Search and analysis of giant radio galaxies with associated nuclei (SAGAN) IV. Interplay with the Supercluster environment

We investigated the prevalence of giant radio galaxies (GRGs), some of the largest structures powered by supermassive black holes, within supercluster environments, and the influence of such environments on their properties. Utilising two large catalogues of superclusters (401) and GRGs (1446), we established the existence of 77 GRGs (5.3%) residing in 64 superclusters (16%) within $\rm 0.05 \leq z \leq 0.42$. Among the 77 GRGs found in superclusters, we identified $\sim$70% as residing within galaxy clusters. Within the subset of GRGs not located in superclusters, which constitutes 94.7% of the sample, a mere 21% are associated with galaxy clusters, while the remaining majority are situated in sparser environments. We examined the influence of differing environments, such as cluster versus non-cluster and supercluster versus non-supercluster regions, on the size of GRGs, while also exploring the driving factors behind their overall growth. Our findings show that the largest GRGs ($\gtrsim$3 Mpc) grow in underdense environments beyond the confines of dense environments. Moreover, we show that $\sim$ 24% of 1446 GRGs reside in galaxy clusters. We conclude that GRGs preferentially grow in sparser regions of the cosmic web and have a significantly larger median size. Finally, we demonstrate the potential of GRGs as astrophysical probes with specific cases where GRGs, exhibiting polarised emissions and located behind superclusters (acting as natural Faraday screens), were used to estimate magnetic field strengths of the supercluster environment at sub-microgauss levels.