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Jet activity on Enceladus linked to tidally driven strike-slip motion along tiger stripes

Nature Geoscience volume 17, pages 385–391 (2024)Cite this article

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Abstract

At Saturn’s moon Enceladus, jets along four distinct fractures called ‘tiger stripes’ erupt ice crystals into a broad plume above the South Pole. The tiger stripes experience variations in tidally driven shear and normal traction as Enceladus orbits Saturn. Here, we use numerical finite-element modelling of a spherical ice shell subjected to tidal forces to show that this traction may produce quasi-periodic strike-slip motion in the Enceladus crust with two peaks in activity during each orbit. We suggest that friction modulates the response of tiger stripes to driving stresses, such that tidal traction on the faults results in a difference in the magnitudes of peak strike slip and delays the first peak in fault motion following peak tidal stress. The simulated double-peaked and asymmetric strike-slip motion of the tiger stripes is consistent with diurnal variations in jet activity inferred from Cassini spacecraft images of plume brightness. The spatial distribution of strike-slip motion also matches Cassini infrared observations of heat flow. We hypothesize that strike-slip motion can extend transtensional bends (for example, pull-apart structures) along geometric irregularities over the tiger stripes and thus modulate jet activity. Tidally driven fault motion may also influence longer term tectonic evolution near the South Pole of the satellite.

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Fig. 1: Examples of tidally driven deformation at Enceladus.
Fig. 2: Modelled traction and lateral slip over tiger stripe faults as a function of mean anomaly.
Fig. 3: Comparison of predicted strike-slip motion along tiger stripes and observations of plume brightness.
Fig. 4: Comparison of the spatial distribution of strike-slip motion and heat flow along the tiger stripes.
Fig. 5: Conceptual relationship between tidally driven normal tractions, strike-slip motion and jet activity through the tidal cycle.

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Data availability

Data used for Fig. 3 (slab densities derived from Cassini ISS images) is publicly available via https://doi.org/10.1016/j.icarus.2019.06.006 (ref. 7). Data used for Fig. 4 (heat flow along the tiger stripe faults derived from Cassini Composite Infrared Spectrometer measurements) is publicly available via https://doi.org/10.2458/azu_uapress_9780816537075-ch008 (ref. 4).

Code availability

The results used in this study were generated using the software package PyLith44,50. PyLith is an open-source finite-element code for modelling geodynamic processes and is available via Zenodo at https://doi.org/10.5281/zenodo.3269486 (ref. 50). The specific PyLith version used in this study was v2.2.2. The full code used to simulate deformation in this work (including modifications Pylith, CUBIT and PETSc and a user manual) are publicly available via https://doi.org/10.5281/zenodo.10585162 (ref. 51). The mesh geometries utilized in this study were created using CUBIT (v15.2), a node-locked licensed software, which is available through the developer Sandia National Laboratories via https://cubit.sandia.gov/2021/09/14/cubit-15-7-released-october-20-2020/ (ref. 48).

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Acknowledgements

This research was supported by the Future Investigators in NASA Earth and Space Science and Technology (FINESST) Program (80NSSC22K1318)(A.B., M.S.). We thank the Keck Institute for Space Studies (KISS) at the California Institute of Technology for organizing two workshops about ‘Next-Generation Planetary Geodesy’ which provided insight, expertise and discussions that inspired this research. We also thank M. Knepley, B. Aagaard and C. Williams for providing valuable advice on how to modify PyLith for our simulations. A portion of this research was supported by a Strategic Research and Technology Development task led by J. T. Keane and R. S. Park at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration (80NM0018D0004)(J.T.K., R.S.P.).

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Authors and Affiliations

  1. Department of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA, USA

    Alexander Berne & Mark Simons

  2. Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA

    James T. Keane, Erin J. Leonard & Ryan S. Park

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Contributions

A.B. conceived and designed this study under the supervision of M.S. A.B. drafted the article and constructed Figs. 1–4. M.S., J.T.K. and A.B. developed numerical models used in the study. R.S.P. provided the shape model necessary for numerical simulations. J.T.K., with the aid of A.B., constructed Fig. 5. E.J.L. provided expertise regarding the geological evolution of the SPT. All authors discussed the results of the study and commented on the manuscript at each stage of revision.

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Correspondence to Alexander Berne.

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Nature Geoscience thanks Douglas Hemingway and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Primary Handling Editor: Tamara Goldin, in collaboration with the Nature Geoscience team.

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Extended data

Extended Data Fig. 1 Similar to upper right and upper left panels of Fig. 2 of the main text except values (driving tractions) are evaluated for a model with slipping faults (μ = 0.4).

