Abstract
The purpose of this thesis is to discuss both phenomenological and experimental aspects of Dark Matter, related to its indirect detection with gamma-ray astronomy. In the MSSM framework, neutralinos arise as natural candidates to non-baryonic and Cold Dark Matter, whose gravitational effects manifest in the Universe at different scales. As they are Majorana particles, they may in principle annihilate in hign density regions, as the centres of galaxies, and produce gamma rays. Nevertheless, the expected fluxes are basically low compared to experimental sensitivities. After estimating gamma fluxes from M31 and Draco galaxies in the MSSM scheme, we first generalize the MSSM couplings by studying an effective Lagrangian. We show that the only constraint of imposing a relic abundance compatible with recent measurements obviously deplete significantly the gamma ray production, but also that predictions in this effective approach are more optimistic for indirect detection than the MSSM. In a second part, we present the indirect searches for Dark Matter performed with the CELESTE Cherenkov telescope towards the galaxy M31. We propose a statistical method to reconstruct spectra, mandatory to discriminate classical and exotic spectra. The M31 data analysis enables the extraction of an upper limit on the gamma ray flux, which is the first worldwide for a galaxy in the energy range 50-500 GeV, and whose astrophysical interest goes beyond indirect searches for Dark Matter.