NIRISS/SOSS Phase Curve Analysis

• NIRISS/SOSS phase curve is a time-resolved spectroscopic technique that maps full-orbit exoplanet brightness to decode atmospheric emissions and reflection.
• It leverages JWST’s NIRISS in SOSS mode along with advanced algorithms like APPLESOSS and ATOCA to achieve precise wavelength calibration and suppress order contamination.
• The method enables detailed atmospheric retrievals by quantifying temperature contrasts, heat recirculation, albedo differences, and chemical compositions in exoplanet atmospheres.

The NIRISS/SOSS phase curve refers to time-resolved, spectroscopic observations obtained in the Single Object Slitless Spectroscopy (SOSS) mode of the Near Infrared Imager and Slitless Spectrograph (NIRISS) aboard the James Webb Space Telescope (JWST), aimed at capturing the full-orbit brightness modulation of exoplanets. By combining continuous spectral monitoring over a full orbital period—including transit, occultation (secondary eclipse), and intermediate phases—these phase curves encode the spatial and temporal distribution of both emission and reflected light from planetary atmospheres. The NIRISS/SOSS configuration leverages its broad 0.6–2.85 μm spectral coverage and high stability to extract physical parameters such as atmospheric composition, temperature structure, energy budget, and cloud properties, while also providing sensitivity to dynamical phenomena like inefficient heat redistribution and chemical gradients.

1. Instrumentation and Observational Mode

The SOSS mode of JWST/NIRISS is purpose-built for high-precision, medium-resolution (R ≈ 650) time-series spectroscopy of bright exoplanet host stars, optimized to capture both primary (transit) and secondary (eclipse) events as well as the intervening and out-of-eclipse phases (Doyon et al., 2023, Albert et al., 2023). The spectroscopic capability is achieved via the GR700XD cross-dispersing grism and a cylindrical defocusing lens that spreads light vertically across the detector, effectively:

• Increasing the brightness threshold before saturation by ∼3 magnitudes,
• Capturing both first and second diffraction orders, and
• Simultaneously covering 0.6–2.8(5) μm (order 1: 0.85–2.8 μm, order 2: 0.6–1.4 μm).

Precise, stable wavelength calibration is vital, as sub-pixel drifts due to pupil wheel misalignments can shift trace positions by up to ~2.5 pixels between visits (Baines et al., 2023). Advanced polynomial regression models, implemented in the PASTASOSS Python package, use detector x-pixel positions and pupil wheel offset to ensure sub-pixel wavelength solutions. This is fundamental for maintaining spectro-photometric accuracy in phase curve analyses, where minute temporal changes in flux are tracked over hundreds or thousands of integrations.

The instrument design achieves a photon conversion efficiency peaking at 55% (1.2 μm, order 1), greatly boosting sensitivity and thereby enabling photometric precision to the level of ~20 ppm on 40-minute timescales after systematic correction (Albert et al., 2023).

2. Spectral Extraction, Order Contamination, and Background Subtraction

SOSS-mode observations record multiple spectral orders on the same detector region, leading to significant (up to ≤1% amplitude) spatial overlap between orders 1 and 2—a fundamental challenge for extracting accurate time-resolved spectra required for phase curve analysis (Radica et al., 2022, Darveau-Bernier et al., 2022). Two data-driven tools/algorithms address this:

• APPLESOSS constructs high-fidelity, order-specific spatial profiles by stitching together direct detector measurements from uncontaminated trace regions with monochromatic PSFs simulated in WebbPSF for the contaminated core/wings (Radica et al., 2022). These spatial profiles feed the ATOCA extraction algorithm.
• ATOCA models the measured flux in each pixel as the sum of contributions from all diffraction orders, convolved against spatial profiles, throughput, and resolution kernels. The solution for the underlying high-resolution spectrum is obtained via regularized linear inversion:

$$M = B \cdot f, \qquad \chi^2_{\text{reg}} = \left\| \frac{D - M}{\sigma} \right\|^2 + \alpha \|\Gamma f\|^2$$

where $B$ encodes the pixel-to-spectrum response, $f$ is the discretized underlying spectrum, and $\Gamma$ is a smoothing operator (Darveau-Bernier et al., 2022).

After application of these techniques, the residual contamination introduced by order overlap is typically suppressed below 10 ppm across the full spectral range, well below the dominant planetary signal (hundreds of ppm), thus preserving both transit depth and orbital phase variability to scientific precision requirements.

Zodiacal light—composed of both scattered and thermal emission—constitutes the main sky background, introducing a strongly structured, order- and position-dependent background pattern that must be carefully subtracted (Baines et al., 10 Sep 2025). Empirically derived background templates, created from dedicated calibration programs with full-frame mosaics, and flexible split-region scaling (independently scaling pre- and post-discontinuity regions near pixel 700), can reduce median residuals by ~10% and the RMSE by ~4% compared to both contemporaneous and static commissioning backgrounds. This improvement directly translates to quantifiable reductions in systematics on phase-dependent spectral measurements.

3. Phase Curve Modeling and Energy Budget Determination

NIRISS/SOSS phase curves, as exemplified by WASP-121 b (Splinter et al., 11 Sep 2025), typically encompass the full orbit, covering primary transit, secondary eclipse, and intermediate phases at 0.6–2.85 μm—capturing 50–83% of the planet's bolometric emission, compared to ~20% for HST/WFC3 or NIRSpec/G395H (Splinter et al., 11 Sep 2025). The high SNR and broad spectral coverage enable:

• Mapping of phase-dependent effective temperatures ($T_{\rm eff}(\phi)$),
• Derivation of the planet's Bond ($A_B$) and geometric ($A_g$) albedos,
• Measurement of the day–night temperature contrast and, by extension, the atmospheric heat recirculation efficiency,
• Assessment of phase curve offsets and their wavelength dependence.

