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Bayesian analysis of Enceladus’s plume data to assess methanogenesis


Observations from NASA’s Cassini spacecraft established that Saturn’s moon Enceladus has an internal liquid ocean. Analysis of a plume of ocean material ejected into space suggests that alkaline hydrothermal vents are present on Enceladus’s seafloor. On Earth, such deep-sea vents harbour microbial ecosystems rich in methanogenic archaea. Here we use a Bayesian statistical approach to quantify the probability that methanogenesis (biotic methane production) might explain the escape rates of molecular hydrogen and methane in Enceladus’s plume, as measured by Cassini instruments. We find that the observed escape rates (1) cannot be explained solely by the abiotic alteration of the rocky core by serpentinization; (2) are compatible with the hypothesis of habitable conditions for methanogens; and (3) score the highest likelihood under the hypothesis of methanogenesis, assuming that the probability of life emerging is high enough. If the probability of life emerging on Enceladus is low, the Cassini measurements are consistent with habitable yet uninhabited hydrothermal vents and point to unknown sources of methane (for example, primordial methane) awaiting discovery by future missions.

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Fig. 1: General modelling framework.
Fig. 2: Cassini observations and the distributions of model outputs over the space of the observables.
Fig. 3: Posterior probabilities of abiotic-habitable and biotic models, and classifier score.

Data availability

Simulated datasets from which the figures were generated are available at

Code availability

The code of the model presented in the article is available at


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We are grateful for discussion with D. Apai, A. Bixel, B. Charnay, Z. Grochau-Wright, B. Kacar, J. Kasting, C. Lineweaver, V. Thouzeau and members of the OCAV Project at PSL University and of NASA’s Nexus for Exoplanet System Science (NExSS) research coordination network and its Earths in Other Solar Systems Project based at the University of Arizona. This work is supported by France Investissements d’Avenir programme (grant numbers ANR-10-LABX-54 MemoLife and ANR-10-IDEX-0001-02 PSL) through PSL IRIS OCAV and PSL–University of Arizona Mobility Program. R.F. acknowledges support from the US National Science Foundation, Dimensions of Biodiversity (DEB-1831493), Biology Integration Institute-Implementation (DBI-2022070) and National Research Traineeship (DGE-2022055) programmes; and from the United States National Aeronautics and Space Administration, Interdisciplinary Consortium for Astrobiology Research programme (grant number 80NSSC21K059).

Author information




R.F., F.G. and S.M. conceived the study. R.F. designed the ecosystem model. F.G. and S.M. designed the geochemical model. A.A. and B.S. refined the models and developed the code. A.A. analysed the results and wrote the first version of the manuscript. All authors finalized the paper.

Corresponding authors

Correspondence to Antonin Affholder or Régis Ferrière.

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Competing interests

The authors declare no competing interests.

Additional information

Peer review informationNature Astronomy thanks David Catling, Ruth-Sophie Taubner and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Overview of the Bayesian inference framework as a two-directional probability tree.

x0 is an observation of system outputs, coming from the Cassini mission: \({\Phi }_{{{\rm{H}}}_{2}}\) the flux of dihydrogen, \({\Phi }_{{{\rm{CH}}}_{4}}\) the flux of methane, and the ratio H2:CH4. θ denotes the set of internal parameters, namely the composition of Enceladus’ putative hydrothermal fluid and ocean as well as hydrothermal fluid temperature. The modelling workflow reads from right to left: the model evaluates ‘habitability’ (H) from a set of parameters and produces so-called pseudo-data x when biological activity (B) contributes to shaping sea-floor waters composition (or not, A, ‘abiotic’); x and θ are thus related through x=π(θ), where π denotes a model. The inference workflow reads from left to right: the goal is to determine the posterior probability P(Bx0), which requires to compute likelihoods (for example, P(x0B)), see Methods.

Extended Data Fig. 2 Biological and chemical default parameter values as well as physical and chemical constants.

Description and standard values of all parameters in the model, with references from which they are taken where applicable. All figures were produced using these parameter values.

