The Mass Spectra of Cores in Turbulent Molecular Clouds and Implications for the Initial Mass Function

We investigate the core mass distribution (CMD) resulting from numerical models of turbulent fragmentation of molecular clouds. In particular we study its dependence on the sonic root-mean-square Mach number $\Ms$. We analyze simulations with $\Ms$ ranging from 1 to 15 to show that, as $\Ms$ increases, the number of cores increases as well while their average mass decreases. This stems from the fact that high-Mach number flows produce many and strong shocks on intermediate to small spatial scales, leading to a highly-fragmented density structure. We also show that the CMD from purely turbulent fragmentation does not follow a single power-law, but it may be described by a function that changes continuously its shape, probably more similar to a log-normal function. The CMD in supersonic turbulent flows does not have a universal slope, and as consequence, cast some doubt on attempts to directly relate the CMD to a universal Initial Mass Function.