# Gap carving by a migrating planet embedded in a massive debris disc

**Authors:** Marc F. Friebe, Tim D. Pearce, Torsten Löhne  
**arXiv:** [2203.03611](https://arxiv.org/abs/2203.03611)  
**Date:** 2022-03-07  
**Summary page:** https://www.summarizepaper.com/en/paper/2203.03611v1/

## Key points

- The study investigates the gap that a single embedded planet would carve in a massive debris disc.
- The typical approach to considering gaps in debris discs can be invalid if the disc is massive because clearing would also cause planet migration.
- An observed gap could be carved by two different planets: either a high-mass, barely-migrating planet or a smaller planet that clears debris as it migrates.
- Depending on disc mass, there is a minimum possible gap width that an embedded planet could carve because smaller planets would actually migrate through the disc and clear a wider region.
- The study provides simple formulae for the planet-to-debris disc mass ratio at which planet migration becomes important, the gap width that an embedded planet would carve in a massive debris disc, and the interaction timescale.
- The authors apply their results to various systems and show that HD 107146's disk can be reasonably well-reproduced with a migrating, embedded planet.
- Potential applications of their work include constraining debris disc masses and finding wider insights into system properties from studying interactions between planets and disks.
- Some caveats must be considered when applying these results such as additional effects seen in simulations like debris being swept up into mean-motion resonances and the importance of considering the pronounced timescale for debris clearing.

## Summary

This study investigates the gap that a single embedded planet would carve in a massive debris disc. The typical approach to considering gaps in debris discs is to invoke clearing by an unseen planet within the gap and derive the planet mass using Wisdom overlap or Hill radius arguments. However, this approach can be invalid if the disc is massive because this clearing would also cause planet migration. This could result in a calculated planet mass that is incompatible with the inferred disc mass because the predicted planet would be too small to carve the gap without significant migration. The authors show that a degeneracy is introduced whereby an observed gap could be carved by two different planets: either a high-mass, barely-migrating planet or a smaller planet that clears debris as it migrates. They find that depending on disc mass, there is a minimum possible gap width that an embedded planet could carve because smaller planets, rather than carving a smaller gap, would actually migrate through the disc and clear a wider region. The study provides simple formulae for the planet-to-debris disc mass ratio at which planet migration becomes important, the gap width that an embedded planet would carve in a massive debris disc, and the interaction timescale. The interaction timescale depends strongly on both planetary and disk masses. If Mplt (planet mass) > Mdisc (disk mass), then Equation 7 characterizes the interaction timescale well; however, if Mplt < Mdisc, then Equation 7 might not hold since disk mass affects planetary migration rates. The authors apply their results to various systems and show that HD 107146's disk can be reasonably well-reproduced with a migrating, embedded planet. Additionally, they discuss potential applications of their work such as constraining debris disc masses and finding wider insights into system properties from studying interactions between planets and disks. Finally, some caveats must be considered when applying these results such as additional effects seen in simulations like debris being swept up into mean-motion resonances and the importance of considering the pronounced timescale for debris clearing. Overall, this study provides valuable insights into Planet-debris disc interactions and their potential applications in understanding planetary systems.