Sub-Neptune Exoplanets
- Sub-Neptune planets are exoplanets with radii of 1.6–4 R⊕ and masses of 2–20 M⊕, characterized by diverse compositions and formation histories.
- Probabilistic mass–radius relationships using hierarchical Bayesian models reveal significant intrinsic scatter, refining our understanding of their structure.
- Atmospheric loss, thermal evolution, and dynamic interactions drive the evolutionary pathways of sub-Neptunes, informing future observational strategies.
Sub-Neptune planets are a distinct class of exoplanets with radii and masses intermediate between those of Earth and Neptune, generally spanning 1.6–4 R⊕ and 2–20 M⊕. These objects lack analogs in the Solar System but are extremely prevalent in the galaxy, dominating the radius and mass distributions revealed by transit and radial velocity surveys. The physical diversity of sub-Neptunes encompasses a broad range of bulk compositions, envelope mass fractions, dynamical states, and evolutionary pathways, reflecting complex formation histories and interactions with their host stars and circumstellar environments. The field has advanced from empirical mass–radius relationships toward comprehensive modeling of structure, evolution, atmospheric properties, and orbital dynamics.
1. Defining Characteristics and Population Properties
Sub-Neptunes are typically identified by their radii (1.6–4 R⊕) and mass (2–20 M⊕) ranges, lying between the terrestrial (super-Earth) regime and ice giant planets like Neptune. Kepler, K2, and TESS have detected thousands of such planets, but Solar System analogs are absent (Bean et al., 2020, Ikuta et al., 22 Jul 2025). The precise definition sometimes varies depending on observational selection, but population studies consistently show a bimodal radius distribution with a “radius valley” at ~1.7–2.0 R⊕, separating smaller rocky planets (“true super-Earths”) from larger gas-rich sub-Neptunes (“gas-rich super-Earths”) (Bean et al., 2020).
Statistically, sub-Neptunes exhibit a wide range of densities, with some examples (e.g., K2-66b, K2-106b, HD 119130 b, K2-182 b) exceeding 5–7 g cm⁻³, indicative of predominantly rocky interiors with minimal envelopes, while others are less dense, implying significant H/He or volatiles (Sinukoff et al., 2017, Luque et al., 2018, Murphy et al., 2021). The diversity in measured densities, envelope mass fractions, and compositions necessitates probabilistic rather than deterministic mass–radius relations (Wolfgang et al., 2015).
2. Probabilistic Mass–Radius Relationships and Intrinsic Scatter
Classical approaches treated the mass–radius (M–R) relationship of exoplanets as deterministic, but empirical data demonstrate a large intrinsic scatter due to variations in composition and evolutionary history. Hierarchical Bayesian modeling frameworks establish that, for sub-Neptunes (R < 4 R⊕), the relation is best captured by a probabilistic power law (Wolfgang et al., 2015):
This means that planets with identical measured radii can span a range of masses due to compositional diversity (e.g., rocky core versus volatile-rich envelope). The σ_M parameter quantifies intrinsic scatter, and credible intervals are derived via MCMC sampling, ensuring parameter uncertainties incorporate both measurement error and astrophysical diversity. Extension to planets with alternative mass measurement techniques (e.g., TTVs) or to wider radius ranges yields systematic shifts in normalization and increased scatter (Wolfgang et al., 2015).
This framework allows for forward modeling and population synthesis, propagating observational and intrinsic uncertainties, and can be extended to include dependencies on orbital period and stellar host properties.
3. Interior Structure and Thermal Evolution
Sub-Neptunes generally comprise a heavy-element core (rocky or icy) surrounded by a modest H/He envelope. Interior structure modeling couples the thermal evolution of the deep interior—typically adiabatic in temperature for massive rock/iron cores—with complex radiative–convective atmospheric layers (Chen et al., 2016, Tang et al., 28 Oct 2024). The thick envelope acts as a thermal blanket, substantially slowing the cooling and solidification of the silicate mantle. For instance, complete mantle solidification within 10 Gyr occurs only for low-mass (≤ 1 M⊕) and thin-enveloped (≤ 0.1%) planets (Tang et al., 28 Oct 2024).
A critical insight is that the transit radius is strongly affected by a low-gravity, extended radiative atmosphere, which can contribute up to 40% of the observed radius. Detailed modeling, including variable gravity, molecular dissociation, and metal enrichment, has shown that low observed densities do not necessarily require large H/He masses—extended atmospheres allow for similar radii at reduced envelope mass fractions (Tang et al., 28 Oct 2024). Metal-rich layers reduce scale height and the transit radius, but do not significantly alter the convective envelope depth.
