JuanCastillo29/space-mission-intelligence-data huggingface dataset:
At low spectral resolution, the Doppler shifts of spectral lines are lost, but the total fraction of star light absorbed by the planet can be measured very precisely by comparing the flux of star light during transit to the flux observed before and after the transit. When the planet rotates during transit, the fraction of absorbed star light can change as a function of time as different atmospheric temperatures and chemical compositions are probed [3]. The analytical form of this function is unknown and thus, we choose a polynomial approximation which represents a Taylor expansion. In the case of the ultrahot Jupiter WASP-121 b, the three-dimensional atmospheric model SPARC/MITgcm [16, 17] predicts the planet to change its apparent radius due to its rotation during transit in a way that can be approximated well by a second-order polynomial (see Methods). Thus, we restrict the Taylor expansion of the planet-tostar radius ratio as a function of time to the second order. To measure these radius changes, we developed a rotational light curve model (Mrot) in which the exoplanet’s radius (Rp) relative to its host star’s radius (R∗) is given by
�
(t −t0)iRi/R∗, (1)
Rp/R∗(t) =
i=0
where t denotes time, t0 is the time of inferior conjunction and Ri/R∗are the polynomial coefficients. In this notation, R0/R∗represents the planet-to-star radius ratio at t0, R1/R∗gives the planet’s linear rate of radius change relative to the star’s radius and R2/R∗gives the curvature of the radius variation in time. This light curve model is qualitatively different from past modeling approaches that adopted either a circle [18], two stacked semi-circles [19] or arbitrarily complex cross-sectional shapes parameterized using Fourier series [20].

Since these models simulate transit light curves by displacing a time-independent planetary cross-sectional shape across the stellar disk, they neglect the changing viewing geometry of the planet during transit that changes its absorbing cross-sectional area as a function of time [3].
We applied the rotational transit model to two transit observations of WASP-121 b observed with the Near Infrared Spectrograph (NIRSpec [21–23]) and the Near Infrared Imager and Slitless Spectrograph (NIRISS, [24, 25]), respectively, onboard the James Webb Space Telescope (JWST). To quantify the statistical significances of the planet’s radius change during transit in these observations, we performed statistical hypothesis tests on the wavelength-integrated (‘white’) light curves with a translational light curve model (Mtra) that prescribes a time-invariant planet radius (i.e., R1/R∗= R2/R∗= 0) as the null hypothesis and Mrot with freely-fit R1/R∗ and R2/R∗as the alternative. In a Bayesian framework, we estimate the ratio of the probabilities of the alternative and the null hypothesis using the Bayes factor (B) calculated by taking the ratio of the Bayesian evidence of Mrot to the Bayesian evidence of Mtra. We ran this test on two independent data reductions of each observation to verify the results against reduction-level assumptions (see Methods). Mrot is significantly preferred [26] over Mtra with ln(B) = 18.0 and ln(B) = 24.8, respectively, in the two NIRISS SOSS data reductions (see Extended Data Table 1) and ln(B) = 11.7 and ln(B) = 23.7 in the two NIRSpec G395H reductions (see Extended Data Table 2). An inspection of the observations and models (see Fig. 1 and Extended Data Fig. 1) suggests that the data between contact points 2 and 3 of the transit drive the detection of the planet’s rotation as the fit to the data using Mtra results in systematic linear residuals in those data that are absent when Mrot is applied. This demonstrates that the planet’s rotation leads to it appearing larger in the second than in the first half of the transit which results in asymmetric light curve shapes in both observations. These asymmetric light curves cannot be adequately fit with a time-independent transit model that models the planet’s cross-section using two semi-circles with a shared center point but different radii (so-called ‘asymmetric limbs’) [23]. Thus, the signal is dominated by the star light transmitting through different longitudes in the planet as a function of time as it rotates during the transit. There is no evidence to fit for a free R2/R∗over setting R2/R∗= 0 in Mrot likely due to a degeneracy of R2/R∗with the host star’s limb darkening (see Extended Data Figs. 2 and 3). To examine the impact of setting R2/R∗= 0 in Mrot, we repeated the hypothesis test and found that the detections of WASP-121 b’s rotationinduced radius change remain significant in both observations with ln(B) = 16.5 and ln(B) = 23.2 in the NIRISS SOSS reductions (see Extended Data Table 1) and ln(B) = 13.6 and ln(B) = 24.9 in the NIRSpec G395H reductions (see Extended Data Table 2). Another degeneracy between the rotation-induced radius change and the host star is driven by WASP-121 A’s gravity darkening caused by its rapid rotation: Data from the Transiting Exoplanet Survey Satellite (TESS) reveal that WASP-121 b NIRSpec, 3.82 - 5.15 µm Data 1.000
