The evolution of the Md–M⋆ and Ṁ–M⋆ correlations traces protoplanetary disc dispersal

Observational surveys of entire star-forming regions have provided evidence of power-law correlations between the disc-integrated properties and the stellar mass, especially the disc mass (Md ∝ M* λm) and the accretion rate (Ṁ ∝ M* λacc). Whether the secular disc evolution affects said correlations is still a matter of debate: while the purely viscous scenario has been investigated, other evolutionary mechanisms could have a different impact. In this paper, we study the time evolution of the slopes λm and λacc in the wind-driven and viscous-wind hybrid case and compare it to the purely viscous prediction. We use a combination of analytical calculations, where possible, and numerical simulations performed with the 1D population synthesis code Diskpop, which we also present and release to the community. Assuming (Md(0) ∝ M* λm,0) and (Ṁ(0) ∝ M* λacc,0) as initial conditions, we find that viscous and hybrid accretion preserve the power-law shape of the correlations, while evolving their slope; on the other hand, magneto-hydrodynamic winds change the shape of the correlations, bending them in the higher or lower end of the stellar mass spectrum depending on the scaling of the accretion timescale with the stellar mass. However, we show how a spread in the initial conditions conceals this behaviour, leading to power-law correlations with evolving slopes as in the viscous and hybrid case. We analyse the impact of disc dispersal, intrinsic in the wind model and due to internal photoevaporation in the viscous case: we find that the currently available sample sizes (~30 discs at 5 Myr) introduce stochastic oscillations in the slopes’ evolution, which dominate over the physical signatures. We show that we could mitigate this issue by increasing the sample size: with ~140 discs at 5 Myr, corresponding to the complete Upper Sco sample, we would obtain small enough error bars to use the evolution of the slopes as a proxy for the driving mechanism of disc evolution. Finally, from our theoretical arguments, we discuss how the observational claim of steepening slopes necessarily leads to an initially steeper Md–M* correlation with respect to Ṁ–M*.