# On the millimetre continuum flux-radius correlation of proto-planetary discs

## TL;DR

This paper demonstrates that the observed flux-radius correlation in proto-planetary discs is a natural consequence of grain growth limited by radial drift, providing insights into dust evolution and observational biases.

## Contribution

It shows that the flux-radius correlation arises from grain growth constrained by radial drift, with implications for disc viscosity and dust mass estimates.

## Key findings

- Correlation indicates grain size limited by radial drift
- Dust masses may be overestimated by a factor of a few
- Correlation should also be observable at longer wavelengths

## Abstract

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.