Orbital evolution of colliding star and pulsar winds in 2D and 3D: effects of dimensionality, EoS, resolution, and grid size

Context. The structure formed by the shocked winds of a massive star and a non-accreting pulsar in a binary system suffers periodic and random variations of orbital and non-linear dynamical origins. The characterization of the evolution of the wind interaction region is necessary for understanding the rich phenomenology of these sources. Aims. For the first time, we simulate in 3 dimensions the interaction of isotropic stellar and relativistic pulsar winds along one full orbit, on scales well beyond the binary size. We also investigate the impact of grid resolution and size, and of different state equations: a (gamma) over cap -constant ideal gas, and an ideal gas with (gamma) over cap dependent on temperature. Methods. We used the code PLUTO to carry out relativistic hydrodynamical simulations in 2 and 3 dimensions of the interaction between a slow dense wind and a mildly relativistic wind with Lorentz factor 2, along one full orbit in a region up to similar to 100 times the binary size. The different 2-dimensional simulations were carried out with equal and larger grid resolution and size, and one was done with a more realistic equation of state than in 3 dimensions. Results. The simulations in 3 dimensions confirm previous results in 2 dimensions, showing: a strong shock induced by Coriolis forces that terminates the pulsar wind also in the opposite direction to the star; strong bending of the shocked-wind structure against the pulsar motion; and the generation of turbulence. The shocked flows are also subject to a faster development of instabilities in 3 dimensions, which enhances shocks, two-wind mixing, and large-scale disruption of the shocked structure. In 2 dimensions, higher resolution simulations confirm lower resolution results, simulations with larger grid sizes strengthen the case for the loss of the general coherence of the shocked structure, and simulations with two different equations of state yield very similar results. In addition to the Kelvin-Helmholtz instability, discussed in the past, we find that the Richtmyer-Meshkov and the Rayleigh-Taylor instabilities are very likely acting together in the shocked flow evolution. Conclusions. Simulations in 3 dimensions confirm that the interaction of stellar and pulsar winds yields structures that evolve non-linearly and become strongly entangled. The evolution is accompanied by strong kinetic energy dissipation, rapid changes in flow orientation and speed, and turbulent motion. The results of this work strengthen the case for the loss of the coherence of the whole shocked structure on large scales, although simulations of more realistic pulsar wind speeds are needed.