Proton acceleration in colliding stellar wind binaries

The interaction between the strong winds in stellar colliding-wind binary (CWB) systems produces two shock fronts, delimiting the wind collision region (WCR). There, particles are expected to be accelerated mainly via diffusive shock acceleration (DSA). We investigate the injection and the acceleration of protons in typical CWB systems by means of Monte Carlo simulations, with both a test-particle approach and a non-linear method modelling a shock locally modified by the backreaction of the accelerated protons. We use magnetohydrodynamic simulations to determine the background plasma in the WCR and its vicinity. This allows us to consider particle acceleration at both shocks, on either side of the WCR, with a realistic large-scale magnetic field. We highlight the possible effects of particle acceleration on the local shock profiles at the WCR. We include the effect of magnetic field amplification due to resonant streaming instability (RSI), and compare results without and with the backreaction of the accelerated protons. In the latter case we find a lower flux of the non-thermal proton population, and a considerable magnetic field amplification. This would significantly increase the synchrotron losses of relativistic electrons accelerated in CWB systems, lowering the maximal energy they can reach and strongly reducing the inverse Compton fluxes. As a result, $\gamma$-rays from CWBs would be predominantly due to the decay of neutral pions produced in nucleon-nucleon collisions. This might provide a way to explain why, in the vast majority of cases, CWB systems have not been identified as $\gamma$-ray sources, while they emit synchrotron radiation.