Terminator Asymmetry in WASP-39b

• Terminator asymmetry in WASP-39b is defined by contrasting atmospheric properties between its cooler, cloudier morning limb and hotter, clearer evening limb.
• JWST transit spectroscopy and 2D retrievals quantify significant differences in transit depths and temperature gradients, with the evening limb showing deeper molecular features.
• 3D circulation and photochemical models demonstrate that zonal winds and haze feedback drive the observed inhomogeneities, refining exoplanet atmospheric analysis.

Terminator asymmetry in WASP-39b refers to spatial variations in atmospheric properties—temperature, composition, and aerosols—between the morning (night-to-day) and evening (day-to-night) limbs as probed by transit spectroscopy. The hot Saturn-mass planet WASP-39b, with its large atmospheric scale height, inflated radius, and extended, metal-rich envelope, has become the archetype for empirical and theoretical investigations of this phenomenon. Recent multi-instrument JWST studies, in combination with 3D circulation models and dedicated retrieval frameworks, now robustly demonstrate that the terminators of WASP-39b are inhomogeneous, in contrast to the long-standing one-dimensional (1D) assumption in transmission spectroscopy.

1. Physical and Dynamical Context: Scale Height, Irradiation, and Sensitivity

WASP-39b ($M_p \approx 0.28\,M_J$, $R_p \approx 1.27\,R_J$, equilibrium temperature $T_{\mathrm{eq}} \approx 1116\,\mathrm{K}$) possesses a low surface gravity and a highly inflated atmosphere (Faedi et al., 2011). The large atmospheric scale height

$H = \frac{k_B T}{\mu m_H g}$

where $k_B$ is the Boltzmann constant, $T$ the local temperature, $\mu$ the atmospheric mean molecular weight, $m_H$ the mass of hydrogen, and $g$ the surface gravity, endows WASP-39b with high sensitivity to limb temperature and compositional structure. Even moderate temperature differences ($\Delta T$) or chemical inhomogeneities near the terminator transform into measurable changes in transit depth ($\Delta R \sim N H$, where $N$ is the number of scale heights affected), enhancing the detectability of terminator asymmetry through spectral and timing diagnostics (Fischer et al., 2016).

The incident stellar irradiation supplies energy to drive robust atmospheric circulation, creating persistent day–night temperature gradients. These gradients, modulated by radiative, advective, and chemical timescales, enable divergent thermal and chemical structures to emerge across the morning and evening limbs.

2. Observational Signatures and Retrieval: Evidence for Inhomogeneous Terminators

High-precision JWST transit spectroscopy (NIRSpec/PRISM, NIRCam, MIRI/LRS, NIRISS) has enabled direct empirical separation of morning and evening limb spectra. Analyses (Espinoza et al., 14 Jul 2024, Chen et al., 1 Apr 2025) show:

• The evening terminator exhibits systematically larger transit depths—on average $405 \pm 88$ ppm greater than the morning leg—in the 2–5 μm window (Espinoza et al., 14 Jul 2024).
• Spectral features, notably H$_2$O ($\sim$2.8–3 μm) and CO$_2$ ($\sim$4.3 μm), are deeper and more pronounced in the evening spectrum, indicating both higher temperatures and reduced cloud opacity on the evening limb.
• Retrievals with limb-separated models yield $T_\text{evening} = 1068^{+43}_{-55}\,\mathrm{K}$ and $T_\text{morning} = 889^{+54}_{-65}\,\mathrm{K}$, so $\Delta T \approx 177^{+65}_{-57}\,\mathrm{K}$ (Espinoza et al., 14 Jul 2024, Chen et al., 1 Apr 2025). These values are consistent with general circulation model (GCM) predictions.

Table: Empirical Differences Between Morning and Evening Terminators

Property	Morning Terminator	Evening Terminator
Temperature (K)	$889^{+54}_{-65}$	$1068^{+43}_{-55}$
Transit Depth (ppm)	shallower	deeper (+$405\pm88$ ppm)
Cloud Opacity	higher (muted features)	lower (clearer features)
C/O Ratio	$\sim$ 0.57	$\sim$ 0.58

The spectral difference between limbs is primarily attributable to thermal structure and aerosol loading rather than bulk chemical composition, as both termini yield C/O ratios consistent with solar.

