Searching for the Imprints of AGN Feedback on the Lyman Alpha Forest Around Luminous Red Galaxies

We explore the potential of using the low-redshift Lyman-$\alpha$ (Ly$\alpha$) forest surrounding luminous red galaxies (LRGs) as a tool to constrain active galactic nuclei (AGN) feedback models. Our analysis is based on snapshots from the Illustris and IllustrisTNG simulations at a redshift of $z=0.1$. These simulations offer an ideal platform for studying the influence of AGN feedback on the gas surrounding galaxies, as they share the same initial conditions and underlying code but incorporate different feedback prescriptions. Both simulations show significant impacts of feedback on the temperature and density of the gas around massive halos. Following our previous work, we adjusted the UV background in both simulations to align with the observed number density of Ly$\alpha$ lines ($\rm dN/dz$) in the intergalactic medium and study the Ly$\alpha$ forest around massive halos hosting LRGs, at impact parameters ($r_{\perp}$) ranging from 0.1 to 100 pMpc. Our findings reveal that $\rm dN/dz$, as a function of $r_{\perp}$, is approximately 1.5 to 2 times higher in IllustrisTNG compared to Illustris up to $r_{\perp}$ of $\sim 10$ pMpc. To further assess whether existing data can effectively discern these differences, we search for archival data containing spectra of background quasars probing foreground LRGs. Through a feasibility analysis based on this data, we demonstrate that ${\rm dN/dz} (r_{\perp})$ measurements can distinguish between feedback models of IllustrisTNG and Illustris with a precision exceeding 12$\sigma$. This underscores the potential of ${\rm dN/dz} (r_{\perp})$ measurements around LRGs as a valuable benchmark observation for discriminating between different feedback models.