Main

Our study was performed using observations of the exoplanet WASP-39 b from the James Webb Space Telescope (JWST) Transiting Exoplanet Community Director’s Discretionary Early Release Science (ERS) programme (ERS-1366; Principal Investigators: N. M. Batalha, J. L. Bean and K. B. Stevenson)18,19. This highly irradiated gas giant exoplanet has a mass of 0.28MJup, a radius of 1.27RJup and an equilibrium temperature of 1,100 K. The ERS observations consisted of four transit events, observed using four different JWST instruments. Combined, these revealed prominent atomic and molecular absorption features in the terminator region, including K, H2O, CO2, CO and even SO2, the latter identified as a photochemical product10,20,21,22,23. Our analysis was performed, in particular, on the near-infrared spectrograph (NIRSpec)/PRISM-mode observations of WASP-39 b10 because this dataset has the widest wavelength coverage while simultaneously presenting minimal instrumental systematics24. This dataset consists of an 8.23 h observation centred around the 10 July 2022 transit of WASP-39 b.

The JWST data were reduced using the FIREFLy pipeline10, as described in ref. 24. Reference 24 also demonstrated that the majority of wavelengths less than 2 μm suffer from detector saturation, and are not in agreement with measurements performed using the near-infrared imaging and slitless spectrograph (NIRISS) single-object slitless spectroscopy (SOSS) instrument across a similar wavelength range21. Because a reliable determination of the transit depth less than 2 μm cannot be obtained using the NIRSpec/PRISM observations, we opted to use only the 2–5 μm data in our present analysis. We fit each individual wavelength-dependent light curve at the pixel-level resolution element of the instrument, using a simple linear term in time as our systematics model, following the work of ref. 10.

The transit light-curve analysis was performed by means of three different methodologies, all of which entailed different assumptions yet provided consistent results (Methods). We report on the results obtained using the catwoman framework25,26, which is arguably the most conservative of the approaches because it allows fitting for morning and evening terminators simultaneously in a single fit. The framework models the terminator as two semicircles of independent radii, thus allowing us to separately retrieve the sizes of both morning and evening limbs as a function of the wavelength from the transit light curves themselves. An example light-curve fit at 4.38 μm, using this methodology and the classic circular occulter method—here, modelled using the batman library27—is presented in Fig. 1. More details on the data analysis are given in the Methods.

Fig. 1: Light-curve modelling and extraction of morning and evening depths.
figure 1

a,b, Transit light-curve modelling of the 10 July 2022 transit at 4.38 μm (in the middle of the CO2 spectral feature in the transmission spectrum) of WASP-39 b (grey datapoints) using both the catwoman framework (a, purple model) and the classic circular occulter model via batman (b, grey model). c,d, Residuals of the best-fit model for the catwoman (c) and batman (d) methodologies. The batman residuals (d) show, in turn, the difference between the catwoman and batman light-curve models (purple line), showcasing the catwoman model’s small (approximately a few hundred parts per million) light-curve asymmetries. Note that the residuals are of comparable magnitude. While it is difficult to conclude the effect is present in each individual light curve, the effect is detectable once all the wavelength-dependent light curves have been analysed (see Fig. 2 and text for details). e,f, Inferences enabled from the catwoman (e) and batman (f) methodologies. The catwoman methodology (e) allows the extraction of morning/evening transit depths (purple ellipses representing the 1, 2 and 3σ posterior contours; dashed grey line indicating equal morning and evening depths), whereas the circular occulter methodology (f) only allows the extraction of a single total transit depth from the light curve. All error bars represent 1-standard deviation.

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The resulting morning and evening terminator spectra inferred from our catwoman light-curve fits are presented in Fig. 2b. We computed an average difference between the evening and morning spectra of 405 ± 88 ppm, finding this difference to be inconsistent with 0 at more than 4.6σ—that is, the spectra showed statistically distinct features in the morning and evening terminators. Qualitatively, both the morning and evening spectra showcase transit depth increases at around the H2O (2.84 μm) and CO2 (4.38 μm) features, with the morning spectra being consistent with somewhat flatter spectra—a behaviour we observed with all our light-curve fitting methodologies. This detection of evening-to-morning spectral differences was, in turn, robust at the 3σ level, even when accounting for the current best uncertainties on the orbital parameters of WASP-39 b. This result does, however, depend on the accuracy and precision of those parameters up to a factor of a few of their current state-of-the-art error bars, which highlights the importance of the accurate and precise determination of exoplanetary orbital parameters when attempting to perform morning-to-evening spectroscopy, as we do in our work (Methods).

