Exploring the AGN population in protoclusters: results from the TNG300 simulation and comparison with observations

In this work, we investigate the physical properties and cosmic evolution of galaxies and AGN in a sample of 280 protoclusters identified in the TNG300 simulation, selected to end up in $z = 0$ clusters with $M_{200, \rm c} > 10^{14} \, {\rm M_{\odot}}$. Our goal is to provide the first statistical view of AGN activity enhancement in a uniformly defined sample of overdense environments, and to identify the physical mechanisms driving it. We identify protoclusters as the progenitors of present-day galaxy clusters through merger-tree reconstruction and compare their galaxy and AGN populations with a control sample of field galaxies across the redshift range $0 \leq z \leq 6$. We investigate galaxy and SMBH demographics, AGN fractions, bolometric luminosity functions, and the SMBH accretion rate density, consistently applying homogeneous selection criteria in all environments. We find that TNG300 protoclusters host systematically more massive galaxies and SMBHs than the field by up to $1 \, {\rm dex}$ at all redshifts, with signatures of accelerated galaxy evolution already visible at $z \sim 3-4$. The AGN fraction increases with stellar mass in both environments and, at fixed host-galaxy stellar mass, is broadly consistent between protoclusters and field galaxies, indicating no strong environmental triggering of SMBH accretion. However, when analysed as a function of redshift, protoclusters exhibit a significant enhancement of AGN activity (by a factor $> 2$), particularly at high luminosities and early cosmic times. We show that this enhancement primarily arises from differences in the stellar-mass distributions of galaxies in overdense regions, where massive systems assemble earlier than in the field. Consistently, protoclusters dominate the bright end of the AGN bolometric luminosity function and contribute up to $\sim 50\%$ of the total SMBH accretion rate density at $z \sim 6$.