Iván Muñoz Rodríguez1,2, Antonis Georgakakis1, Francesco Shankar2 et al. (submitted); e-mail:ivan.rodriguez@noa.gr 1National Observatory of Athens, 2University of Southampton Diﬀerenal evoluon of AGN in clusters Comparisson with observations: We calculate the fraction of X-ray AGN in a cluster parent sample deﬁned as in observations. We compare the results of the models with the observations of Matini et al. (2009, 2013). We select galaxies and AGN in the cluster sample following selection eﬀects as deﬁned in observations. Only galaxies/AGN within the virial radius, brighter than a magnitud limit and within a velocity dispersion are consider a members. The impact of selection eﬀects is illustrated in the ﬁgure on the left. The number of AGN represent the ﬁeld expectation by model construction. Results are shown in the ﬁgure on the right. The model underpredicts the number of AGN at z~1.2 respect the observations. At z~0.75 model prediction is consistent with observations. Finally, at low redshift, z~0.2, the model seems to overproduce AGN respect cluster observations, although ﬁrm conclusions cannot be made since observations only place a lower limit. References: Aird et al. (2018); Behroozi et al. (2019); Georgakakis et al. (2017, 2019); Klypin et al. (2016); Martini et al. (2009, 2013); Peluso et al. (2022) Motivation and semi-empirical model construction: The role of diﬀerent AGN triggering mechanisms remains as one of the open questions in Astrophysics. We studied the inﬂuence of small-scale environment (<1 Mpc) into the AGN triggering mechanism. We developed a novel semi-empirical model (SEM) to construct AGN mock catalogues based on state-of-the-art observations. A graphical workﬂow of this model is shown in the ﬁgure on the left. The starting point are dark matter N-body simulations (MDP2, Klypin et al. 2016), that are populated with galaxies using abundance matching techniques (UNIVERSEMACHINE, Behroozi et al. 2019). Then AGN are painted on this galaxies constrained by the latest observations of AGN populations. The latter step is done under the explicit assumption that accretion events are independent of the environment (i.e halo mass). The ﬁgure shows a 10 Mpc/h slice of a box from MDP2 cosmological simulation with 1000 Mpc/h side size at the snapshot z=0.75. The dots represent the positions of dark matter haloes (top panel), galaxies within these dark matter haloes (middle panel) and AGN within the same dark matter haloes (bottom panel). The key feature of this approach is the reproduction by construction of the predictions and observables (e.g. HMF, SMF and XLF). The key parameter to populate galaxies with AGNs is the speciﬁc accretion rate deﬁned as λ=Lx/M★. It is related with two observables that have been well characterized in the last years thanks to multi-wavelength observations in extragalactic survey ﬁelds. This has allowed to infer its probability distribution P(λ). It describes the probability of a galaxy with mass M★ of hosting an AGN with luminosity Lx. For each galaxy in the catalog we randomly pick a λ from the distribution. This eﬀectively associate an AGN X-ray luminosity to all galaxies. AGN incidence and physical interpretation: Field expectation cannot reproduce the observations. We ﬁnd a diﬀerential evolution of the incidence of AGN in clusters respect to ﬁeld. AGN activity is enhanced at high redshift and suppressed at low redshift in massive clusters respect to ﬁeld. This point to a diﬀerent eﬃciency of AGN triggering mechanisms depending on their small-scale environment (<1 Mpc) that evolves with cosmic time. This could be explained by the diﬀerent physical processes happening in clusters respect low dense environments such as ram-pressure or galaxy interactions. This eﬀects are expected to be stronger in the outskirts of the cluster. Galaxy-Halo connection UNIVERSEMACHINE (Behroozi et al. +19) AGN-Galaxy connection Count galaxies and AGN in the cluster sample Projection of a cluster into sk