Threshold line-masses at the position of the core in dependence of the filament line-mass f_cyl. The beginning of the non-linear evolution in acceleration is given by the cyan points, for the velocity by the orange points. The solid line indicates where the Bonnor-Ebert sphere potential dominates over the filament potential. The vertical dashed-dotted line shows the lower mass limit for a collapsing Bonnor-Ebert sphere and the horizontal dashed line shows the result of calculating the maximum supported Bonnor-Ebert mass assuming a external pressure given by the density within the filament.