Dust clearing by radial drift in evolving protoplanetary discs

Abstract

Recent surveys have revealed that protoplanetary discs typically have dust masses that appear to be insufficient to account for the high occurrence rate of exoplanet systems. We demonstrate that this observed dust depletion is consistent with the radial drift of pebbles. Using a Monte Carlo method we simulate the evolution of a cluster of protoplanetary discs, using a 1D numerical method to viscously evolve each gas disc together with the radial drift of dust particles that have grown to 100 $\mu$m in size. For a 2 Myr old cluster of stars, we find a slightly sub-linear scaling between the gas disc mass and the gas accretion rate ($M_\mathrm{g}\propto\dot{M}^{0.9}$). However, for the dust mass we find that evolved dust discs have a much weaker scaling with the gas accretion rate, with the precise scaling depending on the age at which the cluster is sampled and the intrinsic age spread of the discs in the cluster. Ultimately, we find that the dust mass present in protoplanetary disc is on the order of 10-100 Earth masses in 1-3 Myr old star-forming regions, a factor of 10 to 100 depleted from the original dust budget. As the dust drains from the outer disc, pebbles pile up in the inner disc and locally increase the dust-to-gas ratio by a factor of up to 4 above the initial value. In these high dust-to-gas ratio regions we find conditions that are favourable for planetesimal formation via the streaming instability and subsequent growth by pebble accretion. We also find the following scaling relations with stellar mass within a 1-2 Myr old cluster: a slightly super-linear scaling between the gas accretion rate and stellar mass ($\dot{M}\propto M_\star^{1.4}$), a slightly super-linear scaling between the gas disc mass and the stellar mass ($M_\mathrm{g}\propto M_\star^{1.4}$) and a super-linear relation between the dust disc mass and stellar mass ($M_\mathrm{d}\propto M_\star^{1.4-4.1}$).