Minimum and maximum line-mass perturbation strength for direct collapse as function of the filament line-mass. The minimum is given by the fact that the Bonnor-Ebert sphere potential has to dominate over the filament potential and at the same time the line-mass maximum has to be above f_cyl = 0.66. The maximum is given by the fact that the line-mass cannot exceed a value of 1.0 in equilibrium. The light and dark blue dots show the perturbation strength we used for our test simulations given in Fig. 9.