Galaxy transformation across the cosmic web: The influence zone of filaments

The matter distribution in the Universe exhibits a rich variety of structures forming the cosmic web. These structures arise from the anisotropic gravitational collapse of primordial density fluctuations and define the pathways along which galaxies flow from voids to high-density clusters. Local density variations within these structures play a fundamental role in driving the environmental evolution of galaxies. To characterise filament boundaries, we analysed galaxy overdensity profiles around filaments in two redshift ranges: $0.05 < z < 0.1$ and $0.1 < z < 0.3$. Perpendicular and parallel profiles were derived by averaging galaxy overdensity as a function of distance. Characteristic scales and central overdensities were then analysed by fitting analytical models, specifically exponential and power-law families. We also introduced normalised density profiles to account for survey incompleteness. The perpendicular overdensity profiles show a nearly constant value in the central regions $D_{fila} < 1$ Mpc, decreasing at distances up to $\approx 10$ Mpc. The mean physical widths (scale radii) at $0.05 < z < 0.1$ and $0.1 < z < 0.3$ are $2.39 \pm 0.69$ and $5.56 \pm 2.29$ Mpc, respectively. This scale difference between redshift ranges is also evident in the normalised profiles. Conversely, profiles along filaments remain constant at distances larger than $\approx 20$ Mpc from the nearest intersection. Our results show that the influence zone of cosmic filaments extends up to $\sim 10$ Mpc from their spines. Furthermore, a mild evolution in structural parameters is observed over the past $\sim 4$ Gyr, suggesting that filaments undergo measurable changes even at relatively low redshifts.