JWST Transmission Spectroscopy Follow-Up

• The article presents advanced observational setups and instrument configurations that maximize JWST's infrared wavelength coverage for exoplanet atmosphere studies.
• It details a comprehensive data reduction pipeline that effectively mitigates systematic noise and stellar contamination to achieve photon-noise–limited precision.
• It demonstrates the use of atmospheric retrieval and model comparison techniques to accurately constrain exoplanet atmospheric properties across diverse targets.

The James Webb Space Telescope (JWST) has initiated a transformative era for exoplanet atmospheric characterization using transmission spectroscopy. As the first large-aperture infrared space observatory with multi-instrument, high-precision, wide-wavelength coverage, JWST enables atmospheric retrievals across a comprehensive range of planetary sizes, compositions, thermal regimes, and host star types. Transmission spectroscopy follow-up observations with JWST are designed to resolve atmospheric spectral features during transit, enabling constraints on atmospheric metallicity, chemical composition, temperature–pressure profiles, mean molecular weight, and cloud/haze properties, as well as addressing host star contamination. This article synthesizes fundamental concepts, methodologies, and best practices for JWST transmission spectroscopy follow-ups, with direct reference to early cycle case studies, pipeline strategies, performance metrics, and future directions.

1. Observational Design and Instrument Configuration

JWST transmission spectroscopy follow-up observations utilize multiple instrument modes to maximize simultaneous wavelength coverage, spectral resolving power, and photon-noise–limited precision. The two primary workhorse modes are NIRISS SOSS (0.6–2.8 μm, R≈700) and NIRSpec G395H (2.9–5.2 μm, R≈2700), which together can deliver essentially continuous coverage over 0.6–5.2 μm for a single target (Radica et al., 2023). Subarray selection (e.g., SUBSTRIP256 for SOSS, SUB2048 for NIRSpec) and group count per integration are optimized to balance readout speed, saturation avoidance, persistence, and cosmic-ray rejection.

A typical SOSS configuration for hot Jupiter or Saturn-mass targets employs 280 integrations × 14 groups per integration and covers both diffraction orders (0.6–1.0 μm for order 2, 0.85–2.85 μm for order 1). This enables simultaneous detection of key species such as H₂O, Na, K, CH₄, CO, CO₂, SO₂ within a single visit, minimizing the need for multi-instrument scheduling. An optional short F277W exposure is often included for field-star contamination assessment. Nondestructive up-the-ramp sampling is used, with nonlinearity corrections required above ∼3.5×10⁴ DN but typically minimal for peak pixels.

In the context of the TESS follow-up sample, prioritization via transmission spectroscopy metrics (TSM; see (Hord et al., 2023, Crouzet et al., 2017)) enables efficient allocation of observing time across the planet population. For temperate terrestrial planet programs, the NIRSpec Prism (1–5 μm, R≈100) and split-mode SOSS+G395H (for J≤9) are optimal, with the readout pattern and group count further refined to balance saturation constraints (Batalha et al., 2018, Constantinou et al., 2022).

2. Data Reduction Pipeline Architecture and Calibration Strategies

JWST transmission spectroscopy data reduction requires an end-to-end pipeline that robustly addresses detector-level and astrophysical contaminants. The "supreme-SPOON" pipeline for SOSS is structured in three main phases, augmented by specialized field-star decontamination steps (Radica et al., 2023):

• Detector-level calibrations (Stage 1): GroupScaleStep, DQInitStep, SaturationStep, SuperBiasStep, RefPixStep for initial 1/f noise mitigation.
• Background and 1/f noise subtraction: Scaled 2D zodiacal background models are subtracted per group for each integration, followed by column-median removal of low-frequency streaks. The method corrects for power spectrum components P(f)∝1/f^α.
• Nonlinearity and cosmic-ray correction: LinearityStep for up-the-ramp corrections, JumpStep to flag cosmic ray events, RampFitStep for linear regression of the count rate per pixel.
• Spectroscopic calibrations (Stage 2): FlatFieldStep, BadPixStep for spatiotemporal hot/persistent pixel interpolation, tracing to monitor sub-pixel drift and FWHM.
• 1D spectral extraction (Stage 3): Both box and ATOCA deblending extractions are available, with ATOCA preferred for robust trace overlap disentanglement.
• Field-star contamination: F277W exposures reveal 0th order "smudge" contaminants, while cross-dispersion analysis detects 1st order interlopers. The contamination fraction f_cont(λ) is measured and applied for correction.

