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# Evidence for the volatile-rich composition of a 1.5-Earth-radius planet

## Abstract

The population of planets smaller than approximately 1.7 Earth radii (R) is widely interpreted as consisting of rocky worlds, generally referred to as super-Earths. This picture is largely corroborated by radial velocity mass measurements for close-in super-Earths but lacks constraints at lower insolations. Here we present the results of a detailed study of the Kepler-138 system using 13 Hubble and Spitzer transit observations of the warm-temperate 1.51 ± 0.04 R planet Kepler-138 d ($${T}_{\rm{eq,A_{\rm{B}} = 0.3}}\approx 350\,{\mathrm{K}}$$) combined with new radial velocity measurements of its host star obtained with the Keck/High Resolution Echelle Spectrometer. We find evidence for a volatile-rich ‘water world’ nature of Kepler-138 d, with a large fraction of its mass $M_{\rm{d}}$ contained in a thick volatile layer. This finding is independently supported by transit timing variations and radial velocity observations ($${M}_{{{{\rm{d}}}}}=2.{1}_{-0.7}^{+0.6}\,{M}_{\oplus }$$), as well as the flat optical/infrared transmission spectrum. Quantitatively, we infer a composition of $$1{1}_{-4}^{+3}\%$$ volatiles by mass or ~51% by volume, with a 2,000-km-deep water mantle and atmosphere on top of a core with an Earth-like silicates/iron ratio. Any hypothetical hydrogen layer consistent with the observations (<0.003 M) would have swiftly been lost on a ~10 Myr timescale. The bulk composition of Kepler-138 d therefore resembles those of the icy moons, rather than the terrestrial planets, in the Solar System. We conclude that not all super-Earths are rocky worlds, but that volatile-rich water worlds exist in an overlapping size regime, especially at lower insolations. Finally, our photodynamical analysis also reveals that Kepler-138 c (with a Rc = 1.51 ± 0.04 R and a $${M}_{{{{\rm{c}}}}}=2.{3}_{-0.5}^{+0.6}\,{M}_{\oplus }$$) is a slightly warmer twin of Kepler-138 d (that is, another water world in the same system) and we infer the presence of Kepler-138 e, a likely non-transiting planet at the inner edge of the habitable zone.

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## Data availability

The data used in this paper are deposited on publicly available servers. The data from the HST used in this work can be downloaded from the MAST at https://archive.stsci.edu/proposal_search.php?mission=hst&id=13665. The data from the Spitzer Space Telescope included in our analysis is available on the SHA at https://sha.ipac.caltech.edu/applications/Spitzer/SHA/#id=SearchByProgram&RequestClass=ServerRequest&DoSearch=true&SearchByProgram.field.program=11131&MoreOptions.field.prodtype=aor,pbcd&shortDesc=Program&isBookmarkAble=true&isDrillDownRoot=true&isSearchResult=true. The Keck/HIRES radial velocities are available online as Supplementary Dataset 1. The planet population plots used data from the public NASA Exoplanet Archive (https://exoplanetarchive.ipac.caltech.edu/), which also hosts an interface where the Kepler photometry can be downloaded.

## Code availability

The smint code is publicly available via GitHub at https://github.com/cpiaulet/smint. The RV analysis is based on the publicly available packages george, RadVel and emcee. Further scripts can be provided by the corresponding author upon reasonable request.

