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Jeans escape is collisionless atmospheric escape by particles in the high-speed tail of a thermal distribution at the exobase. The Jeans escape parameter $\lambda =GMm/(k_{B}T{r}_e)$ controls the exponential suppression, and the Jeans escape flux is proportional to $(1+\lambda )e^{-\lambda }$. There is no exact positive-temperature threshold below which the tail vanishes. For $\lambda$ of order a few or smaller, a purely hydrostatic tail model can fail and hydrodynamic atmospheric escape becomes important.

In the 2016 observational context, appropriate choices are as follows.

For atomic species, use optical transit spectra of Na I near $0.589\mu \mathrm{m}$ and K I near $0.770\mu \mathrm{m}$, with Hubble Space Telescope/STIS or ground-based high-resolution instruments on Very Large Telescope/Keck telescope-class telescopes. Neutral/ionized ultraviolet metal lines offer additional diagnostics with Hubble Space Telescope. Resolving a line's shape and distinguishing stellar contamination matters as much as locating its wavelength.

For molecules, use near/mid-IR spectroscopy: water bands near $1.4$, $1.9$ and $2.7\mu \mathrm{m}$, CO near $2.3$ and $4.6\mu \mathrm{m}$, methane near $3.3\mu \mathrm{m}$, and ${\mathrm{CO}}_2$ near $4.3$ or $15\mu \mathrm{m}$. Hubble Space Telescope/WFC3 samples water around $1.1$--$1.7\mu \mathrm{m}$; ground-based Very Large Telescope/CRIRES or Keck telescope/NIRSPEC spectra target accessible near-IR windows such as CO at $2.3\mu \mathrm{m}$. Warm Spitzer Space Telescope provides $3.6$ and $4.5\mu \mathrm{m}$ photometry, while cryogenic Spitzer Space Telescope spectra/longer-wavelength data are archival by 2016. A broadband eclipse point alone does not uniquely identify a molecule.

For atmospheric escape, use ultraviolet transit spectroscopy of H I Ly$\alpha$ at $121.6\mathrm{nm}$, and suitable C/O/metal lines, with Hubble Space Telescope/STIS or COS. Extended, velocity-shifted absorption beyond the optical planet suggests an escaping envelope, although stellar variability, geocoronal emission and interstellar absorption require treatment. Ground-based H$\alpha$ at $656.3\mathrm{nm}$ probes excited hydrogen and is a complementary rather than interchangeable measure of neutral-hydrogen escape.

At fixed mass, three broad controls of a super-Earth-sized body's observed radius are:

Bulk composition, envelope fraction/composition, and thermal/irradiation history are three independent controls. If mass is not fixed, the mass itself is an additional major variable. The label super-Earth does not ensure a rocky composition or an Earth-like atmosphere, and a radius alone does not determine which of these effects dominates.

Three research directions natural in the 2017 setting are:

Small-planet atmospheres, formation through composition, and atmospheric dynamics/variability provide three concrete emerging directions. The examples describe research aims as of the paper's date, rather than treating later discoveries or later operating missions as established in 2017.

Take the logarithm to base ten and write pressure in units of $1\mathrm{bar}$, so its argument is dimensionless. Continuity of the atmospheric pressure-temperature profile givesThusIf the logarithm means $\ln$, the equivalent constant is $C=900/\ln 100\simeq 195.4\mathrm{K}$. A plot of temperature against logarithmic pressure is vertical in each isothermal region and straight between the two endpoints.

The processes can be organized by the supplied pressure ranges, although the exact boundaries require reaction rates, irradiation and mixing information:

The profile identifies plausible chemical regimes, but does not fix their transition pressures by itself. In particular, cloud formation depends on the species-specific condensation curve, and ultraviolet processing depends on shielding.

Three major research directions, appropriate to the scientific questions posed in 2018, are:

These are research goals rather than claims that the relevant mechanisms or habitable atmospheres have already been established.

First refine the ephemeris, planetary mass, stellar radius, and stellar variability using exoplanet transit photometry and the radial-velocity method. Then combine observations that probe different regions rather than relying on one spectrum. A present-day programme could use the following complementary measurements; in the 2019 setting of the paper, James Webb Space Telescope observations would have been a future capability.

Together these address aerosols, molecular composition, elemental enrichment, vertical thermal structure, horizontal heat transport, winds, and escape. Repeat key events and monitor stellar activity, since stellar contamination and instrumental trends can imitate atmospheric signals. Use actual brightness, saturation limits, and predicted feature amplitudes to choose observing modes and exposure times.

The wavelength ranges and time-series capabilities are documented in the NIRISS SOSS guide, NIRSpec overview, MIRI spectroscopy guide, and ESO's CRIRES description.