quintuplet are expected to be such objects. Our findings have strong implications for the stellar upper mass limit and solve the discrepancy between the claimed 150 $\mathrm{M}_\odot$ limit and observations of fours stars with initial masses of 165-320 $\mathrm{M}_\odot$ in R136 and of SN 2007bi, which is thought to be a pair-instability supernova from an initial 250 $\mathrm{M}_\odot$ star. Using the stellar population of R136, we revise the upper mass limit to values in the range 200-500 $\mathrm{M}_\odot$.