A broken debris cascade as a possible source of hot dust emission in transitioning planet-forming disks

Abstract

Planet-forming disks go from gas-rich, massive disks made of dust and gas into planetary systems containing only small amounts dust. This dust is produced by collisions between smaller planetary objects, such as planetesimals, asteroids, and comets. Traditionally, we talk about protoplanetary (age $ 1$\,Myr), transitional (sim 5--10\,Myr), and debris disks (sim 10-hundreds of\,Myr) even though the overlap between these phases may be relevant. We aim to show that in the transition phase of a disk, when the gas surface densities are reduced but not yet negligible, a seemingly small amount of collisional activity may lead to the production of dust on a level that is observationally relevant by creating regions characterised by an optical depth of 1 or above. In particular, we aim to show that the hot dust emission component of transitional disks may in fact be debris dust that has been produced in such collisions. We developed an analytical model to derive the conditions in which observationally relevant amounts of dust can be produced. We focussed on the effect of the gas surface density during the transition phase of a disk from fully gas-dominated to the gas-poor debris stage. We show that the decrease in the gas surface density has an important effect. It allows for smaller planetesimals to become collisional, initiating a cascade. At the same time, small particles are not destroyed by collisions. This interrupted cascade is critical in terms of preserving the produced dust for significant time intervals, allowing for a seemingly minor amount of planetesimal collisions to be effective in producing detectable amounts of dust. The warm emission of low amounts of dust in many transitional planet-forming disks might be caused entirely by second-generation dust, exposing planetary material at a much earlier time than the age that debris disks have traditionally been characterised by.