Table 1. Model parameters used in our study.

Symbol	Name	Definition/value
Enceladus parameters
a	Radius	252 km
δ	Obliquity	27°
H	Global mean ice thickness	20.8 km: (18)
D	Global mean ocean depth	39.2 km: (18)
Ω	Rotation rate	5.307 × 10−5 s−1
g 0	Surface gravity	0.113 m/s2
$\overline{T_{\mathrm{s}}}$	Mean surface temperature	59 K
Europa parameters
a	Radius	1561 km
δ	Obliquity	3.1°
H	Global mean ice thickness	15 km: (53)
D	Global mean ocean depth	85 km: (53)
Ω	Rotation rate	2.05 × 10−5 s−1
g 0	Surface gravity	1.315 m/s2
$\overline{T_{\mathrm{s}}}$	Mean surface temperature	110 K
Physical constants
L f	Fusion energy of ice	334,000 J/kg
Cp	Heat capacity of water	4000 J/kg per Kelvin
Tf(S, P)	Freezing point	Eq. 14
ρi	Density of ice	917 kg/m3
ρw	Density of the ocean	Eq. 12
α, β	Thermal expansion and saline contraction coeff.	Using Gibbs Seawater Toolbox: (23)
κ0	Conductivity coeff. of ice	651 W/m: (74)
p α	Ice dissipation amplification factor	−2 to −1
ηm	Ice viscosity at freezing point	1014 Ps·s
Default parameters in the ocean model
νh, νv	Horizontal/vertical viscosity	10 m2/s
${\tilde{\mathrm{\nu }}}_{\mathrm{h}},{\tilde{\mathrm{\nu }}}_{\mathrm{v}}$	Biharmonic hyperviscosity	109 m4/s
κh, κv	Horizontal/vertical diffusivity	0.005 m2/s
(γT, γS, γM)	Water-ice exchange coeff. for T, S, and momentum	(10−5, 10−5, 10−3) m/s
g	Gravity in the ocean	Eq. 8
P 0	Reference pressure	ρig0H = 2.16 × 106 Pa
θ0	Reference potential temperature	Tf(S0, P0)
ρw0	Reference density of ocean	Eq. 13
ℋcond	Conductive heat loss through ice	Eq. 15, Fig. 7
ℋice	Tidal heating produced in the ice	Eq. 26, Fig. 7
ℋcore	Bottom heat flux powered by the core	Eq. 16, Fig. 7
A	Surface albedo	0.81
T s	Surface temperature profile	Fig. 7