Abstract
Accurate determinations of stellar mass functions and ages of stellar populations are crucial to much of astrophysics. We analyze the evolution of stellar mass functions of coeval main-sequence stars, including all relevant aspects of single and binary star evolution. We show that the slope of the upper part of the mass function in a stellar cluster can be quite different from the slope of the initial mass function. Wind-mass loss from massive stars leads to an accumulation of stars which is visible as a peak at the high-mass end of mass functions, thereby flattening the mass function slope. Mass accretion and mergers in close binary systems create a tail of rejuvenated binary products. These blue straggler stars extend the single star mass function by up to a factor of 2 in mass and can appear up to 10 times younger than their parent stellar cluster. Cluster ages derived from their most massive stars that are close to the turn-off may thus be significantly biased. To overcome such difficulties, we propose the use of the binary tail of stellar mass functions as an unambiguous clock to derive the cluster age because the location of the onset of the binary tail identifies the cluster turn-off mass. It is indicated by a pronounced jump in the mass function of old stellar populations and by the wind-mass loss peak in young stellar populations. We further characterize the binary induced blue straggler population in star clusters in terms of their frequency, binary fraction, and apparent age.