Study of the impact of filamentary structures on the properties of Galaxy Clusters from hydrodynamic simulations and multi-wavelength observations

At megaparsec scales, the large-scale structures we observe today in the Universe are arranged in a filamentary network, known as the Cosmic Web. This distribution of matter, composed of clusters, filaments, walls and underdense regions, originates from primordial random fluctuations of the initial density field, and evolves in a non- linear way to the present times. Within this framework, matter flows anisotropically from areas of lower density to higher density. In particular, the filaments play a central role in matter transportation toward the galaxy clusters’ centre, influencing their accretion and surrounding environment. The main goal of this thesis is to explore the connections between filaments and galaxy clusters’ properties, analysing the extensive dataset of The Three Hundred hydrodynamical simulations. In the first part, I reconstruct the Cosmic Web network from the simulated gas distribution, and analyse the correlation between galaxy clusters’ properties and their connectivity, defined as the number of filaments connected to the galaxy cluster. Specifically, I find that the connectivity is highly correlated with the cluster mass, with more massive clusters being, on average, more connected. Additionally, I find a mild dependence of the connectivity on the redshift, with connectivity decreasing over cosmic time. Finally, no significant dependence on the dynamical state of clusters is observed. In the second part of the thesis, I quantify the effects that may influence the reconstruction of the Cosmic Web from observational data. In this context, I use The Three Hundred simulated regions to study how projection and rotation influence the identification of filaments, and how the choice of the tracer, such as galaxies instead of gas, modifies the connectivity estimates. I further explore the impact of using different gas observables, reconstructing the network from Sunyaev-Zel’dovich effect maps, and quantifying the filaments’ contribution to the radial Compton-y profile in the outskirts of galaxy clusters. Lastly, I analyse the subset of 115 The Three Hundred clusters of the CHEX-MATE Matched Sample, identifying the filamentary structures in the local cluster environment both from mock Emission Measure maps and from mock instrumental X-ray maps that mimic a typical XMM-Newton observation. Overall, the analyses presented in the second part of this thesis provide a reference framework to interpret observational datasets of the Cosmic Web, allowing for the quantification of the impact of projection, tracer choice, and instrumental systematics on the recovery of filamentary structures and their connection to galaxy clusters. This thesis provides a comprehensive study of the role of filamentary structures in shaping galaxy clusters’ properties and of the main observational challenges in reconstructing the Cosmic Web. The results highlight the potential of combining hydrodynamical simulations and mock observations to interpret and optimise future observational analyses of the large-scale structures.