Collisional Cascades in Planetesimal Disks II. Embedded Planets

We use a multiannulus planetesimal accretion code to investigate the growth of icy planets in the outer regions of a planetesimal disk. In a quiescent minimum mass solar nebula, icy planets grow to sizes of 1000–3000 km on a timescale tP ≈ 15 − 20 Myr (a/30 AU), where a is the distance from the central star. Planets form faster in more massive nebulae. Newly-formed planets stir up leftover planetesimals along their orbits and produce a collisional cascade where icy planetesimals are slowly ground to dust. The dusty debris of planet formation has physical characteristics similar to those observed in β Pic, HR 4796A, and other debris disks. The computed dust masses are Md(r . 1 mm) ∼ 10 26 g (M0/MMMSN ) and Md(1 mm . r . 1 m) ∼ 10 27 g (M0/MMMSN ), where r is the radius of a particle, M0 is the initial mass in solids, and MMMSN is the mass in solids of a minimum mass solar nebula at 30–150 AU. The luminosity of the dusty disk relative to the stellar luminosity is LD/L0 ∼ Lmax(t/t0) −m, where Lmax ∼ 10 (M0/MMMSN ), t0 ≈ 10 Myr to 1 Gyr, and m ≈ 1–2. Our calculations produce bright rings and dark gaps with sizes ∆a/a ≈ 0.1. Bright rings occur where 1000 km and larger planets have recently formed. Dark gaps are regions where planets have cleared out dust or shadows where planets have yet to form. Planets can also grow in a planetesimal disk perturbed by the close passage of a star. Stellar flybys initiate collisional cascades, which produce copious amounts of dust. The dust luminosity following a modest perturbation is 3–4 times larger than the maximum dust luminosity of a quiescent planet-forming disk. In 10 Myr or less, large perturbations remove almost all of the planetesimals from a disk. After a modest flyby, collisional damping reduces planetesimal velocities and allows planets to grow from the remaining