The Mass Budgets and Spatial Scales of Exoplanets and Protoplanetary Disks

Planets are born from protoplanetary disks, and observations of these disks are used to constrain the initial conditions of planet formation. However, dust mass measurements of Class II protoplanetary disks with ALMA have called into question whether disks contain enough solids to build the exoplanets that have been detected to date. Here, we show that this apparent mass discrepancy disappears when accounting for observational selection and detection biases in protoplanetary disk and exoplanet surveys.

We calculate the mass and spatial distribution of solid material around sun-like stars probed by exoplanet surveys, and compare those to the observed masses and sizes of protoplanetary disks in the same stellar mass regime. We show that most of the solid reservoir contained in exoplanets, about 10 Earth mass on average, is located in sub-Neptunes between 0.1 and 1 au, with a smaller contribution from giant planets between 1-10 au. In contrast, the same amount of dust in protoplanetary disks is detected at spatial scales that are a factor of 100 larger.

Thus, the posed mass budget problem of protoplanetary disks is instead a surface density problem. The inner regions of Class II protoplanetary disks do not contain enough material to form exoplanets under reasonable assumption for the radial mass distribution.

The frequency of close-in exoplanets can be explained if planet migration is extremely efficient, dust grains experience global-scale radial drift, or if protoplanetary disks have an undetected mass reservoir in the inner disk that is as large as that in the outer disk. Most likely, planet formation is well underway by the time we observe protoplanetary disks, and Class II disks do not represent the initial reservoir of material that forms exoplanets.