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Runaway stars form bow shocks by ploughing through the interstellar medium atsupersonic speeds and are promising sources of non-thermal emission of photons.One of these objects has been found to emit non-thermal radiation in the radioband. This triggered the development of theoretical models predictingnon-thermal photons from radio up to very-high-energy (VHE, E $\geq 0.1$TeV)gamma rays. Subsequently, one bow shock was also detected in X-rayobservations. However, the data did not allow discrimination between a hotthermal and a non-thermal origin. Further observations of different candidatesat X-ray energies showed no evidence for emission at the position of the bowshocks either. A systematic search in the \textit{Fermi}-LAT energy regimeresulted in flux upper limits for 27 candidates listed in the E-BOSS catalogue.Here we perform the first systematic search for VHE gamma-ray emission from bowshocks of runaway stars. Using all available archival H.E.S.S. data we searchfor very-high-energy gamma-ray emission at the positions of bow shockcandidates listed in the second E-BOSS catalogue release. Out of the 73 bowshock candidates in this catalogue, 32 have been observed with H.E.S.S. None ofthe observed 32 bow shock candidates in this population study show significantemission in the H.E.S.S. energy range. Therefore, flux upper limits arecalculated in five energy bins and the fraction of the kinetic wind power thatis converted into VHE gamma rays is constrained. Emission from stellar bowshocks is not detected in the energy range between 0.14 and 18 TeV. Theresulting upper limits constrain the level of VHE gamma-ray emission from theseobjects down to 0.1-1 % of the kinetic wind energy.

Systematic search for very-high-energy gamma-ray emission from bow shocks of runaway stars