The Role of Intrinsic Temperature and Vertical Mixing in Characterizing Sub-Neptune Atmospheres

TL;DR

The paper addresses how a sub-Neptune’s interior heating and vertical transport shape observable atmospheres, tackling degeneracies in interior interpretations by systematically varying the intrinsic temperature $T_{ m int}$ and eddy diffusion $K_{ m zz}$ across a broad grid for K2-18b analogs using a coupled PICASO–VULCAN framework. It demonstrates that CH$_4$, CO$_2$, CO, NH$_3$, and especially HCN are highly sensitive to these parameters, while H$_2$O remains relatively stable, leading to distinct chemical regimes and spectral evolutions from 0.6 to 5 µm. A key finding is that intermediate $T_{ m int}$ (≈$250$–$350$ K) with realistic mixing can reproduce the K2-18b JWST-like spectrum, implying a degeneracy with Hycean-like shallow-surface scenarios and highlighting the need for multi-molecule diagnostics to robustly differentiate interior and atmospheric configurations. The work establishes a diagnostic framework linking quenching chemistry, vertical transport, and condensation to observable features, which has practical impact for interpreting JWST data and guiding future observations of temperate sub-Neptunes. Overall, the study shifts the interpretation of sub-Neptune atmospheres away from fixed-parameter models toward a comprehensive exploration of interior-thermal and mixing parameter space to reliably characterize these abundant worlds.

Abstract

Sub-Neptune planets are often modeled with a dense rocky or metal-rich interior beneath a thick hydrogen/helium (H/He) atmosphere; though their bulk densities could also be explained by a water-rich interior with a thin H/He atmosphere. Atmospheric composition provides a key mechanism to break this degeneracy between competing interior models. However, the overall composition of sub-Neptunes inferred from spectra obtained with the James Webb Space Telescope, remains debated in part due to differences in modeling assumptions. While previous studies explored parameter spaces such as stellar spectra, atmospheric metallicities, and carbon-to-oxygen ratios, they often assumed fixed intrinsic temperatures (Tint) and vertical eddy diffusion coefficients (Kzz) - two critical, yet poorly constrained, drivers of atmospheric chemistry. To address this, we present a self-consistent grid of models that covers the full plausible range of Tint (60 - 450 K) and Kzz (10^{5} - 10^{12} cm^2/s) using the open-source PICASO and VULCAN packages to better characterize sub-Neptune atmospheres. Focusing on K2-18b analogs, we demonstrate that Tint and Kzz significantly impact CH4, CO2, CO, NH3 and HCN abundances, with H2O being largely unaffected. Our work demonstrates that comprehensive parameter space exploration of thermal and mixing parameters is essential for accurate interpretation of sub-Neptune spectra, and that single-parameter assumptions can lead to misclassification of planetary interiors. We provide a diagnostic framework using multi-molecule observations to distinguish between competing atmospheric models and advance robust characterization of sub-Neptunes.

Figures (8)

