Modeling the delivery of dust from discs to ionized winds

A necessary first step for dust removal in protoplanetary disc winds is the delivery of dust from the disc to the wind. In the case of ionized winds, the disc and wind are sharply delineated by a narrow ionization front where the gas density and temperature vary by more than an order of magnitude. Using a novel method that is able to model the transport of dust across the ionization front in the presence of disc turbulence, we revisit the problem of dust delivery. Our results show that the delivery of dust to the wind is determined by the vertical gas flow through the disc induced by the mass loss, rather than turbulent diffusion (unless the turbulence is strong, i.e. $\alpha \gtrsim 0.01$). Using these results we provide a simple relation between the maximum size of particle that can be delivered to the wind and the local mass-loss rate per unit area from the wind. This relation is independent of the physical origin of the wind and predicts typical sizes in the 0.01 -- $1\,\mu m$ range for EUV or X-ray driven winds. These values are a factor $\sim 10$ smaller than those obtained when considering only whether the wind is able to carry away the grains.