The Physical Origin of the Stellar Initial Mass Function

Stars are amongst the most fundamental structures of our Universe. They comprise most of the baryonic and luminous mass of galaxies, synthethise heavy elements, and injec\ t mass, momentum, and energy into the interstellar medium. They are also home to the planets. Since stellar properties are primarily decided by their mass, the so-called \ stellar initial mass function (IMF) is critical to the structuring of our Universe. We review the various physical processes, and theories which have been put forward as well as the numerical simulations which have been carried out to explain the origin of the stellar initial mass function. Key messages from this review are: (1) Gravity and turbulence most likely determine the power-law, high-mass part of the IMF. (2) Depending of the Mach number and the density distribution, several regimes are possible, including $\Gamma _{IMF} \simeq 0$, -0.8, -1 or -1.3 where $d N / d \log M \propto M^{\Gamma_{IMF}}$. These regimes are likely universal, however the transition between these regimes is not. (3) Protostellar jets can play a regulating influence on the IMF by injecting momentum into collapsing clumps and unbinding gas. (4) The peak of the IMF may be a consequence of dust opacity and molecular hydrogen physics at the origin of the first hydrostatic core. This depends weakly on large scale environmental conditions such as radiation, magnetic field, turbulence or metallicity. This likely constitutes one of the reason of the relative universality of the IMF.