On the time evolution of the Md−M⋆ and Ṁ–M⋆ correlations for protoplanetary discs: the viscous time-scale increases with stellar mass.

Large surveys of star-forming regions have unveiled power-law correlations between the stellar mass and the disc parameters, such as the disc mass |$M_{\mathrm{d}} \!-\! {M_{\star }}$| and the accretion rate |$\dot{M} \!-\! {M_{\star }}$|⁠. The observed slopes appear to be increasing with time, but the reason behind the establishment of these correlations and their subsequent evolution is still uncertain. We conduct a theoretical analysis of the impact of viscous evolution on power-law initial conditions for a population of protoplanetary discs. We find that, for evolved populations, viscous evolution enforces the two correlations to have the same slope, λ _m =  λ _acc, and that this limit is uniquely determined by the initial slopes λ _{m, 0} and λ _{acc, 0}. We recover the increasing trend claimed from the observations when the difference in the initial values, δ ₀ = λ _{m, 0}− λ _{acc, 0}, is larger than 1/2; moreover, we find that this increasing trend is a consequence of a positive correlation between the viscous time-scale and the stellar mass. We also present the results of disc population synthesis numerical simulations, that allow us to introduce a spread and analyse the effect of sampling, which show a good agreement with our analytical predictions. Finally, we perform a preliminary comparison of our numerical results with observational data, which allows us to constrain the parameter space of the initial conditions to λ _{m, 0} ∈ [1.2, 2.1], λ _{acc, 0} ∈ [0.7, 1.5]. [ABSTRACT FROM AUTHOR]