Impact of filaments on galaxy cluster properties in The Three Hundred simulation

Galaxy clusters and their filamentary outskirts reveal useful laboratories to test cosmological models and investigate Universe composition and evolution. Their environment, in particular the filaments of the Cosmic Web to which they are connected, plays an important role in shaping the properties of galaxy clusters. In this project, we analyse the gas filamentary structures present in 324 regions of The Three Hundred hydrodynamical simulation extracted with the DisPerSE filament finder. We estimate the number of gas filaments globally connected to several galaxy clusters, i.e. the connectivity k, with a mass range of $10^{13} \leq M_{200} \, h^{-1} \, M_{\odot} \leq 10^{15} $ at redshift $z=0$. We study the positive correlation between the connectivity and mass of galaxy clusters. Moreover, we explore the impact of filaments on the dynamical state of clusters, quantified by the degree of relaxation parameter $\chi$.