Combinations of β Pic d’s mass and semi-major axis for various eccentricities, within observational constraints that successfully reproduce the disk profile at 50 au. The plotting conventions are identical to Fig. 4. The ring limit quickly tends to zero as the eccentricity increases. The minimum semi-major axis stability limit with β Pic b imposes a maximum mass limit (dot-dashed black line), determined by the intersection (black dot) with the fit’s right extremum of the acceptable range of β Pic d’s semi-major axis. This maximum mass limit decreases as eccentricity increases, becoming more restrictive than the observational mass limit for e_d ≳ 0.25, and tends towards zero as eccentricity continues to increase (see Fig. 7).