Numerics and theory of high-energy relativistic astrophysical transients

Recent years have seen massive breakthroughs in the observations of gamma-ray bursts and other high-energy astrophysical transients. Dynamical jet simulations have progressed to a point where it is now becoming possible to fully numerically resolve gamma-ray burst (GRB) jet evolution across scales. However, the modeling of radiative emission is currently lagging behind and makes for a bottleneck severely limiting our efforts to fully interpret the physics of GRBs in the multi-messenger era. In this thesis, I present new numerical developments to resolve this discrepancy and focus on providing insights into GRB afterglow physics. Using numerical simulations, I set out to understand the impact of the presence of multiple emission sites on afterglow light curves. I also investigate the trans-relativistic evolution of the jet and poorly understood behaviour of the spectral breaks in the radiation as the jet decelerates. In order to do this, I develop a new method for the local numerical calculation of non-thermal emission in relativistic shocks. This method combines a moving mesh finite-volume code with the a local description of particle acceleration and corresponding Synchrotron process. In order to inform the theoretical models to simulate, I investigate the GRB X-ray afterglow sample variability using Machine-Learning-based data visualisation techniques. In more details, I first investigate the mechanism responsible for flares in the early X-ray afterglow. Using a one-dimensional Lagrangian relativistic dynamics code, I carry out simulations to show that an erratic shutdown of the central engine in the first few hundred seconds after the burst can produce flares at arbitrarily late times. This erratic shutdown leads to stratification in the ejecta. The radiative flux of the external reverse shock increases when it encounters this stratification. We show that the limitation in the angular extent of the perturbations from transverse causal connection is directly responsible for the observed flare timescale in this scenario. These findings rely on the ability to locally evolve the non-thermal particle populations responsible for emission which is made possible by the increased spatial resolution resulting from the behaviour of the moving mesh. Secondly, I apply the same methods to the study of the trans-relativistic phase of jet evolution. For this multi-dimensional problem, I develop a massively parallel code, GAMMA, in which hydrodynamics are computed on discrete tracks that follow the fluid motion. This code can accurately capture the jet spreading with very high computational efficiency. Thanks to the local particle evolution calculation, it can accurately simulate the afterglow spectral evolution from early to late times. We show that the spectral cooling break shifts by a factor of ~40 compared to previous approaches. The evolution of this break during jet deceleration is also different as it does not shift with time between the relativistic and Newtonian asymptotes when computed from our local algorithm. Finally, I investigate the question whether differences in features between events can be explained by the same model or it is a marker of differences in the phenomenology, and thus separates distinct populations. I explore prospects for acquiring physical inference from Machine Learning models by clustering light curves in an unsupervised manner, and investigate the resulting level of segregation in the Swift X-ray afterglow dataset. We find that the data creates over-densities in the encoded latent space suggesting the presence of dominant light curve types. However, the observed gradual transition in between unifies the prevalent classification of GRBs based on their X-ray data into a single continuum, supporting the idea that light curves of different types should be unified under a single model.