We find that slip along tiger stripe faults induces up to 10% variability in tractions relative to values evaluated for the case of fully-locked interfaces.

Extended Data Fig. 2 Example snapshots of mesh geometry.

Left: South Polar (orthographic) view of mesh geometry showing labelled tiger stripe faults (black traces). Right: perspective view of tiger stripe surfaces with inset closeup image of Alexandria sulcus. Tetrahedra cell edges are colored in blue and range in size from 1 km (over the tiger stripe faults) to 8 km. Approximate distance scale is shown in the lower right panel for reference. Faults are viewed from 130∘W, looking upward from 35∘ below the horizontal.

Extended Data Fig. 3 Spin-up parameter Ξ(t) (see Equation (21)) modelled as a function of time (in units of tidal periods) for several prescribed values for the static coefficient of friction μ.

Ξ(t) = 0 indicates that differences between values at a given mean anomaly are zero (model is fully ‘spun-up’). Plotted lines are colored by value of modelled coefficient of static friction. The x-axis is plotted in log-10 scale.

Extended Data Fig. 4 Simplified model relating driving shear traction τD, normal traction σn, μ, and slip s along the tiger stripe faults.

Upper row: Frictionless fault subject to driving tractions. In this case, the fault cannot support shear traction (resolved shear traction τR = 0) and driving traction τD is resolved along interfaces (s ≠ 0) regardless of the applied σn. Slip results in a concentration of elastic strain at the fixed ends of the fault. The subsequent unloading of the driving shear traction results in a return to zero slip. Center row: frictional fault with time-variable driving shear traction and constant normal traction. In this case, s ≠ 0 when ∣τD∣ > σnμ (that is, τc = ∣τD∣ − σnμ > 0). Constant values of σn result in symmetric slip profiles following the onset of sliding. Bottom row: frictional fault with time-variable driving shear and normal tractions. In this case, variable σn results in an increased magnitude of τD required to initiate sliding and an associated decrease in the amplitude of s during the first occurrence of τc > 0. The resulting slip profile is double-peaked and asymmetric.

Extended Data Fig. 5 Correlation of timing of lateral slip and plume brightness for several values of modelled μ7.

Values are plotted for corresponding values of mean anomaly and are each normalized by maxima over the tidal cycle. Linear regression lines and associated Pearson Correlation Coefficients (R = 1 indicates perfect correlation) shown for reference. Scatter points are colored by value of mean anomaly ranging from 0∘ to 360∘ (that is, periapse to periapse).

Extended Data Fig. 6 Crustal thickness assumed for finite-element models.

The top and bottom images respectively show crustal thickness in cylindrical equidistant and South Polar stereographic projections. We compensate non-hydrostatic surface topography at Enceladus using a formulation for Airy isostatic compensation to generate thickness variations (for details, see Methods ‘Model Geometry’). Surface topography is extracted from a shape model of the full outer surface of Enceladus described in26. Contours denote intervals of 5 km in thickness for both map projections. The labelled thick black lines plotted in the bottom image denote tiger stripes (‘A’ ↔ Alexandria, ‘C’ ↔ Cairo, ‘B’ ↔ Baghdad, and ‘D’ ↔ Damascus).

Extended Data Fig. 7 Correlation of spatial distribution of lateral slip and radiated power per unit length4 for several values of modelled μ.

Values are plotted for corresponding values of surface location (along the tiger stripe faults) and are each normalized by maxima over all interfaces. Linear regression lines and Pearson Correlation Coefficient (R = 1 indicates perfect correlation) shown for reference. Scatter points are colored according to associated fault (Green ↔ Baghdad, Blue ↔ Damascus, Yellow ↔ Cairo, and Red ↔ Alexandria). Values from the endpoints of fault structures are excluded from plots and the computation of R values.

Supplementary information

Supplementary Information

Supplementary Table 1.

Supplementary Video

Movies of tidally driven deformation at Enceladus over the full tidal cycle. Top: South Polar orthographic projections of radial displacement at the surface relative to that produced by models without tiger stripe faults. Bottom: perspective view of lateral slip along tiger stripe faults: ‘A’ Alexandria, ‘C’ Cairo, ‘B’ Baghdad and ‘D’ Damascus. We assign μ = 0.4 to tiger stripe faults for this example. Faults are viewed from 130° W, looking upward from 35° below the horizontal. Mean anomaly value (and relative distance of Enceladus to Saturn) is labelled above (and to the upper left) for reference.

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Berne, A., Simons, M., Keane, J.T. et al. Jet activity on Enceladus linked to tidally driven strike-slip motion along tiger stripes. Nat. Geosci. 17, 385–391 (2024). https://doi.org/10.1038/s41561-024-01418-0

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