# Accretion of aerodynamically large pebbles

**Authors:** Helong Huang, Chris W. Ormel  
**arXiv:** [2304.02044](https://arxiv.org/abs/2304.02044)  
**Date:** 2023-04-04  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2304.02044v1/

## Key points

- Pebble accretion has been extensively studied for aerodynamically small pebbles with Stokes number (St) less than 1
- This study aims to extend the analysis to aerodynamically loosely coupled particles with St greater than 1
- The authors integrate the equation of motion for pebbles, accounting for gas drag, stellar and planetary gravity in a laminar disc's midplane
- They calculate the accretion probability ($\epsilon$) as a function of St, disc pressure gradient index, planet mass and eccentricity
- $\epsilon$(St) first rises for St above unity due to lower drift and aided by a large atmospheric capture radius until it reaches a plateau where efficiency approaches 100%
- At high St values, the plateau region terminates as particles become trapped in resonance
- The study provides semi-analytical "kick-and-drift" models and fully analytical prescriptions for $\epsilon$
- The authors apply their model to $\sim30 \mu$m dust particle accretion in dispersing protoplanetary and secondary (CO-rich) debris discs
- Physically small particles are mainly accreted as aerodynamically large Stokes number pebbles during the debris disc phase
- Earth-mass planets may obtain around 25% of their heavy elements through this late accretion phase
- Overall, this study expands our understanding of pebble accretion beyond aerodynamically small pebbles and highlights its importance in supporting planet formation in different scenarios.

## Summary

The process of pebble accretion has been extensively studied for aerodynamically small pebbles with Stokes number (St) less than 1. However, this study aims to extend the analysis to aerodynamically loosely coupled particles with St greater than 1. The authors integrate the equation of motion for pebbles, accounting for gas drag, stellar and planetary gravity in a laminar disc's midplane. They calculate the accretion probability ($\epsilon$) as a function of St, disc pressure gradient index, planet mass and eccentricity. The results show that $\epsilon$(St) first rises for St above unity due to lower drift and aided by a large atmospheric capture radius until it reaches a plateau where efficiency approaches 100%. At high St values, the plateau region terminates as particles become trapped in resonance. The study provides semi-analytical "kick-and-drift" models and fully analytical prescriptions for $\epsilon$. The authors apply their model to $\sim30 \mu$m dust particle accretion in dispersing protoplanetary and secondary (CO-rich) debris discs. They find that physically small particles are mainly accreted as aerodynamically large Stokes number pebbles during the debris disc phase. Earth-mass planets may obtain around 25% of their heavy elements through this late accretion phase. Overall, this study expands our understanding of pebble accretion beyond aerodynamically small pebbles and highlights its importance in supporting planet formation in different scenarios.