Extended Data Fig. 3 Summary of prior distributions.

For details on the boundaries described here, see Methods.

Extended Data Fig. 4 Model outputs across the prior ranges of internal parameters.

a, Outputs of the purely abiotic model. Blue dots denote uninhabitable simulations, orange dots denote habitable simulations. b, Outputs of the model including biological activity. Green dots denote habitable simulations in which biological methanogenesis occurs. Escape rates of methane and dihydrogen (\({\Phi }_{{{\rm{CH}}}_{4}}\) and \({\Phi }_{{{\rm{H}}}_{2}}\) respectively) are given in mol yr−1 while H2:CH4 has no dimension. All concentrations are given in mol kg-1and temperature is given in Kelvin. Note the log10 scale for every variable but the temperature. Magenta dashed lines indicate the observed values of each observable. See Methods for model equations, Extended Data Table 1 for internal parameter ranges, and Extended Data Table 2 for parameters values.

Extended Data Fig. 5 Likelihood of the Cassini observations: H2 escape rate (\({\Phi }_{{{\rm{H}}}_{2}}\), mol yr−1), CH4 escape rate (\({\Phi }_{{{\rm{CH}}}_{4}}\), mol yr−1), and H2:CH4 ratio under models predicting ‘uninhabitability’, ‘abiotic-habitability’, and ‘biotic’ methane production.

a, c, Likelihood of the observables for the different models when serpentinization is the only modeled abiotic source of methane, for P(BH) =0.5 (a) and P(BH) =0.05 (c). b,d, Likelihood of the observables for the different models when the abiotic methane concentration in the hydrothermal may be much higher, for P(BH) =0.5 (b) and P(BH) =0.05 (d). Blue bars denote the likelihood of the \(\overline{H}\) model (‘uninhabitable’), orange bars denote the likelihood of the Hab model (‘abiotic-habitable’) and green bars denote the likelihood of B (‘biotic’). Likelihood values are obtained by integrating the kernel density estimate approximation of the simulated samples (forexampleFig. 2a,d,f) in the observation interval. The bars are labeled ‘ ≈ 0’ when the likelihood was found to be <10−4. Internal parameters range are explained in Methods and given in Extended Data Table 1, model parameters are given in Extended Data Table 2.

Extended Data Fig. 6 Abiotic and biotic methane production with an increased upper bound on [CH4]f.

a, Outputs of the purely abiotic model. Blue dots indicate ‘uninhabitable’ simulations (\(\overline{H}\)), orange dots indicate ‘abiotic-habitable’ simulations (Hab). b, Outputs of the model including biological activity. Green dots indicate habitable simulations in which biological methanogenesis occurs (B). Magenta dashed lines: Cassini observations. Black dashed lines point to minimum values of CH4 concentration in the HF to explain the lower and upper bounds of observed \({\Phi }_{{{\rm{CH}}}_{4}}\). Internal parameters ranges are explained in Methods and Extended Data Table 1, model parameters are given in Extended Data Table 2.

Extended Data Fig. 7 Cassini observations and distributions of model outputs over the space of observables when higher abiotic methane concentration in the HF is allowed.

a, d, f Univariate distributions for each observable. b, c, e Joint distributions. The color code separates the pseudo-data into simulations that were uninhabitable (\(\overline{H}\), blue), abiotic-habitable (Hab, orange), and biotic (B, green). Magenta dashed lines and stars indicate the observed values of each observable. See Fig. 2 for more details, Methods for model equations, and Extended Data Tables 1 and 2 for definitions of plotted parameters, prior internal parameter ranges, and model parameters.

Extended Data Fig. 8 Parameters of the ABC inference.

Description and values for the parameters of the Approximate Bayesian Computation Random Forest procedure done with the Python Sickit-learn package53.

Supplementary information

Supplementary Information

Supplementary Figs. 1–6, Methods, Results and Discussion.

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Affholder, A., Guyot, F., Sauterey, B. et al. Bayesian analysis of Enceladus’s plume data to assess methanogenesis. Nat Astron (2021).

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