Relativistic Magnetohydrodynamic Modelling of Gamma-ray Burst Jets: From Early Propagation to Afterglow Emission

Gamma-ray bursts are among the most energetic transient phenomena in the Universe. Since their discovery, a dedicated branch of research has been developed to understand their origin and the physics involved. They are thought to arise from ultra-relativistic jets, launched by at least two distinct classes of progenitors: a binary neutron star merger, and the core collapse of a rotating, strongly magnetised massive star. In both cases, the jet is launched by a central engine, harbouring a rotating, newly formed compact object, into a dense and inhomogeneous progenitor environment: the binary neutron star merger ejecta or the collapsing stellar envelope. It is the interaction with this environment that shapes the jet as it reaches the larger scales where electromagnetic emission takes place. The interpretation of observational data is most frequently performed through models that assume an axisymmetric jet configuration described by simple analytical functions. As a consequence, the jet-structure parameters, viewing angles and energetics inferred from afterglow fitting rest on assumptions whose validity in a genuinely three-dimensional setting remains untested. This thesis develops a framework that connects three-dimensional relativistic magnetohydrodynamic simulations of the early jet propagation to the afterglow signal produced at much larger scales, targeting both progenitor channels. The simulations resolve the jet–progenitor interaction during its early-time evolution and follow how the resulting features propagate outwards; the afterglow prediction is carried out within a flexible semi-analytic framework extended to include the full three-dimensional velocity and energy distribution of the jet material. Focussing on the binary neutron star merger scenario, we characterise the dynamical evolution of a fiducial simulation, identifying the formation of a multi-shock structure whose outermost shell carries a non-negligible fraction of the total energy, and the most energetic region evolves into a spherical-cap geometry marked by pronounced angular asymmetries and radial stratification. For the resulting outflow structure to be meaningfully used as input for the afterglow emission predictions, the evolution must be computed up to a time when the jet structure has reached its asymptotic configuration. To this end, we introduce a remapping method that extends three-dimensional jet simulations up to a saturating regime approaching ballistic expansion. We then consider a set of analogous models in which the jet injection parameters are varied around the fiducial configuration in terms of injected energy, magnetisation and launching time. The main qualitative features persist across a range of injection conditions, and the parameter variations enable an assessment of their relative impact on the jet propagation and resulting structure. To bridge the gap between the scales accessible to the simulations and the region where the afterglow is produced, the resulting jet structures are directly fed into the extended semi-analytic model. Accounting for the full three-dimensional structure reveals that the outer shell leaves an observational imprint at early times, only present when the radial velocity stratification is included. The deviations from axisymmetry produce order-of-magnitude differences even for small offsets in the viewing angle, a feature that axisymmetric models cannot reproduce. This azimuthal variation provides an additional degree of freedom when interpreting observational data. A proof-of-concept fit to the afterglow of GRB\,170817A closes the chain, directly connecting jet structural features to the shape of the observed signal. The results show that the resulting jet structures can be brought into good agreement with the reference event within the available observational and theoretical constraints. This highlights the complexity of a direct jet-to-emission connection given the large degeneracy between the parameters involved. The same strategy is then applied, at a preliminary stage, to the massive-star core-collapse channel, addressing the interaction between an incipient relativistic jet and a stellar envelope undergoing a magneto-rotational supernova. The goal is to investigate how this interaction shapes the jet's structure and stability, which conditions determine the successful propagation of the jet beyond the progenitor star, and how the concurrent supernova explosion affects this evolution. This preliminary step provides the basis for a systematic treatment of both classes of gamma-ray burst progenitors within a common framework. Together, these results establish a route from three-dimensional progenitor-scale simulations to observable afterglow signatures, providing a framework for interpreting current and forthcoming gamma-ray burst observations in the multi-messenger era.