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

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Rosotti, GP 
Booth, RA 
Lodato, G 

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 α 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.

accretion, accretion discs, planets and satellites: formation, protoplanetary discs, circumstellar matter, submillimetre: planetary systems
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Monthly Notices of the Royal Astronomical Society: Letters
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Oxford University Press (OUP)
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European Research Council (341137)
European Commission Horizon 2020 (H2020) Marie Sk?odowska-Curie actions (823823)
Science and Technology Facilities Council (ST/N000927/1)
Science and Technology Facilities Council (ST/S000623/1)