Sensitivity limits on bound companions, obtained by combining the constraints from IRDIS/IFS direct imaging and Gaia astrometry (proper motion anomaly and excess noise). The probability to detect a planet of a given mass and semi-major axis is colour-coded with the shade of the map; the darkest area indicates a probability greater than 90%. The mass vs semi-major axis given in Eq. (2) applied for a small body located at a = 60 au (the warp radius) and for various timescales t_sec is shown with coloured lines.