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We summarize a series of numerical experiments of collisional dynamics in dense stellar systems such as globular clusters (GCs) and in weakly collisional plasmas using a novel simulation technique, the so-calledMulti-particle collision (MPC) method, alternative to Fokker-Planck and Monte Carlo approaches. MPC is related to particle-mesh approaches for the computation of self consistent long-range fields, ensuring that simulation time scales with N log N in the number of particles, as opposed to N2 for direct N-body. The collisional relaxation effects are modelled by computing particle interactions based on a collision operator approach that ensures rigorous conservation of energy and momenta and depends only on particles velocities and cell-based integrated quantities.
Understanding the peculiar properties of Ultra Diffuse Galaxies (UDGs) via spectroscopic analysis is a challenging task that is now becoming feasible. The advent of 10m-class telescopes and high sensitivity instruments is enabling the gathering of high quality spectra even for the faintest systems. In addition, advances in the modelling of stellar populations, stellar libraries, and full-spectral fitting codes are allowing the recovery of the stellar content shaping those spectra with unprecedented reliability. In this contribution we report on the extensive tests we have carried out using the inversion code STECKMAP. The similarities between the Star Formation Histories (SFH) recovered from STECKMAP (applied to high-quality spectra) and deep Colour-Magnitude diagrams fitting (resolved stars) in two Local Group dwarf galaxies (LMC and LeoA) are remarkable, demonstrating the impressive performance of STECKMAP. We exploit the capabilities of STECKMAP and perform one of the most complete and reliable characterisations of the stellar component of UDGs to date using deep spectroscopic data. We measure radial and rotation velocities, SFHs and mean population parameters, such as ages and metallicities, for a sample of five UDG candidates in the Coma cluster. From the radial velocities, we confirm the Coma membership of these galaxies. We find that their rotation properties, if detected at all, are compatible with dwarf-like galaxies. The SFHs of the UDG are dominated by old (∼ 7 Gyr), metal-poor ([M/H] ∼ -1.1) and alpha-enhanced ([Mg/Fe]∼ 0.4) populations followed by a smooth or episodic decline which halted ∼ 2 Gyr ago, possibly a sign of cluster-induced quenching. We find no obvious correlation between individual SFH shapes and any UDG morphological properties. The recovered stellar properties for UDGs are similar to those found for DDO 44, a local UDG analogue resolved into stars. We conclude that the UDGs in our sample are extended dwarfs whose properties are likely the outcome of both internal processes, such as bursty SFHs and/or high-spin haloes, as well as environmental effects within the Coma cluster.
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