The relevant theoretical energy balance relations, assuming zero-obliquity and synchronously rotating hot Jupiters, are:

$$T_{\rm day} = T_0 (1 - A_B)^{1/4}(2/3 - 5\epsilon/12)^{1/4} \ T_{\rm night} = T_0 (1 - A_B)^{1/4}(\epsilon/4)^{1/4}$$

with $T_0$ the irradiation temperature and $\epsilon$ the recirculation efficiency (Splinter et al., 11 Sep 2025). Application of these relations yields—for WASP-121 b—$T_{\rm day} = 2717 \pm 17$ K, $T_{\rm night} = 1562^{+18}_{-19}$ K, $A_B = 0.277 \pm 0.016$, and $\epsilon = 0.246 \pm 0.014$. The measured geometric albedo from optical order-2 data is $A_g = 0.093 \pm 0.029$ (3σ upper limit 0.175), reinforcing the observed “albedo paradox” where the Bond albedo substantially exceeds $A_g$ in the optical (Splinter et al., 11 Sep 2025).

Phase offsets, i.e., the longitude of the hottest region (hotspot) relative to the substellar point, are near zero at wavelengths $>1.5\,\mu$m (thermal emission regime), consistent with inefficient heat advection and slow wind speeds (~0.2 km/s as inferred from energy balance modeling).

4. Atmospheric Retrieval and Chemical/Cloud Inference

Spectroscopically resolved phase curves facilitate the retrieval of molecular abundances, cloud/haze properties, and temperature–pressure (T–P) profiles over different longitudes and pressures (Pelletier et al., 25 Aug 2025, Liu et al., 11 Apr 2025). For instance, in WASP-121 b, phase-resolved emission spectra over two secondary eclipses confirm:

• A strong stratospheric inversion, with the upper atmosphere exceeding 3100 K (revealed by water and CO band emission).
• Metal enrichment by approximately a factor of 10 over stellar in both refractories and volatiles, but a pronounced titanium (TiO) deficiency—interpreted as a cold-trap effect removing Ti species from the observable atmosphere (Pelletier et al., 25 Aug 2025).
• The critical importance of including thermal dissociation for species like $\mathrm{H_2O}$ in retrieval analyses; neglecting this introduces order-of-magnitude errors in abundance and derived C/O ratio (Pelletier et al., 25 Aug 2025).

Reflected light in the optical is modeled as an additive component in the secondary eclipse depth:

$$\delta_{\mathrm{ecl}}(\lambda) = A_\mathrm{HS} \frac{F_p(\lambda)}{F_*(\lambda)}\left(\frac{R_p}{R_*}\right)^2 + A_g \left(\frac{R_p}{d}\right)^2$$

where terms represent the thermal emission and the geometric albedo contribution, respectively.

These retrievals place constraints on cloud/haze microphysics: for example, the strong scattering slopes at shorter wavelengths often indicate micron/submicron-sized aerosol populations, while gray cloud decks contribute opacity across broader bands (Liu et al., 11 Apr 2025). Comparison across phase separates dayside versus nightside chemical and condensation processes.

5. Contamination, Noise, and Covariance Estimation

Robust phase curve extraction requires mitigation and quantification of several noise sources:

• 1/f detector noise introduces correlated noise on long timescales; refinement of per-integration background levels, per-column noise subtraction, and inclusion of a "background" term in pixel-level modeling are recommended (Holmberg et al., 2023).
• Contamination from field stars or dispersed background sources is possible due to the slitless design; masking and empirical correction strategies must be employed (Holmberg et al., 2023).
• Correlated noise among adjacent columns/channels propagates into non-diagonal covariance in the extracted time series; empirical estimation and propagation of the full covariance matrix are essential to avoid underestimating uncertainties in binned spectral light curves, especially for high-precision phase curve studies.

Systematic differences between pipelines (e.g., JExoRes, supreme-SPOON, transitspectroscopy, NAMELESS, FIREFly) can yield constant spectral offsets or differences in uncertainty estimates by factors up to 2, primarily due to choices in systematics modeling, covariance treatment, or background subtraction (Holmberg et al., 2023).

6. Applications and Scientific Insights from NIRISS/SOSS Phase Curves

NIRISS/SOSS phase curves have enabled unprecedented constraints on:

• The energy budgets and atmospheric circulation efficiencies of ultra-hot Jupiters (notably WASP-121 b; (Splinter et al., 11 Sep 2025, Pelletier et al., 25 Aug 2025)).
• Quantification of Bond and geometric albedos, offering insight into atmospheric scattering processes and the so-called albedo paradox (Bond albedo significantly higher than geometric).
• Longitude- and pressure-dependent temperature mapping, which constrain wind speeds and atmospheric redistribution.
• Spectral retrievals of metallicity, C/O (Radica et al., 2022), and key atmospheric absorbers including water, CO, VO, and the role of clouds/hazes.
• The vertical distribution and condensation behavior of refractory species (e.g., TiO cold-trapping).
• Systematic improvements in calibration and analysis—e.g., through the implementation of PASTASOSS for wavelength calibration (Baines et al., 2023) and empirical background template libraries for improved sky subtraction (Baines et al., 10 Sep 2025).

The combination of broad spectral coverage, high photometric stability, sophisticated contamination modeling (APPLESOSS/ATOCA), and in-depth atmospheric retrieval has established NIRISS/SOSS phase curves as a benchmark for exoplanet atmospheric characterization and energy budget analysis—enabling many new insights not possible with pre-JWST instrumentation.