Exploring the impact of AGN feedback model variations on the Lyman-$\alpha$ Forest Flux Power Spectrum

We study the effects of varying different Active Galactic Nuclei (AGN) feedback parameters on the Lyman-$\alpha$ (Ly$\alpha$) forest 1D transmitted flux power spectrum (P1D). We use the Cosmological and Astrophysics with Machine Learning Simulations (CAMELS) suite to explore variations on the Simba simulation AGN feedback model. The parameters explored include AGN momentum flux, AGN jet speed, supermassive black hole (SMBH) radiative efficiency, jet velocity threshold, and minimum SMBH mass needed to produce jet feedback. Although all parameters affect the P1D, this work explores the radiative efficiency, jet velocity threshold, and minimum SMBH mass in this context for the first time and finds the following results: Primarily, the most massive SMBHs impact the Ly$\alpha$ forest through the jet feedback mode. While heating AGN jets to the virial temperature at injection aids in the removal of neutral hydrogen from the Ly$\alpha$ forest, this heating also inhibits further jet feedback. Similar behaviors are seen when varying the SMBH radiative efficiency, with higher values resulting in a suppression of SMBH growth and thus a later reduction in AGN feedback and lower values directly reducing the impact of AGN feedback on the Ly$\alpha$ forest P1D. These results imply that increasing the AGN feedback strength in the Simba simulation model suppresses the Ly$\alpha$ forest P1D, but only if the feedback does not impact the number of massive jet producing BHs. Future studies of AGN feedback models will require careful exploration of the unique aspects of the specific subgrid model, and how they interact with one another, for a complete understanding of the potential astrophysical impacts of SMBH feedback.