  Using numerical simulations, we investigate the gravitational evolution of filamentary molecular cloud structures and their condensation into dense protostellar cores. One possible process is the so called 'edge effect', the pile-up of matter at the end of the filament due to self-gravity. This effect is predicted by theory but only rarely observed. To get a better understanding of the underlying processes we used a simple analytic approach to describe the collapse and the corresponding collapse time. We identify a model of two distinct phases: The first phase is free fall dominated, due to the self-gravity of the filament. In the second phase, after the turning point, the collapse is balanced by the ram pressure, produced by the inside material of the filament, which leads to a constant collapse velocity. This approach reproduces the established collapse time of uniform density filaments and agrees well with our hydrodynamic simulations. In addition, we investigate the influence of different radial density profiles on the collapse. We find that the deviations compared to the uniform filament are less than 10%. Therefore, the analytic collapse model of the uniform density filament is an excellent general approach. 
Filament collapse: a two phase process