Evolution of the radial density profile of the core from the linear growth phase until the start of the collapse for a line-mass of f_cyl = 0.25. Shown are snapshots before the first threshold in light blue, between the first and second threshold in blue, and just after the second threshold in dark blue. The density and the radius are normalised to a dimensionless form to compare profiles with different concentrations. The filament profile as defined in Eq. (5) is given as a dotted line and the Bonnor-Ebert sphere profile as a dashed line.