$\eta$ Carinae Detection and Characterisation of the First Colliding-Wind Binary in Very-High-Energy $\gamma$-rays with H.E.S.S.

The exceptional binary star Eta Carinae has been fascinating scientists and the people in the Southern hemisphere alike for hundreds of years. It survived an enormous outbreak, comparable to a supernova energy-wise, and for a short period became the brightest star of the night sky. From observations from the radio regime to X-rays the system's characteristics and its emission in photon energies up to ~ 50 keV are well studied today. The binary is composed of two massive stars of ~ 30 and ~ 100 solar masses. Either star drives a strong stellar wind that continuously carries away a fraction of its mass. The collision of these winds leads to a shock on each side of the encounter. In the wind-wind-collision region plasma gets heated when it is overrun by the shocks. Part of the emission seen in X-rays can be attributed to this plasma. Above ~ 50 keV the emission is no longer of thermal origin: the required plasma temperature exceeds the available mechanical energy input of the stellar winds. In contrast to its observational history in thermal energies observational evidence of Eta Carinae's non-thermal emission has only recently built up. In high-energy gamma-rays Eta Carinae is the only binary of its kind that has been detected unambiguously. Its energy spectrum reaches up to ~ hundred GeV, a regime where satellite-based gamma-ray experiments run out of statistics. Ground-based gamma-ray experiments have the advantage of large photon collection areas. H.E.S.S. is the only gamma-ray experiment located in the Southern hemisphere and thus able to observe Eta Carinae in this energy range. H.E.S.S. measures gamma-rays via electromagnetic showers of particles that very-high-energy gamma-rays initiate in the atmosphere. The main challenge in observations of Eta Carinae with H.E.S.S. is the UV emission of the Carina nebula that leads to a background that is up to 10 times stronger than usual for H.E.S.S. This thesis presents the first detection of a colliding-wind binary in very-high-energy gamma-rays and documents the studies that led to it. The differential gamma-ray energy spectrum of Eta Carinae is measured up to 700 GeV. A hadronic and leptonic origin of the gamma-ray emission is discussed and based on the comparison of cooling times a hadronic scenario is favoured