The MAGIC telescopes located in the Roque de los Muchachos Observatory have been active for 20 years at the time of writing this work. This thesis is dedicated to the innovative exploitation of these imaging atmospheric telescopes as an intensity interferometer to measure the angular size of stars with unprecedented precision in the blue band; and to the search for transient fast radio bursts' counterparts in optical thanks to the central pixel setup in each telescope and very high energy. The work is divided into three main blocks. The first part introduces the history behind the discovery of gamma rays and cosmic rays that gave birth to astroparticle physics. It also introduces the different production, absorption and acceleration mechanisms of gamma rays. These processes are behind the gamma-ray emission of galactic and extragalactic sources, which are also presented. This emission is then observed and detected by space-based and ground-based instruments. MAGIC telescopes will be showcased in more detail since the results presented in this work have been obtained with them. The second part details the historical background of the intensity interferometry technique starting from its predecessor, amplitude interferometry. It will also establish the theoretical basis of the technique and some of the science cases that have been proposed to exploit it. The MAGIC telescopes had to undergo several hardware and software modifications in order to implement this technique, including exploiting its Active Mirror Control to subdivide its mirror dishes into several telescopes. I will explain how I built the star catalogue used for intensity interferometry observations and how I used it to schedule more than 400 h over the curse of 2 years as the official intensity interferometry scheduler. The different steps of the analysis will be explained: photon flux calibration, delay correction, convolution with mirror size and zero baseline correlation as well as several tests that were performed to ensure the consistency of the analysis. For stars whose angular diameter has already been measured directly and in the same optical bandwidth, the measured angular diameter by MAGIC will be compared, and for those stars without it, the MAGIC angular diameter measurement will be provided. A study of the systematics associated to MAGIC intensity interferometry measurements will be also shown. The main objective of this chapter will be to obtain stellar angular diameters for stars whose angular diameter has not been measured before with such high precision and/or in the blue band. Together with distances obtained by other instruments, these stellar angular diameters will help to expand the knowledge of the structure and evolution of massive stars. Finally, the third part describes fast radio bursts (FRBs) possible origins and mechanisms, focusing mainly on the magnetar scenario as a source of repeating FRBs. The potential of MAGIC to detect simultaneous counterparts of FRBs in optical thanks to MAGIC central pixel and in very high energy. As a starting point, the searches performed for the source FRB 121102 in 2017 with MAGIC will be introduced, as well as how this work laid the foundations for the searches performed for this thesis. Standard MAGIC analysis techniques will be described and some non-standard ones that are needed for certain modes of observation, including the analysis of the central pixel data. The results of several observation campaigns of FRB sources will be reported: SGR 1935+2154, FRB 20200120E and FRB 180916.J0158+65. The main objective of this chapter will be the search for optical and very high energy emission, in bursts and persistent, as a counterpart to FRBs, for which the emission mechanism and source populations are still unknown.
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