Observation and detection of pulsars with the H.E.S.S. gamma telescopes and phenomenology of a new pulsed spectral component reaching 20 TeV

The thesis focuses on the search of gamma rays pulsations coming from pulsars with the H.E.S.S. telescopes. The first section is dedicated to the study of statistical tests of periodicity based on Monte Carlo simulations, in particular with scarce data and/or a small signal to noise ratio. In the second section, these tests are used in the analysis of H.E.S.S. observations of Vela and two other pulsars, PSR B1706- 44 and PSR J1509-5850. The pulsations of Vela exhibit a very hard spectrum and are observed at energies ranging from 3 TeV to beyond 20 TeV. These are the most energetic gamma rays ever detected from a pulsar. It is also the first discovery of a pulsed spectral component in discontinuity with that already known at lower energies (GeV) from pulsars. The pulsar B1706-44 is detected from the ground in the 10-80 GeV range, with an index and a flux compatible with those of the LAT instrument onboard the Fermi satellite. Another pulsar, J1509-5850, shows a hint for a TeV emission but it still needs to be confirmed with further data. In the third part, the phenomenology of the spectral component between 3 and 20 TeV of Vela is studied in detail. After a critical review of two recent models suggesting possible interpretations, we explore another and more recent category of models. These rely on magnetic reconnection in the current sheet for the acceleration and on a Lorentz boost, as opposed to previous models. We demonstrate that it is possible to reproduce our data in this framework where the emission is due to an inverse Compton scattering of thermal photons from the neutron star surface. This discovery opening new horizons, we conclude with the study of the perspectives of the field with the future gamma observatory CTA. (author)