High-precision programs universally perform light-curve analysis at the pixel level prior to any spectral binning—this prevents column-wise covariance from biasing photon-limited error propagation. Post-extraction, light curve fitting is decorrelated against trace X/Y position and FWHM, and a linear jitter term is included when necessary.

3. Performance Metrics and Error Budgeting

JWST transmission studies in SOSS mode achieve native pixel-binned precisions of ⟨σbin⟩ ≈ 1.2–1.4×σ_photon, where σ_photon is the photon noise expected from the stellar photon-counting rate (Radica et al., 2023). For the full integration sequence in SOSS, white-light transit-depth precisions are σδF ≈ 76 ppm (order 1) and 120 ppm (order 2) per integration of ~77 s.

The error budget per spectral bin is parameterized as:

$$\sigma_{ \delta F}^2 = \sigma_{\rm photon}^2 + \sigma_{\rm read}^2 + \sigma_{1/f}^2 + \sigma_{\rm sys}^2$$

where σread is typically 5–10 e^{-}, σ{1/f} reaches a few ppm post-correction, and σ_sys captures residual instrumental or model decorrelation. Allan deviation analyses confirm near-ideal white-noise scaling over bin sizes, reduced χ^2 values in white-light fits approach 1.15, and no evidence is seen for significant systematics above the photon floor in the best-observed cases.

Achievable precisions in supporting studies (e.g., LHS 475 b NIRSpec: ~40 ppm per 0.02 μm bin (Lustig-Yaeger et al., 2023), TOI-836 b G395H: 25 ppm per channel (Alderson et al., 29 Mar 2024), WASP-39 b multi-mode: 20–100 ppm (Carter et al., 18 Jul 2024)) further establish JWST as capable of detecting <50 ppm features, provided the source is sufficiently bright and reduction steps mitigate 1/f and other detector systematics.

4. Atmospheric Retrieval and Model Comparison

Transmission spectra are interpreted via self-consistent, 1D radiative–convective grid models (e.g., PICASO, ATMO, ScCHIMERA/CHIMERA (Radica et al., 2023)), as well as Bayesian nested-sampling atmospheric retrievals (e.g., MultiNest, dynesty).

The core statistical framework involves maximizing the Gaussian log-likelihood:

$$\ln \mathcal{L}(\theta) = -½ \sum_i \left[ \frac{(D_i−M_i(\theta))}{\sigma_i} \right]^2 - ½ \sum_i \ln(2\pi\sigma_i^2)$$

with parameter vectors θ spanning metallicity, C/O ratio, cloud/haze parameters, and possibly stellar contamination factors (see below). Model selection is performed using Bayesian evidence differences Δ\ln𝒵 and reduced χ^2 values.

For WASP-96 b, retrievals indicate Z ≈ 1× solar (consistent within 1–5× solar), solar C/O excluded at >3σ for C/O>0.8, optically thick gray clouds only at P_cloud > 1 bar, and enhanced Rayleigh slopes at short wavelengths (log₁₀ a=1.78, γ=4) (Radica et al., 2023). Comparable strategies tightly constrain the permitted parameter space for all investigated targets.

5. Mitigation of Stellar and Astrophysical Contamination

Slitless modes are subject to both photometric dilution by field stars and chromatic flux contamination from unocculted active regions on the host star. Field-star correction uses spatial mapping in "scout" exposures (e.g., F277W), modeling of PSF wings, and quantitative subtraction using the contamination fraction f_cont(λ).

The transit light source effect (TLSE) is corrected by jointly modeling the emergent stellar spectrum as a combination of photosphere and heterogeneity components. For a spot or facula population with covering fraction f_het,

$$\epsilon_{\lambda,\rm het} = \frac{1}{1 - f_{\rm het}\,\left(1 - I_{\lambda}(T_{\rm het})/I_{\lambda}(T_{\rm phot})\right)}$$

where I_λ denotes the surface intensity. Post-correction, atmospheric constraints are robust, but when neglected, inferred abundances (e.g., H₂O, CO₂) and cloud properties can be strongly biased (Fournier-Tondreau et al., 2023, Fournier-Tondreau et al., 22 Dec 2024).

