# Coagulation-Fragmentation Equilibrium for Charged Dust: Abundance of Submicron Grains Increases Dramatically in Protoplanetary Disks

**Authors:** Vitaly Akimkin, Alexei V. Ivlev, Paola Caselli, Munan Gong, Kedron Silsbee  
**arXiv:** [2306.16408](https://arxiv.org/abs/2306.16408)  
**Date:** 2023-06-28  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2306.16408v1/

## Key points

- Dust coagulation in protoplanetary disks is influenced by various factors: bouncing, fragmentation, and radial drift towards the star.
- In UV-shielded regions of the disk, dust grains become negatively charged due to collisions with electrons and ions, resulting in electrostatic repulsion between them.
- Electrostatic repulsion significantly reduces the relative velocities between micron-sized grains and affects their collisions.
- Collisions between larger pebble-sized grains can be too energetic and lead to grain fragmentation.
- The study investigates how electrostatic and fragmentation barriers affect dust evolution in protoplanetary disks.
- The authors numerically solve the Smoluchowski coagulation-fragmentation equation for charged grains under conditions typical for inner disk regions where thermal ionization occurs.
- Results show that dust fragmentation plays an important role in replenishing small grains hindered by the electrostatic barrier.
- Compared to neutral dust cases, there is a significant enhancement of sub-micron grain abundance by several orders of magnitude when considering charged dust.
- Under certain conditions with fragmentation velocities around 1 m/s, macroscopic grains are completely destroyed.
- This study provides valuable insights into how charging and fragmentation processes impact dust evolution in protoplanetary disks.
- It highlights the importance of these processes when studying planet formation and understanding observed properties of young planetary systems.

## Summary

Dust coagulation in protoplanetary disks is a complex process that is influenced by various factors, such as bouncing, fragmentation, and radial drift towards the star. Additionally, in UV-shielded regions of the disk, dust grains become negatively charged due to collisions with electrons and ions, resulting in electrostatic repulsion between them. This repulsion significantly reduces the relative velocities between micron-sized grains and thus affects their collisions. On the other hand, collisions between larger pebble-sized grains can be too energetic and lead to grain fragmentation. In this study, the authors investigate how electrostatic and fragmentation barriers affect dust evolution in protoplanetary disks. To do so, they numerically solve the Smoluchowski coagulation-fragmentation equation for charged grains under conditions typical for inner disk regions where thermal ionization occurs. The results show that dust fragmentation plays an important role in replenishing small grains hindered by the electrostatic barrier; compared to neutral dust cases there is a significant enhancement of sub-micron grain abundance by several orders of magnitude. Moreover, under certain conditions with fragmentation velocities around 1 m/s macroscopic grains are completely destroyed. This study provides valuable insights into how charging and fragmentation processes impact dust evolution in protoplanetary disks and highlights their importance when studying planet formation and understanding observed properties of young planetary systems.