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Table A.1

Expressions for the minimum mass nebula scaling used in this article.

Quantity Description Equation Value

m g Gas molecular mass 3.9 × 10-24 g
σ g Gas collisional cross section (H2) 2 × 10-15 cm2
μ g Gas dynamic viscosity (H2) ~
M Stellar mass 1.989 × 1033 g
Σg Gas surface density
T Disk temperature
ΩK Keplerian frequency
v K Keplerian velocity
c g Isothermal sound speed
h g Disk scale height cg/ ΩK
ρ g Mid-plane gas density
ν g Gas kinematic viscosity (H2) μ g / ρ g ~
ν t Gas turbulent viscosity α c g h g α × 4.9 × 1016rAU cm2 s-1
η Sub-Keplerian factor Eq. (19)
λ g Gas mean free path m g / σ g ρ g
s lim Epstein to Stokes limiting size 9/4 λg
s max Stokes to quadratic limiting size 27λgcg/ (2ηrΩK)
τ s Dimensionless stopping time Eq. (21)
t s Stopping time τs/ ΩK
Stokes to Epstein orbital distance for τs = 1
τ f Dimensionless friction time Eq. (100)
R B Bondi radius Eq. (81) [km]
R H Hill radius Eq. (80) [km]
geometrical-Bondi limit Eq. (82) [km]
Bondi-Hill limit Eq. (83) [km]

Notes. rAUr/ AU; δlims/slim; xlimr/rlim.   μg = 8.76 × 10-5 g cm-1 s-1 × 365.85 K/(T + 72 K)(T/ 293.85 K)3/2 (Sutherland’s formula for H2).

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