Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Helium-enhanced planets along the upper edge of the radius valley

Abstract

The Kepler survey revealed that the radius distribution of sub-Neptunes is bimodal: there is a scarcity of planets between 1.5 and 2.0 R. However, the mechanism that creates the valley is unknown. The low mean densities of sub-Neptunes imply that they formed within a few million years and accreted primordial envelopes. Because these planets receive X-ray and UV fluxes comparable to the gravitational binding energy of their envelopes, their atmospheres are susceptible to mass loss. We model the thermal and compositional evolution of sub-Neptunes undergoing escape with diffusive separation between hydrogen and helium and show that preferential loss of hydrogen can change their atmospheric compositions. Planets with radii between 1.6 and 2.5 R can obtain atmospheric helium mass fractions in excess of 40% from billions of years of photoevaporation. Such enhancement can be detected through transmission spectroscopy, providing a novel observational test to determine whether atmospheric escape creates the radius valley.

This is a preview of subscription content, access via your institution

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Fig. 1: Simulated planet instellation flux–radius relations at ages of 2.5, 5.0, 7.5 and 10.0 Gyr.
Fig. 2: The mass–radius–flux parameter space for helium-enhanced planets orbiting G stars.
Fig. 3: The atmospheric composition (metallicity and helium number fraction) of planets evolved with fractionated mass loss at ages of 2.5, 5.0, 7.5 and 10.0 Gyr.
Fig. 4: Simulated transmission spectra with varying atmospheric compositions.

Data availability

MESA is publicly available (http://mesa.sourceforge.net/). Exo_Transmit is also publicly available (https://github.com/elizakempton/Exo_Transmit). The planet model data from MESA, as well as the Exo_Transmit abundances, are available from the corresponding author upon request.

Code availability

All code is available from the corresponding author upon request.

References

  1. Fulton, B. J. & Petigura, E. A. The California-Kepler Survey. VII. Precise planet radii leveraging Gaia DR2 reveal the stellar mass dependence of the planet radius gap. Astron. J. 156, 264 (2018).

    Article  ADS  Google Scholar 

  2. Fulton, B. J. et al. The California-Kepler Survey. III. A gap in the radius distribution of small planets. Astron. J. 154, 109 (2017).

    Article  ADS  Google Scholar 

  3. Rogers, L. A. Most 1.6 Earth-radius planets are not rocky. Astrophys. J. 801, 41 (2015).

    Article  ADS  Google Scholar 

  4. Rogers, L. A. & Seager, S. Three possible origins for the gas layer on GJ 1214b. Astrophys. J. 716, 1208–1216 (2010).

    Article  ADS  Google Scholar 

  5. Kite, E. S. & Schaefer, L. Water on hot rocky exoplanets. Astrophys. J. Lett. 909, L22 (2021).

    Article  ADS  Google Scholar 

  6. Owen, J. E. & Wu, Y. The evaporation valley in the Kepler planets. Astrophys. J. 847, 29 (2017).

    Article  ADS  Google Scholar 

  7. Watson, A. J., Donahue, T. M. & Walker, J. C. G. The dynamics of a rapidly escaping atmosphere: applications to the evolution of Earth and Venus. Icarus 48, 150–166 (1981).

    Article  ADS  Google Scholar 

  8. Ginzburg, S., Schlichting, H. E. & Sari, R. Core-powered mass-loss and the radius distribution of small exoplanets. Mon. Not. R. Astron. Soc. 476, 759–765 (2018).

    Article  ADS  Google Scholar 

  9. Zeng, L. et al. Growth model interpretation of planet size distribution. Proc. Natl Acad. Sci. USA 116, 9723–9728 (2019).

    Article  ADS  Google Scholar 

  10. Kuchner, M. J. Volatile-rich Earth-mass planets in the habitable zone. Astrophys. J. Lett. 596, L105–L108 (2003).

    Article  ADS  Google Scholar 

  11. Léger, A. et al. A new family of planets? “Ocean-Planets.” Icarus 169, 499–504 (2004).

    Article  ADS  Google Scholar 

  12. Silva Aguirre, V. et al. Ages and fundamental properties of Kepler exoplanet host stars from asteroseismology. Mon. Not. R. Astron. Soc. 452, 2127–2148 (2015).

    Article  ADS  Google Scholar 

  13. Petigura, E. A. et al. The California-Kepler Survey. X. The radius gap as a function of stellar mass, metallicity, and age. Astron. J. 163, 179 (2022).

    Article  ADS  Google Scholar 

  14. Owen, J. E. & Wu, Y. Kepler planets: a tale of evaporation. Astrophys. J. 775, 105 (2013).

    Article  ADS  Google Scholar 

  15. Chen, H. & Rogers, L. A. Evolutionary analysis of gaseous sub-Neptune-mass planets with MESA. Astrophys. J. 831, 180 (2016).

