The time evolution of dusty protoplanetary disc radii: observed and
  physical radii differ
  Proto-planetary disc surveys conducted with ALMA are measuring disc radii in
multiple star forming regions. The disc radius is a fundamental quantity to
diagnose whether discs undergo viscous spreading, discriminating between
viscosity or angular momentum removal by winds as drivers of disc evolution.
Observationally, however, the sub-mm continuum emission is dominated by the
dust, which also drifts inwards, complicating the picture. In this paper we
investigate, using theoretical models of dust grain growth and radial drift,
how the radii of dusty viscous proto-planetary discs evolve with time. Despite
the existence of a sharp outer edge in the dust distribution, we find that the
radius enclosing most of the dust $\textit{mass}$ increases with time, closely
following the evolution of the gas radius. This behaviour arises because,
although dust initially grows and drifts rapidly onto the star, the residual
dust retained on Myr timescales is relatively well coupled to the gas.
Observing the expansion of the dust disc requires using definitions based on
high fractions of the disc $\textit{flux}$ (e.g. 95 per cent) and very long
integrations with ALMA, because the dust grains in the outer part of the disc
are small and have a low sub-mm opacity. We show that existing surveys lack the
sensitivity to detect viscous spreading. The disc radii they measure do not
trace the mass radius or the sharp outer edge in the dust distribution, but the
outer limit of where the grains have significant sub-mm opacity. We predict
that these observed radii should shrink with time.
