Triggering and quenching in the shadow of AGN: How does AGN proximity affect star formation in the EAGLE simulation?

Active galactic nuclei (AGN) are among the most energetic phenomena in the universe, capable of regulating star formation in galaxies via radiative and mechanical feedback. While AGN feedback is well studied in host galaxies, its influence on neighbouring galaxies within the same large-scale environment remains less understood. In this work, we use the EAGLE cosmological hydrodynamical simulation to examine how proximity to AGN affects star formation in nearby star-forming galaxies (SFGs) out to 2 Mpc. A control sample matched in stellar mass and local density allows us to isolate AGN-driven environmental effects, quantified through the $Δ$SFR offset defined as the difference between a galaxy's star formation rate (SFR) and that of its matched controls. We find a significant and mass-dependent impact where $61\%$ of AGN-adjacent SFGs show suppressed star formation, while $39\%$ exhibit enhancement. Although the overall magnitude of these offsets is modest, the trends are statistically robust and consistent across the population. Suppression is prevalent in massive, gas-poor galaxies in high-mass halos, consistent with thermal feedback inhibiting gas cooling. Enhanced SFRs appear in low-mass, gas-rich galaxies, suggesting AGN-driven compression may locally trigger star formation. These trends emerge despite EAGLE implementing AGN feedback as a single-mode, stochastic thermal process, indicating that such models can reproduce both quenching and triggering regimes. Our findings demonstrate that AGN feedback extends well beyond host galaxies, impacting neighbouring systems in a non-uniform, distance-, mass-, and gas-dependent manner. This non-local AGN influence represents a critical, yet often overlooked, mechanism in shaping galaxy evolution within large-scale structures, bridging high-energy astrophysical processes and cosmic-scale environmental regulation.