    Article  ADS  Google Scholar 

  16. Zahnle, K. J. & Kasting, J. F. Mass fractionation during transonic escape and implications for loss of water from Mars and Venus. Icarus 68, 462–480 (1986).

    Article  ADS  Google Scholar 

  17. Hu, R., Seager, S. & Yung, Y. L. Helium atmospheres on warm Neptune- and sub-Neptune-sized exoplanets and applications to GJ 436b. Astrophys. J. 807, 8 (2015).

    Article  ADS  Google Scholar 

  18. Malsky, I. & Rogers, L. A. Coupled thermal and compositional evolution of photoevaporating planet envelopes. Astrophys. J. 896, 48 (2020).

    Article  ADS  Google Scholar 

  19. Deming, D. et al. Spitzer transit and secondary eclipse photometry of GJ 436b. Astrophys. J. Lett. 667, L199–L202 (2007).

    Article  ADS  Google Scholar 

  20. Paxton, B. et al. Modules for Experiments in Stellar Astrophysics (MESA): pulsating variable stars, rotation, convective boundaries, and energy conservation. Astrophys. J. 243, 10 (2019).

    Article  Google Scholar 

  21. Murray-Clay, R. A., Chiang, E. I. & Murray, N. Atmospheric escape from hot Jupiters. Astrophys. J. 693, 23–42 (2009).

    Article  ADS  Google Scholar 

  22. Fortney, J. J. et al. A framework for characterizing the atmospheres of low-mass low-density transiting planets. Astrophys. J. 775, 80 (2013).

    Article  ADS  Google Scholar 

  23. Miller-Ricci, E., Seager, S. & Sasselov, D. The atmospheric signatures of super-Earths: how to distinguish between hydrogen-rich and hydrogen-poor atmospheres. Astrophys. J. 690, 1056–1067 (2009).

    Article  ADS  Google Scholar 

  24. Benneke, B. & Seager, S. Atmospheric retrieval for super-Earths: uniquely constraining the atmospheric composition with transmission spectroscopy. Astrophys. J. 753, 100 (2012).

    Article  ADS  Google Scholar 

  25. Kunimoto, M., Winn, J., Ricker, G. R. & Vanderspek, R. K. Predicting the exoplanet yield of the TESS Prime and extended missions through years 1–7. Astron. J. 163, 290 (2022).

    Article  ADS  Google Scholar 

  26. Mansfield, M. et al. Detection of helium in the atmosphere of the exo-Neptune HAT-P-11b. Astrophys. J. Lett. 868, L34 (2018).

    Article  ADS  Google Scholar 

  27. Spake, J. J. et al. Helium in the eroding atmosphere of an exoplanet. Nature 557, 68–70 (2018).

    Article  ADS  Google Scholar 

  28. Zhang, M., Knutson, H. A., Wang, L., Dai, F. & Barragán, O. Escaping helium from TOI 560.01, a young mini-Neptune. Astron. J. 163, 67 (2022).

    Article  ADS  Google Scholar 

  29. Coc, A. et al. New reaction rates for improved primordial D/H calculation and the cosmic evolution of deuterium. Phys. Rev. D. 92, 123526 (2015).

    Article  ADS  Google Scholar 

  30. Elkins-Tanton, L. T. & Seager, S. Ranges of atmospheric mass and composition of super-Earth exoplanets. Astrophys. J. 685, 1237–1246 (2008).

    Article  ADS  Google Scholar 

  31. Paxton, B. et al. Modules for Experiments in Stellar Astrophysics (MESA). Astrophys. J. 192, 3 (2011).

    Article  Google Scholar 

  32. Paxton, B. et al. Modules for Experiments in Stellar Astrophysics (MESA): planets, oscillations, rotation, and massive stars. Astrophys. J. 208, 4 (2013).

    Article  Google Scholar 

  33. Paxton, B. et al. Modules for Experiments in Stellar Astrophysics (MESA): binaries, pulsations, and explosions. Astrophys. J. 220, 15 (2015).

    Article  Google Scholar 

  34. Paxton, B. et al. Modules for Experiments in Stellar Astrophysics (MESA): convective boundaries, element diffusion, and massive star explosions. Astrophys. J. 234, 34 (2018).

    Article  Google Scholar 

  35. Rogers, L. A., Bodenheimer, P., Lissauer, J. J. & Seager, S. Formation and structure of low-density exo-Neptunes. Astrophys. J. 738, 59 (2011).

    Article  ADS  Google Scholar 

  36. Guillot, T., Chabrier, G., Gautier, D. & Morel, P. Effect of radiative transport on the evolution of Jupiter and Saturn. Astrophys. J. 450, 463–472 (1995).

