Collisional cascades in planetesimal disks. II. Embedded planets.
KENYON S.J. and BROMLEY B.C.
Abstract (from CDS):
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)[a/(30 AU)]3 Myr, 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 in which icy planetesimals are slowly ground to dust. The dusty debris of planet formation has physical characteristics similar to those observed in β Pic and HR 4796A and other debris disks. The computed dust masses are Md(r≲1 mm)∼1026(M0/MMMSN) g and Md(1 mm≲r≲1 m)∼1027(M0/MMMSN) g, 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∼10–3(M0/MMMSN), t0~10-1000 Myr, and m~1-2. Our calculations produce bright rings and dark gaps with sizes Δa/a~0.1. Bright rings occur where planets 1000 km and larger 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 planetesimals. Planet formation timescales are then 2-4 times longer than timescales for undisturbed disks; dust luminosities are 2-4 times smaller.
Stars: Circumstellar Matter - Stars: Planetary Systems: General - Solar System: Formation - Stars: Formation