This Thesis illustrates the activities and the results that I have obtained during my three-year PhD course at the University of Padova.
My work was mainly based on the study of the extreme blazars, or better “extreme high-energy peaked BL Lac objects” (generally referred to as EHBLs). EHBLs are an emerging class of blazars with exceptional spectral properties, presenting a spectral energy distribution peaking with the synchrotron emission in hard X-rays and a high-energy emission in TeV gamma rays. The hard-TeV spectrum of EHBLs is important also for the implications on the indirect estimations of the extragalactic background light and of the intergalactic magnetic fields. The emission processes producing such extremely-high photon energies are currently not completely understood, and may represent a challenge for the standard modelling of these sources. In fact, the standard models are generally able to fit the experimental spectral data, but the parameters they assume are unusual compared to the standard blazar modelling currently available in literature. More complex models, assuming – for example – multiple emission zones or hadronic contributions, may provide more relaxed parameter spaces. In particular, the presence of hadronic processes in the blazar emission might make the EHBLs producers of extragalactic high-energy neutrinos.The number of EHBL objects is currently very limited. Thanks to recent observations, new sources have been classified as candidate EHBLs. Their spectral properties reveal new features that enrich the properties of this class of objects. In this framework, my research work started with the search for new EHBL candidates on the basis of all-sky surveys in hard X-rays. This new method allowed me to select the most promising extreme blazars relying on their X-ray to high-energy gamma-ray flux ratio. The analysis of the spectral properties of this new sample revealed interesting spectral features and systematic differences that are emerging in the EHBL class, especially in TeV gamma rays. This suggests the possible emergence of a sub-classification, and a new population of EHBLs may be unveiled. One specific aspect of my analysis was to predict the feasibility of observations of these objects with the current and next generation of Cherenkov telescopes. In the MAGIC Collaboration, I had the opportunity to propose a list of EHBL candidates for observations. Among them, a source named PGC 2402248 was observed and finally detected in TeV gamma rays, and several others are now being observed with the MAGIC telescopes. These results have been published together with a detailed discussion on the comparison between several theoretical models proposing different interpretations of the spectral properties of these sources. During my PhD, I had the opportunity to contribute to several other projects that complemented my preparation in this field. In the MAGIC Collaboration, I was involved in projects related to the detection of new EHBLs in TeV gamma rays and in the study of interesting blazars like PG 1553+113. I was also involved in two analyses on the relation between extreme blazars and extragalactic background light, and on the selection of extreme blazar candidates from a sample of faint sources in the high-energy gamma-ray band. Finally, an important part of my PhD activity within the MAGIC Collaboration was devoted to a contribution to the discovery of the first association between a high-energy neutrino, the so-called IceCube EHE-170922A event, and the blazar TXS 0506+056. During the analysis of this event, registered on September 2017, I was main analyser of the MAGIC data. Considering the importance of the discovery – with implications about the origin of the very-high-energy cosmic rays – and the intense multi-collaboration work, it was really a unique opportunity for me to gain new experience in this field and to further motivate my interest in the multi-messenger astrophysics