Search

This thesis concerns the use of Gaussian-process mulation (Sacks et al., 1989) to build metamodels of computationally expensive dynamical models of dwarf spheriodal galaxies. These metamodels are computationally cheaper to evaluate than the models that they emulate, and hence have the potential to render tractable previously intractable problems in galactic dynamics. The first part of the thesis deals with the theoretical foundations of Gaussian-process emulation (GPE) while the second part deals with the application of GPE to the modelling of dwarf spheroidal galaxies. I give a description of the general principles of modelling and metamodelling, formally defining a physical model, and showing that the parameter spaces of such models may be made metric or pseudometric spaces. I give a formal treatment of the foundations of GPE and, building on the work of Parzen (1959), give a novel derivation of the GPE predictor and mean-squared error. I also set right some confusion and errors in the literature. In particular, I show that the GPE predictor presented by Rasmussen and Williams (2006) is biased. I quantify this bias, and discuss the circumstances under which it will be significant. In modelling dwarf spheroidal galaxies, I adopt the distribution-function approach, and use GPE to construct a metamodel of the log-likelihood. First, I construct a toy model of a dwarf spheroidal galaxy which I fit using synthetic data drawn from the same toy model. I maximize the log-likelihood using the method of efficient global optimization (Jones et al., 1998), finding that I am able to recover robust confidence regions for the parameter vector, galactic density, and velocity anisotropy with fewer than 100 model evaluations. Second, I construct a more general model. Although the resulting predictions are accurate, the metamodel fails validation, indicating that we may not trust the confidence regions associated with these predictions. We conclude that the usual simplifications made in implementing GPE render it inadequate for the task of predicting the log-likelihood in this case, and that we must consider more general methods.

Understanding the distribution of dark matter (DM) on galactic scales is at the root of constraining the nature of DM and processes of galaxy formation like baryonic feedback. Dwarf spheroidal galaxies (dSphs), lying at the faintest end of the galaxy luminosity function, are the most DM dominated systems known to date. They are a promising candidates to probe the DM distribution on kpc scales. In this work, we study the tidal evolution, abundance and observable properties of dSphs embedded in DM subhaloes. Tidal evolution of subhaloes and dwarf galaxies We run controlled simulations of the tidal evolution of a single cold dark matter subhalo with a centrally-divergent density cusp, tailored to follow the evolution of the subhalo for arbitrarily large fractions of tidally stripped mass. Based on simple dynamical arguments and numerical experiments, we argue that cuspy DM subhaloes cannot be completely disrupted by smooth tidal fields. Using a model of the Tucana III dSph galaxy as an example, we show that tides can strip dSph galaxies down to sub-solar luminosities. The remnant micro-galaxies would appear as co-moving groups of metal-poor, low-mass stars of similar age, embedded in sub-kpc DM subhaloes. Subhalo depletion driven by the galactic disc To further quantify the abundance of subhaloes in Milky Way-like galaxies containing a galactic disc, we use high-resolution re-simulations of all subhaloes of the Aquarius A2 merger tree with masses M > 10^8 Msol at accretion. We model the tidal evolution of subhaloes with both cuspy and cored DM profiles, finding that cuspy models have twice as many surviving subhaloes within the virial radius of the host at redshift z=0 as their cored counterparts. The presence of a galactic disc reduces the number of surviving subhaloes further by a factor of < 2 for subhaloes on orbits that pass through the disc. Mass estimates for Milky Way dwarf galaxies With the aim of comparing observed properties of Milky Way dSph galaxies to simulations, we construct an estimator for enclosed masses based on the virial theorem, insensitive to anisotropy in the velocity dispersion and tailored to yield masses with minimum uncertainty introduced by our ignorance on (i) the shape of the inner DM profile, and (ii) how deeply the stellar component is embedded within the subhalo. Tests against controlled simulations show that the estimator provides unbiased masses with an accuracy of ~10 per cent. Application to published kinematic data of Milky Way dSph galaxies reveals a tight correlation between enclosed mass and luminosity. Comparison against cuspy and cored DM haloes extracted from controlled cosmological simulations shows that the high mass densities of ultrafaint galaxies are not compatible with large DM cores, and that the (total) halo masses of the classical Milky Way dSph galaxies span a remarkably narrow range (8 < log10 M/Msol < 10) at present, showing no clear trend with either galaxy size or luminosity.