Population Synthesis Models Indicate a Need for Early and Ubiquitous Disk Substructures

Large mm surveys of star forming regions enable the study of entire populations of planet-forming disks and reveal correlations between their observable properties. Population studies of disks have shown that the correlation between disk size and millimeter flux could be explained either through disks with strong substructure, or alternatively by the effects of radial inward drift of growing dust particles. This study aims to constrain the parameters and initial conditions of planet-forming disks and address the question of the need for the presence of substructures in disks and, if needed, their predicted characteristics, based on the large samples of disk sizes, millimeter fluxes, and spectral indices available. We performed a population synthesis of the continuum emission of disks, exploiting a two-population model (two-pop-py), considering the influence of viscous evolution, dust growth, fragmentation, and transport varying the initial conditions of the disk and substructure to find the best match to the observed distributions. We show that the observed distributions of spectral indices, sizes, and luminosities together can be best reproduced by disks with significant substructure, namely a perturbation strong enough to be able to trap particles, and that is formed early in the evolution of the disk, that is within 0.4Myr. Agreement is reached by relatively high initial disk masses ($10^{-2.3}M_{\star}\leqslant M_{disk}\leqslant10^{-0.5}M_{\star}$) and moderate levels of turbulence ($10^{-3.5}\leqslant\alpha\leqslant 10^{-2.5}$). Other disk parameters play a weaker role. Only opacities with high absorption efficiency can reproduce the observed spectral indices. Our results extend to the whole population that substructure is likely ubiquitous, so far assessed only in individual disks and implies that most "smooth" disks hide unresolved substructure.