| Abstract
| - Context. Runaway stars produce bowshocks that are usually observed at infrared (IR) wavelengths. Non-thermal radio emission has been detected so far only from the bowshock of BD+43°3654, whereas the detection of non-thermal radiation from these bowshocks at high energies remains elusive. Aims. We aim at characterising in detail the radio, X-ray, and γ-ray emission from stellar bowshocks accounting for the structure of the region of interaction between the stellar wind and its environment. Methods. We develop a broadband-radiative, multi-zone model for stellar bowshocks that takes into account the spatial structure of the emitting region and the observational constraints. The model predicts the evolution and the emission of the relativistic particles accelerated and streaming together with the shocked flow. Results. We present broadband non-thermal spectral energy distributions for different scenarios, synthetic radio-cm synchrotron maps that reproduce the morphology of BD+43°3654, and updated predictions in X-ray and γ-ray energy ranges. We also compare the results of the multi-zone model applied in this work with those of a refined one-zone model. Conclusions. A multi-zone model provides better constraints than a one-zone model on the relevant parameters, namely the magnetic field intensity and the amount of energy deposited in non-thermal particles. However, one-zone models can be improved by carefully characterising the intensity of the IR dust photon field and the escape rate of the plasma from the shocked region. Finally, comparing observed radio maps with those obtained from a multi-zone model enables constraints to be obtained on the direction of stellar motion with respect to the observer.
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