Forming the cores of giant planets from the radial pebble flux in protoplanetary discs

The formation of planetary cores must proceed rapidly in order for the giant planets to accrete their gaseous envelopes before the dissipation of the protoplanetary gas disc (less than or similar to 3 Myr). In orbits beyond 10 AU, direct accumulation of planetesimals by the cores is too slow. Fragments of planetesimals could be accreted faster, but planetesimals are likely too large for fragmentation to be efficient, and resonant trapping poses an additional hurdle. Here we instead investigate the accretion of small pebbles (mm-cm sizes) that are the natural outcome of an equilibrium between the growth and radial drift of particles. We construct a simplified analytical model of dust coagulation and pebble drift in the outer disc, between 5 AU and 100 AU, which gives the temporal evolution of the solid surface density and the dominant particle size. These two key quantities determine how core growth proceeds at various orbital distances. We find that pebble surface densities are sufficiently high to achieve the inside-out formation of planetary cores within the disc lifetime. The overall efficiency by which dust gets converted to planets can be high, close to 50% for planetary architectures similar to the solar system. Growth by pebble accretion in the outer disc is sufficiently fast to overcome catastrophic type I migration of the cores. These results require protoplanetary discs with large radial extent (greater than or similar to 100 AU) and assume a low number of initial seed embryos. Our findings imply that protoplanetary discs with low disc masses, as expected around low-mass stars (<1 M-circle dot), or with sub-solar dust-to-gas ratios, do not easily form gas-giant planets (M greater than or similar to 100 M-E), but preferentially form Neptune-mass planets or smaller (M less than or similar to 10 M-E). This is consistent with exoplanet surveys which show that gas giants are relatively uncommon around stars of low mass or low metallicity.