Fig. 2: The morning and evening spectra of WASP-39 b from JWST NIRSpec/PRISM observations.
figure 2

a,b, The total transit depth, from adding the morning and evening spectra (a), along with the individual morning (blue points) and evening (red points) spectra of WASP-39 b, as derived from our light-curve modelling (b). The large points are datapoints at a resolution (R) of 30, shown for illustration, the smaller points are at R = 100. The best-fit, chemically consistent models (solid black line in a, solid red and blue lines in b; fitted to the R = 100 spectra) are consistent with a hotter evening terminator (see text for details). c,d, Residuals from the best-fit model (red points for the evening (c), blue points for the morning (d)), the dashed line marks 0. All error bars represent 1-standard deviation.

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Next, we performed forward modelling and atmospheric retrievals to explore the physical mechanism behind the difference in the observed morning and evening spectra. In particular, we used the ATMO forward-model grid28 and the chemically consistent CHIMERA retrieval framework29, with modifications that allowed them to perform morning and evening inference simultaneously and account for the covariance between these limb depths26. We thus fitted the morning and evening spectra of WASP-39 b simultaneously to constrain their individual temperatures, C/O ratios and cloud properties (Methods). The best-fit solutions from both of those frameworks are qualitatively similar; in Fig. 2, we show the CHIMERA median model as solid blue and red lines for the morning and evening, respectively. Both modelling frameworks returned similar constraints on the morning and evening temperatures and C/O ratios. Our CHIMERA retrievals converge to a \({\rm{C}}/{{\rm{O}}}_{{\rm{evening}}}=0.5{8}_{-0.16}^{+0.13}\) and \({\rm{C}}/{{\rm{O}}}_{{\rm{morning}}}=0.5{7}_{-0.23}^{+0.17}\), which are consistent with each other. These are, in turn, consistent with the ratios derived from the transmission spectroscopy analysis reported by the ERS team from the NIRSpec/PRISM observations10—that is, C/O ≈ 0.3–0.5. Our derived metallicity (assumed to be common for both limbs) is also consistent with the approximately 10× solar metallicity reported in that work. Interestingly, the CHIMERA retrievals support a significantly hotter, \(106{8}_{-55}^{+43}\) K, evening than the morning retrieved temperature of \(88{9}_{-65}^{+54}\) K, the difference being \(17{7}_{-57}^{+65}\) K—significant at more than a 3σ level. This result qualitatively follows predictions from three-dimensional (3D) general circulation models (GCMs), from which hotter evening limbs arise due to superrotating equatorial jets on highly irradiated exoplanets, such as WASP-39 b14,15,23,30,31. In addition, while the retrieval suggests a relatively constrained cloud-top location in the evening limb at about 1–10 mbar, the cloud-top location in the morning limb is relatively unconstrained, allowing multiple possible configurations, given this data. This is probably a consequence of the relatively flatter morning spectrum, combined with the relatively large uncertainties on our NIRSpec/PRISM limb spectra, allowing for a wide range of possibilities for the morning cloud properties. While this suggests that most of the variations observed in the NIRSpec/PRISM morning and evening limb spectra could be attributed to temperature differences between the morning and evening limbs, the treatment of clouds as grey opacity sources in the frameworks used to perform our inferences might be preventing us from further constraining the cloud properties in the morning and evening limbs of WASP-39 b.

To explore the possibilities enabled by aerosols and chemical processes, we compared the observations to predictions from GCMs, which are hydrodynamics models that simulate the 3D wind and temperature structure in planetary atmospheres, self-consistently predicting differences between the evening and morning terminator. A range of processes influence terminator differences in the spectra, including temperature differences driven by atmospheric circulation, condensate clouds, photochemical hazes and the transport-induced disequilibrium chemistry of gaseous species (Fig. 3). No single GCM is currently able to self-consistently simulate all of these processes simultaneously. We thus explored multiple different models32,33,34,35.

Fig. 3: Comparison of morning and evening spectra using GCMs.
figure 3

a–h, Comparison between the predictions from GCMs and the observed transit depths for the morning and evening terminators, as derived with catwoman. The left-hand column shows the spectra (a, c, e and g) and the right-hand column shows the difference between the morning and evening terminator (b, d, f and h). A vertical offset of −600 ppm was applied to the spectra in c, e and g to facilitate comparison with the observed spectra. a,b, Condensate cloud model together with the equilibrium chemistry taking into account elemental depletion by clouds compared against the morning (blue) and evening (red) spectra (a), and against the difference between the spectra (b, in black); the grey line indicates zero difference. This model qualitatively provides the best match to the morning terminator spectrum. c,d, Photochemical haze model based on the SPARC/MITgcm, with equilibrium chemistry gas-phase abundances. e,f, Clear-atmosphere equilibrium chemistry model. g,h, Clear-atmosphere model, including transport-induced disequilibrium chemistry (diseq. chem.). The clear-atmosphere models provide the best match to the evening terminator spectrum. All error bars represent 1-standard deviation.

