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Sublimation-driven convection in Sputnik Planitia on Pluto

Abstract

Sputnik Planitia is a nitrogen-ice-filled basin on Pluto1. Its polygonal surface patterns2 have been previously explained as a result of solid-state convection with either an imposed heat flow3 or a temperature difference within the 10-km-thick ice layer4. Neither explanation is satisfactory, because they do not exhibit surface topography with the observed pattern: flat polygons delimited by narrow troughs5. Internal heating produces the observed patterns6, but the heating source in such a setup remains enigmatic. Here we report the results of modelling the effects of sublimation at the surface. We find that sublimation-driven convection readily produces the observed polygonal structures if we assume a smaller heat flux (~0.3 mW m−2) at the base of the ice layer than the commonly accepted value of 2–3 mW m−2 (ref. 7). Sustaining this regime with the latter value is also possible, but would require a stronger viscosity contrast (~3,000) than the nominal value (~100) considered in this study.

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Fig. 1: Surface topography as a function of the driving buoyancy source.
Fig. 2: Pattern of convection obtained as a function of viscosity contrast and Rayleigh number.
Fig. 3: Application of cases in the polygonal regime to SP.

Data availability

All results necessary to produce the figures are available in the Zenodo repository https://doi.org/10.5281/zenodo.5511744.

Code availability

The convection code StagYY is the property of Paul J. Tackley and Eidgenössische Technische Hochschule Zürich. Researchers interested in using StagYY should contact Paul J. Tackley (paul.tackley@erdw.ethz.ch). Scripts for the treatment of results and drawing of figures have been written in Python (https://www.python.org/) using the StagPy package (https://github.com/StagPython/StagPy) and are available in the Zenodo repository, along with the data.

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Acknowledgements

We are grateful to P. Tackley for providing his mantle convection code StagYY, which we used for our calculations. We gratefully acknowledge support from the Pôle Scientifique de Modélisation Numérique of the ENS de Lyon for the computing resources. G.C. acknowledges the support from the Agence Nationale de la Recherche (France) under grant number ANR-20-CE49-0010.

Author information

Authors and Affiliations

Authors

Contributions

All authors developed the theory and designed the study together. A.M. modified the StagYY code; A.M. and S.L. ran the calculations and developed the analysis Python scripts. All authors contributed to the paper.

Corresponding author

Correspondence to Stéphane Labrosse.

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Extended data figures and tables

Extended Data Fig. 1 Topography slope.

Slope of topography for cases # 14 (left) and 15 (right), with the mean value written in the upper left corner.

Extended Data Fig. 2 Time evolution of output diagnostics for case # 14.

Evolution with time of the surface heat flux (a), the mean temperature (b), the RMS velocity (c), the effective Rayleigh number (d) and viscosity contrast (e) in the case of Fig. 2b, e of the main text. The first three quantities have been rendered dimensional using the nominal values of the parameters, see Table 1 of the main text.

Extended Data Fig. 3 Effective temperature as function of effective Rayleigh number for case # 14.

Evolution of the dimensionless temperature as function of the internal heating Rayleigh number, using secular cooling as effective internal heating source (see methods), for case # 14. The dashed line shows a guide to the eye for the expected scaling law in steadily cooling situation. The circled numbers correspond to snapshots, some being presented on Extended Data Fig. 4, the red ones being in the polygonal regime, which is first established at snapshot 18.

Extended Data Fig. 4 Pattern maturation for case # 14.

Four snapshots (# 2, 10, 18 and 30) of the surface topography (left) and mid-depth temperature anomaly (right) for case # 14, each associated with a circled number on Extended Data Fig. 3.

Extended Data Fig. 5 Temperature profiles during decaying convection.

Evolution of the horizontal minimum (blue), mean (red) and maximum (green) temperature profiles following the application of a zero heat flux at the upper surface of an established convecting system, case #14.

Extended Data Fig. 6 Decaying time-scale of convection.

Time evolution of the temperature anomalies (a, b) and the RMS velocity (c) after the surface heat flow has been set to zero. (a) shows the vertical mean of Tmax(z) − Tmin(z). (b) shows the RMS of \(T-\bar{T}(z)\), with \(\bar{T}(z)\) the horizontal mean of temperature. The exponential fit has been performed on values for time ≥55 kyr.

Extended Data Fig. 7 Time evolution of output diagnostics for a time-varying boundary condition.

Time evolution of the same diagnostics as in Extended Data Fig. 2 for a time varying boundary condition at the surface. The insets in each panel shows a zoom on the last 5 periods of the oscillations.

Extended Data Fig. 8 Convection pattern for a time-varying boundary condition.

Surface topography and mid-depth temperature anomaly at the end of the time varying run presented on Extended Data Fig. 7.

Extended Data Fig. 9 Evolution of the layer with an imposed bottom heat flux qbot = 0.26 mW m−2.

Panel (a) shows the evolution of the surface and bottom heat fluxes, (b) the mean temperature, (c) the RMS velocity, (d) the effective Rayleigh number, (e) the effective viscosity contrast and the bottom ones, snapshots of the topography at times written on their respective upper left corners.

Extended Data Fig. 10 Evolution of the layer with an imposed bottom heat flux qbot = 1.3 mW m−2.

Panel (a) shows the evolution of the surface and bottom heat fluxes, (b) the mean temperature, (c) the RMS velocity, (d) the effective Rayleigh number, (e) the effective viscosity contrast and the bottom ones, snapshots of the topography at times written on their respective upper left corners.

Extended Data Fig. 11 Evolution of the layer for Ra = 109 and \({{\boldsymbol{R}}}_{{\boldsymbol{\eta }}}^{\infty }={{\bf{10}}}^{{\bf{4}}}\) with a zero imposed bottom heat flux.

Panel (a) shows the evolution of the surface and bottom heat fluxes, (b) the mean temperature, (c) the RMS velocity, (d) the effective Rayleigh number, (e) the effective viscosity contrast and the bottom ones, snapshots of the topography at times written on their respective upper left corners.

Extended Data Fig. 12 Evolution of the layer for Ra = 109 and \({{\boldsymbol{R}}}_{{\boldsymbol{\eta }}}^{\infty }={{\bf{10}}}^{{\bf{4}}}\) with an imposed bottom heat flux qbot = 1.3 mW m−2.

Panel (a) shows the evolution of the surface and bottom heat fluxes, (b) the mean temperature, (c) the RMS velocity, (d) the effective Rayleigh number, (e) the effective viscosity contrast and the bottom ones, snapshots of the topography at times written on their respective upper left corners.

Extended Data Table 1 Input parameters and output diagnostics

Supplementary information

41586_2021_4095_MOESM1_ESM.pdf

Supplementary information This file presents some diagnostics for the last snapshot of each studied case, as listed in Extended Data Table 1. For each case, the second column shows the surface topography, the temperature anomaly at mid-depth and the vertical profile of the r.m.s. of the horizontal velocity, all figures being dimensionless.

Peer Review File

Supplementary Video 1

Supplementary video showing the evolution with time of the topography (left) and mid-depth temperature anomaly in case 14.1.

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Morison, A., Labrosse, S. & Choblet, G. Sublimation-driven convection in Sputnik Planitia on Pluto. Nature 600, 419–423 (2021). https://doi.org/10.1038/s41586-021-04095-w

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