Long-term stability of Enceladus’ uneven ice shell

Čadek, O.; Souček, Ondřej; Běhounková, M.; Choblet, G.; Tobie, G.; Hron, J.

doi:10.1016/j.icarus.2018.10.003

Cited by 71 publications

(98 citation statements)

References 44 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…At a given time, the ice layer may further vary laterally. For objects such as Enceladus, and owing to a small internal pressure, lateral variations in ice shell thickness could be as large as the average value (e.g., Čadek et al, ), provided that the viscosity is sufficiently high to overcome the viscous relaxation. In the specific case of Europa, numerical models typically report lateral variations in the ice shell thickness in the range 5–10 km (Tobie et al, ), while more recent studies suggest that preserving such variations against viscous relaxation would require unrealistically large viscosities (Čadek et al, ).…”

Section: Melting In Icy Satellitesmentioning

confidence: 99%

Tidally Heated Convection and the Occurrence of Melting in Icy Satellites: Application to Europa

et al. 2020

Self Cite

View full text Add to dashboard Cite

Observations of icy satellites have revealed widespread marks of cryovolcanism. Because aqueous cryomagmas are negatively buoyant, two processes are required to explain these observations: one mechanism to generate melt close enough to the surface and another one to transport this melt to the surface. Here, we investigate the generation of melting in a systematic way, using a set of 85 numerical simulations where we vary the viscosity contrast, Rayleigh number, and tidal heating rate. Applied to Europa, considering a hydrosphere composed of pure water, our simulations suggest that isolated melt pockets can be generated close to the surface ( ∼5 km) as long as the ice layer thickness ( d*) remains modest ( 15≤d*≤35 km). However, the generation of melting becomes increasingly difficult as the amount of antifreeze compounds in the subsurface ocean increases. Furthermore, the proportion of melting increases very sharply with increasing tidal heating rate. In particular, when the tidal heating rate exceeds a threshold, an asymptotic regime is reached where the surface heat flux remains constant indicating that the tidal heat generated above this threshold is only used for melting the ice shell. In that regime, we found a direct relationship between the surface heat flux and d*. Finally, we provide a new assessment of Europa's thermal state. Based on available constraints, we propose that the ice shell thickness should exceed 15 km. However, d*∼15–35 km implies a tidal power ( >2 TW) much larger than expected. An extrapolation of the trends suggested by our results indicates that a more reasonable tidal power ( ∼1 TW) would involve d*∼50–90 km.

show abstract

Section: Melting In Icy Satellitesmentioning

confidence: 99%

Tidally Heated Convection and the Occurrence of Melting in Icy Satellites: Application to Europa

et al. 2020

Self Cite

View full text Add to dashboard Cite

show abstract

“…Equation states that in a steady state, the change in mass of ice due to the phase transition (melting, freezing) must be counterbalanced by the flow of ice at the base of the ice shell. This flow is driven by variations in hydrostatic pressure along the phase boundary, which are a consequence of uneven ice shell thickness; the thickness is reduced in areas of melting and increased in areas of freezing (for a detailed discussion of equation , see section 4 in Čadek et al, ). The term on the left‐hand side of equation can be neglected only if the viscosity of ice near the bottom boundary is very high and

boldv \to bold0

.…”

Section: Dynamic Model Of the Ice Crustmentioning

confidence: 99%

“…Calculations are performed for a shell that has the same size as the ice shell of Enceladus, a small moon of Saturn discussed in recent studies of isostasy (Beuthe et al, ; Čadek et al, ; Hemingway & Matsuyama, ). The parameters of the model are as follows:

R_{1} = 252.1

km,

R_{2} = 232.1

km,

ρ_{1} = 926

kg/m

^{3}

, and

ρ_{2} = 1,

010 kg/m

^{3}

.…”

Section: Dynamic Model Of the Ice Crustmentioning

confidence: 99%

“…The parameters of the model are as follows:

R_{1} = 252.1

km,

R_{2} = 232.1

km,

ρ_{1} = 926

kg/m

^{3}

, and

ρ_{2} = 1,

010 kg/m

^{3}

. The gravitational potential (

V

in equations , and ) is evaluated assuming that the core of the moon is a sphere of radius 194 km and density 2,366 kg/m