3. Atmospheric Chemistry and Photochemistry: SO₂, H₂O, CO₂, and Metallicity

The identification of SO₂ as a robust photochemical tracer stands out among the molecular species detected (Rustamkulov et al., 2022, Tsai et al., 2022, Powell et al., 10 Jul 2024). Photolytic conversion of H$_2$O and H$_2$S under stellar UV irradiation produces SO₂ at ppm levels, with the efficacy of these reactions controlled by local temperature and metallicity: $\mathrm{H_2S + 2H_2O \rightarrow SO_2 + 3H_2}$ Photochemical modeling reveals that the cooler morning limb ($\sim 150{-}200\,\mathrm{K}$ lower than the evening limb) yields more efficient SO₂ formation due to enhanced conversion via H and OH radicals, while the warmer evening limb suppresses SO₂ production (Tsai et al., 2022). Nevertheless, global circulation and horizontal mixing homogenize these differences, and the observed SO₂ absorption features (notably at 4.05, 7.7, 8.5 μm in NIRSpec and MIRI/LRS data) can be matched by limb-averaged abundances in the range 0.5–25 ppm, depending on the band (Powell et al., 10 Jul 2024).

Atmospheric metallicity is well-constrained by multi-band transmission spectra to be $\sim$7–10× solar (Ahrer et al., 2022, Rustamkulov et al., 2022, Feinstein et al., 2022, Powell et al., 10 Jul 2024, Kirk et al., 2019). Enhanced metallicity increases mean molecular weight, reduces scale height, and, for a fixed temperature, accentuates metallic absorbers (SO₂, H₂O, CO₂) and strengthens the sensitivity of resulting band depths to composition and spatial gradients. The C/O ratio is uniform across the limb, retrieved as $0.57^{+0.17}_{-0.23}$ (morning) and $0.58^{+0.13}_{-0.16}$ (evening) (Espinoza et al., 14 Jul 2024, Chen et al., 1 Apr 2025).

4. 3D General Circulation, Cloud/Haze Effects, and Mechanisms for Asymmetry

3D GCMs and cloud/haze microphysical models consistently predict persistent asymmetry between the morning and evening terminators. The circulation in WASP-39b is dominated by a fast superrotating jet that advects heat and chemical species from the substellar point eastward, producing a hotter, clearer evening limb and a cooler, more frequently cloud-covered morning limb (Mak et al., 27 Jul 2025).

Specifically, small-particle haze (e.g., Titan-like, water-world-like, soot-like; particle radius ≈1.5 nm) undergoes complex advection, radiative feedback, and eddy mixing. Models show that radiative heating by absorbing hazes enhances the strength of the equatorial jet and drives haze accumulation over the morning terminator. This effect is encapsulated by: $$\frac{Dq}{Dt} = -\nabla \cdot (\mathbf{u}q) - \nabla \cdot (\mathbf{u}'q')$$ where $q$ is haze mass mixing ratio, $\mathbf{u}$ is the wind vector, and primes denote deviations from the mean flow. For sufficiently absorbing haze, the morning limb is predicted to yield higher opacity and larger UV-optical transit depth—an inverse trend relative to the infrared gas-phase signal, which is dominated by the hotter, clearer evening limb (Mak et al., 27 Jul 2025).

Thus, the observed limb asymmetry is a composite effect of (i) advective-dynamical control of the temperature structure, (ii) radiative-haze feedback on circulation, (iii) spatially variable aerosol formation, and (iv) the interplay between gas-phase absorption features and cloud/haze opacities.

5. Retrieval Methodologies: 2D Models, Bayesian Evidence, and Data-Model Interplay

The advent of high signal-to-noise, broad-wavelength JWST spectra has motivated the development of two-dimensional (2D) retrieval approaches that independently parameterize the morning and evening limbs (Chen et al., 1 Apr 2025, Espinoza et al., 14 Jul 2024). These frameworks retrieve limb-specific temperatures, cloud/haze opacities, and (when warranted) chemical abundances. Dynamically-motivated priors, such as enforcing a temperature difference from shallow-water theory ($\Delta T \sim 150\,\mathrm{K}$), help mitigate degeneracies and encourage physical realism.

