Elliptical instability in terrestrial planets and moons

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Table 6

Stability results in the extreme case of optical librations (ϵ = 2e and β from this table and Table 5).

	Io	Europa	Ganymede	Callisto	Titan

	core	core	core	core	core
R₂/R	0.52^a^b	0.38^b	0.27^c	−	−
η	0	0	0	−	−
E (×10¹⁴)	2.7	14	20	−	−
β (×10⁴)	60^a	9.7^d	3.7^e	−	−
Λ (×10⁷)	42	4.1	0.7	−	−
σ (yr^-1)	0.016	0.0025	−3 × 10^-4	−	−

	ocean	ocean	ocean	ocean	ocean
Crust (km)	−	10^g	100^h	150ⁱ	70^j
Depth (km)	−	100^g	150^h	150ⁱ	200^j
R₂/R	−	0.99	0.96	0.94	0.97
η	−	0.94	0.94	0.93	0.92
E (×10¹⁴)	−	2.0	1.5	4.5	3.5
β (×10⁴)	−	9.7^d	3.7^e	0.72^e	1.2^f
Λ ( × 10¹³)	−	21	3.5	0.9	0
σ (yr^-1)	−	0.0016	−6 × 10^-4	−4 × 10^-4	−10^-4

Notes. For the liquid cores, we take σ_e = 4 × 10⁵ S.m^-1, ρ₀ = 8000 kg m^-3 and ν = 10^-6 m² s^-1 as typical values, consistent with a Fe/Fe-S composition. For the subsurface oceans, we take σ_e = 0.25 S m^-1 (Hand & Chyba 2007), ρ₀ = 1000 kg m^-3, and ν = 10^-6 m² s^-1 as typical values.

^(a)

Kerswell & Malkus (1998), considering the static tidal bulge.

^(b)

Hussmann & Spohn (2004).

^(c)

Bland et al. (2008).

^(d)

with k₂ ≈ 0.3 (Wahr et al. 2006; Baland & Van Hoolst 2010).

^(e)

Equation (5) with k₂ ≈ 0.3.

^(f)

k₂ ≈ 1 (Goldreich & Mitchell 2010).

^(g)

Wahr et al. (2006).

^(h)

Bland et al. (2009).

⁽ⁱ⁾

Kuskov & Kronrod (2005).

^(j)

Sohl et al. (2003).

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