Theories of the initial mass function

Patrick Hennebelle, Gilles Chabrier

Published 2010-11-11, updated 2011-01-08Version 2

We review the various theories which have been proposed along the years to explain the origin of the stellar initial mass function. We pay particular attention to four models, namely the competitive accretion and the theories based respectively on stopped accretion, MHD shocks and turbulent dispersion. In each case, we derive the main assumptions and calculations that support each theory and stress their respective successes and failures or difficulties.