transits a brighter part of its host star’s disk at the end of the transit than in the beginning, also creating an asymmetric light curve (see Extended Data Fig. 4). WASP-121 A’s gravity darkening affects the NIRISS SOSS data, but is only a minor effect in the NIRSpec G395H data thanks to the latter instrument probing the transit in longer wavelengths (see Methods). Because of the degeneracy of R2/R∗with the host star’s limb darkening and the contamination of the NIRISS SOSS data with the star’s gravity darkening, we derive WASP-121 b’s transmission spectrum as a function of orbital phase from fits to the spectroscopic light curves of NIRSpec G395H with Mrot adopting R2/R∗= 0. The polynomial coefficients as functions of wavelength in those data are shown in Extended Data Fig. 5. The transmission spectra at the orbital phases at the beginning and end of the transit (see Fig. 2) firstly reveal that the fraction of star light absorbed by the planet increases as a function of time through the entire bandpass. Secondly, the CO absorption feature between 4.3 µm and 5.2 µm grows by ∼200 ppm relative to the rest of the spectrum between contact points 2 and 3. This increase of CO absorption is observed with a consistent amplitude in the NIRISS SOSS data (see Extended Data Fig. 6). And thirdly, the H2O feature shortward of 3.8 µm remains approximately constant, possibly shrinking slightly. Additionally, the absorption from SiO that occurs between 4.0 µm to 4.3 µm appears to slightly increase, though not as strongly as the CO absorption. With the narrow wavelength range of the SiO absorption feature and thus few data, however, it is challenging to draw definite conclusions.
[Figure: Fig. 2 Visualization of WASP-121 b’s orbital motion and phase-dependent transmission spectrum. The transmission spectra at contact points two (t2) and three (t3) are shown in the lower row. The spectra were measured with NIRSpec G395H using the Firefly reduction and modeled adopting R2/R∗= 0. Circles depict medians and error bars indicate the 1 σ range of 125,000 posterior samples. The planet’s orbit and star’s radius are shown to scale, but the planet’s and its atmosphere’s size are exaggerated for visual clarity. The color map on the planet depicts an equatorial cross-section of the planet’s atmospheric temperature from the SPARC/MITgcm. The blue and magenta arrows in the zooms into the planet’s temperature map indicate the approximate heights at which the atmosphere becomes opaque. In the t3 map, dotted blue lines correspond to the heights probed at t2 to demonstrate how the trailing limb grows while the leading limb shrinks as the planet rotates. In the transmission spectra, colored regions underneath the data points indicate which molecule is the dominant absorber in each wavelength channel [23].]
We propose that the changes of WASP-121 b’s transmission spectrum throughout the transit are driven by the different distributions of molecules in WASP-121 b’s atmosphere: H2O thermally dissociates on the dayside [15, 28–30], leading to a higher abundance on the nightside, while CO is abundant in the entire atmosphere thanks to its stability against thermal dissociation [17]. Thus, the progressively hotter gas rotating into view on the trailing limb becomes more and more depleted in H2O, while the CO abundance remains approximately constant. Therefore, the increase of the transit depth is strong in the CO band owing to the increase in atmospheric scale height, but this effect is overwhelmed in the H2O band due to thermal dissociation of H2O as temperatures increase. The slight increase of SiO absorption as the transit progresses could indicate that SiO thermally dissociates less than H2O, but the limited constraining power due to its narrow absorption feature makes the interpretation difficult.
