Distribution of the angular separation between eRASS1 X-ray source positions and the Gaia/unWISE QSOs. The red dots correspond to the observed number of associations at a given angular separation bin, δR_X−Opt. We use only eRASS1 X-ray sources with Galactic latitudes in the range |b| = 30–70°(i.e. extragalactic sky), DET_LKE_0 > 7, with more than 30 counts, are not spatially extended (parameter EXT = 0) and are not identified as potentially spurious by the algorithms described in Sect. 5.2. The dashed line is the model described in the text for parameters fixed to the median of the corresponding posteriors.