Dust delivery and entrainment in photoevaporative winds

We model the gas and dust dynamics in a turbulent protoplanetary disc undergoing extreme-UV photoevaporation in order to better characterise the dust properties in thermal winds (e.g. size distribution, flux rate, trajectories). Our semi-analytic approach allows us to rapidly calculate these dust properties without resorting to expensive hydrodynamic simulations. We find that photoevaporation creates a vertical gas flow within the disc that assists turbulence in supplying dust to the ionisation front. We examine both the delivery of dust to the ionisation front and its subsequent entrainment in the overlying wind. We derive a simple analytic criterion for the maximum grain size that can be entrained and show that this is in good agreement with the results of previous simulations where photoevaporation is driven by a range of radiation types. We show that, in contrast to the case for magnetically driven winds, we do not expect large scale dust transport within the disc to be effected by photoevaporation. We also show that the maximum size of grains that can be entrained in the wind ($s_{\rm max}$) is around an order of magnitude larger than the maximum size of grains that can be delivered to the front by advection alone ($s_{\rm crit} \lesssim 1$ $\mu{\rm m}$ for Herbig Ae/Be stars and $\lesssim 0.01$ $\mu{\rm m}$ for T Tauri stars). We further investigate how larger grains, up to a limiting size $s_{\rm limit}$, can be delivered to the front by turbulent diffusion alone. In all cases, we find $s_{\rm max} \gtrsim s_{\rm limit}$ so that we expect that any dust that is delivered to the front can be entrained in the wind and that most entrained dust follows trajectories close to that of the gas.