This thesis is devoted to the application of high-resolution numerical methods for relativistic hydrodynamics (RHD) to the study of gamma-ray bursts (GRBs), as well as to the development of new schemes able to describe radiative transfer in relativistic magnetized and unmagnetized flows.
On one side, we have performed RHD simulations of relativistic plasma outbursts within the binary-driven hypernova model, developed throughout the last years in the International Center of Relativistic Astrophysics Network (ICRANet). This model is based on the so-called induced gravitational collapse scenario, proposed to explain the observed temporal coincidence of GRBs and supernovae (SN) of type Ic. This scenario considers a carbon-oxigen star (CO core) forming a tight binary system with a companion neutron star (NS). When the collapse of the CO core produces a type Ic SN, part of the ejected material is accreted by the NS, which in turn collapses and forms a black hole (BH). It has been proposed, although the details of this process are a matter of current research, that this collapse creates an optically thick electron-positron plasma around the BH that expands due to its own internal pressure and originates a GRB. Our work in this context has focused on the description of such expanding plasma and its interaction with the surrounding SN ejecta, for which we have followed a hydrodynamical approach using the open-source code PLUTO. This allowed us to study this process in high-density regions that had not been explored thus far, and to perform consistency checks of the model taking into account both theoretical and observational constraints such as the system’s size, the initial plasma energy, the observed timing and the Lorentz factor of the outbursts. Three different scenarios are here considered: (I) the expansion of the plasma in low-density regions, proposed to produce most of the GRB emission in the prompt phase; (II) a model in which X-ray flares are produced due to the breakout of shocks created when the plasma interacts with high-density regions of the SN ejecta; and (III) a model for the emission of secondary bursts due to the creation of reflected waves caused by the same interaction.
The second part of this thesis is devoted to the main part of our work, which consists in the development of a numerical code for radiative transfer integrated in PLUTO. Our implementation is able to solve the equations of relativistic radiation magnetohydrodynamics (Rad-RMHD) under the so-called M1 closure, which allows the radiation transport to be handled in both the free-streaming and diffusion limits. Since we use frequency-averaged opacities, this approach is unable to describe frequency-dependent phenomena; instead, the main focus is put on the transport of total energy and momentum. To avoid numerical instabilities arising due to the possibly large timescale disparity caused by the radiation–matter interaction terms, the Rad-RMHD equations are integrated following implicit–explicit (IMEX) schemes. In this way, interaction terms are integrated implicitly, whereas transport and all of the remaining source terms are solved explicitly by means of the same Godunov-type solvers included in PLUTO. Among these, we have introduced a new Harten–Lax–van Leer–contact (HLLC) solver for optically thin radiation transport. The code is suitable for multidimensional computations in Cartesian, spherical, and cylindrical coordinates using either a single processor or parallel architectures. Adaptive grid computations are also made possible by means of the CHOMBO library. We explain in this work the implementation of all of these methods, after which we show the code’s performance in several problems of radiative transfer in magnetized and unmagnetized flows. We pay particular attention to the behavior of the solutions in the free-streaming and diffusion limits, and show the efficiency and scalability properties of the code as compared with its usual nonradiative implementation. Finally, we show an application of this code to the mentioned model for X-ray flares
