Multi-wavelength continuum sizes of protoplanetary discs: scaling relations and implications for grain growth and radial drift

TL;DR

This study uses multi-wavelength ALMA observations to analyze protoplanetary disc sizes and properties, revealing consistent size-luminosity relations across wavelengths and supporting the presence of large grains or optically thick substructures.

Contribution

It provides the first comprehensive multi-wavelength size analysis of protoplanetary discs, confirming size-luminosity relations and supporting grain growth models with new observational evidence.

Findings

Size-luminosity relation holds at 1.3 mm, steeper at 3.1 mm

Discs are only 9% smaller at 3.1 mm than at 0.9 mm, less than models predict

Large grains ($a_{max}>1$ mm) explain spectral and size observations

Abstract

We analyse spatially resolved ALMA observations at 0.9, 1.3, and 3.1 mm for the 26 brightest protoplanetary discs in the Lupus star-forming region. We characterise the discs multi-wavelength 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 millimeter continuum size - luminosity relation already observed at 0.9 mm is also present at 1.3 mm with an identical slope, and at 3.1 mm with a steeper slope, confirming that emission at longer wavelengths becomes increasingly optically thin. Second, when observed at 3.1 mm the discs appear to be only 9% smaller than when observed at 0.9 mm, in tension with models of dust evolution which 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 ($a_\mathrm{max}>1 $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 0.9-1.3 mm 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.