The Stellar Initial Mass Function

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The outcome of star formation are stars and sub-stellar objects with a range of masses. Astrophysicists refer to the distribution of masses as the initial mass function (IMF). The IMF together with the time-modulation of the star-formation rate dictates the evolution and fate of galaxies and star clusters, and is therefore a fundamental astrophysical distribution function. Because stars cannot be weighed directly the shape of the IMF in star-forming regions and in entire galaxies remains uncertain. The project outlined here addresses the following issues: (i) the form and time-variation of the stellar IMF integrated over whole galaxies and the implications for their chemo-photometric evolution over cosmological time scales and the red-shift dependent supernova rate, (ii) the existence of a maximum stellar mass, (iii) the shape of the IMF for massive stars and corrections for a high stellar multiplicity, and (iv) the shape of the MF for low-mass stars using a novel iterative scheme, and (v) the possible shape and variation of the IMF across the hydrogen-burning mass limit and in the brown-dwarf mass regime. This project thus deals with issues ranging from cosmological problems down to local star-formation in the stellar and sub-stellar regimes.