VARIATIONS ON DEBRIS DISKS. III. COLLISIONAL CASCADES AND GIANT IMPACTS IN THE TERRESTRIAL ZONES OF SOLAR-TYPE STARS

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, alpha t(-n) with n approximate to 1.1-1.2 instead of 1. Size distributions derived from the numerical calculations follow analytic predictions at r less than or similar to 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 approximate to 0.5-0.8 instead of 1.1-1.2. Throughout this decline, giant impacts produce large, observable spikes in dust luminosity that last similar to 0.01-0.1 Myr and recur every 1-10 Myr. If most solar-type stars have Earth mass planets with a less than or similar to 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 greater than or similar to 30 Myr old stars agrees with our calculations, the observed frequency of warm debris among 5-20 Myr old stars is smaller than predicted.