# Growth after the streaming instability: from planetesimal accretion to pebble accretion

## TL;DR

This study investigates how planetesimals grow into super-Earths via streaming instability, focusing on the effects of initial size distributions, pebble flux, disk turbulence, and pebble properties.

## Contribution

It demonstrates that diverse initial planetesimal size distributions enable super-Earth formation within disk lifetimes, highlighting the importance of dynamical friction and pebble flux.

## Key findings

- Mono-dispersed 400 km planetesimals cannot form Earth-mass planets.
- Poly-dispersed and bimodal distributions facilitate super-Earth formation.
- Higher pebble flux, lower turbulence, and larger Stokes number favor super-Earth growth.

## Abstract

Streaming instability is a key mechanism in planet formation, clustering pebbles into planetesimals. It is triggered at a particular disk location where the local volume density of solids exceeds that of the gas. After their formation, planetesimals can grow by feeding from other planetesimals in the birth ring as well as by accreting inwardly drifting pebbles from the outer disk. To investigate the growth of planetesimals at a single location by the streaming instability, we test the conditions under which super-Earths are able to form within the lifetime of the gaseous disk. We modify the \texttt{Mercury} N-body code to trace the growth and dynamical evolution of a swarm of planetesimals at the ice line for a solar-mass star. Three distributions of planetesimal sizes are investigated: (i) a mono-dispersed population of 400 km radius planetesimals, (ii) a poly-dispersed populations of planetesimals from 200 km up to 1000 km, (iii) a bimodal distribution with a single runaway body and a swarm of smaller, 100 km size planetesimals. The mono-disperse population of 400 km size planetesimals cannot form $\gtrsim$ Earth mass protoplanets. Their velocity dispersions are quickly excited, which suppresses both planetesimal and pebble accretion. Planets can form from the poly-dispersed and bimodal distributions. In these circumstances, the two-component nature damps the random velocity of the large embryo by small planetesimals' dynamical friction, allowing the embryo to accrete pebbles efficiently when it approaches $10^{-2}$ Earth mass. We find that super-Earth planets are preferred to form when the pebble mass flux is higher, the disk turbulence is lower, or the Stokes number of the pebbles is higher.