Standing on the shoulders of giants

Trojan Earths and vortex trapping in low mass self-gravitating protoplanetary disks of gas and solids

¹ Department of Physics and Astronomy, Uppsala Astronomical Observatory, Box 515, 75120 Uppsala, Sweden e-mail: wlyra@astro.uu.se
² Leiden Observatory, Leiden University, PO Box 9513, 2300 RA Leiden, The Netherlands
³ Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany

Received: 13 August 2008
Accepted: 28 October 2008

Abstract

Context. Centimeter and meter-sized solid particles in protoplanetary disks are trapped within long-lived, high-pressure regions, creating opportunities for collapse into planetesimals and planetary embryos.

Aims. We aim to study the effect of the high-pressure regions generated in the gaseous disks by a giant planet perturber. These regions consist of gas retained in tadpole orbits around the stable Lagrangian points as a gap is carved, and the Rossby vortices launched at the edges of the gap.

Methods. We performed global simulations of the dynamics of gas and solids in a low mass non-magnetized self-gravitating thin protoplanetary disk. We employed the Pencil code to solve the Eulerian hydro equations, tracing the solids with a large number of Lagrangian particles, usually 100 000. To compute the gravitational potential of the swarm of solids, we solved the Poisson equation using particle-mesh methods with multiple fast Fourier transforms.

Results. Huge particle concentrations are seen in the Lagrangian points of the giant planet, as well as in the vortices they induce at the edges of the carved gaps. For 1 cm to 10 cm radii, gravitational collapse occurs in the Lagrangian points in less than 200 orbits. For 5 cm particles, a 2 planet is formed. For 10 cm, the final maximum collapsed mass is around 3. The collapse of the 1 cm particles is indirect, following the timescale of gas depletion from the tadpole orbits. Vortices are excited at the edges of the gap, primarily trapping particles of 30 cm radii. The rocky planet that is formed is as massive as 17, constituting a Super-Earth. Collapse does not occur for 40 cm onwards. By using multiple particle species, we find that gas drag modifies the streamlines in the tadpole region around the classical L4 and L5 points. As a result, particles of different radii have their stable points shifted to different locations. Collapse therefore takes longer and produces planets of lower mass. Three super-Earths are formed in the vortices, the most massive having 4.5.

Conclusions. A Jupiter-mass planet can induce the formation of other planetary embryos at the outer edge of its gas gap. Trojan Earth-mass planets are readily formed; although not existing in the solar system, might be common in the exoplanetary zoo.