Giant planet formation with pebble accretion

In the core accretion model for giant planet formation, a solid core forms by coagulation of dust grains in a protoplanetary disk and then accretes gas from the disk when the core reaches a critical mass. Both stages must be completed in a few million years before the disk gas disperses. The slowest stage of this process may be oligarchic growth in which a giant-planet core grows by sweeping up smaller, asteroid-size planetesimals. Here, we describe new numerical simulations of oligarchic growth using a particle-in-a-box model. The simulations include several processes that can effect oligarchic growth: (i) planetesimal fragmentation due to mutual collisions, (ii) the modified capture rate of planetesimals due to a core’s atmosphere, (iii) drag with the disk gas during encounters with the core (so-called “pebble accretion”), (iv) modification of particle velocities by turbulence and drift caused by gas drag, (v) the presence of a population of mm-to-m size “pebbles” that represent the transition point between disruptive collisions between larger particles, and mergers between dust grains, and (vi) radial drift of small objects due to gas drag. Collisions between planetesimals rapidly generate a population of pebbles. The rate at which a core sweeps up pebbles is controlled by pebble accretion dynamics. Metre-size pebbles lose energy during an encounter with a core due to drag, and settle towards the core, greatly increasing the capture probability during a single encounter. Millimetre-size pebbles are tightly coupled to the gas and most are swept past the core during an encounter rather than being captured. Accretion efficiency per encounter increases with pebble size in this size range. However, radial drift rates also increase with size, so metre-size objects encounter a core on many fewer occasions than mm-size pebbles before they drift out of a region. The net result is that core growth rates vary weakly with pebble size, with the optimal diameter being about 10 cm. The main effect of planetesimal size is to determine the rate of mutual collisions, fragment production and the formation of pebbles. 1-km-diameter planetesimals collide frequently and have low impact strengths, leading to a large surface density of pebbles and rapid core growth via pebble accretion. 100-km-diameter planetesimals produce fewer pebbles, and pebble accretion plays a minor role in this case. The strength of turbulence in the gas determines the scale height of pebbles in the disk, which affects the rate at which they are accreted. For an initial solid surface density of 12 g/cm² at 5 AU, with 10-cm diameter pebbles and a disk viscosity parameter α=10^-4, a 10-Earth mass core can form in 3 My for 1-10 km diameter planetesimals. The growth of such a core requires longer than 3 My if planetesimals are 100 km in diameter.