Best practices include simultaneous retrieval of stellar and planetary parameters, pixel-level light-curve fitting, masking or modeling spot-crossing events, and, where relevant, utilization of multi-component (spot+facula) models to capture the diversity of stellar surface structures.

6. Target Selection, Scheduling, and Program Design

Efficient use of JWST resources demands judicious target selection and observing strategy:

• TESS targets prioritized via TSM (Kempton et al.), with highest-yield objects (e.g., J≲10, Rp>1.5 R⊕, moderate host R_*) scheduled for SOSS+G395H two-transit programs (Hord et al., 2023, Crouzet et al., 2017).
• For mini-Neptunes and cloudy K/M dwarf planets, instrument choice and wavelength coverage are dictated by cloud-top pressure; single SOSS/G235H visit suffices for P_cloud≳10 mbar, multi-instrument for higher altitude decks (Constantinou et al., 2022).
• For temperate terrestrial M dwarf planets, optimal precision is realized by stacking up to ten NIRSpec Prism or SOSS+G395H transits; information gain plateaus beyond N_transit ≈10 (Batalha et al., 2018).
• Scheduling recommendations include roll angle selection to avoid field contaminants, timing repeat visits across stellar rotation to average down heterogeneity signals (Cadieux et al., 21 Jun 2024, May et al., 2023), and acquisition of simultaneous ground-based monitoring where possible.

Future programmatic recommendations stress the utility of pre-JWST reconnaissance (e.g., ETSI (Oelkers et al., 5 Mar 2025)), robust ephemeris refinement, and flexible strategy adaptation in light of evolving systematics and retrieved atmospheric properties.

7. Best Practices and Future Recommendations

A synthesis of emerging guidelines for JWST transmission spectroscopy follow-up includes:

• Apply pixel-level light-curve extraction and spectral fitting before any spectral or spatial binning to preserve error covariances and maximize photon-limited S/N (Radica et al., 2023, Carter et al., 18 Jul 2024).
• Couple 1/f noise correction with contemporaneous background subtraction at the group level; integration-level approaches yield ∼20% higher scatter (Radica et al., 2023).
• Jointly fit system geometry and stellar/planetary parameters; bin transit depths after fitting, not before.
• Employ informative Gaussian limb-darkening priors from 3D stellar models to stabilize fits (Radica et al., 2023, Carter et al., 18 Jul 2024).
• Fit at multiple spectral resolutions (pixel scale, R=125–500) to check inference robustness and minimize sensitivity to limb-darkening or systematic bias (Radica et al., 2023).
• Combine radiative–convective equilibrium forward grids with free-chemistry retrievals to bracket atmospheric modeling uncertainties.
• For small planets and shallow features (≲30 ppm amplitude), plan ≥2 visits and use ≥2 independent pipelines to confirm statistical significance and reproducibility (Alderson et al., 29 Mar 2024, May et al., 2023).
• For active hosts, combine spot/facula modeling in both light-curve and spectral retrieval frameworks, leveraging multi-order coverage to break degeneracies between stellar and atmospheric chromaticity (Fournier-Tondreau et al., 22 Dec 2024, Fournier-Tondreau et al., 2023).

Collectively, these practices allow JWST follow-up observations to reach precise atmospheric constraints for a diverse exoplanetary sample, with achievable metallicity precisions of a factor of a few, C/O ratio to ≈0.2 dex, and haze or alkali detection in a single transit. The generalizable framework for observation, reduction, and interpretation enumerated here provides a roadmap for the efficient and rigorous exploitation of JWST for transmission spectroscopy science, from both a technical and strategic standpoint (Radica et al., 2023, Carter et al., 18 Jul 2024, Cadieux et al., 21 Jun 2024, Fournier-Tondreau et al., 2023, Fournier-Tondreau et al., 22 Dec 2024).