Star formation is one of the key processes of cosmic evolution as it influences phenomena from the formation of galaxies to the formation of planets, and the development of life. Unfortunately, there is no comprehensive theory of star formation, despite intense effort on both the theoretical and observational sides, due to the large amount of complicated, non-linear physics involved (e.g. MHD, gravity, radiation). A possible approach is to formulate simple, easily testable models that allow us to draw a clear connection between phenomena and physical processes.
In the first part of the talk I will focus on the origin of the IMF peak, the characteristic scale of stars. There is debate in the literature about whether the initial conditions of isothermal turbulence could set the IMF peak. Using detailed numerical simulations, I will demonstrate that not to be the case, the initial conditions are "forgotten" through the fragmentation cascade. Additional physics (e.g. feedback) is required to set the IMF peak.
In the second part I will Use simulated galaxies from the Feedback in Realistic Environments (FIRE) project to show that most star formation theories are unable to reproduce the near universal IMF peak of the Milky Way.
Finally, I will present analytic arguments (supported by simulations) that a large number of observables (e.g. IMF slope) are the consequences of scale-free structure formation and are (to first order) unsuitable for differentiating between star formation theories.