Combinations of β Pic d’s mass and semi-major axis within observational constraints that successfully reproduce the disk profile at 50 au. For several values of m_d, the corresponding acceptable ranges of a_d are displayed in green. A power-law fit, according to Eq. (7), is overlaid in blue, taking into account the ranges of the semi-major axis. Shaded areas are not accessible byβ Pic d. The limits in semi-major axis are similarly presented as in Fig. 2. Additionally, above a mass of 1 M_Jup, corresponding to the observational limit (solid red line), β Pic d would have already been detected in previous observations (Lagrange et al. 2020). And below 0.15 M_Jup, corresponding to the ring limit (dashed red line), β Pic d does not completely clear the inner zone.