A new method for the reconstruction of very-high-energy gamma-ray spectra and application to galatic cosmic-ray accelerators

In this thesis, high-energy (HE; E>0.1 GeV) and very-high-energy (VHE; E>0.1 TeV) γ-ray data were investigated to probe Galactic stellar clusters (SCs) and star-forming regions (SFRs) as sites of hadronic Galactic cosmic-ray (GCR) acceleration. In principle, massive SCs and SFRs could accelerate GCRs at the shock front of the collective SC wind fed by the individual high-mass stars. The subsequently produced VHE γ rays would be measured with imaging air-Cherenkov telescopes (IACTs). A couple of the Galactic VHE γ-ray sources, including those potentially produced by SCs, fill a large fraction of the field-of-view (FoV) and require additional observations of source-free regions to determine the dominant background for a spectral reconstruction. A new method of reconstructing spectra for such extended sources without the need of further observations is developed: the Template Background Spectrum (TBS). This methods is based on a method to generate skymaps, which determines background in parameter space. The idea is the creation of a look-up of the background normalisation in energy, zenith angle, and angular separation and to account for possible systematics. The results obtained with TBS and state-of-the-art background-estimation methods on H.E.S.S. data are in good agreement. With TBS even those sources could be reconstructed that normally would need further observations. Therefore, TBS is the third method to reconstruct VHE γ-ray spectra, but the first one to not need additional observations in the analysis of extended sources. The discovery of the largest VHE γ-ray source HESSJ1646-458 (2.2 in size) towards the SC Westerlund 1 (Wd1) can be plausibly explained by the SC-wind scenario. But owing to its size, other alternative counterparts to the TeV emission (pulsar, binary system, magnetar) were found in the FoV. Therefore, an association of HESSJ1646-458 with the SC is favoured, but cannot be confirmed. The SC Pismis 22 is located in the centre of the previously reported, but unidentified extended TeV γ-ray source HESSJ1614-518. Unpublished H.E.S.S. data and archival multi-wavelength (MWL) data (radio, X-ray, and He data) as well various astrophysical objects in the FoV were investigated in search of a counterpart. The energy-dependent TeV morphology (with at least two source regions) can hardly be reconciled with the MWL data. A SC-wind scenario appears unlikely and the FoV lacks plausible counterpart, but a relic pulsar wind nebula could explain the lack of prominent X-ray emission. The VHE γ-ray source remains unidentified. The analysis of unpublished H.E.S.S. data on the SFR the Gould Belt (GB) did not provide any firm evidence of VHE γ-ray emission, and upper limits on the flux and the cosmic-ray enhancement were derived. The analysis of current IACTs. Towards Orion A, a possible discovery of extended VHE γ rays with flux of 10.8 % of the Crab Nebula is found with TBS, but cannot be confirmed and could be an artifact od the analysis of this region. Observations with the H.E.S.S. telescope system motivate that SCs and SFRs can accelerate GCRs. However, further H.E.S.S. observations are needed for further morphological and spectral studies. Also, more X-ray observations (in the case of HESSJ1614-518) and further studies on the background-estimation methods and their systematics (in the case of the GB) are required.