No abstract

The final orbital position of growing planets is determined by their migration speed, which is essentially set by the planetary mass. Small mass planets migrate in type I migration, while more massive planets migrate in type II migration, which is thought to depend mostly on the viscous evolution rate of the disc. A planet is most vulnerable to inward migration before it reaches type II migration and can lose a significant fraction of its semi-major axis at this stage. We investigated the influence of different disc viscosities, the dynamical torque and gas accretion from within the horseshoe region as mechanisms for slowing down planet migration. Our study confirms that planets growing in low viscosity environments migrate less, due to the earlier gap opening and slower type II migration rate. We find that taking the gas accretion from the horseshoe region into account allows an earlier gap opening and this results in less inward migration of growing planets. Furthermore, this effect increases the planetary mass compared to simulations that do not take the effect of gas accretion from the horseshoe region. Moreover, combining the effect of the dynamical torque with the effect of gas accretion from the horseshoe region, significantly slows down inward migration. Taking these effects into account could allow the formation of cold Jupiters (a > 1 au) closer to the water ice line region compared to previous simulations that did not take these effects into account. We thus conclude that gas accretion from within the horseshoe region and the dynamical torque play crucial roles in shaping planetary systems.

Recent detailed observations of protoplanetary discs revealed a lot of sub-structures which are mostly ring-like. One interpretation is that these rings are caused by growing planets. These potential planets are not yet opening very deep gaps in their discs. These planets instead form small gaps in the discs to generate small pressure bumps exterior to their orbits that stop the inflow of the largest dust particles. In the pebble accretion paradigm, this planetary mass corresponds to the pebble isolation mass, where pebble accretion stops and efficient gas accretion starts. We perform planet population synthesis via pebble and gas accretion including type-I and type-II migration. In the first stage of our simulations, we investigate the conditions necessary for planets to reach the pebble isolation mass and compare their position to the observed gaps. We find that in order to match the gap structures 2000 M E in pebbles is needed, which would be only available for the most metal rich stars. We then follow the evolution of these planets for a few My to compare the resulting population with the observed exoplanet populations. Planet formation in discs with these large amounts of pebbles result in mostly forming gas giants and only very little super-Earths, contradicting observations. This leads to the conclusions that either (i) the observed discs are exceptions, (ii) not all gaps in observed discs are caused by planets or (iii) that we miss some important ingredients in planet formation related to gas accretion and/or planet migration.

In the general classical picture of pebble-based core growth, planetary cores grow by accretion of single pebble species. The growing planet may reach the so-called pebble isolation mass, at which it induces a pressure bump that blocks inward drifting pebbles exterior to its orbit, thereby stalling core growth by pebble accretion. In recent hydrodynamic simulations, pebble filtration by the pressure bump depends on several parameters including core mass, disc structure, turbulent viscosity and pebble size. We investigated how accretion of multiple, instead of single, pebble species affects core growth rates, and how the dependence of pebble isolation mass on turbulent viscosity and pebble size sets the final core masses. We performed numerical simulations in viscous 1D disc, where maximal grain sizes were regulated by grain growth, fragmentation and drift limits. We confirm that core growth rates and final core masses are sensitive to three key parameters: threshold velocity at which pebbles fragment on collision, turbulent viscosity and distribution of pebble species, which yield a diversity of planetary cores. With accretion of multiple pebble species, planetary cores can grow pretty fast, reaching over 30 – 40 ME in mass. Potential cores of cold gas giants were able to form from embryos initially implanted as far as 50 AU. Our results suggest that accretion of multi-species pebbles could explain: the estimated 25 – 45 ME heavy elements abundance inside Jupiter’s core; massive cores of extrasolar planets; disc rings and gaps at wider orbits; early and rapid formation of planetary bodies.