Table A.2.
Explanations of variables related to the planet used in our model.
| Parameter | Explanation |
|---|---|
| Jp | angular momentum of the planet |
| M | Mass of the planet |
| ap | distance of planet to the star |
| τM | Migration timescale |
| Γ | Torque that acts on the planet |
| L | accretion luminosity of the planet |
| Ṁpeb | accretion rates of pebbles onto the planet |
| Θ | numerical parameter used for the dynamical torque |
 |
numerical gap parameter |
 |
Reynolds number |
| RH | Hill radius |
| q | mass ratio of planet to host star |
| fgap | relative Depth of surface density gap caused by planet |
 |
gravitational gap depth |
| fA | gap depth caused by accretion |
| τII | Migration timescale for type II migration |
| Mt | transition mass, where pebble accretion becomes efficient |
| Miso | pebble isolation mass |
| Ma | mass of planetary envelope |
| Racc | impact radius of pebble accretion |
| ρpeb | density of pebbles in the disk |
| δv | approach speed of pebbles |
| Hpeb | pebble scale hight |
| αz | vertical mixing of pebbles |
| Ṁgas, Ikoma | Ikoma gas accretion rate |
 |
Kelvin-Helmholtz contraction rate |
| Mc | Core mass of the planet |
| κenv | envelope opacity |
| Ṁgas, low | low branch of the Machida gas accretion rate |
| Ṁgas, high | high branch of the Machida gas accretion rate |
| ṀHS | horseshoe depletion rate |
| THS | synodic period at the border of the horseshoe region |
| ΩHS | synodic orbital frequency at the border of the horseshoe region |
| rHS | half width of the horseshoe region |
| xs | half width of the horseshoe region normed to planetary position |
| h | aspect ratio at the planetary position |
| Δt | numerical time step |
| ΣHS | surface density of the horseshoe region |
| ℵ | gap profile |
| σ | std. deviation of gap profile |
| F⋆ | stellar insulation at planetary position |
| γa, γb | Fit parameter for heavy element content |
| MZ | mass of heavy elements in planet |
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