Predicted masses of fragments caused by disk instabilities as a function of semi-major axis for the massive star κ And. Formation of planets by disk instability is possible when the Toomre criterium is exceeded (solid lines) and when the disk can cool rapidly enough (long-dashed lines). The allowed formation space (in yellow) lies in-between these two criteria. Companions cannot be formed in situ at separations shorter than the ones indicated by the dotted lines. We superimpose the semi-major axis and mass estimates of κ And b (magenta dot) estimated from “hot-start” models for Columba ages ( Myr; dark gray shaded area) and considering an upper-limit corresponding to the highest age for the Pleiades cluster ( Myr; light gray shaded area). We also report the lower limit on the companion mass inferred from “warm-start” models (gray arrows, see Sect. 3.4.2). We show the corresponding primordial disk-mass reservoir (10, 20, 50%) at a given separation needed to form given clumps/companions. The Toomre parameter is independent of stellar metallicity.