Multiwavelength continuum sizes of protoplanetary discs: scaling relations and implications for grain growth and radial drift

We analyse spatially resolved ALMA observations at 0.9, 1.3, and 3.1mm for the 26 brightest protoplanetary discs in the Lupus star-forming region. We characterize the discs multiwavelength brightness profiles by fitting the interferometric visibilities in a homogeneous way, obtaining effective disc sizes at the three wavelengths, spectral index profiles, and optical depth estimates. We report three fundamental discoveries: first, the millimetre continuum size-luminosity relation already observed at 0.9mm is also present at 1.3mm with an identical slope, and at 3.1mm with a steeper slope, confirming that emission at longer wavelengths becomes increasingly optically thin. Second, when observed at 3.1mm the discs appear to be only 9 percent smaller than when observed at 0.9mm, in tension with models of dust evolution that predict a starker difference. Third, by forward modelling the sample of measurements with a simple parametric disc model, we find that the presence of large grains (mm) throughout the discs is the most favoured explanation for all discs as it reproduces simultaneously their spectral indices, optical depth, luminosity, and radial extent in the 0.9-1.3mm wavelength range. We also find that the observations can be alternatively interpreted with the discs being dominated by optically thick, unresolved, substructures made of mm-sized grains with a high scattering albedo.