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Table A.1

List of notations.

Symbol Description
ε3D or ε2D 3D or 2D pebble accretion efficiency (probability of capture)
ε0 Pebble accretion efficiency for planets on circular orbits
εset Pebble accretion efficiency in the settling regime
εbal Pebble accretion efficiency in the ballistic regime
A2D Prefactor of pebble accretion efficiency in 2D
am Acceleration for type I migration
ae Acceleration for the eccentricity damping
ap Planet semimajor axis
b Impact parameter in the local frame
bset Accretion radius in the settling regime
bbal Accretion radius in the ballisitc regime
ep Planet eccentricity
eeq Equilibrium eccentricity at resonance
Ωp Keplerian angular velocity at planet’s location
η Headwind prefactor
Σgas Gas surface density
ΣP Pebble surface density
ρgas Gas volume density
ρP Pebble volume density
fset Attenuation factor
Hgas Gas disk scaleheight
HP Pebble disk scaleheight
hgas Gas disk aspect ratio
hP Pebble disk aspect ratio
Mp Planet mass
Mp,sio Pebble isolation mass
M Star mass
Nhit Number of pebbles hit onto the planet in the global simulation
Ntot Total number of pebbles initially given in the global simulation
P gas disk pressure
qp Mass ratio between the planet and the star
RH Hill radius of the planet
RBondi Bondi radius of the planet
Rp Planet physical radius
rp Distance between the planet and the central star
r Distance between the pebble and the central pebble
tstop Stopping time of the pebble
tsyn Synodical time of the pebble
τm Type I migration timescale
τe Eccentricity damping timescale
τs Dimensionless stopping time (τs = tsΩK)
vesc Planet escape velocity
v* Transition velocity from the settling regime to the ballistic regime
vr Radial drift velocity of the pebble
vϕ Azimuthal velocity of the pebble
vhw Headwind velocity of disk gas
vsh Keplerian shear velocity between the planet and the pebble
vecc Relative velocity between a planet on an eccentric and a circular orbit
vcir Relative velocity between the pebble and the planet on a circular orbit
vK Keplerian velocity at planet’s location
PA Pebble mass accretion rate onto the planet
disk Pebble mass flux in the disk
Δrp Distance between the pebble and the planet
Δv Relative velocity between the pebble and the planet

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