Determining the mechanisms that drive the evolution of protoplanetary disks is a necessary step toward understanding how planets form. For this work, we measured the mass accretion rate for young stellar objects with disks at age > 5 Myr, a critical test for the current models of disk evolution. We present the analysis of the spectra of 36 targets in the ∼5–10 Myr old Upper Scorpius star-forming region for which disk masses were measured with ALMA. We find that the mass accretion rates in this sample of old but still surviving disks are similarly high as those of the younger (∼1−3 Myr old) star-forming regions of Lupus and Chamaeleon I, when considering the dependence on stellar and disk mass. In particular, several disks show high mass accretion rates ≳10−9 M⊙ yr−1 while having low disk masses. Furthermore, the median values of the measured mass accretion rates in the disk mass ranges where our sample is complete at a level ∼60−80% are compatible in these three regions. At the same time, the spread of mass accretion rates at any given disk mass is still > 0.9 dex, even at age > 5 Myr. These results are in contrast with simple models of viscous evolution, which would predict that the values of the mass accretion rate diminish with time, and a tighter correlation with disk mass at age > 5 Myr. Similarly, simple models of internal photoevaporation cannot reproduce the observed mass accretion rates, while external photoevaporation might explain the low disk masses and high accretion rates. A possible partial solution to the discrepancy with the viscous models is that the gas-to-dust ratio of the disks at ∼5–10 Myr is significantly different and higher than the canonical 100, as suggested by some dust and gas disk evolution models. The results shown here require the presence of several interplaying processes, such as detailed dust evolution, external photoevaporation, and possibly MHD winds, to explain the secular evolution of protoplanetary disks.

In this paper, we compare simple viscous diffusion models for the disc evolution with the results of recent surveys of the properties of young protoplanetary discs. We introduce the useful concept of 'disc isochrones' in the accretion rate -disc mass plane and explore a set of Montecarlo realization of disc initial conditions. We find that such simple viscous models can provide a remarkable agreement with the available data in the Lupus star forming region, with the key requirement that the average viscous evolutionary timescale of the discs is comparable to the cluster age. Our models produce naturally a correlation between mass accretion rate and disc mass that is shallower than linear, contrary to previous results and in agreement with observations. We also predict that a linear correlation, with a tighter scatter, should be found for more evolved disc populations. Finally, we find that such viscous models can reproduce the observations in the Lupus region only in the assumption that the efficiency of angular momentum transport is a growing function of radius, thus putting interesting constraints on the nature of the microscopic processes that lead to disc accretion.

In this paper we analyse giant gap-opening planet migration in protoplanetary discs, focusing on the type II migration regime. According to standard type II theory, planets migrate at the same rate as the gas in the disc, as they are coupled to the disc viscous evolution; however, recent studies questioned this paradigm, suggesting that planets migrate faster than the disc material. We study the problem through 2D long-time simulations of systems consistent with type II regime, using the hydrodynamical grid code FARGO3D. Even though our simulations confirm the presence of an initial phase characterised by fast migration, they also reveal that the migration velocity slows down and eventually reaches the theoretical prediction if we allow the system to evolve for enough time. We find the same tendency to evolve towards the theoretical predictions at later times when we analyse the mass flow through the gap and the torques acting on the planet. This transient is related to the initial conditions of our (and previous) simulations, and is due to the fact that the shape of the gap has to adjust to a new profile, once the planet is set into motion. Secondly, we test whether the type II theory expectation that giant planet migration is driven by viscosity is consistent with our simulation by comparing simulations with the same viscosity and different disc mass (or viceversa). We find a good agreement with the theory, since when the discs are characterised by the same viscosity, the migration properties are the same.