In the scenario of turbulent fragmentation, the characteristic stellar mass and the IMF turnover at lower masses are determined by the gas density PDF, as large density enhancements are required for the local Bonnor-Ebert mass to be as small as the mass of low-mass stars and brown dwarfs (Padoan, Nordlund and Jones 1997, MNRAS 288, 145). The power-law shape of the IMF above 1-2 solar masses results from the scale-free nature of the turbulence, as more massive cores in the turbulent flow are always gravitationally unstable (Padoan and Nordlund 2002, ApJ 576, 870).
We test the theory with simulations:
i) without gravity to study the effect of the turbulence in isolation
Padoan et al. 2007 ApJ 661, 972
ii) with gravity and sink particles to test the combined effect of gravity, turbulence and dynamical interactions
Protostellar Infall and Luminosity
Simple protostellar collapse models are not able to predict the observed luminosity distribution of protostars, not even the mean of such distribution. Various models of episodic accretion have been proposed to explain the observations. We have shown that in the scenario of turbulent fragmentation the random velocity field results in protostellar infall rates that vary randomly in time and from star to star. More importantly, the infall rate tend to decrease with time, which appears to be the main solution to the protostellar luminosity problem:
Padoan et al. 2014, ApJ 797, 32
More recent syntetic observations of similar simulations have successfully reproduced the protostellar luminosity function (Frimann et al. 2016, ApJ 797, 32) and the simulations are now coupled with the MESA stellar evolution code in order to produce synthetic HR diagrams (Jensen and Haugbølle 2017).
We model the SFR assuming the gas density PDF is Lognormal, because of supersonic turbulence, and computing the mass fraction above a critical density, divided by a characteristic time. Different choices of critical density and characteristic time result in different SFR models.
We test the models with simulations of:
i) small-scale (few pc) regions with random driving, for parameter studies
Padoan et al. 2012, ApJ 759, 27
Padoan et al. 2011, ApJ 730, 40
ii) large scale (250 pc) regions with SN driving, to generate SF clouds ab initio (realistic initial and boundary conditions)
Padoan et al. 2017, ApJ 840, 48