A tension between dust and gas radii: The role of substructures and external photoevaporation in protoplanetary disks

Context. Protoplanetary disk substructures are thought to play a crucial role in disk evolution and planet formation. Population studies of disks large-sample size surveys show that not only substructure, but also their rapid formation, are needed to reproduce the observed spectral indices. Moreover, they enable the simultaneous reproduction of the observed spectral index and size-luminosity distributions. Aims. This study is aimed at investigating the need for substructures and predicting their characteristics in reproducing the gas-to-dust size ratios observed in the Lupus star-forming region. Methods. We performed a population synthesis study of gas and dust evolution in disks using a two-population model (two-pop-py) and the DustPy code. We considered the effects of viscous evolution, dust growth, fragmentation, transport, and external photoevaporation. The simulated population distributions were obtained by post-processing the resulting disk profiles of surface density, maximum grain size, and disk temperature. Results. Although substructures do help in reducing the discrepancy between simulated and observed disk gas-to-dust size ratios, even when accounting for external photoevaporation, they do not fully resolve it. Only specific initial conditions in disks undergoing viscous evolution with external photoevaporation are able to reproduce the observations, highlighting a fine-tuning problem. Even in cases where substructured disks successfully reproduce the dust size and spectral index, they tend to overestimate gas radii. Conclusions. These results ultimately highlight the main challenge of simultaneously reproducing gas and dust sizes. One possible explanation is that the outermost substructure is linked to the disk truncation radius, which determines the gas radius. Alternatively, it might be the case that substructures are frequent enough to always be located near the outer radius of the gas.