Stochastic modelling of galactic cosmic rays: spectral features and diffuse emission

Cosmic rays are ubiquitous in our Galaxy and bombard the Earth continuously from all directions. They also interact with the interstellar medium throughout the Galaxy, producing so-called diffuse emission in -rays and neutrinos. Direct observations by space-borne high-precision experiments such as AMS-02, DAMPE, and CALET provide measurements of the local cosmic-ray spectrum, while ground-based -ray and neutrino observatories such as LHAASO and IceCube are beginning to probe diffuse emission at energies beyond 100 TeV, extending the energy range of previous experiments such as Fermi-LAT. Cosmic rays are commonly assumed to be accelerated at the shock fronts of supernova remnants. However, observations indicate that Galactic cosmic-ray sources must accelerate particles efficiently up to the so-called cosmic-ray knee at energies around 3 PeV. Achieving such energies is theoretically challenging, and realistic source models must address this issue. Magnetic field amplification through streaming instabilities provides a possible solution, but it also influences the time at which cosmic rays escape into the interstellar medium. In this thesis, we introduce a model that incorporates energy-dependent cosmic-ray injection times. Models of Galactic cosmic rays are inherently limited by our incomplete knowledge of the spatial distribution and ages of their sources. To address this, we adopt a stochastic approach to model the population of Galactic cosmic-ray sources, treating their positions and ages as random variables. Using extensive Monte Carlo simulations, we characterise the impact of individual sources, quantify the uncertainties arising from the unknown source population, and investigate whether observations of the local cosmic-ray spectrum and diffuse emission can constrain source properties. Our results demonstrate a close connection between the statistical properties of cosmic-ray intensities and those of the resulting diffuse emission. Finally, we show that the proposed energy-dependent injection model leaves distinct features in the local cosmic-ray spectrum. Using machine-learning techniques, we explore the potential to distinguish between different injection scenarios based on direct cosmic-ray measurements. We highlight the prospects of this approach for current and future experimental analyses.