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## Acknowledgements

We gratefully acknowledge the open-source software that made this work possible: LDTK34, batman35, emcee36, TTVFast37, REBOUND38, WHFast39, nestle (https://github.com/kbarbary/nestle; refs. 40,41,42,43), astropy126,127, numpy128, ipython129, matplotlib130, RadVel44, george45, smint14 and GNU parallel78. This work is based on observations with the NASA/ESA HST, obtained at the Space Telescope Science Institute (STScI) operated by AURA, Inc. We received support for the analysis by NASA through grants under the HST-GO-13665 programme (PI B.B). This work relies on observations made with the Spitzer Space Telescope, which was operated by the Jet Propulsion Laboratory, California Institute of Technology, under a contract with NASA. This paper includes data collected by the Kepler mission. Funding for the Kepler mission is provided by the NASA Science Mission directorate. This study has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for DPAC has been provided by national institutions, particularly the institutions participating in the Gaia Multilateral Agreement. Data presented in this paper were obtained from the Mikulski Archive for Space Telescopes (MAST) and the Spitzer Heritage Archive (SHA). This research has made use of NASA’s Astrophysics Data System and the NASA Exoplanet Archive, which is operated by the California Institute of Technology, under contract with NASA within the Exoplanet Exploration Program. Parts of this analysis have been run on the Lesta cluster kindly provided by the Observatoire de Genève. C.P. acknowledges financial support from the Fonds de Recherche Québécois—Nature et Technologie (FRQNT; Quebec), the Technologies for Exo-Planetary Science (TEPS) Trainee Program and the Natural Sciences and Engineering Research Council (NSERC) Vanier Scholarship. D.D. acknowledges support from the TESS Guest Investigator Program grant number 80NSSC19K1727 and NASA Exoplanet Research Program grant number 18-2XRP18_2-0136. B.B. acknowledges financial support from the NSERC of Canada and the FRQNT. I.W. is supported by an appointment to the NASA Postdoctoral Program at the NASA Goddard Space Flight Center, administered by Oak Ridge Associated Universities under contract with NASA. C.V.M. acknowledges HST funding through grant number HST-AR-15805.001-A from STScI.

## Author information

Authors

### Contributions

C.P. and B.B. conceived the project. C.P. wrote the manuscript and carried out the reduction of the HST and Spitzer data, as well as the TTV, RV, atmospheric escape, atmospheric retrieval and planetary structure analyses, under the supervision of B.B and with the help of M.S.P. for the TTV analysis and contributions from D.K. to the upper atmosphere modelling. J.M.A. realized the photodynamical analysis and the transit search for Kepler-138 e. D.D. provided the Spitzer observations. H.A.K., A.W.H., H.I., L.M.W. and C.A.B. conducted the observations and reduction of the HIRES RVs. D.T. provided the grid of interior models. R.A. constrained the stellar age. All co-authors provided comments and suggestions on the manuscript.

### Corresponding author

Correspondence to Caroline Piaulet.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

## Peer review

### Peer review information

Nature Astronomy thanks the anonymous reviewers for their contribution to the peer review of this work

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## Extended data

### Extended Data Fig. 1 Three-planet photodynamical fit results.

a,b,c Same as Fig. 1a-c, for a photodynamical fit including only the three previously-known planets Kepler-138 b,c, and d. This illustrates the extent to which the timescale over which the predicted transit times of Kepler-138d are modulated (the super-period) is underestimated by the three-planet solution. This discrepancy was already hinted at by the mismatch with the Kepler transit times but revealed at high significance by the now longer baseline over which we obtained transits with HST and Spitzer, at times beyond BJD=2457000.

### Extended Data Fig. 2 Folded Kepler transits of Kepler-138 b, c, and d, and search for the transit of Kepler-138 e.

The four panels show the corrected light curve of Kepler-138 (open circles) folded in a 2 day window around the expected transit epochs of Kepler-138 b, c, d, and e from the photodynamical fit (see Methods). Transit models corresponding to the median retrieved planet parameters are superimposed to the data (solid colored lines), conservatively assuming an Earth-like composition to estimate the radius of Kepler-138 e. The transits of Kepler-138 b, c, and d are detected in the Kepler light curve, but while Kepler-138 e should be larger than Kepler-138 b, its transit is not detected. We interpret this as originating from a likely non-transiting configuration of Kepler-138 e’s orbit, with an inclination of  89 consistent with the photodynamical solution, too low to occult the stellar disk from our perspective.

### Extended Data Fig. 3 Search for prominent periodicities in the RV and photometric dataset.

From top to bottom, Lomb-Scargle periodogram of the RV dataset, the Kepler light curve, the activity indicator (S-index) and the window function of the RVs. The orbital periods of the four planets, the rotational period of the star and its first harmonic are shown. False-alarm probability levels of 0.1, 1 and 10% are indicated by dashed gray lines in the top two panels. Significant signals are detected at the stellar period and its first harmonic in the light curve. No significant periodicity is detected in the RV and S-index time series.

