We describe calculations for the formation of icy planets and debris disks at 30–150 AU around 1–3 M _ { \odot } stars .
Debris disk formation coincides with the formation of planetary systems .
As protoplanets grow , they stir leftover planetesimals to large velocities .
A cascade of collisions then grinds the leftovers to dust , forming an observable debris disk .
Stellar lifetimes and the collisional cascade limit the growth of protoplanets .
The maximum radius of icy planets , r _ { max } \approx 1750 km , is remarkably independent of initial disk mass , stellar mass , and stellar age .
These objects contain \lesssim 3 % –4 % of the initial mass in solid material .
Collisional cascades produce debris disks with maximum luminosity \sim 2 \times 10 ^ { -3 } times the stellar luminosity .
The peak 24 \mu m excess varies from \sim 1 % times the stellar photospheric flux for 1 M _ { \odot } stars to \sim 50 times the stellar photospheric flux for 3 M _ { \odot } stars .
The peak 70–850 \mu m excesses are \sim 30–100 times the stellar photospheric flux .
For all stars , the 24–160 \mu m excesses rise at stellar ages of 5–20 Myr , peak at 10–50 Myr , and then decline .
The decline is roughly a power law , f \propto t ^ { - n } with n \approx 0.6–1.0 .
This predicted evolution agrees with published observations of A-type and solar-type stars .
The observed far-IR color evolution of A-type stars also matches model predictions .