Indirect searches of dark matter and the galactic center at very high energy with H.E.S.S.

H.E.S.S. (High Energy Stereoscopic System) is an array of four identical imaging atmospheric Cherenkov telescopes, designed to observe very high energy gamma-rays (E > 100 GeV). The observation of such gamma-rays plays a crucial role in the understanding of extreme non-thermal phenomena in the Universe. These gamma-rays can be used for instance to search for annihilations of dark matter particles in dense environments of the Universe. This thesis presents a series of data analysis and phenomenological studies on two main subject of the gamma-ray astronomy: the indirect searches of dark matter, and the study of the Galactic Center region. The indirect dark matter searches focus on the study of two classes of targets: dwarf galaxies and galaxy clusters. A detailed study of the H.E.S.S. observations towards the Sculptor and Carina dwarf galaxies, and towards the Fornax galaxy cluster are presented. In the absence of a significant signal coming from these object, constraints on the annihilation cross section of dark matter particle candidates are derived. Particular consideration is given to different processes from particle physics and astrophysics which might give rise to additional contributions to the signal expected from a dark matter particle annihilation, such as the Sommerfeld effect and dark matter halo substructures. The current H.E.S.S. dark matter constraints towards the Sagittarius are updated in light of recent realistic dark matter halo models. A prospect on the sensitivity of the future generation of Cherenkov telescopes, i.e. CTA (Cherenkov Telescope Array), for the detection of a dark matter annihilation signal and conventional gamma-ray emissions are also given. The second subject of this thesis provides a detailed analysis of the VHE gamma-ray data from the Galactic Center region observed by H.E.S.S. This was possible thanks to the deep exposure of this region, achieved by the H.E.S.S. experiment throughout the 2004-2011 period. The analysis and spectral reconstruction of the central source and the diffuse emission around this region are presented. A spectral subtraction of the diffuse emission contribution to the HESS J1745-290 spectral is performed and allows to recover the intrinsic central source spectrum. The spectral morphology of the diffuse emission region suggests the possibility of various accelerators being responsible for the observed emission.