    Article  ADS  Google Scholar 

  37. Miller, N., Fortney, J. J. & Jackson, B. Inflating and deflating hot Jupiters: coupled tidal and thermal evolution of known transiting planets. Astrophys. J. 702, 1413–1427 (2009).

    Article  ADS  Google Scholar 

  38. Freedman, R. S. et al. Gaseous mean opacities for giant planet and ultracool dwarf atmospheres over a range of metallicities and temperatures. Astrophys. J. 214, 25 (2014).

    Article  Google Scholar 

  39. Owen, J. E. & Jackson, A. P. Planetary evaporation by UV & X-ray radiation: basic hydrodynamics. Mon. Not. R. Astron. Soc. 425, 2931–2947 (2012).

    Article  ADS  Google Scholar 

  40. Sanz-Forcada, J. et al. Estimation of the XUV radiation onto close planets and their evaporation. Astron. Astrophys. 532, A6 (2011).

    Article  Google Scholar 

  41. Erkaev, N. V. et al. Roche lobe effects on the atmospheric loss from “Hot Jupiters”. Astron. Astrophys. 472, 329–334 (2007).

    Article  ADS  Google Scholar 

  42. Rodrigo, R. & Lara, L. M. Photochemistry of planetary atmospheres. In The Evolving Sun and its Influence on Planetary Environments (eds Montesinos, B. et al.) 133-150 (Astronomical Society of the Pacific, 2002).

  43. Yelle, R. Aeronomy of extra-solar giant planets at small orbital distances. Icarus 170, 167–179 (2004).

    Article  ADS  Google Scholar 

  44. Koskinen, T. T., Lavvas, P., Harris, M. J. & Yelle, R. V. Thermal escape from extrasolar giant planets. Philos. Trans. R. Soc. Lond. A 372, 20130089 (2014).

    ADS  Google Scholar 

  45. Tucker, O. J., Erwin, J. T., Deighan, J. I., Volkov, A. N. & Johnson, R. E. Thermally driven escape from Pluto’s atmosphere: a combined fluid/kinetic model. Icarus 217, 408–415 (2012).

    Article  ADS  Google Scholar 

  46. Erwin, J., Tucker, O. J. & Johnson, R. E. Hybrid fluid/kinetic modeling of Pluto’s escaping atmosphere. Icarus 226, 375–384 (2013).

    Article  ADS  Google Scholar 

  47. Johnson, R. E., Volkov, A. N. & Erwin, J. T. Molecular–kinetic simulations of escape from the ex-planet and exoplanets: criterion for transonic flow. Astrophys. J. 768, L4 (2013).

    Article  ADS  Google Scholar 

  48. Volkov, A. N. & Johnson, R. E. Thermal escape in the hydrodynamic regime: reconsideration of parker’s isentropic theory based on results of kinetic simulations. Astrophys. J. 765, 90 (2013).

    Article  ADS  Google Scholar 

  49. Mason, E. A. & Marrero, T. R. The diffusion of atoms and molecules. Adv. At. Mol. Phys. 6, 155–232 (1970).

    Article  ADS  Google Scholar 

  50. Schunk, R. W. & Nagy, A. F. Ionospheres of the terrestrial planets. Rev. Geophys. 18, 813–852 (1980).

    Article  ADS  Google Scholar 

  51. Hunten, D. M., Pepin, R. O. & Walker, J. C. G. Mass fractionation in hydrodynamic escape. Icarus 69, 532–549 (1987).

    Article  ADS  Google Scholar 

  52. Zahnle, K., Kasting, J. F. & Pollack, J. B. Mass fractionation of noble gases in diffusion-limited hydrodynamic hydrogen escape. Icarus 84, 502–527 (1990).

    Article  ADS  Google Scholar 

  53. Hunten, D. M. The escape of light gases from planetary atmospheres. J. Atmos. Sci. 30, 1481–1494 (1973).

    Article  ADS  Google Scholar 

  54. Carroll, B. W. & Ostlie, D. A. An Introduction to Modern Astrophysics (Addison-Wesley, 1996).

  55. Lodders, K. Solar system abundances and condensation temperatures of the elements. Astrophys. J. 591, 1220–1247 (2003).

    Article  ADS  Google Scholar 

  56. Mbarek, R. & Kempton, E. M. R. Clouds in super-Earth atmospheres: chemical equilibrium calculations. Astrophys. J. 827, 121 (2016).

    Article  ADS  Google Scholar 

  57. Kempton, E. M.-R., Lupu, R., Owusu-Asare, A., Slough, P. & Cale, B. Exo-Transmit: an open-source code for calculating transmission spectra for exoplanet atmospheres of varied composition. Publ. Astron. Soc. Pac. 129, 044402 (2017).

