Star formation and the initial mass function

Supersonic turbulence fragments the interstellar medium into dense sheets, filaments, cores and large low-density voids, thanks to a complex network of highly radiative shocks. The turbulence is driven on large scales, predominantly by supernovae. While on scales of the order of the galactic disk thickness the magnetic energy is in approximate equipartition with the kinetic energy of the turbulence, on scales of a few pc the turbulent kinetic energy significantly exceeds the magnetic energy. The scaling properties of supersonic turbulence are well described by a new analytical theory, which allows to predict the structure functions of the density and velocity distributions in star-forming clouds up to very high order. The distribution of core masses depends primarily on the power spectrum of the turbulent flow, and on the jump conditions for isothermal shocks in a. magnetized gas. For the predicted velocity power spectrum index beta = 1.74; consistent with results of numerical experiments of supersonic turbulence as well as with Larson's velocity-size relation, one obtains by scaling arguments a power law mass distribution of dense cores with a slope equal to 3/(4 - beta) = 1.33, consistent with the slope of the Salpeter stellar initial mass function (IMF). Results from numerical simulations confirm this scaling. The analytical model for the stellar IMF and its numerical estimate show that turbulent fragmentation may explain the origin of brown dwarfs, but only if the critical mass for collapse under dynamical conditions is an order of magnitude smaller than the Jeans' mass from a linear stability analysis. The main conclusion is that the stellar IMF directly reflects the mass distribution of prestellar cores, due predominantly to the process of turbulent fragmentation.