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While the gas-phase chemistry results (Unified Model) reproduced the shape of the spectral features well at the evening terminator, the condensate cloud model (ExpeRT/MITgcm) performed qualitatively better at reproducing the reduced feature amplitude at the morning terminator, especially the suppressed CO2 feature at 4.3 μm. The photochemical haze model predicted large methane (CH4) features at the morning limb and a larger morning limb in the CH4 bands (centred at 2.3 and 3.3 μm), in conflict with the observations. This was driven by colder temperatures at low pressures in this GCM (Substellar and Planetary Atmospheric Radiation and Circulation (SPARC)/MITgcm) combined with the equilibrium chemistry. Photochemical hazes themselves have a smaller effect on limb differences. The condensate cloud model is the only one that predicted the largest limb difference to be in the centre of the CO2 feature (even though the difference is substantially smaller than observed). This finding is in line with another recently published cloud-microphysics study36. A comparison with cloud-free spectra from the same GCM as our condensate cloud model (not shown) revealed that the limb difference in the centre of the 4.3 μm CO2 feature is determined by the temperature difference, but, at other wavelengths, is dominated by clouds. We thus suggest, as a tentative explanation, a relatively cloud-free evening terminator and a cloudier morning terminator, in line with the inferences performed with the ATMO forward models and CHIMERA retrievals described above. Detailed follow-up studies, exploring a larger parameter space with cloud-formation models, will be needed to test this explanation.

Methods

Dataset

In this work, we use the JWST NIRSpec PRISM dataset, obtained for WASP-39 b as part of the JWST Transiting Exoplanet Community Director’s Discretionary ERS programme18,19 (ERS-1366; Principal Investigators: N. M. Batalha, J. L. Bean, K. B. Stevenson), which has already been introduced in ref. 10. We selected this dataset for the morning and evening exploration of WASP-39 b because, among the four ERS datasets, it has the widest wavelength coverage and presented relatively minor challenges in the light-curve data analysis, which is how we obtained constraints on the morning and evening of the exoplanet in this work.

Data analysis

We used the FIREFLy pipeline’s reduction of the dataset, as presented in refs. 10,37 and subsequently used in ref. 24. To summarize, the pipeline performs initial calibrations using the package jwst, adding in group-stage 1/f noise destriping before the ramp-fitting stage. It then scrubs the time series of bad pixels and cosmic rays, and shift-stabilizes each integration to correct for millipixel-level correlated jitter of the spectral trace. Following the authors of ref. 24, who delved deeply into the deleterious effects of saturation, we elected to use only the unsaturated 2.0–5.0 μm region of the spectrum due to its weak systematic noise and reproducible transmission spectrum. The approximately 0.7–2.0 μm region showed significant deviations relative to the unsaturated NIRISS-SOSS spectrum21, increasing in magnitude towards the saturation centre at 1.3 μm. The region also suffered from a significantly lower signal-to-noise ratio because fewer groups are available for use there. We omitted this region to avoid the possibility of drawing spurious conclusions about the planet’s nature. We noted that WASP-39 b’s 2.0–5.0 μm spectrum has relatively larger feature amplitudes, spanning more chemical species, than the NIR region. The PRISM spectrophotometry is well-fit by a linear trend varying in wavelength, and displays no other significant systematic noise.

Transit light-curve analysis

Physical and orbital parameters of the system

The physical and orbital parameters of WASP-39 b used in this work are the ones reported in ref. 24. These were fixed in our wavelength-dependent light-curve fits. In particular, we fixed the period to P = 4.0552842 days, the scaled-to-stellar-radius semi-major axis to a/R* = 11.390 and the impact parameter to b = 0.4498, and set the mid-transit time for NIRSpec/PRISM to T0 = 2,459,771.335647 days.

Wavelength-dependent light-curve analysis

To explore the evidence for morning and evening signatures on the wavelength-dependent NIRSpec/PRISM light curves, we performed analyses following three different approaches:

  1. 1.

