Detecting Preheating in Protoclusters with Ly? Forest Tomography

Studies of low redshift galaxy clusters suggest the intra-cluster medium (ICM) has experienced non-gravitational heating during formation phase clusters. Using simple phenomenological prescriptions, we simulate effect this preheating nascent ICM in proto-clusters and examine its on Lyman-$\alpha$ (Ly$\alpha$) forest tomographic maps. We analyse a series cosmological zoom-in simulations within framework Ly$\alpha$ transmission-dark matter (DM) density distribution. find that more energy is injected into proto-ICM at $z$ = 3, distribution high DM tilts towards higher transmission. This been confirmed both low-resolution adopting scheme based entropy floors, as well higher-resolution with another floors. The evolution slope shown to vary redshift. methodology developed here can be applied current upcoming survey data help constrain feedback models proto-clusters.