Dynamics of multiple protoplanets embedded in gas and pebble discs and its dependence on Σ and ν parameters

¹ Institute of Astronomy, Charles University, Prague, V Holešovičkách 2, 18000 Prague 8, Czech Republic
e-mail: mira@sirrah.troja.mff.cuni.cz
² Department of Space Studies, Southwest Research Institute, 1050 Walnut St., Suite 300, Boulder, CO 80302, USA
³ Lund Observatory, Department of Astronomy and Theoretical Physics, Lund University, Box 43, 22100 Lund, Sweden

Received: 13 July 2018
Accepted: 3 October 2018

Abstract

Protoplanets of super-Earth size may get trapped in convergence zones for planetary migration and form gas giants there. These growing planets undergo accretion heating, which triggers a hot-trail effect that can reverse migration directions, increase planetary eccentricities, and prevent resonant captures of migrating planets. In this work, we study populations of embryos that are accreting pebbles under different conditions, by changing the surface density, viscosity, pebble flux, mass, and the number of protoplanets. For modelling, we used the FARGO-THORIN two-dimensional (2D) hydrocode, which incorporates a pebble disc as a second pressure-less fluid, the coupling between the gas and pebbles, and the flux-limited diffusion approximation for radiative transfer. We find that massive embryos embedded in a disc with high surface density (Σ = 990 g cm⁻² at 5.2 au) undergo numerous “unsuccessful” two-body encounters that do not lead to a merger. Only when a third protoplanet arrives in the convergence zone do three-body encounters lead to mergers. For a low-viscosity disc (ν = 5 × 10¹³ cm² s⁻¹), a massive co-orbital is a possible outcome, for which a pebble isolation develops and the co-orbital is further stabilised. For more massive protoplanets (5 M_⊕), the convergence radius is located further out, in the ice-giant zone. After a series of encounters, there is an evolution driven by a dynamical torque of a tadpole region, which is systematically repeated several times until the co-orbital configuration is disrupted and planets merge. This may be a way to solve the problem that co-orbitals often form in simulations but they are not observed in nature. In contrast, the joint evolution of 120 low-mass protoplanets (0.1 M_⊕) reveals completely different dynamics. The evolution is no longer smooth, but rather a random walk. This is because the spiral arms, developed in the gas disc due to Lindblad resonances, overlap with each other and affect not only a single protoplanet but several in the surrounding area. Our hydrodynamical simulations may have important implications for N-body simulations of planetary migration that use simplified torque prescriptions and are thus unable to capture protoplanet dynamics in its full glory.