Final masses and semimajor axes of formed planets from planetesimal rings at (a) 30 AU and (b) 100 AU orbital distances based on Toomre’s surface density criterion. The filled dots represent the final bodies from the planetesimal population (Eq. (5)) that grow by 50% from their initial masses and are greater than 0.1 M_⊕ at t = 1 Myr. The unfilled circles denote the single largest planetesimal that only undergoes pebble accretion, for comparison. The three unfilled circles from small to large refer to the mass at t = 1, 2, and 3 Myr, respectively. Red, blue, and yellow correspond to the pebble flux of 100, 200, and 300 M_⊕ Myr⁻¹, respectively. In order to distinguish the mass more clearly, we artificially shift the blue and yellow unfilled circles slightly away from the birth locations. The black dotted horizontal lines represent the gap-opening masses based on Eq. (35) of Liu et al. (2019a) at 30 AU and 100 AU.