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Table 1

Parameterization of the circumplanetary disk as described in Heller & Pudritz (2015).

Symbol Meaning Fiducial value

Constant or parameterized planetary disk parameters

r distance to the planet
RH planetary Hill radius
rcf centrifugal radius
rc transition from optically thick to optically thin (viscously spread) outer part 27.22 / 22 × rcf a
rd outer disk radius RH/ 5 bc
Λ(r) radial scaling of Σ(r)
Tm(r) midplane temperature
Ts(r) surface temperature
Σ(r) gas surface density
h(r) effective half-thickness
ρ0(r) gas density in the midplane
ρs(r) gas density at the radiative surface level
zs(r) radiative surface level, or photospheric height
qs(r) vertical mass coordinate at the radiative surface
cs(Tm(r)) speed of sound
α viscosity parameter 0.001d
ν(r,Tm) gas viscosity
Γ adiabat exponent, or ratio of the heat capacities 1.45
χ dust enrichment relative to the protostellar, cosmic value 10c
Xd dust-to-mass fraction 0.006 ef
μ mean molecular weight of the H/He gas 2.34 kg / mol g

Variable planetary disk parameters

κP Planck mean opacity 10-3−10-1 m2 kg-1 h
ks fraction of the solar radiation flux contributing to disk heating at zzs 0.1−0.5 c
shut shutdown accretion rate for moon formation 100,10,1 MGan/ Myr

Notes. See Heller & Pudritz (2015) and additional references for details about the respective parameter values or ranges.


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