2018ApJ...854..112M

We present a semi-analytical population synthesis model of protoplanetary clumps formed by disk instability at radial distances of 80-120 au. Various clump density profiles, initial mass functions, protoplanetary disk models, stellar masses, and gap opening criteria are considered. When we use more realistic gap opening criteria, we find that gaps open only rarely, which strongly affects clump survival rates and their physical properties (mass, radius, and radial distance). The inferred surviving population is then shifted toward less massive clumps at smaller radial distances. We also find that populations of surviving clumps are very sensitive to the model assumptions and used parameters. Depending on the chosen parameters, the protoplanets occupy a mass range between 0.01 and 16 M_J and may either orbit close to the central star or as far out as 75 au, with a sweet spot at 10-30 au for the massive ones. However, in all of the cases we consider, we find that massive giant planets at very large radial distances are rare, in qualitative agreement with current direct imaging surveys. We conclude that caution should be taken in deriving population synthesis models as well as when comparing the models' results with observations.