Abstract
It is proposed that the initial mass function (IMF) for star formation in galaxies is not a monotonic function of stellar mass but is double-peaked or bimodal. In models with a bimodal IMF the star formation rate (SFR) can be strongly decreasing function of time, and stellar remnants can constitute an important or dominant fraction of the total mass. A bimodal model is constructed that accounts for all of the unseen mass in the solar neighbourhood as remnants, and it is shown that this model is consistent with all of the available constraints on the evolution and stellar content of the solar neighbourhood. The properties of the inner discs of our Galaxy and M83 can be accounted for by similar models in which the high-mass mode of star formation is more dominant than in the solar neighbourhood, and remnants constitute a large fraction of the mass. Bimodal models with a rapidly decreasing SFR and a mass dominated by remnants account better than conventional models for the observed colours, mass-to-light ratios, and gas contents of spiral galaxies, and also allow the increase of both metallicity and mass-to-light ratio with mass in giant elliptical galaxies to be understood. All of the data are consistent with a picture in which the formation of massive stars is favoured at times and in regions where the SFR is high. An extension of such a picture to the earliest stages of star formation in galaxies may allow the dark mass in galactic haloes to be accounted for as remnants of early generations of massive stars.

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