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

TL;DR

This study investigates whether substructures and external photoevaporation can reconcile the observed gas-to-dust size ratios in Lupus protoplanetary disks. Using a population synthesis with the two-pop-py model and complementary DustPy simulations including external FUV radiation, the authors compute millimeter fluxes, dust radii, gas radii, and spectral indices to compare with Lupus observations. They find that substructures improve the match for dust properties and the spectral index but tend to overestimate gas radii, while external photoevaporation helps reduce gas radii but can hinder dust trapping, leaving a residual tension in reproducing both gas and dust sizes simultaneously. The results suggest that the outer disk edge or the proximity of pressure traps to the gas edge may play a critical role, and point toward incorporating wind-driven disk evolution, internal photoevaporation, or more complex substructure formation to fully resolve the tension.

Abstract

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.

Figures (10)

• Figure 1: Gas-dust size distribution (first row), spectral index distribution (second row) and size-luminosity distribution (third row) for the parameter space of the initial conditions selecting disks with a spectral index $0 \leq \alpha_{\mathrm{0.89-3.1mm}}\leq 4$, $e-3Jy\leq F_{\rm{1mm}}\leq 10Jy$, $e-3Jy\leq F_{\rm{0.89mm}}\leq 10Jy$, $10^{0.1}\,au\leq R_{\rm{dust(68\%)}}\leq 10^{2.6}\,au$, $1au\leq R_{\rm{dust(90\%)}}\leq 200au$ and $0.1\leq R_{\rm{gas(90\%)}}/R_{\rm{dust(90\%)}}\leq 20$. Left plots: smooth disks. Middle plots: substructured disks with one planet randomly inserted in a range between 0.1-0.4 Myr from the start of the disk evolution. Right plots: substructured disks with two planets randomly inserted in a range between 0.1-0.4 Myr (innermost planet) and between 0.5-0.8 Myr (outermost planet) from the start of the disk evolution. Heatmap of the observed disks with the black dots representing each single observed disk. The black and red lines refer to the simulated results and the observational results respectively. In particular, the continuous lines encompass $30\%$ of the cumulative sum of the disks produced from the simulations or observed. The dashed lines encompass instead the $90\%$.
• Figure 2: Evolution in the $R_{\rm{gas(90\%)}}/R_{\rm{dust(90\%)}}$ vs $R_{\rm{dust(90\%)}}$ space for some test substructured disks evolved with DustPy code with external photoevaporation ($F_{\rm{FUV}} = 4\mathrm{G}_{0}$) in a low viscosity regime ($\alpha=10^{-3.5}$) for different values of the characteristic radius $r_{\rm{c}}$. The points associated with each trajectory represent the snapshots taken at 0Myr, 1Myr, 2Myr, and 3Myr, respectively.
• Figure 3: Evolution in the $R_{\mathrm{gas(90\%)}}/R_{\mathrm{dust(90\%)}}$ vs $R_{\mathrm{dust(90\%)}}$ space for some test substructured disks evolved with DustPy code in a low viscosity regime ($\alpha=10^{-3.5}$) for different values of the characteristic radius $r_\mathrm{c}\xspace$. The points associated with each trajectory represent the snapshots taken at 0Myr, 1Myr, 2Myr, and 3Myr, respectively. Solid line: external photoevaporation ($F_{\rm{FUV}} = 4\mathrm{G}_{0}$). Dashed line: no external photoevaporation ($F_{\rm{FUV}} = 0\mathrm{G}_{0}$).
• Figure 4: Evolution in the spectral index, size-luminosity, and $R_{\mathrm{gas(90\%)}}/R_{\mathrm{dust(90\%)}}$ vs $R_{\mathrm{dust(90\%)}}$ spaces of substructured disks evolved with DustPy code with external photoevaporation ($F_{\rm{FUV}} = 4\mathrm{G}_{0}$). Low viscosity regime ($\alpha=10^{-3.5}$) and disk characteristic radius fixed to $r_{c}=50au$. Different values of the position of the inserted substructure $r_{p}$ have been explored. The points associated with each trajectory represent the snapshots taken at 0Myr, 1Myr, 2Myr, and 3Myr, respectively. Top row: $M_{\rm{disk}}=0.1\mathrm{M_{star}}$. Bottom row: $M_{\rm{disk}}=0.01\mathrm{M_{star}}$.
• Figure 5: Same as Figure \ref{['fig:1substr_50rc']}, but disks with characteristic radius fixed to $r_\mathrm{c}\xspace=100au$.