Phase-resolved observations of the Hα line in WASP-121 b obtained using the four-unit telescope (4-UT) mode of the Echelle Spectrograph for Rocky Exoplanets and Stable Spectroscopic Observations (ESPRESSO) at the Very Large Telescope (VLT) were used in a past study to trace the longitudinal variation of temperature in the uppermost part of the atmosphere where the planet’s atmosphere escapes into space [14]. These data are sensitive to very low pressures in the atmosphere on the level of microbars where the atmosphere is extremely hot (T > 8000 K). The JWST observations presented here are sensitive to higher pressures than that around milibars, complimenting the existing temperature gradient constraints from high-resolution observations. Regarding chemical gradients in WASP-121 b, phase-resolved atmospheric retrievals [8] were carried out on ESPRESSO data obtained in its one-unit telescope (1-UT) mode [31]. The data are sensitive to atomic species such as Fe and did not reveal chemical gradients around the planet’s terminators, but abundances consistent with homogeneous distributions [8]. Since chemical gradients of atoms in exoplanets are driven by rain-out or ionization, the lack of atomic gradients is not in tension with the gradient in H2O driven by thermal dissociation we observe with JWST. Regarding longitudinal gradients of molecular abundances, the Doppler shifts of CO and H2O lines in WASP-121 b were previously measured as functions of orbital phase during three transits observed using the Immersion Grating Infrared Spectrometer (IGRINS) on the Gemini-South Telescope [15]. The data revealed CO lines to become increasingly blueshifted during the transits indicating that CO absorption predominantly originates in the trailing limb that rotates toward the observer. The blueshift of H2O lines, in contrast, decreased as the transits progressed, revealing H2O absorption to be dominated by the leading limb that rotates away from the observer [32]. These results are in line with the JWST observations presented here that also suggest CO, but not H2O, absorption to trace the temperature increase in the trailing limb as the planet rotates during transit due to the thermal dissociation of H2O. Thus, the consistency between the Gemini-South and JWST observations highlights the synergy between phase-resolved ground-based and space-based observations.
With the detection of WASP-121 b’s rotational transit and subsequently its phaseresolved transmission spectrum, the longitudinal gradients of temperature and chemistry around the planet’s terminators become observable in transit at low spectral resolution. Beyond WASP-121 b, the phase-dependent transmission spectra of several other exoplanets might be measurable with JWST. We propose to use exoplanets’ rotations during transit, their equilibrium temperatures (delivering a proxy for their longitudinal temperature gradients), and their transmission spectroscopy metrics (TSM [33], giving an estimate of the signal-to-noise ratio of a planet’s atmospheric features in transit) to guide the expectation for the signal amplitudes caused by rotational transits. Under these considerations, WASP-121 b is one of the stand-out targets (see Fig. 3). Some of the other promising targets, such as WASP-33 b, WASP-189 b and KELT-9 b, orbit rapidly-rotating A-type stars for which gravity darkening has been shown to impact the planets’ transit light curves by introducing asymmetric transits [34–36]. Thus, constraints on these planets’ rotational transits will require careful modeling of the stars’ gravity darkening by combining transit light curves from different wavelength ranges as it was done in the present study using data from JWST and TESS.
Jupiter size Earth size
HAT-P-67 b
Equilibrium Temperature [K]
HAT-P-32 b
TSM
KELT-9 b
0 10 20 30 40 50 Rotation during transit [◦]

[Figure: Fig. 3 Known transiting exoplanets’ TSMs and rotations during transit estimated assuming synchronous rotation and zero eccentricity. Dot colors represent equilibrium temperatures and dot sizes are proportional to planet radii. The names of some of the planets that rotate the most during transit and are the most promising for atmospheric characterization using transmission spectroscopy are indicated. The data were taken from the NASA Exoplanet Archive [37].]
JWST also observed a phase curve of WASP-121 b using the Near Infrared Imager and Slitless Spectrograph (NIRISS) instrument starting before a planetary eclipse on October 10, 2023 (UTC) and ending 43.85 hours later after a second eclipse event. This observation was part of observing program GTO 1201 (PI: Lafreni`ere) and used the single object slitless spectroscopy (SOSS) mode with the SUBSTRIP256 subarray with 6 groups per integration. The observations were reduced starting from the uncalibrated (uncal.fits) images using the Firefly reduction suite [38–40], which has been adapted for SOSS data [42] with further details available in ref. [42–44]. A notable recent addition is the removal of 1/f noise at the group-level stage, as described in ref. [45]. From the cosmic ray, bad pixel, 1/f-removed, background-removed 2D images, we summed the white light curve using an aperture width of 34 pixels which produced a first order white light curve which minimized the light curve scatter, found to have a standard deviation of 110 ppm and a median absolute deviation of 83 ppm as characterized by a near-flat 100 integration segment shortly before transit. We also performed a NIRISS SOSS reduction independent of the Firefly reduction using steps as outlined in ref. [46] (hereafter labeled the ‘Fu’ reduction). It starts with the uncalibrated (uncal.fits) files, and we used the default JWST pipeline to produce the rampfitsstep.fits. Then, we did background and 1/f subtraction using pixels in the bottom 50 percentile in flux for column median subtraction and extracted the time series two-dimensional spectra. Based on the 100 points right before transit, we measured a standard deviation of 116 ppm and a median absolute deviation of 88 ppm.
