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 less than or similar to 0.001. In this case, the relation has an almost universal normalization, 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 normalization factor that scales as the square of the observing frequency as in the optically thick case.