We analyze two new sets of coagulation calculations for solid particles orbiting within the terrestrial zone of a solar-type star .
In models of collisional cascades , numerical simulations demonstrate that the total mass , the mass in 1 mm and smaller particles , and the dust luminosity decline with time more rapidly than predicted by analytic models , \propto t ^ { - n } with n \approx 1.1–1.2 instead of 1 .
Size distributions derived from the numerical calculations follow analytic predictions at r \lesssim 0.1 km but are shallower than predicted at larger sizes .
In simulations of planet formation , the dust luminosity declines more slowly than in pure collisional cascades , with n \approx 0.5–0.8 instead of 1.1–1.2 .
Throughout this decline , giant impacts produce large , observable spikes in dust luminosity which last \sim 0.01–0.1 Myr and recur every 1–10 Myr .
If most solar-type stars have Earth mass planets with a \lesssim 1–2 AU , observations of debris around 1–100 Myr stars allow interesting tests of theory .
Current data preclude theories where terrestrial planets form out of 1000 km or larger planetesimals .
Although the observed frequency of debris disks among \gtrsim 30 Myr old stars agrees with our calculations , the observed frequency of warm debris among 5–20 Myr old stars is smaller than predicted .