Efficiency of coherent vortices to trap dust particles in the solar nebula

Pierre-Henri Chavanis

doi:10.1051/epjconf/20134606004

Abstract

We develop the idea proposed by Barge & Sommeria (1995) that large-scale vortices present in the solar nebula can concentrate dust particles and facilitate the for- mation of planetesimals and planets. We introduce an exact vortex solution of the incom- pressible 2D Euler equation (Kida vortex) and study the motion of dust particles in that vortex. In particular, we derive an analytical expression of the capture time as a function of the friction coecient and determine the parameters leading to an optimal capture.

Highlights

Many astrophysical objects, ranging from young stars to massive black holes, are surrounded by widespread gaseous disks
It seems natural to expect their presence in accretion disks. Their existence was first proposed by Von Weizäcker in 1944 to explain the regularity of the planet distribution in the solar system: the famous Titius-Bode law. This idea has been reintroduced more recently by Barge and Sommeria [1] who demonstrated that anticyclonic vortices in a rotating disk are able to capture and concentrate dust particles
We study the trajectories of dust particles in that vortex and derive an analytical expression for the capture time as a function of the friction coefficient

Summary

Introduction

Many astrophysical objects, ranging from young stars to massive black holes, are surrounded by widespread gaseous disks. Their existence was first proposed by Von Weizäcker in 1944 to explain the regularity of the planet distribution in the solar system: the famous Titius-Bode law This idea has been reintroduced more recently by Barge and Sommeria [1] who demonstrated that anticyclonic vortices in a rotating disk are able to capture and concentrate dust particles. The density of the dust cloud is increased by a large factor which is sufficient to trigger locally the gravitational instability and facilitate the formation of the planetesimals or the cores of giant planets This trapping mechanism is quite rapid (a few rotations) and can reduce substantially the time scale of planet formation. We find that the capture is optimal for particles whose friction coefficient is close to the local disk angular velocity

The vortex model

The capture time

Conclusion