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Table A.1
Definitions of symbols.
| Symbol | Definition |
|
|
|
| τ s | tstopΩ: Stokes number |
| χ |
|
| ζ |
|
| κ | cutoff of cross section defined by Eq. (38) |
| τ s,crit1 | dust migration is faster than growth for τs>τs,crit1 (Eq. (47)) |
| τ s,crit2 | runaway dust growth occurs for τs>τs,crit2 (Eq. (51)) |
| r snow | snow line at T ~ 170 K (Eq. (15) or (16)) |
| r vis - irr | viscously-heated and irradiation boundary (Eq. (14)) |
| r ES | Epstein and Stokes drag boundary (Eq. (49)) |
| r pf | pebble formation front |
| λ mfp | gas mean free path |
| h g | cs/ Ω: gas scale height |
| h p | (1 + τs/α)− 1/2hg ~ (α/τs)1/2hg: pebble scale height |
| ĥ g | h g / r |
| ĥ p | h p / r |
| Σg | gas surface density |
| Σp | pebble surface density |
| η |
|
| η ′ | χη |
| Ṁ | pebble mass accretion rate onto a planetary embryo |
| Ṁ F | pebble mass flux (accretion rate) through the disk |
| Ṁ ∗ | gas accretion rate through the disk |
| Δv | relative velocity between the embryo and a pebble |
| b | radius of the collision cross section |
| M | embryo mass |
| M BH | transitional embryo mass between Bondi and Hill regimes (Eq. (40)) |
| M 2D3D | transitional embryo mass between 2D and 3D accretion (Eq. (66)) |
| R | embryo physical radius |
|
|
|
| q | ĥg ∝ rq |
| q = 1/20 [viscous],2/7 [irradiation] | |
| p | τs ∝ rp |
| γ | T ∝ r− γ; |
| γ = −2q + 1 = 9/10 [viscous],3/7 [irradiation] | |
| ξ | Σg ∝ r− ξ |
| ξ = 2q + 1/2 = 3/5 [viscous], 15/14 [irradiation] | |
|
|
|
| M ∗ 0 | M∗/ 1 M⊙ |
| L ∗ 0 | L∗/ 1 L⊙ |
| α 3 | α/ 10-3 |
| Ṁ ∗ 8 | Ṁ∗/ 10-8M⊙ yr-1 |
| Ṁ F4 | ṀF/ 10-4M⊕ yr-1 |
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