We approximate the rotation-induced change of the planet’s transit radius with a second-order polynomial in time (see main text). We implemented this light curve model using the Batman package [18], in which the planet-to-star radius ratio is a constant. To calculate light curve models with time-dependent planet radii, we set up a Batman model for each data point of the time-series observation and set the planet-to-star radius ratio in the series of Batman models according to equation 1. To measure WASP-121 b’s phase-resolved transmission spectrum, we analyze a cutout of the light curves that includes the data taken during both full eclipses and from 3.5 hours before to 3.5 hours after the transit mid-time output from both reductions of both the NIRSpec and NIRISS observations. Including the adjacent eclipses into the transit analysis is needed, because the planet’s rotation around the transit results in a variation of its emitted flux as a function of time that would contaminate the transmission spectrum if it were not separated from the systematics’ baseline [23]. The full model we use to fit the observations is Mrot = (c0 + c1t) × (T(θ) + P(p0, p1, p2)) , (2) where (c0 + c1t) is the stellar and instrumental baseline, T(θ) is the modified Batman model with transit parameters θ, and � 0 during secondary eclipse p0 + p1t + p2t2 else (3)
P(p0, p1, p2) =
is an approximation of WASP-121 b’s partial phase curve around the transit. The translational light curve model Mtra we use as a null hypothesis is identical to Mrot apart from prescribing R1/R∗= R2/R∗= 0.
30]. These differences in chemistry might also be responsible for the deviations of the model’s transmission spectrum at the point of conjunction from the observations (Fig. 5, blue diamonds in the upper panel), namely, the too steep H2O feature and the underestimation of the CO feature between 4.3 µm and 5.2 µm. To simulate the effect of a colder morning terminator, we modified the ‘nominal’ SPARC/MITgcm by setting the vertical temperature structure from 240◦to 302◦in longitude to its structure at 240◦(see Extended Data Fig.

7). With this modified temperature field (labeled the ‘muted leading limb’ model in Extended Data Fig. 5), the model predictions for R1/R∗increase in all wavelengths, because the planet’s rotation does not lead to a shrinking of the leading limb anymore due to a vertical temperature structure that is constant in longitude. With this modification, the model predictions for R1/R∗are larger than the observations between 3.05 µm and 4.0 µm where H2O is the dominant molecular absorber [23]. At wavelengths larger than 4.3 µm where CO is the strongest absorbing molecule [23], the model values for R1/R∗are smaller than the data (see Extended Data Fig. 5), though the lower limits of four of the five data points’ 1σ intervals overlap with the model predictions. Thus, the order of magnitude of the transit asymmetry observed with NIRSpec G395H NRS2 can be reproduced by the longitudinal temperature gradient around the evening terminator in the SPARC/MITgcm, when the longitudinal temperature gradient around the morning terminator is muted. The SPARC/MITgcm predicts negative R2/R∗through the whole spectrum, suggesting a local maximum of the planet’s cross-sectional area during transit. When adopting Gaussian priors on the limb darkening in the light curve analysis, we find consistently positive R2/R∗(see Extended Data Fig. 5), implying a local radius minimum during transit. The SPARC/MITgcm does not include any tidal deformation of the planet and thus the local maximum during transit in the model is solely caused by the atmospheric structure. The tidal deformation of WASP-121 b would lead to an elongation of the planet along the planet-star axis [55] which, together with the planet’s rotation, would cause a local minimum of its cross-sectional area during transit [3]. Thus, the observed tendency to positive R2/R∗might be a hint at the planet’s tidal deformation. Measuring the planet’s tidal deformation from this observation would be dependent on the assumption that the adopted limb darkening priors are accurate. However, their degree of precision is unknown and thus, we refrain from attempting to constrain WASP-121 b’s tidal Love number that quantifies its tidal deformation.
