Conditions for water ice lines and Mars-mass exomoons around accreting super-Jovian planets at 1−20 AU from Sun-like stars

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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
R_H	planetary Hill radius
r_cf	centrifugal radius
r_c	transition from optically thick to optically thin (viscously spread) outer part	27.22 / 22 × r_cf ^a
r_d	outer disk radius	R_H/ 5 ^b^c
Λ(r)	radial scaling of Σ(r)
T_m(r)	midplane temperature
T_s(r)	surface temperature
Σ(r)	gas surface density
h(r)	effective half-thickness
ρ₀(r)	gas density in the midplane
ρ_s(r)	gas density at the radiative surface level
z_s(r)	radiative surface level, or photospheric height
q_s(r)	vertical mass coordinate at the radiative surface
c_s(T_m(r))	speed of sound
α	viscosity parameter	0.001^d
ν(r,T_m)	gas viscosity
Γ	adiabat exponent, or ratio of the heat capacities	1.45
χ	dust enrichment relative to the protostellar, cosmic value	10^c
X_d	dust-to-mass fraction	0.006 ^e^f
μ	mean molecular weight of the H/He gas	2.34 kg / mol ^g

	Variable planetary disk parameters

κ_P	Planck mean opacity	10^-3−10^-1 m² kg^-1 ^h
k_s	fraction of the solar radiation flux contributing to disk heating at z ≤ z_s	0.1−0.5 ^c
Ṁ_shut	shutdown accretion rate for moon formation	100,10,1 M_Gan/ Myr

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

Reference.

^(a)

Machida et al. (2008);

^(b)

Sasaki et al. (2010);

^(c)

Makalkin & Dorofeeva (2014);

^(d)

Keith & Wardle (2014);

^(e)

Lunine & Stevenson (1982);

^(f)

Hasegawa & Pudritz (2013);

^(g)

D’Angelo & Bodenheimer (2013);

^(h)

Bell et al. (1997).

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