Protoplanetary disc population synthesis I. Constraining disc parameters to reproduce disc observations

Abstract: Context. Protoplanetary discs are the birthplaces of planets. Recent studies highlight the role of stellar mass sampling in determining disc lifetimes from the observed fraction of stars with discs. Low-mass stars tend to host longer-lived discs, allowing planet formation via solid accretion. Observations also reveal a strong correlation between stellar (and substellar) mass and accretion rate, typically following $\dot{M}\propto M_\star^2$. Aims. We aim to identify the optimal parameters of a disc evolution model that reproduces both the observed disc fractions and accretion rates in young stellar populations. Methods. We performed a population synthesis study exploring different dependencies of the viscosity parameter $\alpha$ on stellar mass. Disc evolution includes viscous accretion and photoevaporation (internal and external). Initial disc masses and radii were drawn from observationally motivated distributions, while stellar masses followed a given distribution and a time-dependent star formation rate (SFR) was introduced. Results. Matching observed disc fractions and accretion trends requires $\alpha$ to increase with stellar mass. External photoevaporation is necessary to produce low-mass discs with high accretion rates, and a time-dependent SFR enhances accretion in young clusters while extending disc lifetimes in older ones. A stellar mass cut-off reproduces the distance-dependent biases in observed disc fractions. Conclusions. Both stellar and environmental effects are essential to explain the observed properties of protoplanetary discs. A stellar-mass-dependent viscosity reproduces the $\dot{M}$-$M_\star$ relation, while external photoevaporation and extended star formation histories shape the accretion rate distribution across environments.