A dusty origin for the correlation between protoplanetary disc accretion
  rates and dust masses
  Recent observations have uncovered a correlation between the accretion rates
(measured from the UV continuum excess) of protoplanetary discs and their
masses inferred from observations of the sub-mm continuum. While viscous
evolution models predict such a correlation, the predicted values are in
tension with data obtained from the Lupus and Upper Scorpius star forming
regions; for example, they underpredict the scatter in accretion rates,
particularly in older regions. Here we argue that since the sub-mm observations
trace the discs' dust, by explicitly modelling the dust grain growth,
evolution, and emission, we can better understand the correlation. We show that
for turbulent viscosities with $\alpha \lesssim 10^{-3}$, the depletion of dust
from the disc due to radial drift means we can reproduce the range of masses
and accretion rates seen in the Lupus and Upper Sco datasets. One consequence
of this model is that the upper locus of accretion rates at a given dust mass
does not evolve with the age of the region. Moreover, we find that internal
photoevaporation is necessary to produce the lowest accretion rates observed.
In order to replicate the correct dust masses at the time of disc dispersal, we
favour relatively low photoevaporation rates $\lesssim
10^{-9}~M_{\odot}~\mathrm{yr^{-1}}$ for most sources but cannot discriminate
between EUV or X-ray driven winds. A limited number of sources, particularly in
Lupus, are shown to have higher masses than predicted by our models which may
be evidence for variations in the properties of the dust or dust trapping
induced in substructures.
