Protoplanetary disc population synthesis I. Linking mass-dependent viscosity, star formation history and environment to observations

Abstract

Context. Recent studies highlight the importance of stellar mass sampling when determining disc lifetimes through observed disc fractions. Low-mass stars host discs with average lifetimes exceeding 5~Myr, and accretion rates show a strong correlation with stellar mass ($\dot{M} \propto M_\star^2$). Aims. We aim to identify the optimal parameters of a protoplanetary disc evolution model capable of reproducing both observed disc fractions and mass accretion rates in young stellar populations. Methods. We conducted a population synthesis study modelling disc evolution via viscous accretion and internal/external photoevaporation. Initial disc masses and radii were drawn from observational distributions. We explored the viscosity parameter $\alpha$ as a function of stellar mass, and incorporated a stellar mass distribution and a star formation rate (SFR). Results. Matching observed disc fractions and accretion trends requires that $\alpha$ increases with stellar mass. External photoevaporation and a systematic underestimation of gas disc masses (due to dust evolution and hidden solids) are needed to reproduce the $\dot{M}-M_{\rm d}$ plane. Accounting for a time-dependent SFR enhances accretion in young clusters and extends disc lifetimes in older ones. Introducing a stellar mass cut-off reproduces distance-dependent biases in cluster disc fractions. Conclusions. Stellar and environmental dependencies are both essential to explain observed disc properties. A stellar-mass-dependent viscosity recovers the $\dot{M}-M_\star$ relation, while external photoevaporation and extended star formation histories shape accretion rate distributions across environments, emphasizing the value of multi-faceted population synthesis models.