Temperature profiles of the hot galaxy cluster intracluster medium (ICM) have a complex non-linear structure that traditional parametric modelling may fail to fully approximate. For this study, we made use of neural networks, for the first time, to construct a data-driven non-parametric model of ICM temperature profiles. A new deconvolution algorithm was then introduced to uncover the true (3D) temperature profiles from the observed projected (2D) temperature profiles. An auto-encoder-inspired neural network was first trained by learning a non-linear interpolatory scheme to build the underlying model of 3D temperature profiles in the radial range of [0.02-2] R$_{500}$, using a sparse set of hydrodynamical simulations from the THREE HUNDRED PROJECT. A deconvolution algorithm using a learning-based regularisation scheme was then developed. The model was tested using high and low resolution input temperature profiles, such as those expected from simulations and observations, respectively. We find that the proposed deconvolution and deprojection algorithm is robust with respect to the quality of the data, the morphology of the cluster, and the deprojection scheme used. The algorithm can recover unbiased 3D radial temperature profiles with a precision of around 5\% over most of the fitting range. We apply the method to the first sample of temperature profiles obtained with XMM{\it -Newton} for the CHEX-MATE project and compared it to parametric deprojection and deconvolution techniques. Our work sets the stage for future studies that focus on the deconvolution of the thermal profiles (temperature, density, pressure) of the ICM and the dark matter profiles in galaxy clusters, using deep learning techniques in conjunction with X-ray, Sunyaev Zel'Dovich (SZ) and optical datasets.

The Fornax dwarf spheroidal galaxy (dSph) represents a challenge for some globular cluster (GC) formation models, because an exceptionally high fraction of its stellar mass is locked in its GC system. In order to shed light on our understanding of GC formation, we aim to constrain the amount of stellar mass that Fornax has lost via tidal interaction with the Milky Way (MW). Exploiting the flexibility of effective multi-component $N$-body simulations and relying on state-of-the-art estimates of Fornax's orbital parameters, we study the evolution of the mass distribution of the Fornax dSph in observationally justified orbits in the gravitational potential of the MW over 12 Gyr. We find that, though the dark-matter mass loss can be substantial, the fraction of stellar mass lost by Fornax to the MW is always negligible, even in the most eccentric orbit considered. We conclude that stellar-mass loss due to tidal stripping is not a plausible explanation for the unexpectedly high stellar mass of the GC system of the Fornax dSph and we discuss quantitatively the implications for GC formation scenarios.

We study the interplay between mass-loss and dynamical friction (DF) on the orbital decay of the Fornax dwarf spheroidal galaxy in the potential of the Milky Way (MW). Using a simplified single particle approach combined with a mass-loss rate extrapolated by $N-$body simulations we find that the the effect of a time-dependent mass partially compensates DF, and typically produces a much less evident decay of the pergalactic distance, thus confirming that $N-$body simulations in smooth MW potentials without DF can be taken as a good model of the dynamics of dwarf satellite galaxies.