A two-phase code for protoplanetary disks

¹ Laboratoire d'Astrophysique de Marseille, CNRS, BP 8, 13376 Marseille Cedex 12, France e-mail: satoshi.inaba@oamp.fr
² Department of Earth and Planetary Sciences, Tokyo Institute of Technology, 2-12-1 Oookayama, Meguro-ku, Tokyo 152-8551, Japan
³ EPU - UMR CNRS 6595, 5 rue Enrico Fermi, 13453 Marseille Cedex 13, France
⁴ ProgetSMASH - INRIA, 2004 route des Lucioles, 06902 Sophia Antipolis, France

Received: 14 April 2004
Accepted: 21 October 2004

Abstract

A high accuracy 2D hydrodynamical code has been developed to simulate the flow of gas and solid particles in protoplanetary disks. Gas is considered as a compressible fluid while solid particles, fully coupled to the gas by aerodynamical forces, are treated as a pressure-free diluted second phase. The solid particles lose energy and angular momentum which are transfered to the gas. As a result particles migrate inward toward the star and gas moves outward. High accuracy is necessary to account for the coupling. Boundary conditions must account for the inward/outward motions of the two phases. The code has been tested on one and two dimensional situations. The numerical results were compared with analytical solutions in three different cases: i) the disk is composed of a single gas component; ii) solid particles migrate in a steady flow of gas; iii) gas and solid particles evolve simultaneously. The code can easily reproduce known analytical solutions and is a powerful tool to study planetary formation at the decoupling stage. For example, the evolution of an over-density in the radial distribution of solids is found to differ significantly from the case where no back reaction of the particles onto the gas is assumed. Inside the bump, solid particles have a drift velocity approximately 16 times smaller than outside which significantly increases the residence time of the particles in the nebula. This opens some interesting perspectives to solve the timescale problem for the formation of planetesimals.