Top panel: radial profiles of the mean over-densities (Eq. (3)) of DM (solid lines with triangles), gas (dotted lines with circles), and stars (dash-dotted lines with crosses) for short and long filaments, respectively in orange and blue. The pink, green, and cyan lines denote respectively the fitting results of the DM, gas, and stellar profiles to the generalised β-model of Eq. (5) in the r < 3 Mpc range. Bottom panel: impact of the resolution of the simulation. The black curves correspond to the profiles obtained with the reference TNG300-1 simulation (same profiles as in Fig. 3a). Pink and green curves present respectively the results from the TNG300-2 (low resolution) and TNG100-1 (high resolution) boxes.