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The standard model for GRB afterglow emission treats the accelerated electron population as a simple power law, N(E) proportional to E-p for p greater than or similar to 2. However, in standard Fermi shock acceleration, a substantial fraction of the swept-up particles do not enter the acceleration process at all. Additionally, if acceleration is efficient, then the nonlinear back-reaction of accelerated particles on the shock structure modifies the shape of the nonthermal tail of the particle spectra. Both of these modifications to the standard synchrotron afterglow impact the luminosity, spectra, and temporal variation of the afterglow. To examine the effects of including thermal particles and nonlinear particle acceleration on afterglow emission, we follow a hydrodynamical model for an afterglow jet and simulate acceleration at numerous points during the evolution. When thermal particles are included, we find that the electron population is at no time well fitted by a single power law, though the highest-energy electrons are; if the acceleration is efficient, then the power-law region is even smaller. Our model predicts hard-soft-hard spectral evolution at X-ray energies, as well as an uncoupled X-ray and optical light curve. Additionally, we show that including emission from thermal particles has drastic effects (increases by factors of 100 and 30, respectively) on the observed flux at optical and GeV energies. This enhancement of GeV emission makes afterglow detections by future gamma-ray observatories, such as CTA, very likely.
Massive runaway stars produce bow shocks through the interaction of their winds with the interstellar medium, with the prospect for particle acceleration by the shocks. These objects are consequently candidates for non-thermal emission. Our aim is to investigate the X-ray emission from these sources. We observed with XMM-Newton a sample of five bow shock runaways, which constitutes a significant improvement of the sample of bow shock runaways studied in X-rays so far. A careful analysis of the data did not reveal any X-ray emission related to the bow shocks. However, X-ray emission from the stars is detected, in agreement with the expected thermal emission from stellar winds. On the basis of background measurements we derive conservative upper limits between 0.3 and 10 keV on the bow shocks emission. Using a simple radiation model, these limits together with radio upper limits allow us to constrain some of the main physical quantities involved in the non-thermal emission processes, such as the magnetic field strength and the amount of incident infrared photons. The reasons likely responsible for the non-detection of non-thermal radiation are discussed. Finally, using energy budget arguments, we investigate the detectability of inverse Compton X-rays in a more extended sample of catalogued runaway star bow shocks. From our analysis we conclude that a clear identification of non-thermal X-rays from massive runaway bow shocks requires one order of magnitude (or higher) sensitivity improvement with respect to present observatories.