Coagulation of small grains in disks: the influence of residual infall and initial small-grain content

Abstract

Turbulent coagulation in protoplanetary disks is known to operate on a timescale far shorter than the lifetime of the disk. In the absence of mechanisms that replenish the small dust grain population, protoplanetary disks would rapidly lose their continuum opacitybearing dust. This is inconsistent with infrared observations of disks around T Tauri stars and Herbig Ae/Be stars, which are usually optically thick at visual wavelengths and show signatures of small (a 3 μm) grains. A plausible replenishing mechanism of small grains is collisional fragmentation or erosion of large dust aggregates, which model calculations predict to play an important role in protoplanetary disks. If optically thick disks are to be seen as proof for ongoing fragmentation or erosion, then alternative explanations for the existence of optically thick disks must be studied carefully. In this study we explore two scenarios. First, we study the effect of residual, low-level infall of matter onto the disk surface. We find that infall rates as low as 10 −11 M /yr can, in principle, replenish the small grain population to a level that keeps the disk marginally optically thick. However, it remains to be seen if the assumption of such an inflow is realistic for star+disk systems at the age of several Myrs, at which winds and jets are expected to have removed any residual envelope. The effectiveness of even a low level infall can be understood by the strongly non-linear behavior of the coagulation equation: a high, fine-grain, dust density at any given time leads to very fast, effective removal of these small grains, while a low fine-grain density lasts for a far longer time. We then consider a second scenario in which, during the buildup phase of the disk, an intermediate fine-grain dust abundance is generated that is sufficiently low to ensure longevity of the state yet sufficiently high for the disk to remain optically thick. While our models confirm that such an "initial condition" can be constructed, we argue that these special initial conditions cannot be achieved during the disk build-up phase. In summary, fragmentation or erosion still appear to be the most promising processes to explain the abundant presence of small grains in old disks.

Dust Filtration by Planet-Induced Gap Edges: Implications for Transitional Disks

“…It may only take 10 3 yr for dust particles to grow from submicron sizes to 1000 μm at 1 AU (e.g., models S3 and S4 in Dullemond & Dominik 2005). One way to stop the rapid dust growth is by collisional fragmentation (Dullemond & Dominik 2005;Dominik & Dullemond 2008), in which case large particles are shattered to replenish small dust grains. Thus, the growth and fragmentation maintains a quasi-stationary dust size distribution function.…”

Dust Evolution in Protoplanetary Disks

“…Dullemond and Dominik, 2005;Birnstiel et al, 2009;Zsom et al, 2011) or by continuous infall (e.g. Mizuno et al, 1988;Dominik and Dullemond, 2008).…”

THE PROPAGATION OF Lyα IN EVOLVING PROTOPLANETARY DISKS

“…Not only does grain growth affect the optical properties of individual grains, but also the radial and vertical drift of solids relative to gas causes a segregation of the grainsize population (Weidenschilling 1977;Dullemond & Dominik 2004). The majority of the grain opacity at FUV wavelengths is attributable to relatively small grains with radii a < 1 μm, which subsequently reemit absorbed energy at infrared wavelengths, making it possible to estimate their abundance (Dominik & Dullemond 2008). Observationally, the abundance of small grains (per H nucleus) relative to that found in the interstellar medium (ISM), , typically takes a value much less than one, for example, in the Taurus star-forming region the median value is ∼ 0.01 (Furlan et al 2006).…”