Difference in proper motions between the HIPPARCOS and the Gaia epochs. Each dot represents a trial from our N = 20 000 saved simulation trial points, and the red and yellow encircled areas show which values are compatible within 1 − σ of the actual measured value when applying the HIPPARCOS proper motions from Perryman et al. (1997) and van Leeuwen (2007), respectively (see Sect. 2 for discussion). Higher-mass companions induce stronger Δμ, as indicated by the colour scheme. The colours of the encircled areas of the measured proper motions are not reflected by the defined colour scheme in mass, and serve only to differentiate between the two proper-motion solutions.