Dust trapping around Lagrangian points in protoplanetary disks

TL;DR

This study uses hydro-simulations to investigate dust trapping at Lagrangian points in protoplanetary disks, revealing vortex-driven dust accumulation and asymmetries between L4 and L5 that inform Trojan planet formation theories.

Contribution

It demonstrates the role of vortices in dust trapping at Lagrangian points and explores the impact of planetary migration and dust source regions on Trojan dust distribution.

Findings

L4 traps more submm particles than L5.

Total dust mass is greater in L5 despite L4's larger particle trapping.

Planet migration does not alter L4-L5 asymmetry.

Abstract

Trojans are defined as objects that share the orbit of a planet at the stable Lagrangian points $L_4$ and $L_5$. In the Solar System, these bodies show a broad size distribution ranging from micrometer($\mu$m) to centimeter(cm) particles (Trojan dust) and up to kilometer (km) rocks (Trojan asteroids). It has also been theorized that earth-like Trojans may be formed in extra-solar systems. The Trojan formation mechanism is still under debate, especially theories involving the effects of dissipative forces from a viscous gaseous environment. We perform hydro-simulations to follow the evolution of a protoplanetary disk with an embedded 1--10 Jupiter-mass planet. On top of the gaseous disk, we set a distribution of $\mu$m--cm dust particles interacting with the gas. This allows us to follow dust dynamics as solids get trapped around the Lagrangian points of the planet. We show that large vortices generated at the Lagrangian points are responsible for dust accumulation, where the leading Lagrangian point $L_4$ traps a larger amount of submillimeter (submm) particles than the trailing $L_5$, which traps mostly mm--cm particles. However, the total bulk mass, with typical values of $\sim M_{\rm moon}$, is more significant in $L_5$ than in $L_4$, in contrast to what is observed in the current Solar System a few gigayears later. Furthermore, the migration of the planet does not seem to affect the reported asymmetry between $L_4$ and $L_5$. The main initial mass reservoir for Trojan dust lies in the same co-orbital path of the planet, while dust migrating from the outer region (due to drag) contributes very little to its final mass, imposing strong mass constraints for the in situ formation scenario of Trojan planets.