Extension of the empirical accretion law to lower-mass planets

Determine whether the empirical gas-accretion formula given by Eq. 24 can be extended to planets with masses below the approximately one-to-three-Jupiter-mass range studied in the three-dimensional simulations.

Background

The study calibrates its empirical accretion-rate relation using gap-opening planets with planet-to-star mass ratios of 10^-3 to 3 × 10^-3, corresponding to roughly one to three Jupiter masses around a solar-mass star. The authors explicitly identify the extrapolation of this relation to lower planet masses as unresolved. In that regime, gas approaches the planet subsonically because of the narrowing corotation region, which may suppress shock dissipation and produce a qualitatively different dependence of accretion on cooling time.