C.G. analyzed the JWST data and wrote the manuscript with assistance from A.F, T.M.E.-S., D.K.S, S.D. and E.-M.A. A.F. provided model light curves derived from the SPARC/MITgcm using Pytmosph3R. T.M.E.-S., V.P. and J.L. supported the interpretation of the results. D.K.S and E.-M.A. reduced the JWST/NIRSpec observations. D.K.S and G.F. reduced the JWST/NIRISS observations. S.D. analyzed the TESS data and the JWST/NIRSpec NRS2 data with a gravity darkening model.
Instrumental systematics causing the observed asymmetric light curve shapes would require an instrumental effect that impacts the NIRISS SOSS and NIRSpec G395H’s NRS2 data that show a transit asymmetry, but not NIRSpec G395H’s NRS1 observations that deliver a symmetric transit light curve (see Fig. 1 and Extended Data Fig. 1). Considering that past observations suggested the NRS2 detector to be less affected by instrumental systematics than NRS1 (see, e.g., ref. [21, 56, 57]) and the coincidence of systematics required during the precise time span of the transit to create the observed signal in both the NIRISS SOSS and the NIRSpec G395H observations, such a scenario appears unlikely.

Therefore, the transit asymmetry is likely a signal from either WASP-121 b or its host star.
JWST/NIRISS’s and JWST/NIRSpec G395H’s bandpasses include one CO band each. To examine, if WASP-121 b’s radius change is consistent between both observed CO bands, we integrated both detectors’ light curves over the heads of the two CO bands and fit both Mtra and Mrot with R2/R∗= 0 using least-squares approaches and MCMCs as before to the light curves. In these fits, the orbital parameters were fixed to the two observations’ white light curve fit results. The fits to the observations (see Extended Data Fig.

6) reveal that WASP-121 b’s rotation-induced radius change results in residuals on the order of 250 ppm between contact points 2 and 3 when Mtra is used in both the NIRISS and NIRSpec light curve, though the NIRISS data suffer from a lower signal-to-noise ratio due to the probed CO band being narrower than the one in NIRSpec. The MCMC posteriors of R1/R∗are 650+188 −189 ppm hr−1 in NIRISS and 580+90 −91 ppm hr−1 in NIRSpec and thus consistent between both observations. The slightly stronger increase of WASP-121 b’s apparent radius as a function of time in NIRISS compared to NIRSpec might be the result of contamination with gravity darkening. We note, however, that the linear rate of radius change in the white light curve of NIRISS (409+53 −53 ppm hr−1, see Supplementary Table 4) is smaller than the rate measured from the light curve integrated over the CO band (650+188
−189 ppm hr−1).
Gravity darkening monotonically decreases with wavelength and since the CO band in NIRISS is located on the long-wavelength end of the detector, there has to be an additional source of an asymmetric light curve that elevates the R1/R∗measurement over that from the white light curve. Thus, both the NIRISS and the NIRSpec data point toward increasing CO absorption in the planet as a function of orbital phase with quantitatively consistent amplitudes. This demonstrates JWST’s remarkable capability to measure phase-dependent absorption in transiting exoplanets consistently between different observations and instruments.
The JWST and TESS data used in this study are publicly available on the Barbara A. Mikulski Archive for Space Telescopes at https://mast.stsci.edu. The JWST/NIRSpec observation analyzed here is part of JWST observing program G.O. 1729 (P.I.: T.M.E.-S.; co-P.I.: Tiffany Kataria) and can be retrieved from ref. [70]. The JWST/NIRISS observation is associated with JWST observing program G.T.O. 1201 (P.I.: David Lafreni`ere) and can be retrieved from ref. [71].
The following software packages were used to perform the data analysis and model interpretation: astropy [72–74], batman [18], corner [75], dynesty [50], eclipsoid [65], emcee [49], Eureka! [41], ExoTIC-LD [51], FIREFly [38–40], lmfit [48], matplotlib [76], numpy [77], NumPyro [66], pandas [78], scipy [79]
This work is based on observations made with the NASA/ESA/CSA James Webb Space Telescope. The data were obtained from the Mikulski Archive for Space Telescopes at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-03127 for JWST.

This research has made use of the NASA Exoplanet Archive, which is operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program.