SAGAN-VI: When Jets Meet Filaments -- Environmental Imprints on the Growth of Giant Radio Galaxies

Giant radio galaxies (GRGs) represent the largest individual astrophysical structures, rivalling galaxy clusters in physical extent. Understanding how they attain such scales demands examining their large scale cosmic surroundings, particularly the under explored filament environment. We quantify the three dimensional (3D) distance of GRGs from the nearest filament spine; test how this distance correlates with their growth and formation of different morphological classes; assess whether their radio jets exhibit preferred orientations relative to filament axes; and examine how filament anisotropy from spine to periphery modulates radio morphology. We employed a filament catalogue from the SDSS together with the largest GRG catalogue currently available. For each source, we measured the comoving distance to the nearest filament spine, the projected jet spine orientation angle, and quantified lobe asymmetry via the arm length ratio (ALR). These metrics trace proximity, directionality, and the impact of filamentary environment on morphology. We then compared GRGs with a control sample of small radio galaxies (SRGs) to constrain the environmental factors that regulate the attainment of giant sizes. We validated the robustness of our results via bootstrap resampling and non parametric statistical tests. Our results show that GRGs and SRGs have similar filament occupancy. By contrast, GRGs preferentially display larger alignment angles relative to filament spines, while SRG orientations are consistent with a random distribution. GRGs further show enhanced morphological asymmetry, reflected in lower ALR values than SRGs. Attainment of giant sizes is not governed by proximity to filaments; rather, it correlates with jet filament alignment. Abridged.