Roles of SN and AGN Feedback in Shaping the Baryonic Content in a Wide Range of Dark Matter Halo Mass

We build upon FEGA25 (Contini et al 2025), a previously introduced semi-analytic model for galaxy formation and evolution, focusing on its enhanced treatment of supernova and active galactic nucleus feedback mechanisms. In addition to the traditional AGN feedback modes, negative (suppressing cooling), and the new positive mode (triggering star formation), we introduce two implementations of a third mode: the ejection of hot gas beyond the virial radius, AGNeject1 and AGNeject2. This component addresses a longstanding issue in semi-analytic models and hydrodynamical simulations: the overestimation of hot gas fractions in low and intermediate mass halos. FEGA25 is calibrated via MCMC using a suite of cosmological N-body simulations YS50HR, YS200, and YS300, and a comprehensive set of observed stellar mass functions across a wide redshift range. We find that supernova feedback dominates gas ejection in halos with logM₇₀₋₎ < approximately 12, while AGN feedback becomes increasingly important at higher halo masses. The AGNeject2 model, which activates primarily at late times, redshift < 1, reproduces a characteristic cavity, a U shaped feature in the baryon fraction at redshift zero, similar to trends observed in simulations like SIMBA and IllustrisTNG. Conversely, AGNeject1 yields a smoother, redshift independent evolution. Both models preserve the stellar and cold gas components and successfully reproduce the stellar to halo mass relation up to redshift 3. Our results emphasize that a physically motivated AGN driven mechanism capable of selectively removing hot gas is essential to accurately model the baryon cycle, particularly in intermediate halo mass regimes.