Simulating gamma-ray binaries with a relativistic extension of RAMSES

Gamma-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, resulting in the observed high energy emission. We study the impact of special relativity on the structure and stability of the colliding wind region and highlight the differences with colliding winds from massive stars. We focus on evolution 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 the pulsar wind Lorentz factors by orders of magnitude. We use high resolution numerical simulations with a relativistic extension to the hydrodynamics code RAMSES we have developed. Using 2D simulations, we focus on the region close to the binary, neglecting orbital motion. We use different values of the Lorentz factor of the pulsar wind, up to 16. We find analytic scaling relations between stellar wind collisions and gamma-ray binaries. They provide the position of the contact discontinuity. The position of the shocks strongly depends on the Lorentz factor, 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. We provide guidance for extrapolation towards more realistic values of the Lorentz factor of the pulsar wind. We extended the adaptive mesh refinement code RAMSES to relativistic hydrodynamics. This code is suited for the study of astrophysical objects such as pulsar wind nebulae, gamma-ray bursts or relativistic jets and will be part of the next public release of RAMSES. Using this code we performed simulations of gamma-ray binaries, highlighting the limits and possibilities of current hydrodynamic models of such systems.