^{3}

(Čadek et al, ). Enceladus is an example of a small icy moon where the thickness of the crust is relatively large compared to the mean radius.…”

Section: Dynamic Model Of the Ice Crustmentioning

confidence: 99%

“…In many applications, the difference between the shape and the topography is assumed to be small and Airy isostasy is formulated in terms of the shape anomalies, which facilitates the evaluation of gravity anomalies (gravity depends on the shape, not the topography). However, this approach may lead to physically incorrect results if the difference between the shape and the topography is large as, for example, in the case of Saturn's moon Enceladus (see Figure 1 in Čadek et al, ). For this reason, all models of Airy isostasy considered in the present study (equations –) are formulated in terms of the topographic anomalies.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Is Airy Isostasy Applicable to Icy Moons?

Čadek

Souček

Běhounková

2019

Geophysical Research Letters

View full text Add to dashboard Cite

Airy isostasy is commonly used in planetary science to explain the relationship between crustal thickness variations and topography. Recently, several researchers have questioned the validity of this concept and proposed alternative approaches. Here we examine the accuracy of these approaches by comparing their results with those obtained from the numerical solution of the equations governing the flow in the crust of a small icy moon with a subsurface ocean. We find that the traditional approach based on application of Archimedes' principle with elevations referred to the geoid, provides a satisfactory estimate of crustal thickness for low harmonic degrees. The alternative approach, based on the deviatoric stress minimization, gives correct results for isoviscous model, but its accuracy deteriorates as the viscosity contrast increases. The other alternative approach, in which the deviatoric stress is neglected, is significantly less accurate than other methods, leading to biased results for models with a thick crust. Plain Language Summary Airy isostasy is a concept based on simple application ofArchimedes' principle, which is broadly used in solid Earth geophysics and planetary science to explain the relationship between crustal thickness variations and topography. However, the application of Airy isostasy to icy bodies is problematic due to large variations in ice viscosity and phase transitions occurring in the interior. Recently, several researchers have questioned the validity of the traditional approach to Airy isostasy and proposed alternative approaches. Here we examine the accuracy of these approaches by comparing their results with those obtained from the numerical solution of the equations governing the flow in the crust of a small icy moon with a subsurface ocean. The results of our modeling suggest that the traditional approach to Airy isostasy provides a satisfactory estimate of crustal thickness variations on large spatial scales. The alternative approach based on the deviatoric stress minimization gives correct results for isoviscous model, but its accuracy deteriorates as the viscosity contrast increases. The other alternative approach, in which the deviatoric stress is neglected, is significantly less accurate than the other methods, leading to biased results for models with a thick crust.The original concept of Airy isostasy (Airy, 1855) is based on the application of Archimedes' principle to Earth's crustal blocks. According to this concept, the crustal blocks, which are rigid and do not interact with each other, are floating on a fluid-like mantle of greater density than the crust (for a historical review,

show abstract

Estimating the 3D structure of the Enceladus ice shell from flexural and Crary waves

Marusiak

Tharimena

Panning

et al. 2022

Preprint

View full text Add to dashboard Cite

A seismic investigation on Saturn's moon Enceladus could determine the thickness of the ice shell, along with variations from the mean thickness, by recovering phase and group velocities, and through the frequency content of surface waves. Here, we model the Enceladus ice shell with uniform thicknesses of 5 km, 20 km, and 40 km, as well as with ice topography ranging from 5-40 km. We investigate several approaches for recovering the mean ice shell thickness. We show that surface wave dispersions could be used to determine the mean ice shell thickness. Flexural waves in the ice only occur if the shell is thinner than a critical value < 20 km. Rayleigh waves dominate only in thicker ice shells. The frequency content of Crary waves depends on the ice shell thickness.

show abstract

Long-term stability of Enceladus’ uneven ice shell

Cited by 71 publications

References 44 publications

Tidally Heated Convection and the Occurrence of Melting in Icy Satellites: Application to Europa

Tidally Heated Convection and the Occurrence of Melting in Icy Satellites: Application to Europa

Is Airy Isostasy Applicable to Icy Moons?

Estimating the 3D structure of the Enceladus ice shell from flexural and Crary waves

Contact Info

Product

Resources

About