Orford, Nicola Diane2015-05-062015-05-062015-05-06http://hdl.handle.net/10539/17651A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of requirements for the degree of Master of Science. Johannesburg, February 6, 2015.We explore indirect detections of Dark Matter, focusing on deep radio observations of six dwarf spheroidal galaxies (dSph), Carina, Fornax, BootesII, Hercules, Segue2, Sculptor. We discuss the WIMP Dark Matter particle annihilation process and describe brie y the particles produced in this process. We consider the emissions, which can result from electrons and positrons produced. We describe why dSph are the best observational targets for indirect Dark Matter detection at radio frequencies. We describe the theoretical framework for predicting Dark Matter synchrotron emissions and make some predictions for the six dSph of interest to us. We discuss ATCA observations of these dSph and explore the background source subtraction process in detail. We obtain an upper limit on the WIMP mass and compare our results to various other experiments. We discuss prospects for this work towards attaining an indirect Dark Matter detection.enDark matter.Dwarf galaxies.Radio frequency.Thesis