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

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 substructures, and 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. This study aims to investigate the necessity of substructures and predict their characteristics to reproduce gas-to-dust size ratios observed in the Lupus star-forming region. 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. Although substructures help reduce 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 can reproduce the observations, highlighting a fine-tuning problem. While substructured disks reproduce dust size and spectral index, they tend to overestimate gas radii. The 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, or that substructures are frequent enough to always be near the gas outer radius.

💡 Research Summary

This paper investigates why observed gas‑to‑dust radius ratios (R_CO/R_dust) in the Lupus star‑forming region cluster around 2–4, whereas many theoretical models predict values >5. The authors perform a two‑stage population synthesis. In the first stage they run 10⁵ disk evolutions with the two‑population model (two‑pop‑py), which couples viscous gas evolution (parameterized by α) with dust growth, fragmentation, and radial drift. Disk initial conditions (stellar mass, disk mass, characteristic radius, α, fragmentation velocity) are drawn from realistic probability distributions. Substructures are introduced by mimicking planetary gaps: a local increase in α_gas creates a gap in the gas surface density, trapping dust at the pressure maximum. In the second stage they use DustPy, augmented with an external photoevaporation module based on the FRIEDv2 grid, to model the effect of a moderate far‑ultraviolet field (≈4 G₀, typical for Lupus). Photoevaporation removes gas outside a truncation radius that evolves with time.

Results show that smooth disks quickly develop large R_CO/R_dust (>5) because dust drifts inward efficiently. Adding substructures reduces the ratio to ≈3–5 by retaining dust in pressure bumps, but the simulated gas radii remain too large. Including external photoevaporation modestly shrinks the gas disk, yet the ratio still exceeds the bulk of the observations unless the outermost substructure coincides with the truncation radius. Only a narrow region of parameter space—low α (10⁻³–10⁻⁴), moderate characteristic radii (20–100 au), disk‑to‑star mass ratios of 0.01–0.1, and early formation of relatively massive planets—reproduces the observed distribution. This fine‑tuning highlights a tension: current models can match either dust spectral indices and size‑luminosity relations or gas‑to‑dust ratios, but not all simultaneously. The authors propose two possible resolutions: (1) the outermost pressure bump physically sets the disk truncation radius, linking substructure location to gas size; (2) substructures are ubiquitous and typically lie near the gas edge, naturally yielding low R_CO/R_dust. They conclude that more sophisticated treatments—including magnetohydrodynamic winds, internal photoevaporation, and a broader range of substructure morphologies—are required to fully reconcile theory with the observed gas and dust sizes.