The growth of super-Earths: The importance of a self-consistent treatment of disk structures and pebble accretion

Abstract

The conditions in the protoplanetary disk are determinant for the various planet formation mechanisms. We present a framework that combines self-consistent disk structures with the calculations of the growth rates of planetary embryos via pebble accretion, in order to study the formation of super-Earths. We first perform 2D hydrodynamical simulations of the inner disks, considering a grain size distribution with multiple chemical species and their corresponding size and composition dependent opacities. The resulting aspect ratios are almost constant with orbital distance, resulting in radially constant pebble isolation masses, the mass where pebble accretion stops. This supports the "peas-in-a-pod"constraint from the Kepler observations. The derived pebble sizes are used to calculate the growth rates of planetary embryos via pebble accretion. Disks with low levels of turbulence (expressed through the α-viscosity) and/or high dust fragmentation velocities allow larger particles, hence lead to lower pebble isolation masses, and the contrary. At the same time, small pebble sizes lead to low accretion rates. We find that there is a trade-off between the pebble isolation mass and the growth timescale; the best set of parameters is an α-viscosity of 10-3 and a dust fragmentation velocity of 10 m s-1, mainly for an initial gas surface density (at 1 AU) greater than 1000 g cm-2. A self-consistent treatment between the disk structures and the pebble sizes is thus of crucial importance for planet formation simulations.