Precise Constraints on the Energy Budget of WASP-121 b from its JWST NIRISS/SOSS Phase Curve

TL;DR

This study delivers the first JWST NIRISS/SOSS spectroscopic phase curve for an ultra-hot Jupiter (WASP-121 b), enabling a robust, near-complete accounting of its energy budget across 0.6–2.85 μm and constraining both reflected and thermal components. By employing two independent reductions and a forward model that separately treats planetary emission, reflection, and ellipsoidal effects, the authors derive $A_ ext{B}\approx0.28$–0.31 and $\epsilon\approx0.19$–0.25, with a near-1 bar mixed layer depth suggested by energy-balance modeling and very slow global winds. They measure a low geometric albedo, $A_g\approx0.09$, and find evidence for eastward reflected light at short wavelengths, emphasizing the albedo paradox in hot Jupiters. The results underscore the critical influence of nightside flux treatment on energy-transport inferences and demonstrate JWST’s capability to tightly constrain exoplanetary energy budgets across multiple atmospheric layers.

Abstract

Ultra-hot Jupiters exhibit day-to-night temperature contrasts upwards of 1000 K due to competing effects of strong winds, short radiative timescales, magnetic drag, and H2 dissociation/recombination. Spectroscopic phase curves provide critical insights into these processes by mapping temperature distributions and constraining the planet's energy budget across different pressure levels. Here, we present the first NIRISS/SOSS phase curve of an ultra-hot Jupiter, WASP-121 b. The instrument's bandpass [0.6 - 2.85 micron] captures an estimated 50-83% of the planet's bolometric flux, depending on orbital phase, allowing for unprecedented constraints on the planet's global energy budget; previous measurements with HST/WFC3 and JWST/NIRSpec/G395H captured roughly 20% of the planetary flux. Accounting for the unobserved regions of the spectrum, we estimate effective day and nightside temperatures of T_day = 2717 +/- 17 K and T_night = 1562 +/- 19 K corresponding to a Bond albedo of A_B = 0.277 +/- 0.016 and a heat recirculation efficiency of epsilon = 0.246 +/- 0.014. Matching the phase-dependent effective temperature with energy balance models yields a similar Bond albedo of 0.3 and a mixed layer pressure of 1 bar consistent with photospheric pressures, but unexpectedly slow winds of 0.2 km/s, indicative of inefficient heat redistribution. The shorter optical wavelengths of the NIRISS/SOSS Order 2 yield a geometric albedo of A_g = 0.093 +/- 0.029 (3 sigma upper limit of 0.175), reinforcing the unexplained trend of hot Jupiters exhibiting larger Bond albedos than geometric albedos. We also detect near-zero phase curve offsets for wavelengths above 1.5 micron, consistent with inefficient heat transport, while shorter wavelengths potentially sensitive to reflected light show eastward offsets.

Figures (16)

• Figure 1: Left:(a) Order 1 white light-curve fit to the flux that is normalized to the first eclipse. The red line is the best-fit full model. (b) Components of the systematics model in ppm, including the linear trend in green; the PCA model in pink; the tilt jump model in blue; the GP model in purple; the ellipsoidal variation contribution in black; and the stellar sinusoid model in red (Order 2 only). (c) Detrended light-curve created after removing all contributions from (b). The remaining planetary signal is shown in green. (d) Residuals of the best-fit model to the data. Darker blue points are residuals binned for visual purposes. The rms in ppm is printed in the bottom left. Right: same as the left plot except for Order 2.
• Figure 2: Estimated captured flux of the planet assuming the planet radiates as a blackbody. The captured flux is calculated as the ratio of the integrated blackbody emission within the instrument's bandpass to the total emission over all wavelengths, i.e., $\gamma =\int_{\lambda_{\rm min}}^{\lambda_{\rm max}} B(\lambda, T)\, d\lambda / \int_{0}^{\infty} B(\lambda, T)\, d\lambda$. The captured flux fraction is shown for NIRISS SOSS [0.6–2.85 $\mu$m] (red line); Hubble WFC3 [1.12–1.64 $\mu$m] (dashed green line); NIRSpec G395H [2.7–5.15 $\mu$m] (dash-dotted blue line). The red-shaded region shows the temperature range on WASP-121 b based on our $T_{\rm eff}$ estimates. Red dashed lines indicate the boundaries of the planet's temperature range within the NIRISS SOSS captured flux fraction. From this we estimate that these observations capture between 55% and 82% of the planet's bolometric flux, depending on orbital phase. Using the minimum temperature from the NAMELESS fit, this estimate decreases to 50%. In either case, the wavelength coverage of NIRISS exceeds that of any other instrument.
• Figure 3: Inferred Bond albedo (A$_\mathrm{B}$) and heat recirculation efficiency ($\epsilon$) of WASP-121 b derived from dayside and nightside emission measurements using irradiation temperature $T_{0} = 3398$ K. The blue contours represent 1$\sigma$, 2$\sigma$ and 3$\sigma$ confidence intervals from the fit to the exoTEDRF reduction, while the red contours correspond to the NAMELESS reduction. The gold contours show the results from the Hubble WFC3 phase curve presented by Mikal-Evans2022, using the brightness temperatures reported in Morello2023. The purple and teal contours correspond to brightness temperatures from NIRSpec NRS1 and NRS2, respectively Mikal-Evans2023. For the Spitzer 3.6 $\mu$m phase curve (brown contours), we use brightness temperatures from Morello2023; while the magenta contours represent results from the comprehensive analysis of the 4.5 $\mu$m phase curve by Dang2025. Top: Inferred contours when using standard uncertainties of day- and nightside. Only NIRISS SOSS measurements fully propogate astrophysical uncertainties. Bottom: Inferred contours when uncertainties are inflated by 1/$\gamma$, i.e. the captured flux fraction for a given instrument at the reported temperature. When accounting for captured flux, only NIRISS provides constraints on both the Bond albedo and heat recirculation efficiency. Our phase measurements show a Bond albedo of 20--35% and relatively poor day-to-night heat transport.
• Figure 4: Phase offset versus normalized phase amplitude from the spectroscopic fits of WASP-121 b. The normalized phase amplitude is given by $(F_{\rm max} - F_{\rm min})/F_{\rm max}$. The phase offset is defined such that 0$^\circ$ corresponds to mid-eclipse with positive offset values indicating an eastward shift and negative a westward. Symbols are colored by wavelength with blue indicating the shortest wavelengths and red the longest. Order 2 values are binned with three points per bin for visual clarity. Relative amplitudes above 1 correspond to Order 2 wavelengths with a negative minimum flux. The values from the white light-curve fits are also shown as stars with colored cyan edges for Order 2 and red for Order 1. We robustly detect an eastward offset of 5.1 $\pm$ 1.4$^\circ$ in Order 1 and an insignificant offset of 10.5 $\pm$ 9.9$^\circ$ in Order 2.
• Figure 5: Top: Reflected light and thermal emission components from the Order 2 detrended white light-curve. Model is described in Section \ref{['sec:Slice-Model']} and was fit four longitudinal slices across the planet; slices are centered at $\phi$ = 45$^\circ$, 135$^\circ$, 225$^\circ$, 315$^\circ$. Red shows thermal emission, blue shows reflected light and black shows the full model. Solid lines show the median retrieved value while shaded regions show the 1 $\sigma$ uncertainties on each model component. The detrended data are shown in black, binned with 20 points per bin for visual clarity. Bottom: Residuals of median model to the data. Larger points are residuals binned to 20 points per bin.