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The bow shock current (BSC) plays an important role in supplying the magnetosphere with solar wind energy, in particular during times of low solar wind magnetosonic Mach numbers. Since the magnetic pile-up in the magnetosheath has to be maintained, the BSC cannot close locally, but must instead connect to magnetospheric current systems. However, the details of this closure remain poorly understood. For east–west interplanetary magnetic field (IMF) it has been hypothesized that the BSC partly closes to the high-latitude ionosphere, as field-aligned currents (FACs) on open field lines, but there is still no statistical evidence of this. In order to investigate this hypothesis, we use 9 years of Defense Meteorological Satellite Program (DMSP) data to construct normalized FAC maps of the northern hemisphere polar cap. We sort them according to different IMF clock angles, IMF magnitudes and magnetosonic Mach numbers. By separating opposite polarity FACs, we show that, on average, a unipolar FAC exists in the dayside polar cap when the IMF (Formula presented.), regardless of the sign of the IMF (Formula presented.). This current flows out of (into) the ionosphere in the northern hemisphere for IMF (Formula presented.) (Formula presented.) and is thus of the correct polarity to connect to the north–south component of the BSC. Moreover, it is strongest when the BSC flows predominantly in the north–south direction. These results constitute the first statistical evidence in support of at least a partial closure of the BSC to the ionosphere during non-zero IMF (Formula presented.).