Eliot Ayache

Gamma-ray bursts are extremely powerful explosions resulting from the collapse of a massive star or the merger of two neutron stars that produce relativistic jets. Internal mechanisms in the jet are responsible for an initial burst of gamma-rays, called the prompt emission. Later on, as the jet collides with the external medium, a shock wave is formed ahead of the swept- up material. Energy is transferred to electrons at the shock front, causing them to emit synchrotron radiation covering the whole electromagnetic spectrum. This is called the afterglow. Explaining the features of the light-curve (brightness evolution with time) of the afterglow is a great pathway towards understanding the overall GRB mechanism, from the properties of the progenitor and the remnant, to the microphysical processes involved in the radiative emission.
In order to get some understanding of the light curve, and since the emission mechanism is linked to the formation of shock waves, one has to accurately model the dynamics of the explosion. Unfortunately, analytical approaches fail to accurately capture their dynamics because of their transition from relativistic to non-relativistic speeds, as well as the overall complexity of the flow, and we have to rely on numerical simulations.
Numerical simulations are still challenging as they need to be resolved over a large range of spatial scales. Indeed, the ejecta forms a very narrow shell that has to be followed from early to very late times to properly account for the resulting emitted radiation. Downstream of the shocks, the electron will also lose their energy (or “cool down”) rapidly, increasing the resolution constraint around the shocks. So far, most studies have relied on an analytical description of this cooling. However, one needs to numerically follow the local evolution of the population of particles responsible for the emission in order to build models valid from radio to X-ray.
We have developed a parallel multi-dimensional relativistic hydrodynamics code that includes this local treatment of the particle population on a moving mesh for the first time. The code uses finite-volume methods where we compute the averaged conserved physical quantities in a grid of volumes (the cells). For each time-step we compute the flux in these conserved quantities between each cell and evolve the grid accordingly. We allow the mesh to move in one dimension only (and update the fluxes accordingly) in order to avoid expensive re-gridding operations. Choosing this dimension as the main direction of travel of the fluid improves computational efficiency while naturally increasing the resolution around shock fronts.
As a first application, we investigate the cause of the frequently observed flares (sudden, temporary increase in brightness) in the early X-ray afterglow with one-dimensional simulations. We can follow the fluid from ejection to deceleration. We can also compute synthetic light-curves across the whole electromagnetic spectrum and show that flares can be the result of an initial perturbation at the back of the ejected material.
Going forward, we present the first preliminary outputs of two-dimensional simulations using our code. We confirm the ability of the code to correctly account for transverse flow both in cartesian and spherical coordinates and run coarse simulations of a relativistic jet propagating in a diffuse environment. As expected, we observe the formation of a shock wave ahead of the swept-up material.
Using this code, we now intend to study the influence of the jet-launching parameters on the radiation. Moreover, understanding the interplay between large scale jet dynamics and local particle shock acceleration will allow us to derive better constraints from observations across the electromagnetic spectrum on fundamental plasma physics of particle acceleration and magnetic field generation in relativistic shocks.