The evolution of the flux-size relationship in protoplanetary discs by viscous evolution and radial pebble drift

¹ Lund Observatory, Division of Astrophysics, Department of Physics, Lund University, Box 43, 22100 Lund, Sweden
² Center for Star and Planet Formation, Globe Institute, University of Copenhagen, Øster Voldgade 5-7, 1350 Copenhagen, Denmark
³ Centre for Star and Planet Formation, Niels Bohr Institute & Natural History Museum of Denmark, University of Copenhagen, Øster Voldgade 5–7, 1350 Copenhagen K., Denmark
⁴ Leiden Observatory, Leiden University, PO Box 9531, 2300 RA Leiden, The Netherlands
⁵ Academia Sinica Institute of Astronomy & Astrophysics, 11F of Astronomy-Mathematics Building, AS/NTU, No.1, Sec. 4, Roosevelt Rd, Taipei 10617, Taiwan
⁶ National Radio Astronomy Observatory, 520 Edgemont Rd., Charlottesville, VA 22903, USA

^★ Corresponding author; Anders.Johansen@sund.ku.dk

Received: 30 May 2024
Accepted: 6 January 2025

Abstract

In this paper we study the evolution of radiative fluxes, flux radii and observable dust masses in protoplanetary discs, in order to understand how these depend on the angular momentum budget and on the assumed heat sources. We use a model that includes the formation and viscous evolution of protoplanetary gas discs, together with the growth and radial drift of the dust component. We find that we are best able to match the observed fluxes and radii of class 0/I discs when we assume (i) an initial total angular momentum budget corresponding to a centrifugal radius of 40 au around solar-like stars, and (ii) inefficient viscous heating. Fluxes and radii of class II discs appear consistent with disc models with angular momentum budgets equivalent to centrifugal radii of both 40 or 10 au for solar-like stars, and with models where viscous heating occurs at either full efficiency or at reduced efficiency. During the first ∼0.5 Myr of their evolution discs are generally optically thick at λ = 1.3 mm. However, after this discs are optically thin at mm-wavelengths, supporting standard means of dust mass estimates. Using a disc population synthesis model, we then show that the evolution of the cumulative evolution of the observable dust masses agrees well with that observed in young star forming clusters of different ages.