On the millimetre continuum flux-radius correlation of proto-planetary
  discs
  A correlation between proto-planetary disc radii and sub-mm fluxes has been
recently reported. In this Letter we show that the correlation is a sensitive
probe of grain growth processes. Using models of grain growth and drift, we
have shown in a companion paper that the observed disc radii trace where the
dust grains are large enough to have a significant sub-mm opacity. We show that
the observed correlation emerges naturally if the maximum grain size is set by
radial drift, implying relatively low values of the viscous $\alpha$ parameter
$ \lesssim 0.001$. In this case the relation has an almost universal
normalisation, while if the grain size is set by fragmentation the flux at a
given radius depends on the dust-to-gas ratio. We highlight two observational
consequences of the fact that radial drift limits the grain size. The first is
that the dust masses measured from the sub-mm could be overestimated by a
factor of a few. The second is that the correlation should be present also at
longer wavelengths (e.g. 3mm), with a normalisation factor that scales as the
square of the observing frequency as in the optically thick case.
