Population plot of core formation for 1000 protoplanets randomly initialized from Fig. 11 (top). We indicate M_iso with gray dashed-dotted lines. We zoom in in the outer regions where the protoplanets reach M_iso, and we indicate the metal content of the giant planets in the Solar System (see Sect. 5.4 for discussion). A medium or high pebble Stokes number is required to form a planet with JupiterΫs metallicity. Protoplanets that accrete gas via the pebble decay pathway (purple dots) acquire a significantly less massive core. Population plot including gas accretion for t_f = 5 Myr (bottom). The pebble isolation mass M_iso, 1 M_Jup and 10 M_Jup are indicated as reference lines, as well as the giant planets in the Solar System and the protoplanets PDS 70 b and c are indicated with red error bars (data from Wang et al. 2021). With a medium Stokes number and a short-lasting pebble flux, the formation of wide-orbit gas giants located up to 40 AU is possible due to the pebble decay pathway.