Nested-grid calculations of disk-planet interaction

¹ Astrophysikalisches Institut und Universitäts-Sternwarte, Schillergäßchen 2–3, 07745 Jena, Germany
² Computational Physics, Auf der Morgenstelle 10, 72076 Tübingen, Germany

Corresponding author: G. D'Angelo, gennaro@astro.uni-jena.de

Received: 16 May 2001
Accepted: 24 January 2002

Abstract

We study the evolution of embedded protoplanets in a protostellar disk using very high resolution nested-grid computations. This method allows us to perform global simulations of planets orbiting in disks and, at the same time, to resolve in detail the dynamics of the flow inside the Roche lobe of the planet. The primary interest of this work lies in the analysis of the gravitational torque balance acting on the planet. For this purpose we study planets of different masses, ranging from one Earth-mass up to one Jupiter-mass, assuming typical parameters of the protostellar disk. The high resolution supplied by the nested-grid technique permits an evaluation of the torques, resulting from short and very short range disk-planet interactions, more reliable than the one previously estimated with the aid of numerical methods. Likewise, the mass flow onto the planet is computed in a more accurate fashion. The obtained migration time scales are in the range from few times 10⁴ years, for intermediate mass planets, to 10⁶ years, for very low and high mass planets. These are longer than earlier assessments due to the action of circumplanetary material. Typical growth time scales depend strongly on the planetary mass. Below 64 Earth-masses, we find this time scale to increase as the -power of the planet's mass; otherwise it rises as the -power. In the case of Jupiter-size planets, the growth time scale is several times ten thousand years.