Abstract
Context. Large millimeter surveys of star-forming regions enable the study of entire populations of planet-forming disks and reveal correlations between their observable properties. The ever-increasing number of these surveys has led to a flourishing of population study, a valuable tool and approach that is spreading in ever more fields. 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.
Aims. 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.
Methods. 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 with the observed distributions. Disks both with and without substructure have been examined. We obtained the simulated population distribution for the disk sizes, millimeter fluxes, and spectral indices by post-processing the resulting disk profiles (surface density, maximum grain size, and disk temperature).
Results. 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 that is strong enough to be able to trap particles, that is formed early in the evolution of the disk, and that is within 0.4 Myr. Agreement is reached by relatively high initial disk masses (10−2.3 M⋆ ⩽ Mdisk ⩽ 10−0.5 M⋆) and moderate levels of turbulence (10−3.5 ⩽ α ⩽ 10−2.5). Other disk parameters play a weaker role. Only opacities with a high absorption efficiency can reproduce the observed spectral indices.
Conclusions. Disk population synthesis is a precious tool for investigating and constraining the parameters and initial conditions of planet-forming disks. The generally low observed spectral indices call for significant substructure, like that which planets in the mass range of Saturn to a few Jupiters would induce, to already be present before 0.4 Myr. Our results indicate that substructure, which so far has only been assessed in individual disks, is likely ubiquitous and extends to the whole population, and imply that most “smooth” disks hide unresolved substructure.