Why do semi-analytic models predict higher scatter in the stellar mass-halo mass relation than cosmological hydrodynamic simulations?

Semi-analytic models (SAMs) systematically predict higher stellar-mass scatter at a given halo mass than hydrodynamical simulations and most empirical models. Our goal is to investigate the physical origin of this scatter by exploring modifications to the physics in the SAM Dark Sage. We design two black hole formation models that approximate results from the IllustrisTNG 300-1 hydrodynamical simulation. In the first model, we assign a fixed black hole mass of $10^{6}\, \mathrm{M}_{\odot}$ to every halo that reaches $10^{10.5}\, \mathrm{M}_{\odot}$. In the second model, we disregard any black hole growth as implemented in the standard Dark Sage model. Instead, we force all black hole masses to follow the median black hole mass-halo mass relation in IllustrisTNG 300-1 with a fixed scatter. We find that each model on its own does not significantly reduce the scatter in stellar mass. To do this, we replace the native Dark Sage AGN feedback model with a simple model where we turn off cooling for galaxies with black hole masses above $10^{8}\, \mathrm{M}_{\odot}$. With this additional modification, the SMBH seeding and fixed conditional distribution models find a significant reduction in the scatter in stellar mass at halo masses between $10^{11-14}\, \mathrm{M}_{\odot}$. These results suggest that AGN feedback in SAMs acts in a qualitatively different way than feedback implemented in cosmological simulations. Either or both may require substantial modification to match the empirically inferred scatter in the Stellar Mass Halo Mass Relation (SMHMR).