Simulating gamma-ray binaries with a relativistic extension of RAMSES

Context. γ-ray binaries are composed of a massive star and a rotation-powered pulsar with a highly relativistic wind. The collision between the winds from both objects creates a shock structure where particles are accelerated, which results in the observed high energy emission. Aims. We want to understand the impact of the relativistic nature of the pulsar wind on the structure and stability of the colliding wind region and highlight the differences with colliding winds from massive stars. We focus on how the structure evolves with increasing values of the Lorentz factor of the pulsar wind, keeping in mind that current simulations are unable to reach the expected values of pulsar wind Lorentz factors by orders of magnitude. Methods. We use high resolution numerical simulations with a relativistic extension to the hydrodynamics code RAMSES we have developed. We use two-dimensional simulations, and focus on the region close to the binary, where orbital motion can be neglected. We use different values of the Lorentz factor of the pulsar wind, up to 16. Results. We determine analytic scaling relations between stellar wind collisions and γ-ray binaries. They provide the position of the contact discontinuity. The position of the shocks strongly depends on the Lorentz factor. We find that the relativistic wind is more collimated than expected based on non-relativistic simulations. Beyond a certain distance, the shocked flow is accelerated to its initial velocity and follows adiabatic expansion. Finally, we provide guidance for extrapolation towards more realistic values of the Lorent