Inference of Dark Matter Density Profiles of Dwarf Spheroidal Galaxies via Distribution Functions

Abstract

Dark matter consist of about 25% of our universe, yet the nature of the dark matter is still unknown. Our current understanding of the cosmology is presented in the theory of?CDM. The theory predicts a cold dark matter (CDM). It is very successful at explaining large-scale structures in the distribution of galaxies and of the cosmic microwave background. However, at small-scale there are controversies. One persistent controversy regards the darkmatter density profi?le at the center of the dwarf galaxy. The theory of CDM predicts a steep profi?le that diverges as r-1, while the observations tend to suggest a flatter pro?file.The resolution of this controversy could provide a milestone in our understanding of the nature of dark matter. This work is intended to contribute to that eff?ort by studyingthe dark matter density profi?les of the dwarf spheroidal galaxies (dSph). Dwarf satellite galaxies around Milky Way are some of the most dark matter dominated system we know, and without active star formation they are excellent laboratories to resolve this dichotomy. This thesis presents new methodology that analyzes data with foreground contamination to create the ?first fully consistent inferences of dSph mass density pro?file. We analyze Fornaxand Sculptor dSph as the fi?rst applications. Direct Bayesian inference is made with the kinematic data of each galaxy, using both Osipkov-Merritt and Strigari Frenk and White(SFW) stellar distribution functions. The result shows that Fornax has enough data to constrain the dark matter central density profi?le. It also shows that depending on theconsistency of modeling foreground contaminants, totally opposite results in central density profi?le can be obtained. That shows the importance and the need for consistent treatment of foreground contaminants in future analysis. For the cases where likelihood calculation becomes intractable, kernel density estimation is applied to sample points to approximate the underlying density. Test inferences show that the approximation can reliably recover dark matter density profi?les. Machine learning methods are also applied to address this challenge. Mixture Density Network (MDN) shows great promise, although improvement in training is needed to narrow down the prediction uncertainty.