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.
Highlights
Observational data have so far shown that planets of a few Earth masses are one of the most abundant groups of planets in the exoplanetary systems (e.g., Borucki et al 2010; Batalha et al 2013; Fressin et al 2013; Petigura et al 2013; Mulders et al 2018)
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 focus on the innermost parts of a disk to study how the grain size distribution and the chemical compositions of the grains affect the formation of super-Earths
Summary
Observational data have so far shown that planets of a few Earth masses are one of the most abundant groups of planets in the exoplanetary systems (e.g., Borucki et al 2010; Batalha et al 2013; Fressin et al 2013; Petigura et al 2013; Mulders et al 2018). The super-Earth planets have recently been shown to be of similar sizes within the same planetary system (Weiss et al 2018), even though this was put into question by another analysis (Zhu et al 2018). There are several conditions that limit dust growth, such as the fragmentation barrier, the bouncing barrier, and the radial drift barrier (Brauer et al 2007; Birnstiel et al 2010; Zsom et al 2010). These barriers help in the rapid formation of millimeter- to centimeter-sized particles or pebbles, which is an essential contributor to planet formation
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