Core cooling timescales may be comparable to or exceed system ages (1–10 Gyr), and delayed core cooling can inflate the atmosphere and thus the observed radius by up to 30% at Gyr ages, introducing degeneracy into interpretations based solely on mass and radius (Vazan et al., 2017).
4. Atmospheric Loss, Evolutionary Pathways, and Population Features
Atmospheric escape is a critical process in the evolutionary trajectories of sub-Neptunes, driven by photoevaporative mass loss via high-energy stellar irradiation and/or core-powered envelope loss. Models predict that for planets with H/He envelope mass fractions of ~1%, the mass-loss timescale τ_env is maximized, creating a convergent evolution that leads many close-in sub-Neptunes to "pile up" at this fraction (Chen et al., 2016). This "convergent evaporation" is consistent with empirical radius distributions.
The "photoevaporation desert"—a region of parameter space (e.g., 2.2–3.8 R⊕, F ≳ 650 S⊕) almost devoid of planets—arises because planets in this regime are particularly susceptible to envelope loss, as exemplified by high-density, bare core planets such as K2-66b (Sinukoff et al., 2017). Population-level studies have also revealed a gap in the planet mass–period distribution for sub-Neptunes with P < 20 d: the best-fit boundary is ΔM/ΔP ≈ –1 M⊕/d with a width of ~4 M⊕. This gap is statistically very significant (ΔBIC ≈ –20 for bimodal Gaussian mixture fits) and likely results from a combination of tidal interactions, dynamical and accretion boundaries, and migration traps (Armstrong et al., 2019).
In situ formation and disk-driven migration are both considered important; multi-planet resonant chains (e.g., Kepler-223) provide evidence for migration and resonant locking, while the observed distribution of orbital period ratios, especially the peak–trough asymmetry near first-order resonances, can be quantitatively reproduced by short-scale (~10%) migration under the damping influence of a gas-poor disk (Mills et al., 2016, Choksi et al., 2020).
5. Composition Diversity: Rocky, Water-Rich, and Gas-Rich Sub-Neptunes
The density and inferred composition of sub-Neptunes span a wide range even for similar masses and radii. Ultra-dense examples such as HD 119130 b, K2-66b, and K2-182 b have densities > 5–7 g cm⁻³, consistent with minimal envelopes and silicate-rich interiors; by contrast, less dense planets likely retain significant volatile layers (H/He and/or H₂O) (Luque et al., 2018, Murphy et al., 2021). Modeling and precise mass–radius measurements in multiple systems (including M dwarf hosts) show many sub-Neptunes cannot be fit by purely rocky models but instead require volatiles—either H/He or thick ice/water mantles (Hori et al., 21 May 2024, Ikuta et al., 22 Jul 2025).
A fundamental ambiguity arises because different compositions (rocky core + thin H/He, water world, or gas-dominated) can yield similar bulk densities. This degeneracy motivates the emerging use of atmospheric spectroscopy and direct imaging to determine dominant atmospheric species and surface properties, breaking M–R degeneracy (Hu et al., 20 Sep 2025).
Mechanisms such as the “fugacity crisis” have been invoked to explain the abundance and size distribution: around 3 R⊕, the base-of-atmosphere pressure enables efficient dissolution of H₂ into a molten silicate mantle, arresting further growth in atmospheric thickness and causing a sharp cutoff in planet radii (Kite et al., 2019).
6. Observational Advances: Atmospheres, Chemistry, and Prospects
Transmission spectroscopy, both space- and ground-based, has matured with the advent of JWST and high-precision RV follow-up. The first robust detection of carbon-bearing molecules (CH₄, CO₂) in the habitable zone sub-Neptune K2-18 b demonstrates chemical disequilibrium and supports the presence of H₂-rich atmospheres (Madhusudhan et al., 23 Sep 2025). More generally, atmospheric retrievals reveal departures from equilibrium, evidence for vertical mixing, photochemistry, and a diversity of atmospheric and interior states.