### Extended Data Fig. 4 Gaussian Process fit to the Kepler photometry.

Zoom on the last 200 days of the Kepler photometric observations (black points) and the best-fitting stellar activity model using a GP (gray shading). The mean is the solid line and the variance is shown as the shaded region. The lower panel shows residuals around the best-fit model divided by the single-point scatter. Posterior constraints on the stellar rotation period from rotational brightness modulations are shown on the right. The GP model reproduces the photometric variability and provides tight constraints on the covariance structure of the stellar signal.

### Extended Data Fig. 5 Median four-planet Keplerian orbital model for Kepler-138.

A trained GP model was used to account for stellar activity in the RV fit. The model corresponding to the median retrieved parameters is plotted in purple while the corresponding parameters are annotated in each panel. We add in quadrature the RV jitter term (Supplementary Table 2) with the measurement uncertainties for all RVs. a, Full HIRES time series. b, Residuals to the best fit model. c, RVs phase-folded to the ephemeris of planet b. The phase-folded model for planet b is shown (purple line), while Keplerian orbital models for all other planets have been subtracted. d,e,f, Same as c for Kepler-138 c, d, and e.

### Extended Data Fig. 6 Illustration of the coupling of interior and atmosphere models.

a, Temperature-pressure and b, temperature-radius profiles computed to generate a complete planet model for a mass of 2.36 M, a H2/He mass fraction of 3%, and no water layer. Self-consistent atmosphere models are shown down to the radiative–convective boundary (dotted, black), for the irradiation of Kepler-138 d, but varying the reference radius at a pressure of 1 kbar. Interior models are displayed for the same composition but different specific entropies (solid, colors). For consistency, full-planet models with a given planet mass and composition are obtained from the combination of interior and atmosphere model that have both matching temperatures and radii at the radiative–convective boundary (bold profiles show the closest match in this example).

### Extended Data Fig. 7 Composition of Kepler-138 d for the hydrogen-free scenario.

We show the joint and marginalized posterior distributions of the planet structure fit for Kepler-138 d in the case of a hydrosphere lying on top of a rock/iron core. The 1, 2 and 3σ probability contours are shown. As expected, the water mass fraction is strongly correlated with the relative amount of rock and iron. The correlation between irradiance temperature and water mass fraction is weak across the considered temperature range.

### Extended Data Fig. 8 Impact of unocculted stellar spots on the Kepler transit depth measurement.

Transmission spectrum of Kepler-138 d (black points) superimposed with three scenarios for the level of stellar contamination: spot covering fractions of 0.1, 3 or 10% (colored lines, colored filled circles show bandpass-integrated values). The potential impact of unocculted stellar spots on the radius in the Kepler bandpass is small compared to its measurement uncertainty.

### Extended Data Fig. 9 Composition of Kepler-138 c for the hydrogen-free scenario.

Same as Extended Data Figure 7, for Kepler-138 c.

### Extended Data Fig. 10 Constraints on the atmospheric composition from transmission spectroscopy.

a, Optical-to-IR transmission spectrum of Kepler-138 d, compared with three representative forward models: a H2/He atmosphere with a solar composition, a high-metallicity cloud-free atmosphere and a cloudy hydrogen-dominated atmosphere. b, Joint posterior probability density of the cloud top pressure Pcloud and atmospheric metallicity, along with the corresponding mass fraction of metals Z assuming a solar C/O ratio. The color encodes the density of posterior samples in each bin and the contours indicate the 2 and 3σ constraints. The location in the parameter space of the three models from panel a is shown with ‘x’ markers. The constraints reflect the well-documented degeneracy between increasing mean molecular weight of the atmosphere and cloud top pressure in terms of the strength of absorption features77. The cloud-free, solar-metallicity scenario is excluded at 2.5σ. The new planet mass leads to an increased surface gravity which motivates further spectroscopic follow-up to obtain more precise constraints on the atmospheric composition.

## Supplementary information

### Supplementary Information

Supplementary Figs. 1–13 and Tables 1–3.

### Supplementary Dataset 1

Machine-readable table of the Keck/HIRES RVs of Kepler-138.

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Piaulet, C., Benneke, B., Almenara, J.M. et al. Evidence for the volatile-rich composition of a 1.5-Earth-radius planet. Nat Astron 7, 206–222 (2023). https://doi.org/10.1038/s41550-022-01835-4

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• DOI: https://doi.org/10.1038/s41550-022-01835-4