Joint probability contours (68.3, 95, and 99%) on the mass and post-formation entropy of β Pic b from log (L/L_⊙) = −3.90 ± 0.07 and an age of 21 ± 4 Myr using a flat prior on S_i and a prior flat in mass (dashed black curves) or given by the radial-velocity and astrometry constraints for a linear K prior (solid dark-blue curves). Using the logarithmic-K prior of Fig. 1 gives nearly identical results. The long-dashed orange line shows the combinations matching log (L/L_⊙) = −3.90 at 12 Myr, i.e. allowing for an extreme 9 Myr formation delay. The open circles indicate the cold-start post-formation entropies for different final core masses (labeled) or for hot starts (Mordasini 2013, App. B of MC14). The bottom panel displays the mass priors (dotted lines) and the marginalized posterior distributions (black and blue lines), whereas the side panel shows the marginalized S_i posterior and the non-flat mass prior’s 90- and 95-% lower limits (up to S_i ~ 14).