  Runaway stars produce shocks when passing through interstellar medium at
supersonic velocities. Bow shocks have been detected in the mid-infrared for
several high-mass runaway stars and in radio waves for one star. Theoretical
models predict the production of high-energy photons by non-thermal radiative
processes in a number sufficiently large to be detected in X-rays. To date, no
stellar bow shock has been detected at such energies. We present the first
detection of X-ray emission from a bow shock produced by a runaway star. The
star is AE Aur, which was likely expelled from its birthplace by the encounter
of two massive binary systems and now is passing through the dense nebula IC
405. The X-ray emission from the bow shock is detected at 30" to the northeast
of the star, coinciding with an enhancement in the density of the nebula. From
the analysis of the observed X-ray spectrum of the source and our theoretical
emission model, we confirm that the X-ray emission is produced mainly by
inverse Compton upscattering of infrared photons from dust in the shock front.