    Article  ADS  Google Scholar 

  58. Virtanen, P. et al. SciPy 1.0: fundamental algorithms for scientific computing in Python. Nat. Methods 17, 261–272 (2020).

    Article  Google Scholar 

  59. Akeson, R. L. et al. The NASA Exoplanet Archive: data and tools for exoplanet research. Publ. Astron. Soc. Pac. 125, 989 (2013).

    Article  ADS  Google Scholar 

  60. Kempton, E. M.-R. et al. A framework for prioritizing the TESS planetary candidates most amenable to atmospheric characterization. Publ. Astron. Soc. Pac. 130, 114401 (2018).

    Article  ADS  Google Scholar 

  61. Kreidberg, L. et al. Clouds in the atmosphere of the super-Earth exoplanet GJ 1214b. Nature 505, 69–72 (2014).

    Article  ADS  Google Scholar 

  62. Foreman-Mackey, D. corner.py: scatterplot matrices in Python. J. Open Source Softw. 1, 24 (2016).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

I.M. thanks E. Rauscher, N. Calvet, N. Choksi and M. Cowherd, who provided editorial suggestions on drafts of this manuscript. I.M. acknowledges support from the Michigan Space Grant under Grant No. 80NSSC20M0124. I.M. also thanks N. Merhle, who provided code used to convolve the simulated spectra. L.R. gratefully acknowledges support from NSF FY2016 AAG Solicitation 12-589 award number 1615089 and the Research Corporation for Science Advancement through a Cottrell Scholar Award. This research has made use of the NASA Exoplanet Archive, which is operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program. This work was also completed in part with resources provided by the University of Chicago’s Research Computing Center.

Author information

Authors and Affiliations

Authors

Contributions

L.R. conceived the study and L.R. and I.M. designed the project together. I.M. wrote the numerical additions to MESA and other code necessary for the simulated spectra and data analysis. E.M.-R.K. provided input for the simulated spectra and N.M. analysed the atmospheric chemistry models. I.M. and L.R. wrote the manuscript with input from E.M.-R.K. and N.M.

Corresponding author

Correspondence to Isaac Malsky.

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.

Additional information

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

Extended data

Extended Data Fig. 1 The atmospheric compositions expressed as number fraction ratios planets evolved for 10 Gyr around a G type host star with homopause temperatures of 3,000 K.

The atmospheric compositions expressed as number fraction ratios planets evolved for 10 Gyr around a G type host star with homopause temperatures of 3,000 K. All model parameters are identical to those in Fig. 1. The colored dots correspond to the compositions reached at 10 Gyr. We also show the four compositions used for generating transmission spectra (Fig. 4), for both the helium enhanced compositions (the two blue Xs) and the solar H/He compositions (the two black pluses). Note, the helium to hydrogen number ratios and metallicities plotted represent the overall elemental abundances in the planet envelope, while the mean molecular weights are calculated for gas phase species after condensation is taken into account. Furthermore, we expect the metallicity of the two cases with mean molecular weights of 4.00 to be nearly identical as helium has a mean molecular weight of approximately 4.00.

Extended Data Fig. 2 The mean molecular weights as a function of pressure and the optical depths as a function of pressure for the for the solar Y/X and the maximum Y/X composition models.

The mean molecular weights as a function of pressure (top panel) and the optical depth (at a wavelength of 5.9 × 10−7 m, near the rest wavelength of the Na D-lines) as a function of pressure (bottom panel) for the solar Y/X composition atmospheres and the maximum Y/X composition atmospheres corresponding to the transmission spectra in Fig. 4.

Extended Data Fig. 3 The ratios of the solar Y/X composition abundance tables divided by the maximum Y/X composition abundance tables at 10x solar metallicity and 100x solar metallicity for H2O, CH4, CO2, and Na.

The ratios of the solar Y/X composition abundance tables divided by the maximum Y/X composition abundance tables at 10x solar metallicity and 100x solar metallicity for H2O, CH4, CO2, and Na. These tables show the abundances at different X/Y ratios but constant metallicities (defined as the number ratio between Fe and H atoms).

Extended Data Fig. 4 The distribution of surface gravities, radii, and equilibrium temperatures for all planets with Y ≥ 0.4 in our simulations after 10 Gyr.

The distribution of surface gravities, radii, and equilibrium temperatures for all planets with Y ≥ 0.4 in our simulations after 10 Gyr. All model parameters are identical to those in Fig. 1. The figure was made using the Foreman-Mackey62 open source software package.

Supplementary information

Supplementary Information

Supplementary methods, results and Figs. 1–11.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Malsky, I., Rogers, L., Kempton, E.MR. et al. Helium-enhanced planets along the upper edge of the radius valley. Nat Astron (2022). https://doi.org/10.1038/s41550-022-01823-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1038/s41550-022-01823-8

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing