Variations on Debris Disks III. Collisional Cascades and Giant Impacts in the Terrestrial Zones of Solar-type Stars

TL;DR

This paper presents numerical simulations of debris disk evolution around solar-type stars, revealing faster mass decline than analytic models, the impact of giant impacts on dust luminosity, and implications for planet formation theories.

Contribution

It introduces new coagulation models for collisional cascades and planet formation, highlighting differences from analytic predictions and observational constraints.

Findings

Mass and dust luminosity decline faster than analytic models predict.

Giant impacts cause observable spikes in dust luminosity every 1-10 Myr.

Current observations challenge theories with large planetesimals in planet formation.

Abstract

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 radii less than 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 roughly 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.