Can the giant planets of the Solar System form via pebble accretion in a smooth protoplanetary disc?

Prevailing $N$-body planet formation models typically start with lunar-mass embryos and show a general trend of rapid migration of massive planetary cores to the inner Solar System in the absence of a migration trap. This setup cannot capture the evolution from a planetesimal to embryo, which is crucial to the final architecture of the system. We aim to model planet formation with planet migration starting with planetesimals of $\sim10^{-6}$ -- $10^{-4}M_\oplus$ and reproduce the giant planets of the Solar System. We simulated a population of 1,000 -- 5,000 planetesimals in a smooth protoplanetary disc, which was evolved under the effects of their mutual gravity, pebble accretion, gas accretion, and planet migration, employing the parallelized $N$-body code SyMBAp. We find that the dynamical interactions among growing planetesimals are vigorous and can halt pebble accretion for excited bodies. While a set of results without planet migration produces one to two gas giants and one to two ice giants beyond 6 au, massive planetary cores readily move to the inner Solar System once planet migration is in effect. Dynamical heating is important in a planetesimal disc and the reduced pebble encounter time should be considered in similar models. Planet migration remains a challenge to form cold giant planets in a smooth protoplanetary disc, which suggests an alternative mechanism is required to stop them at wide orbits.