Timescale diagnostics for saving viscous and MHD-wind-driven dusty discs from external photoevaporation

Context. The evolution of protoplanetary discs is a function of their internal processes and of the environment in which the discs are located. It is unclear if angular momentum is mainly removed viscously or by magnetic winds or by a combination of the two. While external photoevaporation is expected to severely influence disc evolution and eventually dispersal, there are observational limitations towards highly irradiated discs. Consequently, the interplay between these ingredients and their combined effects on the gas and dust distributions within the disc are poorly understood.Aims. We investigate, for the first time, the evolution of both the gaseous and solid components of viscous, MHD-wind, or hybrid discs, in combination with external far-ultraviolet (FUV) driven mass loss. We tested which combinations of parameters may protect discs from the external irradiation, allowing the solid component to live long enough to allow planet formation to succeed.Methods. We ran a suite of 1D simulations of smooth discs with varying initial sizes, different levels of viscous and MHD-wind stresses (modelled via an alpha parametrisation), and strengths of the external FUV environment. We then tracked disc properties such as their radii, various lifetime diagnostics, and the amount of dust removed by the photoevaporative wind, as a function of the underlying parameters.Results. We find that the biggest role in determining the fate of discs is played by a combination of a disc's ability to spread radially outwards and the strength of FUV-driven erosion. While MHD wind-driven discs experience less FUV erosion due to the lack of spread, they do not live for longer amounts of time compared to viscously evolving discs, especially at low-to-moderate FUV fluxes, while higher fluxes (greater than or similar to 100 G0) yield disc lifetimes that are rather insensitive to the disc's angular momentum transport mechanism. Specifically, for the solid component, the biggest role is played by a combination of inward drift and removal by FUV winds. This points to the importance of other physical ingredients, such as disc substructures, even in highly irradiated disc regions, to retain solids.