On the use of tracer particles in simulations of binary neutron stars

In grid-based codes that provide the combined solution of the Einstein equations and of relativistic hydrodynamics, the history of the fluid is not simple to track, especially when compared with particle-based codes. The use of tracers, namely massless particles that are advected with the flow, represents a simple and effective way to solve this problem. Yet, the use of tracers in numerical relativity is far from being settled and several issues, such as the impact of different placements in time and space of the tracers, or the relation between the placement and the description of the underlying fluid, have not yet been addressed. In this paper we present the first detailed discussion of the use tracers in numerical-relativity simulations focussing on both unbound material -- such as the one leading to r-process nucleosynthesis in binary mergers of neutron stars -- and on bound material -- such as the one in the core of the object produced from the merger of two neutron stars. In particular, when interested in unbound matter, we have evaluated four different placement schemes that could be used to initially distribute the tracers and how well their predictions match those obtained when using information from the actual fluid flow. Countering our naive expectations, we found that the most effective method does not rely on the rest-mass density distribution nor on the fluid that is unbound, but simply distributes tracers uniformly in rest-mass density. This prescription leads to the closest matching with the information obtained from the hydrodynamical solution. When considering bound matter, we demonstrate that tracers can provide insight into the fine details of the fluid motion as they can be used to track the evolution of fluid elements or to calculate the variation of quantities that are conserved along streamlines of adiabatic flows.