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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/k 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

Notes. Quantities defined for the unperturbed axis-symmetric gas disc are denoted with a 0 subscript. The values provided for t0, h, and Qc correspond to the values at 50 AU.

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