Understanding the mechanisms—AGN and stellar feedback—that drive the expulsion and redistribution of baryons in collapsed structures remains a cornerstone of our paradigm for galaxy formation and evolution. These processes are simultaneously the greatest strength and the most significant challenge for theoretical models. While current models can successfully reproduce key observables, such as the evolution of the galaxy stellar mass function and the hot gas content of massive clusters, they diverge considerably in their predictions for:

 

• The amount and distribution of baryons in low-mass halos.

• The mass, temperature, and metal gradients of the circum-galactic medium (CGM) surrounding central galaxies.

• The ability to balance feedback mechanisms such that they effectively evacuate gas from low-mass halos to match observed gas fractions while avoiding over-quenching the bulk of the galaxy population.

• The regulation of star formation activity and evolution of central and satellite galaxies from clusters to low mass groups

 

Different feedback implementations lead to strikingly divergent outcomes, and observational uncertainties persist regarding when, where, and how much energy is deposited into different environments. Constraining the AGN feedback–gas interplay across all scales is therefore critical not only for advancing our understanding of galaxy evolution but also for accurately modelling the formation and evolution of large-scale structures in the Universe.

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At high redshifts, particularly beyond z >1.5, we observe a stormy CGM around central galaxies in bright clusters, characterized by filaments, multi-temperature, and multiphase gas. This environment, often associated with accretion from surrounding filaments and mergers with substructures, plays a crucial role in the feedback mechanisms that shape both the cluster core and the evolution of the central galaxy. In this context, the interplay between AGN feedback, gas inflow, and the resulting star formation activity becomes more complex. In some distant clusters, widespread star formation is observed deep into the cluster core, in stark contrast to the suppression seen in clusters at lower redshifts. However, in other cases, we also find signs of significant star formation suppression in the central regions, suggesting a diversity of early cluster environments and evolutionary paths.

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The study of low-mass halos and galaxy groups introduces another layer of complexity. While in massive clusters, feedback primarily impacts the cluster core and the fate of the central galaxy, in low-mass halos, the situation is quite different. In these systems, the energy injected by AGN feedback can be comparable to the binding energy of the halo itself, potentially leading to the complete removal of the gas from the system. Depending on the implementation of feedback in state-of-the-art hydrodynamical simulations, predictions for the hot gas content in low-mass halos vary significantly. Some simulations predict halos that are entirely devoid of gas, while others generate groups that are overly X-ray bright. This disparity underscores the critical importance of constraining the hot gas content in galaxy groups as a means of testing and refining feedback models.

 

This workshop will review the latest observational results, focusing on X-ray and SZ data that probe the hot phase of the elusive intra-group and CGM in low-mass halos. With its exceptional sensitivity in the soft X-ray band, eROSITA has proven to be an excellent "filament and group-finding machine," delivering groundbreaking insights. Complementary efforts, such as upcoming deep XMM surveys of local groups and stacking analyses of existing SZ datasets, are poised to further enhance our understanding of hot gas in the virialized and circum-galactic regions of these systems, while we wait for Athena.

 

The workshop will also highlight the multiphase nature of the CGM and the critical role of the central galaxy, leveraging the latest data from integral field unit (IFU) spectrographs (e.g., ESO/MUSE, ESO/KMOS, KCWI), UV spectrographs (e.g., HST/COS), JWST, and submillimeter and radio observations (e.g., ALMA, LOFAR). These datasets allow us to study the interconnection between the CGM, halo gas on larger scales, and AGN-driven outflows and galactic components on smaller scales.

 

The feedback mechanisms, including AGN and stellar processes, must be considered across a broad range of scales—spanning not only the ~100 kpc around the galaxy in its CGM, but also the entire halo gas, extending up to the virial region in low-mass halos. By synthesizing these new observational results and comparing them with theoretical predictions, the MMC workshop will provide a comprehensive picture of the interplay between feedback, baryons, and the evolution of the central galaxy within the virialized dark matter halo population, with a particular focus on the feedback processes in low-mass halos and their impact on gas content and star formation.