Architectures of planetary systems formed by pebble accretion

In models of planetary accretion, pebbles form by dust coagulation and rapidly migrate toward the central star. Planetesimals may continuously form from pebbles over the age of the protoplanetary disk by yet uncertain mechanisms. Meanwhile, large planetary embryos grow efficiently by accumulation of leftover pebbles that are not incorporated in planetesimals. Although this process, called pebble accretion, is offering a new promising pathway for formation of giant planets' cores, architectures of planetary systems formed through the process remain elusive. In the present paper, we perform simulations of formation of planetary systems using a particle-based hybrid code, to which we implement most of the key physical effects as precisely as possible. We vary the size of a protoplanetary disk, the turbulent viscosity, the pebble size, the planetesimal formation efficiency, and the initial mass distribution of planetesimals. Our simulations show that planetesimals first grow by mutual collisions if their initial size is the order of $100$ km or less. Once planetesimals reach $\sim$ 1000 km in size, they efficiently grow by pebble accretion. If pebble supply from the outer region continues for a long period of time in a large protoplanetary disk, planetary embryos become massive enough to commence runaway gas accretion, resulting in gas giant planets. Our simulations suggest that planetary systems like ours form from protoplanetary disks with moderately high turbulent viscosities. If the disk turbulent viscosity is low enough, a planet opens up a gap in the gas disk and halts accretion of pebbles even before the onset of runway gas accretion. Such a disk produces a planetary system with several Neptune-size planets.