Atmospheric water vapor abundances show a temperature dependence, with a critical temperature (empirically near 350 K) above which the cold trap is lifted and the atmosphere transitions from H₂-dominated with low observable H₂O (cold trap) to "steamy" water-rich regimes, consistent with theoretical cold-trapping models (Madhusudhan et al., 23 Sep 2025). These observations support an emerging chemical taxonomy: “hycean worlds” (H₂ envelope, liquid water ocean), “steam worlds” (hot, supercritical water-hydrogen envelopes), and mini-Neptunes/gas dwarfs (thick H₂/He, lower metal content).
Future missions such as the Habitable Worlds Observatory (HWO) will leverage optical/NIR spectroscopy and polarimetry to diagnose atmospheric composition (H₂, H₂O, CH₄, CO₂) and scattering properties (e.g., Rayleigh scattering, ocean glint) to distinguish between rocks, water worlds, and gas-rich sub-Neptunes, overcoming M–R compositional degeneracies. Polarization analysis can probe atmospheric properties and surface types over phase angle and wavelength baselines, providing powerful discrimination (Hu et al., 20 Sep 2025).
7. Dynamical and Spin-Orbit Architectures
Dynamical architectures, including system obliquity and multiplicity, are key for diagnosing formation and migration histories. Recent Rossiter–McLaughlin measurements for single sub-Neptunes (e.g., TOI-1759A b: |λ|=4° ± 18°, ψ=24° ± 12°) reveal a tendency toward aligned systems, particularly for R < 4 R⊕ and compact multi-planet configurations (Polanski et al., 6 Jul 2025). Isolated, larger sub-Neptunes (4 < R < 8 R⊕) are more often misaligned, consistent at ~3σ confidence, supporting a picture where compact multi-planet systems form via migration in dynamically cool disks, while isolated systems may have experienced dynamical perturbations, possibly due to unseen massive companions.
Case studies of planets in the "evaporation desert" with high eccentricity and short periods (e.g., TOI-5800 b, e ≈ 0.39, P ≈ 2.6 d) provide laboratories to paper tidal heating, atmospheric inflation, and photoevaporative erosion in real time (Jenkins et al., 15 May 2025). These systems are high-value targets for time-resolved atmospheric spectroscopy with JWST.
Summary Table: Key Physical Properties and Mechanisms
| Property | Observed Range / Model Value | Significance |
|---|---|---|
| Radii | 1.6–4 R⊕ | Defining sub-Neptune class |
| Masses | 2–20 M⊕ | Intermediate regime, diverse compositions |
| Probabilistic M–R law | μ = 2.7 (R/R⊕)1.3, σ = 1.9 M⊕ | Captures intrinsic scatter (compositional spread) |
| Envelope Mass Fraction | 0.1–a few % (typ. 1%) | Modest; set by atmospheric escape/magma equil. |
| Metallicity Effects | 10–50 × solar metals? | Contracts radiative atm., lowers transit radius |
| Spin–Orbit Obliquity | Most R < 4 R⊕: aligned | Dynamically cool histories, disk migration |
| "Photoevaporation desert" | 2.2–3.8 R⊕, F ≳ 650 S⊕ | Region of reduced occurrence, envelope stripping |
| Key processes | Photoevaporation, core-powered mass loss, core cooling, magma–atm. equilibration, disk migration, tidal heating | Drivers of observed diversity |
References
- Probabilistic M–R relations and intrinsic scatter: (Wolfgang et al., 2015)
- Photoevaporation and convergent mass loss: (Chen et al., 2016)
- Core cooling and inflated radii: (Vazan et al., 2017, Tang et al., 28 Oct 2024)
- Population-level mass/radius gaps: (Armstrong et al., 2019)
- Magma-atmosphere equilibration ("fugacity crisis"): (Kite et al., 2019)
- Bimodal radius distributions, atmospheric loss: (Bean et al., 2020)
- Dynamical architectures, resonant chains, obliquities: (Mills et al., 2016, Choksi et al., 2020, Polanski et al., 6 Jul 2025)
- Diverse compositions, ultra-dense sub-Neptunes: (Sinukoff et al., 2017, Luque et al., 2018, Murphy et al., 2021)
- Atmospheric observations, chemical taxonomy, habitability: (Madhusudhan et al., 23 Sep 2025, Hu et al., 20 Sep 2025)
The sub-Neptune population encapsulates the complexity of planet formation and evolution. The lack of a Solar System analog necessitates direct empirical and theoretical paper. Emerging taxonomies, framed by atmospheric observations (notably with JWST), hierarchical modeling, and dynamical characterization, are transforming sub-Neptunes from a taxonomic gap into a key laboratory for comparative planetology and the search for habitable environments.
