The evolution of the $M_{\mathrm{d}}-M_{\star }$ and $\dot{M}-M_{\star }$ correlations traces protoplanetary disc dispersal

Abstract

(Abridged) Observational surveys of entire star-forming regions have provided evidence of power-law correlations between the disc properties and the stellar mass, especially the disc mass (${M_d\propto M_{\ast }}^{{\lambda }_m}$) and the accretion rate ($\dot{M}\propto {M_{\ast }}^{{\lambda }_{acc}}$). Whether the secular disc evolution affects said correlations is still debated: while the purely viscous scenario has been probed, other mechanisms could impact differently. We study the evolution of the slopes ${\lambda }_m$ and ${\lambda }_{acc}$ in the wind-driven and hybrid case and compare it to the viscous prediction, using a combination of analytical calculations and numerical simulations (performed with the 1D population synthesis code Diskpop, that we also present and release). Assuming $M_d(0)\propto {M_{\ast }}^{{\lambda }_{m,0}}$ and $\dot{M}(0)\propto {M_{\ast }}^{{\lambda }_{acc,0}}$ as initial conditions, we find that viscous and hybrid accretion preserve the shape of the correlations and evolve their slope; on the other hand, MHD winds change the shape of the correlations, bending them according to the scaling of the accretion timescale with the stellar mass. We also show how a spread in the initial conditions conceals this behaviour. We then analyse the impact of disc dispersal, and find that the currently available sample sizes ($\sim 30$ discs at 5 Myr) introduce stochastic oscillations in the slopes evolution, which dominate over the physical signatures. Increasing the sample size could mitigate this issue: $\sim 140$ discs at 5 Myr, corresponding to the complete Upper Sco sample, would give small enough error bars to use the evolution of the slopes as a proxy for the driving mechanism of disc evolution. Finally, we discuss how the observational claim of steepening slopes necessarily leads to an initially steeper $M_d-M_{\ast }$ correlation with respect to $\dot{M}-M_{\ast }$.

14 pages, 5 figures and 3 tables (plus Appendix). Accepted for publication in A&A. Includes Diskpop and popcorn software release

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