Dust clearing by radial drift in evolving protoplanetary discs

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 sublinear scaling between the gas disc mass and the gas accretion rate (M-g proportional to 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 discs is on the order of 10-100 M-circle plus in 1-3 Myr-old star-forming regions, a factor of 10-100 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 up to a factor of four above the initial value. In these regions of high dust-to-gas ratio 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 ( M proportional to M-star(1.4) M proportional to M star 1.4 ), a slightly super-linear scaling between the gas disc mass and the stellar mass ( M-g proportional to M-star(1.4) Mg proportional to M star 1.4 ), and a super-linear relation between the dust disc mass and stellar mass ( M-d proportional to M-star(1.4-4.1) Md proportional to M star 1.4-4.1 ).