Filament fragmentation: Density gradients suppress end dominated collapse

The onset of star formation is set by the collapse of filaments in the interstellar medium. From a theoretical point of view, an isolated cylindrical filament forms cores via the edge effect. Due to the self-gravity of a filament, the strong increase in acceleration at both ends leads to a pile-up of matter which collapses into cores. However, this effect is rarely observed. Most theoretical models consider a sharp density cut-off at the edge of the filament, whereas a smoother transition is more realistic and would also decrease the acceleration at the ends of the filament. We show that the edge effect can be significantly slowed down by a density gradient, although not completely avoided. However, this allows perturbations inside the filament to grow faster than the edge. We determine the critical density gradient for which the timescales are equal and find it to be of the order of several times the filament radius. Hence, the density gradient at the ends of a filament is an essential parameter for fragmentation and the low rate of observed cases of the edge effect could be naturally explained by shallow gradients.