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Some runaway stars are known to display IR arc-like structures around them,resulting from their interaction with surrounding interstellar material. Theproperties of these features as well as the processes involved in theirformation are still poorly understood. We aim at understanding the physicalmechanisms that shapes the dust arc observed near the runaway O star AEAur(HD34078). We obtained and analyzed a high spatial resolution map of theCO(1-0) emission that is centered on HD34078, and that combines data from boththe IRAM interferometer and 30m single-dish antenna. The line of sight towardsHD34078 intersects the outer part of one of the detected globulettes, whichaccounts for both the properties of diffuse UV light observed in the field andthe numerous molecular absorption lines detected in HD34078's spectra,including those from highly excited H2 . Their modeled distance from the staris compatible with the fact that they lie on the 3D paraboloid which fits thearc detected in the 24 {\mu}m Spitzer image. Four other compact CO globulettesare detected in the mapped area. These globulettes have a high density andlinewidth, and are strongly pressure-confined or transient. The good spatialcorrelation between the CO globulettes and the IR arc suggests that they resultfrom the interaction of the radiation and wind emitted by HD 34078 with theambient gas. However, the details of this interaction remain unclear. A windmass loss rate significantly larger than the value inferred from UV lines isfavored by the large IR arc size, but does not easily explain the low velocityof the CO globulettes. The effect of radiation pressure on dust grains alsomeets several issues in explaining the observations. Further observational andtheoretical work is needed to fully elucidate the processes shaping the gas anddust in bow shocks around runaway O stars. (Abridged)

Dense molecular globulettes and the dust arc towards the runaway O star AE Aur (HD 34078)