Impact of Cosmic Ray Acceleration on the Early Evolution of Bow Shocks around Massive Runaway Stars
Bow shocks generated from the interaction of winds from massive runaway stars with the interstellar medium have been shown to be prominent particle accelerators through recent $γ$-ray and radio synchrotron observations. Here, we study particle acceleration from bow shocks by conducting 3D ideal cosmic ray magnetohydrodynamic simulations in the advection-diffusion limit. We use the Eulerian grid-based code FLASH, where stellar winds are injected through tabulated wind velocities and mass loss rates. We implement a gradient-based shock detection algorithm to resolve the shocked regions where the CRs are injected dynamically. Simulations are performed for different values of the CR diffusion coefficient and star velocities within an ISM-like environment up to 180 kyr to showcase the impact of dynamical CR injection on the early evolution of the wind-driven bow shock. With a simplified spectral model in post-processing, we calculate the expected upper limits of $γ$-ray and synchrotron emission and compare with those from current observations. We observe that variations of CR diffusion rates can strongly dictate the morphology of the bow shock and the overall $γ$-ray and radio synchrotron luminosity due to the balance between the CR injection efficiency and diffusion. Our results yield qualitatively comparable results with current observations, primarily attributed to the high-energy protons and electrons contributing to non-thermal emission from efficient acceleration at the forward shock through the approximations and assumptions in the injection algorithm. We conclude that CR acceleration, with varying CR diffusion rates, may substantially affect the morphology of wind-driven bow shocks and their non-thermal emission, if there is efficient particle acceleration in the forward shock. [abridged]