Dwarf Spheroidal galaxies (dSphs) are the nearest and the most dark matter dominated galaxies in the Universe. In this thesis, we study their kinematics and dynamics using Monte Carlo methods. First, we study the kinematics of stellar subpopulations in dwarf spheroidal galaxies and present a robust Monte Carlo based method for interpretation of the sub-population data in dSphs. We apply the mehod to new spectroscopic data for twenty six stars in the recently-discovered Canes Venatici I (CVn I) dSph, obtained with the GMOS-N spectroscope on the Gemini North telescope. We use these data to investigate the recent claim of the presence of two dynamically different stellar populations in this system (Ibata et al., 2006).\ud While we find no evidence for kinematically distinct sub-populations in our sample, we also show that the available kinematic data sets in CVn I might be too small to draw robust conclusions about its sub-populations. Second, we introduce a Markov Chain Monte Carlo based method for studying the dynamics of dSphs. We perform a large number of N-body simulations of the Carina dSph, modelling it with different dark matter halo profiles in the presence of tidal interactions. We show that due to the uncertainties in the data, it is possible to find several good models that can match Carina’s observed data. We show the differences in the mass, density, compactness and orbital eccentricities that result from different split power halo profiles, as well as mass follows light models. Finally, using high resolution re-simulations of some of our best models, we show the robustness of our results and perform a more detailed analysis of the models, looking at their mass evolution, and general tidal signatures that should be looked for in future observations
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