JWST Eclipse Mapping Techniques

• JWST eclipse maps are spatially resolved inferences from secondary eclipse data that reveal exoplanet brightness, temperature, and spectral structures.
• They employ techniques like spherical harmonic decomposition and eigencurve models to extract atmospheric dynamics and mitigate instrument systematics.
• Observations have quantified hotspot shifts and day–night temperature contrasts in hot Jupiters, advancing our understanding of exoplanet climates.

JWST eclipse maps are spatially resolved inferences of exoplanetary dayside (and, more rarely, nightside) brightness, temperature, or spectral structure, extracted from time-series photometry during secondary eclipses by the James Webb Space Telescope. By analyzing the subtle deviations from a uniform eclipse shape caused by the planet’s non-uniform emission profile as it is progressively occulted by its host star (ingress/egress), and combining this with out-of-eclipse phase curve information, researchers invert these modulations using parameterized or data-driven basis functions to reconstruct two-dimensional (2D) or even three-dimensional (3D) atmospheric maps. These maps provide quantitative constraints on atmospheric circulation, energy balance, hotspot offsets, chemical heterogeneity, and vertical temperature structure in a mathematically robust and instrumentally calibrated framework.

1. Principles and Parameter Space of JWST Eclipse Mapping

JWST eclipse mapping operates by decomposing the observed time-varying flux during secondary eclipse into spatial information about the planet’s dayside emission profile. The ingress and egress of an eclipse encode a one-dimensional projection of the two-dimensional surface brightness, which, when analyzed alongside system geometry constraints (from transits and phase curves), allows for the recovery of large-scale planetary features. Key parameters affecting observability include planetary radius, orbital period, impact parameter (which controls latitudinal vs longitudinal resolution), atmospheric mean molecular weight, equilibrium temperature, and host star properties. Hot Jupiters and Neptunes represent optimal mapping targets due to their large radii and bright emission; for terrestrial planets only the absolute brightest and closest systems (e.g., within 10 pc around M dwarfs) are accessible for such studies (Belu et al., 2010).

Mapping uses parameterizations such as spherical harmonics up to a chosen maximum degree $\ell_{\mathrm{max}}$, with the basis truncated according to the achievable signal-to-noise ratio (S/N) and the light-curve information content. The S/N for eclipse features scales as

$$\mathrm{S/N} \propto \frac{N_{\rm transit}^{1/2}}{\mathrm{d} \, \mu}$$

where $N_{\rm transit}$ is the number of stacked eclipses, $d$ is the distance to the system, and $\mu$ the mean molecular weight (for transmission features), with detailed noise budgeting including photon, readout, zodiacal, and instrumental contributions (Belu et al., 2010, Boone et al., 2023).

2. Theoretical Foundations and Information Limits

The math of eclipse mapping relies on the decomposition of the planet’s flux map $Z(\theta, \phi)$ into a basis of spherical harmonics or sinusoids, each of which projects onto the light curve as a (potentially) orthogonal “eigencurve” (Rauscher et al., 2018, Challener et al., 2023). However, not all map components are observable: the so-called “null space” arises because many spatial brightness patterns (especially small-scale or those symmetric about directions not occulted by the star) have no effect on the observed light curve. This limitation is formalized by singular value decomposition (SVD) of the design matrix $A$, with observable modes $P$ and null modes $N$ such that $Z = Z_{•} + Z_{∘}$, where only $Z_{•}$ affects the data (Challener et al., 2023).

The impact parameter $b$ and the “stellar edge angle” $\theta_0$ control which features (in latitude or longitude) are best constrained; low $b$ enhances longitudinal but diminishes latitudinal resolution, and vice versa (Boone et al., 2023). The attainable mapping resolution is quantified via metrics such as the Eclipse Mapping Metric (EMM):

$$\mathrm{EMM}_x = 180^{\circ} \times \frac{2\sqrt{6 \ln 2}}{\pi^2 \sqrt{1-b^2}} \left[\cdots\right]^{-1/(3+1/2)}$$

with similar expressions for $\mathrm{EMM}_y$ (latitudinal resolution), showing that S/N, planetary radius, and geometry set the number of spatial modes that can be recovered.

