Open Access
Table 3
Parameter definitions.
| Symbol | Definition/value | Description |
|---|---|---|
| r | Normalised radius at 1 AU | |
| σ | Gas surface-density | |
| P | Vertically integrated pressure | |
| T |  |
Gas temperature |
| v | Gas velocity-field | |
| v′ | v − ΩK reθ | Relative gas-velocity (with respect to the angular gas velocity) |
| Φ⊙ | Central object potential | |
| ΦSG | Gas SG potential | |
| Φind | Indirect potential (offset of Φ⊙) | |
| ΩK |  |
Pressure-supported rotation-rate |
| γ | 1.4 | Adiabatic index |
| cs |  |
Gas sound-speed |
| H |  |
Pressure scale-height |
| h(r) |  |
Disc aspect ratio |
| Q | Ωkcs/(πGσ) | Local Toomre’s parameter |
| Q0 | Ωkcs/(πGσ0) | Toomre’s parameter at 50 AU for the Axis-symmetric disc |
| Qc | 1/h = 20 | Critical Toomre parameter |
| q0 | Q0/Qc | SG parameter |
| Ro | ∇ × v′/2Ωk | Rossby number |
 |
〈Ro〉core | Vortex spin |
| χ | Vortex aspect-ratio | |
| Δr | Vortex radial-width | |
| δ | Δr/H | Vortex radial-extent |
| t0 | 353 yr | Orbital period at 50 AU |
| Cσ | σ/σ0 − 1 | Density contrast |
| CP | P/P0 − 1 | Pressure contrast |
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