• Figure 1: Transiting exoplanets with measured masses and radii from the exoatlasTransiting Exoplanets catalog (Berta-Thompson2025). The gray points represent the sub-neptune population extracted from exoatlas. The selected possible Hycean worlds from Madhusudhan2021 are labeled with error bars for reference; point color encodes equilibrium temperature (K) ranging from 200 K to 600 K using values taken from the NASA Exoplanet Archive (Christiansen2025) assuming zero albedo. K2-18b analogs -- sub-Neptunes with comparable bulk properties and equilibrium temperatures (250-300 K) that occupy the compositional transition region where both Hycean world and gas-rich sub-Neptune interpretations remain plausible, are highlighted within this population. The regime boundaries between super-Earth/rocky composition (light purple) and sub-Neptune/gas-rich (blue) are based on the radius criterion of $1.6 R_{\oplus}$ from Rogers2015, with sub-Neptunes defined as planets with radii between 1.6 and $3.2 R_{\oplus}$. Solid and dashed composition curves from Zeng2008Zeng2019 for rocky and hydrogen-rich planets showcase the degeneracy in mass-radius space. Shaded regions are not strict classifications.
• Figure 2: Left: Pressure-temperature profiles for a K2-18b-like atmosphere generated by PICASO across varying intrinsic interior temperatures ($T_{\mathrm{int}}$) from $60$ to $450~\mathrm{K}$. The color gradient represents different $T_{\mathrm{int}}$ values, with cooler interiors in blue and hotter interiors in purple. The dashed black line shows the reference case with $T_{\mathrm{int}} = 60~\mathrm{K}$, which has been commonly adopted in previous atmospheric models of K2-18b. The curvature around 0.1 bar shown in Figure \ref{['fig:PT-Profile and Kzz Profile']} is expected in these PT profiles because that is where the incident stellar irradiation is absorbed by atmospheric gases. Right: Pressure-dependent eddy diffusion coefficient ($K_{\mathrm{zz}}$) profile for a sub-Neptune model of K2-18b with $100\times$ solar metallicity. The purple line shows the model $K_{\mathrm{zz}}$ profile used in this study, which follows a Jupiter-like eddy diffusion profile in the upper atmosphere ($1~\mathrm{bar}$ to $10^{-8}~\mathrm{bar}$) as adopted from Hu2021Wogan2024. The deep atmosphere ($500~\mathrm{bar}$ to $1~\mathrm{bar}$) uses constant $K_{\mathrm{zz}}$ values from $10^{5}$ - $10^{12}$ cm$^2$/s. Black dashed vertical lines indicate the range of constant $K_{\mathrm{zz}}$ values used in our model grid.
• Figure 3: Mean $\log_{10}$ abundance averaged over $10^{-3}$ -- $10^{-4}$ bar as a function of intrinsic temperature ($60$ -- $450$ K, y-axis) and vertical eddy diffusion coefficient $K_{\mathrm{zz}}$ ($10^{5}$ - $10^{12}\ \mathrm{cm}^{2}\ \mathrm{s}^{-1}$, x-axis) for key atmospheric molecules: (a) methane (CH$_4$): yellow to orange, (b) carbon monoxide (CO): red dark to red, (c) carbon dioxide (CO$_2$): light green to dark green, (d) ammonia (NH$_3$): light blue to purple), (e) hydrogen cyanide (HCN): pink to magenta), and (f) water (H$_2$O): light blue to dark blue. More saturated colors (Darker) indicate higher abundances, while lighter colors indicate depletion. The column labeled Variable represents modeled grid using $K_{\mathrm{zz}}$ profile shown in Figure \ref{['fig:PT-Profile and Kzz Profile']} as adopted from Hu2021 and Wogan2024.
• Figure 4: Vertical abundance profiles of key atmospheric molecules as a function of pressure for mini-Neptune models with different eddy diffusion prescriptions. Panels (a)--(d) show constant $K_{\mathrm{zz}}$ cases: $10^{5}$, $10^{8}$, $10^{10}$, and $10^{12}\ \mathrm{cm}^{2}\ \mathrm{s}^{-1}$. Panel (e) shows the variable-$K_{\mathrm{zz}}$ case adopted from Hu2021 and Wogan2024. Each panel shows mixing-ratio profiles for CH$_4$ (blue), CO$_2$ (green), CO (orange), H$_2$O (red), NH$_3$ (purple), and HCN (pink) at three intrinsic temperatures: $60$ K (solid lines), $250$ K (dashed lines), and $450$ K (dotted lines). The atmosphere is divided into three regions: the equilibrium zone (dark gray, $>100$ bar), the quenching zone (gray, $1$--$100$ bar), and the photochemistry zone (light gray, $<1$ bar).
• Figure 5: Spectrum grid with varying intrinsic temperature and $K_{zz}$ profile. The $K_{zz}$ profile follows the parameterization from Wogan2024 for mini-Neptune atmospheres. The grid showcases atmospheric temperature pressure profiles spanning intrinsic temperatures ($T_\mathrm{int}$) from 60 to 450 K with the $K_{zz}$ profile applied across all models, while metallicity and C/O ratio are held constant. Note that the benchmark spectrum (black line) exhibits some artificially sharp features due to the spectral resolution and binning used in the original Wogan2024 analysis, which we maintain for direct comparison.