Gravitoviscous Protoplanetary Discs with a Dust Component. IV. Disc Outer Edges, Spectral Indices, and Opacity Gaps

Abstract

The crucial initial step in planet formation is the agglomeration of micron-sized dust into macroscopic aggregates. This phase is likely to happen very early during the protostellar disc formation, which is characterised by active gas dynamics. We present numerical simulations of protostellar/protoplanetary disc long-term evolution, which includes gas dynamics with self-gravity in the thin-disc limit, and bidisperse dust grain evolution due to coagulation, fragmentation, and drift through the gas. We show that the decrease of the grain size to the disc periphery leads to sharp outer edges in dust millimetre emission, which are explained by a drop in dust opacity coefficient rather than by dust surface density variations. These visible outer edges are at the location where average grain size $\approx λ/2π$, where $λ$ is the observational wavelength, so discs typically look more compact at longer wavelengths if dust size decreases outwards. This allows a simple recipe for reconstructing grain sizes in disc outer regions. Discs may look larger at longer wavelengths if grain size does not reach $λ/2π$ for some wavelength. Disc visible sizes evolve non-monotonically over the first million years and differ from dust and gas physical sizes by factor of a few. We compare our model with recent observation data on gas and dust disc sizes, far-infrared fluxes and spectral indices of protoplanetary discs in Lupus. We also show that non-monotonic variations of the grain size in radial direction can cause wavelength-dependent opacity gaps, which are not associated with any physical gaps in the dust density distribution.