Bayesian model comparison (ln $\mathcal{B}$) strongly disfavors homogeneous (1D) models; 2D retrievals, whether free or dynamically-constrained, provide significantly improved explanation of limb-resolved spectral features. However, small ln $Z$ differences between “free” and “fixed” 2D models imply model selection is not always decisive. Both approaches consistently retrieve hotter, clearer evening limbs and cooler, cloudier mornings, with uniform C/O (Chen et al., 1 Apr 2025).

Sensitivity studies with different cloud prescriptions (e.g., grey vs. non-grey, Mie-scattering particle size) and chemistry complexity reveal that the minimal set of detected species and the retrieved elemental abundances are instrument- and model-dependent (Lueber et al., 4 May 2024). This underlines the importance of careful multi-instrument cross-validation and methodological transparency when diagnosing limb asymmetry.

6. Photochemistry, Horizontal Transport, and Reduction of Chemical Asymmetry

Photochemical models incorporating 2D transport demonstrate that, though vertical mixing and temperature differences enable SO₂ and CH₄ to vary steeply between limbs in 1D, the effect of rapid zonal winds is to homogenize the limb-to-limb abundances, especially for major photochemical species (Tsai et al., 2023). The resulting atmospheric composition is thus only weakly asymmetric, particularly in the upper atmosphere, although residual temperature- and opacity-driven differences persist and remain observable in the transmission spectrum.

Horizontal mixing is quantitatively described by the continuity equation (for species $i$ number density $n_i$): $$\frac{\partial n_i}{\partial t} = \mathcal{P}_i - \mathcal{L}_i - \frac{\partial \phi_{i,z}}{\partial z} - \frac{\partial \phi_{i,x}}{\partial x}$$ where $\mathcal{P}_i,\ \mathcal{L}_i$ are the production/loss rates, $\phi_{i,z}$ the vertical flux (including turbulent mixing), and $\phi_{i,x} = -n_i v_x$ the horizontal flux (zonal wind transport). Fast winds efficiently advect dayside photochemical SO₂ to the nightside, flattening the morning-evening gradient in the observable upper atmosphere (Tsai et al., 2023).

7. Synthesis and Implications for Exoplanet Atmospheric Studies

Multi-dimensional observations and models of WASP-39b demonstrate that terminator asymmetry is a detectable, quantifiable feature of hot Jupiter atmospheres. Key empirical signatures—e.g., a measured $405 \pm 88$ ppm asymmetry in infrared transit depth and a $177^{+65}_{-57}$ K day-to-night limb temperature gradient (Espinoza et al., 14 Jul 2024, Chen et al., 1 Apr 2025)—are robustly attributable to spatial contrasts in temperature and cloud/haze distribution, with a secondary role for chemical composition. General circulation models confirm that superrotating jets, radiative haze feedback, and 3D cloud microphysics are central to establishing the observed asymmetry.

A concise summary of core findings:

Aspect	Dominant Driver	Observational Impact
Temperature (ΔT)	Day–night irradiation gradients, jets	Spectral feature depth/shape
Aerosol/Haze Distribution	Night–day advection, radiative feedback	UV/optical transit depth, muted IR features
SO₂ / Photochemistry	UV-driven S–oxidation, metallicity	Mid-IR/IR bands (4–8.5 μm), enhanced with metallicity
C/O Ratio	Subsolar/solar, uniform	Major absorbers (H₂O, CO₂) spectral shape & strength

These advances necessitate a shift to multi-dimensional retrievals and reinforce the importance of physically-motivated, dynamically-consistent modeling in future studies. The WASP-39b case establishes that even moderately irradiated exoplanets exhibit measurable and complex limb inhomogeneities, and that high-precision, multi-epoch transmission spectroscopy is a critical tool for revealing the three-dimensional nature of exoplanetary atmospheres.