3. Mapping Methodologies: Harmonics, Eigencurves, and Cross-Validation

Eclipse mapping employs either direct (truncated) spherical harmonic models, data-driven eigencurve decompositions, or hybrid PCA/SVD approaches for computational and statistical robustness (Rauscher et al., 2018, Challener et al., 2021, Hammond et al., 31 May 2024). The generic mapping model is:

$F(t) = \sum_{i} c_i f_i(t)$

where each $f_i(t)$ is the light curve resulting from the occultation of a spherical harmonic map $z_i(\theta,\phi)$; $c_i$ are the coefficients to be fit. In eigencurve methods, a PCA is performed on a suite of model light curves to construct an orthogonal basis:

$$E_n(t) = \sum_{\ell,m} \lambda_{n,\ell,m} F^{\ell m}(t)$$

with corresponding eigenmaps $Z_n(\theta,\phi)$, so that

$$Z_p(\theta,\phi) = c_0 Y_0^0(\theta,\phi) + \sum_{n} c_n Z_n(\theta,\phi)$$

This basis is truncated according to variance- or information-criteria (e.g., BIC) or out-of-sample predictive power (e.g., leave-one-out cross-validation (Challener et al., 2023) or k-fold cross-validation (Hammond et al., 31 May 2024)).

Cross-validation metrics (elpd$_{\text{LOO}}$, $\Delta$CV) guide the choice of model complexity, especially to avoid spurious overfitting in the presence of the null space and in the case of limited robustness in latitudinal structure (Hammond et al., 31 May 2024). Regularization is further enhanced with spatial entropy penalties:

$\hat{p} = p - 2\alpha S$

where $S$ measures the spatial entropy of the map, and $\alpha$ is tuned via cross-validation.

Recent studies emphasize the necessity of explicitly accounting for the null space in uncertainty estimation; models that ignore it can yield spuriously precise but non-physical constraints, particularly on latitudinal features (Challener et al., 2023). Fitting must also ensure physically meaningful brightness distributions, typically enforcing non-negativity (positive-flux constraint).

4. Results from JWST Observations: Mapping Outcomes and Atmospheric Insights

JWST has, since Cycle 1, delivered eclipse maps of several hot Jupiters with unprecedented detail. For WASP-43b, MIRI/LRS and NIRSpec/G395H observations yielded two-dimensional maps revealing:

• A meridionally-averaged hotspot shift of $(7.75 \pm 0.36)^\circ$ eastward at $7-12\,\mu$m, corresponding to robust atmospheric advection (Hammond et al., 25 Apr 2024).
• Distinct longitudinal ($\sim$250 ppm) and latitudinal ($\sim$200 ppm) mapping signals, with the latter measured in the ingress/egress shape beyond what a purely longitudinal model could explain.
• In NIRSpec/G395H, a %%%%32$\mu$33%%%% southward latitudinal hotspot offset of $(-13.4^{+3.2}_{-1.7})^\circ$, constituting the first significant detection of a non-equatorial hotspot in an exoplanet atmosphere (Challener et al., 14 Jun 2024). This latitudinal offset is robust when transit constraints are applied.

For HD 189733b, a 2-component, 5th-degree spherical harmonic model combining high-SNR JWST MIRI and archival Spitzer data yields an eastward hotspot offset of $33.0^{+0.7}_{-0.9}$ degrees, with higher-degree latitudinal models strongly disfavored, ruling out strong hemispheric asymmetry (Lally et al., 26 Mar 2025). WASP-17b exhibits a day–night contrast of $\sim1000$ K and an eastward hotspot offset of $18.7^{+11.1}_{-3.8}$ degrees from a single MIRI/LRS eclipse (Valentine et al., 10 Oct 2024).

Atmospheric maps derived with these methods consistently reveal strong eastward zonal jets, with the degree of hotspot offset and day–night contrast constraining the efficiency of heat redistribution. Forward atmospheric modeling of these systems (with GCMs) generally predicts offsets of $\sim 10^\circ-50^\circ$ (varying by incident flux, metallicity, drag, and cloud properties), in agreement with the derived maps, though variations persist among models and observed systems (Hammond et al., 25 Apr 2024, Lally et al., 26 Mar 2025).

