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Characterization of the regimes of hydrodynamic escape from low-mass exoplanets

Nature Astronomy volume 8, pages 920–928 (2024)Cite this article

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Abstract

Atmospheric hydrodynamic escape sculpts the population of low-mass close-in planets. However, distinguishing between the driving mechanisms responsible for the hydrodynamic escape of hydrogen-rich atmospheres is a complex task due to the involvement of many physical factors. Using simulations, I show that hydrodynamic escape can be driven solely by thermal energy deposited in the lower layers of the atmosphere, but only if the planet’s Jeans parameter is below 3. Otherwise, additional exogenous drivers are necessary. To characterize these drivers, an upgraded Jeans parameter that takes into account tidal forces is introduced. When the upgraded Jeans parameter falls below 3 or exceeds 6, atmospheric escape is primarily driven by tidal forces or extreme ultraviolet radiation from the host star, respectively. In the range 3 to 6, both factors can trigger the escape of the atmosphere. The upgraded Jeans parameter, which is closely related to the underlying physics, provides a concise method for categorizing the driving mechanisms of hydrodynamic escape. The results can also be applied to planetary evolution calculations.

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Fig. 1: Ratios of mass-loss rates without and with tidal forces.
Fig. 2: Mass-loss rates of planets with different FXUV/ρ.
Fig. 3: Neutral and ionized atmospheres.
Fig. 4: Product of the heating efficiency (η) and \((R_\mathrm{XUV}/R_\mathrm{p})^{2}\).

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Data availability

The data that support the results and plots within this paper are available from the corresponding author upon reasonable request.

Code availability

The codes used in this study are based on previously published works, and references are provided in the manuscript. Those references include most details. The results of this paper can be reproduced by incorporating the details supplied within the paper.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant No. 12288102) and the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB 41000000). I also acknowledge support from the National Natural Science Foundation of China (Grant No. 11973082) and the National Key R&D Program of China (Grant No. 2021YFA1600400/2021YFA1600402). I gratefully acknowledge the PHOENIX Supercomputing Platform jointly operated by the Binary Population Synthesis Group and the Stellar Astrophysics Group at Yunnan Observatories, Chinese Academy of Sciences.

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  1. Yunnan Observatories, Chinese Academy of Sciences, Kunming, China

    J. H. Guo

  2. University of Chinese Academy of Sciences, Beijing, China

    J. H. Guo

  3. Key Laboratory for the Structure and Evolution of Celestial Objects, CAS, Kunming, China

    J. H. Guo

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Extended data

Extended Data Fig. 1 The distributions of density, separation and Jean parameter λ for planets with different driving mechanisms.

The symbols are the same as those in Fig. 2. (a) the distributions of λ and XUV flux; (b) the distributions of separation and mean density. In generally, the planets have smaller density if their hydrodynamic escapes are TE- and tidally-driven. In contrast, the trend is contrary to the planets with XUV-driven. For TE-driven escape, their λ values are smaller than ∼3. For tidally-driven escape, the values of λ* is smaller than 3. In the regime of tidally-XUV-driven transition regime, the values of λ* are in the range of 3-6. The values of λ* are greater than 6 in XUV-driven regime (see Fig. 1).

Extended Data Fig. 2 The TE-driven escape of the atmosphere.

“Black square”: the atmosphere is composed of hydrogen atoms and Helium; “Red circle”: the atmosphere of Hydrogen molecular; “Green triangle”: the atmosphere is composed of hydrogen molecules and Helium. The two solid lines are λ=2.8 and 3.5, and the region between two solid lines represents the regime of transonic escape for the atmospheres of H2 and H2+He. The dashed line is λ=3.3 that denote the limit of supersonic escape for mon-atomic gases. All filled symbols are supersonic outflow while the triangles and circles denote the case of transonic escape. I also marked the Mach numbers of the lower boundary for the three examples with the lowest mass loss rates. Note that the velocities at the lower boundary are not imposed to equal with the sound speed such that my model predicts very high the mass loss rates. Also note that the tidal forces, XUV irradiation and all chemical reactions are ignored for all planets in the figure.

Extended Data Fig. 3 The atmospheric structures of the TE-driven escape in diatomic atmospheres.

I show two samples with different values of λ. The escapes of both the two planets are driven by their thermal energy, but one is supersonic and the other is transonic.

Extended Data Fig. 4 The distribution of RRoche/Rs-Rxuv/Rs and the relationship between the location of sonic point and optical depths of XUV spectrum.

The dependence of the altitude distribution of the Roche radius, average absorption radius of XUV radiation and position of the sound point on the upgraded Jeans parameter. All planets orbiting G- and M-type are included. “red circle”: λ* < 3; “green triangle”: 3 < λ* < 6; “blue star”: λ* > 6.

Extended Data Fig. 5 The structure of the atmosphere for two planets around the turning point of neutral and ionized wind.

The XUV flux received by them is 5.4 × 104erg/s/cm2. The black lines denote the case of neutral atmosphere (Mp = 12M⊕, Rp = 1R⊕, and gravitational potential ϕ = 7.50 × 1012 erg/g) while the red lines are the ionized atmosphere (Mp = 20M⊕, Rp = 1R⊕, gravitational potential ϕ = 1.25 × 1013 erg/g). ‘Solid line”: the number density of hydrogen atoms; ‘Dashed line”: the number density of hydrogen ions; ‘Dotted line”: the temperature profiles.

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Supplementary Discussion and Figs. 1–3.

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Guo, J.H. Characterization of the regimes of hydrodynamic escape from low-mass exoplanets. Nat Astron 8, 920–928 (2024). https://doi.org/10.1038/s41550-024-02269-w

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