  We present results of our Chandra/ACIS observations of the field centered on
the fast, runaway O star AE Aur and its bow shock. Previous XMM-Newton
observations revealed an X-ray "blob" near the IR arc tracing the bow shock,
possibly a nonthermal source consistent with models of Inverse Compton
scattering of dust IR photons by electrons accelerated at the shock. The new,
subarcsecond resolution Chandra data, while confirming the presence of the
XMM-Newton source, clearly indicate that the latter is neither extended nor
coincident with the IR arc and strongly suggest it is a background AGN.
Motivated by results published for the bow shock of BD+43 3654, we extended our
study to the radio domain, by analyzing archival EVLA data. We find no radio
emission from the AE Aur bow shock either. The corresponding upper limits for
the absorbed (unabsorbed) X-ray flux of 5.9(7.8)x10^-15 erg/cm^2/s (3 sigma)
and, in the radio range, of 2 mJy (1.4 GHz), and 0.4 mJy (5.0 GHz), are used to
put constraints on model predictions for particle acceleration within the bow
shock. In the "classical" framework of Diffusive Shock Acceleration, we find
that the predicted X-ray and radio emission by the bow shock is at least two
orders of magnitude below the current upper limits, consistent with the
systematic non-detections of up to 60 stellar bow shocks. The only exception so
far remains that of BD+43 3654, probably the result of its very large mass-loss
rate among runaway O stars.