5. Instrumental Systematics and Data-Driven Detrending

Achieving robust eclipse maps requires precise modeling and removal of instrument systematics. For JWST MIRI, a dominant “detector settling” ramp—an exponential decay whose timescale scales with the target’s brightness—can corrupt ingress/egress signals critical for mapping. A frame-normalized principal component analysis (FN-PCA) approach identifies and removes such systematics in a data-driven manner, preserving the uniform stellar + planetary eclipse signal (Connors et al., 2 Jul 2025). The detector settling time is empirically found to follow

$$T_{\mathrm{set}}\,[\mathrm{hours}] = 0.063\,\exp^{0.427\,m_K} - 0.657$$

where $m_K$ is the apparent K-band magnitude. Identifying and modeling these systematics across targets and datasets is critical for controlling false mapping signals and ensuring uniformity in characterization, especially in surveys of rocky planets at 15 μm.

Cross-instrument checks (e.g., comparison between NIRSpec NRS1 and NRS2 channels) confirm that mapping results—such as hotspot location—are consistent within uncertainties, validating the instrumental calibration and repeatability of the mapping approach (Challener et al., 14 Jun 2024).

6. Practical Resolution Limits, Target Selection, and Large-Scale Mapping Prospects

The theoretical and instrumental constraints combine to set the practical spatial resolution achievable with current JWST eclipse mapping. For bright, large exoplanets, the “maximum spherical harmonic order” $N_{\max}$ attainable is a function of flux precision, target geometry, and mapping metric (EMM), with longitudinal resolution typically exceeding latitudinal resolution especially for low-to-moderate impact parameters (Boone et al., 2023, Valentine et al., 3 Oct 2025). Best-case EMM values for JWST (NIRISS/SOSS, NIRSpec/G395H, MIRI/LRS) are found for bright systems such as HD 189733b, WASP-18b, WASP-43b, and WASP-17b, with achievable mapping of $\ell_{\max}=2-5$ modes and longitudinal hotspot offset errors down to $\sim$1 degree. For fainter targets or those without extensive phase or transit coverage, the effective mapping signal vanishes, and regularization or model selection criteria penalize overfitting (Hammond et al., 31 May 2024).

As the field approaches population-level mapping, the upcoming Ariel mission, with its extensive time allocation and planned uniform survey of 1000 transiting exoplanets, will be able to map $\sim$100 targets with similar techniques by stacking repeated eclipse and phase curve observations, despite a smaller aperture compared to JWST (Valentine et al., 3 Oct 2025). The mapping focus for Ariel will be predominantly on longitudinal brightness features (day–night contrast, hotspot offset), with limited practical latitudinal mapping except for the brightest systems.

7. Scientific Impact and Future Directions

JWST eclipse maps have shifted exoplanet atmospheric research from global-average spectra to spatially resolved climate and circulation constraints. They provide direct evidence for eastward equatorial jets, quantitative day–night temperature contrasts, and, for the first time, statistically robust detection of latitudinal hotspot asymmetries. The insights from these maps tightly constrain three-dimensional general circulation models, atmospheric metallicity, cloud coverage, radiative and advective timescales, and, by extension, planet formation history and evolution pathways (Hammond et al., 25 Apr 2024, Schlawin et al., 2018, Challener et al., 2021).

Developments in inversion techniques (eigencurve decomposition, information-cross-validation), systematics mitigation (FN-PCA), and the integration of mapping with high-fidelity spectroscopic retrievals (CHIMERA, PICASO, TauREx, ThERESA) continue to push the attainable precision and complexity of exoplanet atmospheric characterization. Remaining challenges include the null space limitations, the risk of overinterpretation in the absence of cross-validation, and the requirement for careful instrument and astrophysical model validation, particularly as mapping campaigns expand to cooler, lower-S/N worlds or population-level surveys with Ariel.

JWST eclipse mapping stands as a cornerstone for multi-dimensional exoplanet science—bridging observational inversion, atmospheric modeling, and planetary formation theory—providing both detailed individual system insights and a framework for comparative exoplanetology in the era of next-generation surveys.