The Formation of Faint and Ultra-Faint dwarf spheroidal galaxies: Modeling the formation of Ursa Major II using AMUSE

Faint and Ultra-Faint dwarf spheroidal (UFD) galaxies have generated significant scientific interest due to their extremely faint luminosities (L < 10^{5} L_{☉}), large dark matter (DM) content (≥ 100 M_{☉}/L_{☉}), and old stellar populations (≥ 10 Gyr). In this project, we model the UFD galaxy Ursa Major II (UMa II) by performing numerical simulations using the AMUSE framework and the direct N-body integrator ph4 to study a new formation model for UFDs: the dissolving star cluster scenario. We consider 4000 stars with virial equilibrium velocities and equal masses (M_{*} = 1 M_{☉}), representing the total luminosity of UMa II. The stars are randomly placed in a fractal distribution within the central part of a DM halo modeled with both analytical Plummer and NFW potentials, building up the luminous component of the simulated galaxy. We find that the size of the resulting UFD galaxy at 2 Gyr depends mainly on the scale-length of the analytical DM halo and only marginally on the initial size of the fractal. In essence, this implies that by measuring the half-light radius of the UFD, we can deduce the scale-length of the DM distribution.