Variations on debris disks. II. ICY planet formation as a function of the bulk properties and initial sizes of planetesimals

Abstract

We describe comprehensive calculations of the formation of icy planets and debris disks at 30-150 AU around 1-3M · stars. Disks composed of large, strong planetesimals produce more massive planets than disks composed of small, weak planetesimals. The maximum radius of icy planets ranges from ∼ 1500km to 11,500km. The formation rate of 1000km objects - "Plutos" - is a useful proxy for the efficiency of icy planet formation. Plutos form more efficiently in massive disks, in disks with small planetesimals, and in disks with a range of planetesimal sizes. Although Plutos form throughout massive disks, Pluto production is usually concentrated in the inner disk. Despite the large number of Plutos produced in many calculations, icy planet formation is inefficient. At the end of the main sequence lifetime of the central star, Plutos contain less than 10% of the initial mass in solid material. This conclusion is independent of the initial mass in the disk or the properties of the planetesimals. Debris disk formation coincides with the formation of planetary systems containing Plutos. As Plutos form, they stir leftover planetesimals to large velocities. A cascade of collisions then grinds the leftovers to dust, forming an observable debris disk. In disks with small (≲1-10km) planetesimals, collisional cascades produce luminous debris disks with maximum luminosity ∼ 10-2 times the stellar luminosity. Disks with larger planetesimals produce debris disks with maximum luminosity 5 × 10-4 (10km) to ∼ 5 × 10-5 (100km) times the stellar luminosity. Following peak luminosity, the evolution of the debris disk emission is roughly a power law, f α t -n with n ≈ 0.6-0.8. Observations of debris disks around A-type and G-type stars strongly favor models with small planetesimals. In these models, our predictions for the time evolution and detection frequency of debris disks agree with published observations. We suggest several critical observations that can test key features of our calculations. © 2010. The American Astronomical Society. All rights reserved.