X-ray Clusters in Conformal Gravity

We present Conformal Gravity (CG) which is an alternative theory for Standard Gravity where no Dark Matter need to be added a posteriori. The differences between Standard Gravity and CG and its main implications for large-scale structures are pointed out. As a main point, explicit calculation for the potential of the extended sphere is performed. Then, we provide an overview of the main properties of galaxy clusters such as the $\beta$-model for the Intracluster Medium (ICM) distribution and the thermal processes which occur in clusters. We also explain how the cluster has been modeled for the numerical simulations. The GADGET code used for these simulations is based on the Smoothed Particle Hydrodynamics (SPH) formalism, which depends on the kernel function. We focus on how this function enables the calculation of the physical observables within the cluster. In order to consider CG terms, the code had to be modified to be used as a N-body integrator. Simulation outcomes point out the major problems for large-structure formation within CG which concerns cluster thermodynamics. Finally, the additional inmprovements included into the code are presented: we first study the effect of the CG extra terms, namely the quadratic term in $r$; and then we explain how we can add cooling and heating processes. We show the results obtained and discuss whether the increasing temperature profile can be corrected or not.