The dSphs which surround the Milky Way are vital laboratories in which to test theories of galaxy formation. Not only are they are the lowest mass stellar systems known to contain dark matter but they also populate the faint end of the galaxy luminosity function. Over the past 15 years, several issues have been identified which appear to place cosmological galaxy formation simulations in tension with observations: (1) simulations which contain only dark matter over-predict the numbers of objects around a Milky Way-like galaxy by at least an order of magnitude (the “missing satellites” problem; Moore et al., 1998); (2) simulated haloes exhibit central density cusps in their dark matter profiles, while observations are often claimed to be more consistent with uniform density central cores (the “cusp-core problem); (3) simulations predict the existence of dark haloes whose masses should have allowed them to form stars but which are apparently missing from the census of observed galaxies (the “too big to fail problem”; Boylan-Kolchin et al., 2012). The resolution of all three issues requires knowledge of the masses of the dwarf satellites both at the present epoch and at the time of their formation.

Despite the availability of large observed data sets containing measured velocities for 1000s of stars in several of the brighter Milky Way satellites, previous analyses of their mass distributions have made many simplifying assumptions. In particular, most models assume that the dwarf galaxy is in dynamical equilibrium and isolated from external perturbations. For small Milky Way satellite galaxies, both these assumptions are of questionable validity. N-body simulations provide a natural way to relax these assumptions and explore the impact of the Milky Way on the evolution of a dwarf galaxy. We have combined a Markov-Chain-Monte-Carlo algorithm with an N-body simulation code to explore the parameter space of models of the Carina dwarf galaxy using 20,000 medium-resolution simulations.

We identified the Carina dSph as an interesting target for this initial study due to the large amount of available kinematic data and the fact that there were already hints that its outer regions are being disturbed by the Milky Way (e.g. Muñoz et al., 2006). Our algorithm was able to constrain the present-day mass of Carina to be (7±3)×10⁷ solar masses. More interestingly, we were also able to constrain Carina’s mass at the time it first fell into the Milky Way to be 3.9 (−2.4;+3.9)×10⁸ solar masses. Our mass estimate is significantly lower than the halo mass generally associated with dSphs of comparable luminosity to Carina. In Ural et al. (2015), we suggested that this may be evidence that galaxy formation becomes stochastic in low-mass haloes.

The calculations for this project consumed approximately 1M core hours on the Complexity cluster of DiRAC-2, as a very significant number of simulations were required to verify the efficacy of the method using artificial data sets before it could be applied to the observed data with confidence. By using the Complexity cluster we were able to run multiple MCMC chains in parallel which greatly reduced the overall time required to complete the project. The work is reported in Ural, Wilkinson, Read & Walker, 2015 (Nature Communications, 6, 7599).