The dynamical role of the circumplanetary disc in planetary migration

Numerical simulations of planets embedded in protoplanetary gaseous discs are a precious tool for studying the planetary migration ; however, some approximations have to be made. Most often, the selfgravity of the gas is neglected. In that case, it is not clear in the literature how the material inside the Roche lobe of the planet should be taken into account. Here, we want to address this issue by studying the influence of various methods so far used by different authors on the migration rate. We performed high-resolution numerical simulations of giant planets embedded in discs. We compared the migration rates with and without gas selfgravity, testing various ways of taking the circum-planetary disc (CPD) into account. Different methods lead to significantly different migration rates. Adding the mass of the CPD to the perturbing mass of the planet accelerates the migration. Excluding a part of the Hill sphere is a very touchy parameter that may lead to an artificial suppression of the type III, runaway migration. In fact, the CPD is smaller than the Hill sphere. We recommend excluding no more than a 0.6 Hill radius and using a smooth filter. Alternatively, the CPD can be given the acceleration felt by the planet from the rest of the protoplanetary disc. The gas inside the Roche lobe of the planet should be very carefully taken into account in numerical simulations without any selfgravity of the gas. The entire Hill sphere should not be excluded. The method used should be explicitly given. However, no method is equivalent to computing the full selfgravity of the gas.

💡 Research Summary

The paper tackles a subtle but crucial methodological issue in numerical studies of planet–disk interactions: how to treat the gas that resides inside a planet’s Roche (Hill) sphere when the self‑gravity of the gas is neglected. Because most hydrodynamic simulations omit gas self‑gravity to save computational cost, the material bound to the planet—typically a circum‑planetary disc (CPD)—must be handled in an ad‑hoc manner. The authors ask whether different prescriptions for the CPD lead to measurable differences in the migration rate of giant planets.

Using high‑resolution two‑dimensional simulations of a Jupiter‑mass planet embedded in a protoplanetary gas disc, they run two families of experiments. In the first, they compare runs that include the full gas self‑gravity with runs that do not. When self‑gravity is present, the CPD and the surrounding disc interact gravitationally, effectively increasing the planet’s perturbing mass and accelerating the standard Type II inward drift. In the non‑self‑gravity runs, the CPD behaves as a fixed mass “blob” attached to the planet. If the CPD’s mass is added to the planet’s perturbing mass, the migration speeds up, but the torque budget is not physically identical to the self‑gravity case.

The second set of experiments investigates how much of the Hill sphere should be excluded from the torque calculation. A common practice is to cut out the entire Hill sphere, but this removes the CPD’s contribution to the torque entirely. The authors show that such an aggressive exclusion artificially suppresses Type III (runaway) migration, which relies on strong, asymmetric corotation flows that are generated precisely in the planet’s immediate vicinity. By systematically varying the exclusion radius, they find that cutting out only the innermost 0.6 R_H, together with a smooth Gaussian filter at the boundary, preserves the essential torque while avoiding numerical singularities.

An alternative approach they test is to let the CPD experience the same acceleration that the planet feels from the rest of the disc. In effect, the CPD becomes a dynamically responsive component rather than a static mass. This method reproduces many of the torque features seen in the self‑gravity runs, yet it still cannot capture fully non‑linear phenomena such as spiral wave feedback, vortex formation, or multi‑planet resonant interactions that would naturally arise if the gas self‑gravity were computed.

From these experiments the authors draw several practical recommendations for future migration studies that cannot afford full self‑gravity:

1. Explicitly state the CPD treatment – whether its mass is added to the planet’s perturbing mass, excluded, or given the disc‑induced acceleration.
2. Do not exclude the entire Hill sphere – limit exclusion to ≤ 0.6 R_H and apply a smooth filter to avoid sharp force discontinuities.
3. If possible, apply the disc‑induced acceleration to the CPD – this yields a more realistic torque without the full cost of self‑gravity.

Nevertheless, they caution that none of these shortcuts is equivalent to a simulation that includes the full gas self‑gravity. The residual discrepancies become especially important in massive, high‑density discs where the CPD can contain a non‑negligible fraction of the planet’s total mass and where Type III migration can dominate the orbital evolution.

In summary, the paper demonstrates that the handling of gas inside the Roche lobe is not a minor technical detail but a decisive factor that can change migration rates by tens of percent or even suppress runaway migration altogether. By quantifying these effects and proposing a balanced, reproducible prescription, the authors provide a valuable guideline for the community, while also underscoring the ultimate need for self‑gravity‑inclusive simulations as computational resources continue to improve.