Modelling the secular evolution of protoplanetary disc dust sizes - a comparison between the viscous and magnetic wind case

For many years, protoplanetary discs have been thought to evolve viscously: angular momentum redistribution leads to accretion and outward disc spreading. Recently, the hypothesis that accretion is due, instead, to angular momentum removal by magnetic winds gained new popularity: no disc spreading is expected in this case. In this paper, we run several 1D gas and dust simulations to make predictions on the time evolution of disc sizes in the dust and to assess whether they can be used to understand how discs evolve. We show that viscous and magnetic wind models have very different dust disc radii. In particular, magnetohydrodynamic wind models are compact and their sizes either remain constant or decrease with time. On the contrary, discs become larger with time in the viscous case (when alpha greater than or similar to 10(-3)). Although current observations lack enough sensitivity to discriminate between these two scenarios, higher sensitivity surveys could be fruitful to this goal on a 1-10 Myr age range. When compared with the available ALMA (Atacama Large Millimeter/submillimeter Array) Band 7 data, both viscous and magnetic wind models are compatible with the observationally inferred dust radii in Lupus, Chamaeleon I, and Upper Sco. Furthermore, in the drift-dominated regime, the size-luminosity correlation is reproduced in Lupus, both in Band 7 and 3, while in Upper Sco a different slope than in the data is predicted. Sub-structures (potentially undetected) can explain several outliers with large observed sizes. Higher angular-resolution observations will be helpful to test our predictions in the case of more compact discs, expected in both frameworks, particularly at the age of Upper Sco.