Connecting AGN feedback in galaxy formation simulations to recent and upcoming multi-wavelength observations

Massive black holes (MBHs) play a crucial role in galaxy formation simulations, significantly impacting surrounding gas and reducing star formation through feedback effects. While cosmological galaxy formation models are effective at quenching massive galaxies and suppressing cooling flows, the detailed mechanisms of active galactic nucleus (AGN) feedback remain uncertain. This talk outlines new progress in linking AGN feedback - via jets and winds - to observed multi-wavelength signatures. Using cosmological and isolated cluster simulations with jet feedback, I will show how AGN jets influence cluster thermodynamics and turbulence as measured using X-ray data from XRISM, and discuss modelling radio emissions with a Fokker-Planck solver for non-thermal electrons to compare spectral aging and multifrequency observations, in particular low-frequency LOFAR data. Additionally, I'll share initial findings on connecting AGN activity to warm ionized and neutral gas phases traced by H-alpha, [OIII] emission and NaID absorption, and compare to recent JWST NIRSpec results.