On the Absence of Non-thermal X-ray emission around Runaway O stars

Theoretical models predict that the compressed interstellar medium around runaway O stars can produce high-energy non-thermal diffuse emission, in particular, non-thermal X-ray and $\gamma$-ray emission. So far, detection of non-thermal X-ray emission was claimed for only one runaway star AE Aur. We present a search for non-thermal diffuse X-ray emission from bow shocks using archived XMM-Newton observations for a clean sample of 6 well-determined runaway O stars. We find that none of these objects present diffuse X-ray emission associated to their bow shocks, similarly to previous X-ray studies toward $\zeta$ Oph and BD$+$43${}^{\circ }$3654. We carefully investigated multi-wavelength observations of AE Aur and could not confirm previous findings of non-thermal X-rays. We conclude that so far there is no clear evidence of non-thermal extended emission in bow shocks around runaway O stars.