  Planetary migration is a major challenge for planet formation theories. The
speed of Type I migration is proportional to the mass of a protoplanet, while
the final decade of growth of a pebble-accreting planetary core takes place at
a rate that scales with the mass to the two-thirds power. This results in
planetary growth tracks (i.e., the evolution of a protoplanet's mass versus its
distance from the star) that become increasingly horizontal
(migration-dominated) with rising mass of the protoplanet. It has been shown
recently that the migration torque on a protoplanet is reduced proportional to
the relative height of the gas gap carved by the growing planet. Here we show
from 1-D simulations of planet-disc interaction that the mass at which a planet
carves a 50% gap is approximately 2.3 times the pebble isolation mass. Our
measurements of the pebble isolation mass from 1-D simulations match published
3-D results relatively well, except at very low viscosities where the 3-D
pebble isolation mass is significantly higher, possibly due to gap edge
instabilities not captured in 1-D. The pebble isolation mass demarks the
transition from pebble accretion to gas accretion. Gas accretion to form
gas-giant planets therefore takes place over a few astronomical units of
migration after reaching first the pebble isolation mass and, shortly after,
the 50% gap mass. Our results demonstrate how planetary growth can outperform
migration, both during core accretion and during gas accretion, even when the
Stokes number of the pebbles is small, St~0.01, and the pebble-to-gas flux
ratio in the protoplanetary disc is in the nominal range of 0.01-0.02. We find
that planetary growth is very rapid in the first million years of the
protoplanetary disc and that the probability for forming gas-giant planets
increases with the initial size of the protoplanetary disc and with decreasing
turbulent diffusion.