    Catwoman light-curve fits. In this approach, we performed light-curve fits to the wavelength-dependent light curves using the catwoman framework introduced in refs. 25,26. This framework models the transiting object passing in front of the star as two stacked semicircles, each one representing the effective transit depth from the morning and evening terminators of WASP-39 b. We performed two sets of fits using this approach, led by co-authors M.M. (MM) and N.E. (NE), respectively, both of which set the rotation angle of the limbs to 90°. The NE catwoman fits were performed using limb-darkening coefficients taken from the limb-darkening38 package as priors, using ATLAS models with the same stellar parameters as WASP-39, and passing those through the Synthetic-Photometry/Atmosphere-Model (SPAM) algorithm of ref. 39 to obtain the final estimates for the limb-darkening coefficients. The MM fits fixed the limb-darkening coefficients to those obtained from the ExoCTK40 library also obtained from ATLAS models with the same stellar parameters as WASP-39. Both light-curve fits used a quadratic limb-darkening law. The NE fits used the limb-darkening parametrization in ref. 41, with a prior that followed a truncated normal centred around theoretical transformed coefficients (q1, q2), and with limits set at between 0 and 1 for each. The standard deviation of that prior distribution was set to 0.1 for both transformed coefficients, based on the findings of ref. 42, who found 0.1 to be the maximum offset between quadratic and empirical limb-darkening coefficients when comparing theoretical coefficients to those obtained via precise Transiting Exoplanet Survey Satellite photometry. Both fits also included a slope in time as a free parameter for modelling the visit-long slope seen in the NIRSpec/PRISM data in ref. 10, along with a baseline flux offset. The NE fits include, in addition, a jitter term added in quadrature to the NIRSpec/PRISM light-curve error bars. In total, the MM fits had four free parameters (two semicircle radii, slope and baseline flux offset) for each wavelength-dependent light curve, whereas the NE fits had seven free parameters (the same as MM plus two limb-darkening coefficients and a jitter term).

  2. 2.

    Ingress/egress (Tiberius) light-curve fits. In this approach, we performed transit light-curve fits to the wavelength-dependent light curves using the batman27 framework via the Tiberius library43,44, but fitting the half-ingress (where contributions mainly from the morning limb are expected) and half-egress (where contributions mainly from the evening limb are expected) independently. To find the contact points of the transit event, a transit light curve was generated using the orbital parameters described above, and limb-darkening was set to zero to find the discontinuity points in the light-curve-marking contact points—1 (start of ingress), 2 (end of ingress), 3 (beginning of egress) and 4 (end of egress). With this, the half-ingress (contact point 1.5—mean of contact 1 and 2) and half-egress (contact point 3.5—mean of contact 3 and 4) contact points were derived. The half-ingress (all datapoints before contact point 1.5 and after contact point 4) and half-egress (all datapoints after contact point 3.5 and before contact point 1) light curves were then fit as follows. First, the full light curve is fit for each wavelength bin, with a model that fits for a slope and baseline flux offset, the planet-to-star radius ratio and the linear term of a quadratic limb-darkening law, with the quadratic term fixed to limb-darkening coefficients obtained from 3D models in the Exo-TiC library45. Then, the half-ingress and half-egress light curves are fit by leaving all parameters fixed to the best-fit parameters obtained from the full transit fit, with the only free parameter being the planet-to-star radius ratios. These define the morning and evening transit depth, respectively, using this methodology.

  3. 3.

    Wavelength-dependent mid-transit time. The transit-time spectrum is sensitive to 0th-order wavelength-dependent opacity-centroid shifts along the planet’s orbit, imparted by spatial inhomogeneity in the composition and temperature of its terminator12,15,26,46. A hotter, more extended trailing terminator casts a positive deflection in the relative transit time (ΔT0 > 0), with the planet appearing to transit slightly later due to the subtle trailing-limb inflation of its τ = 1 surface. A colder leading terminator spectrum, or one with feature-muting grey clouds, would likewise cast a monochromatic positive deflection on the transit-time spectrum. The effect amplitude scales inversely with the planet’s orbital velocity and impact parameter, and the difference in each terminator’s mean transit-cord altitude. The time spectrum shown in Extended Data Fig. 1c is the result of a Levenburg–Marquardt least-squares fit to the spectrophotometry, with bins wider than those used in ref. 10. At each wavelength channel, we fixed WASP-39 b’s orbital parameters to those of ref. 24, while fitting for its limb-darkening coefficients, transit depth and transit centre time using batman27. We found that the time signature is robust against the selection of fitted and fixed parameters, resulting in less than or equal to 1σ differences. Statistically significant greater than or equal to 3σ positive deflections were detected with wavelengths corresponding to the spectral features of H2O (roughly 2–3.5 μm), H2S (roughly 3.78 μm), SO2 (roughly 4.06 μm) and CO2 (roughly 4.2–4.5 μm).

The results from the methodologies described above are presented in Extended Data Fig. 1. Both catwoman (NE, MM) and the half-ingress and half-egress approaches seem to be consistent with each other within the error bars, and in judging the overall structure of the resulting morning and evening spectra. In general, it appears the morning spectral features of H2O and CO2 are damped in comparison with the same features observed in the evening—a picture that is consistent with the analysis performed on the wavelength-dependent transit times, where the largest offsets are observed for the H2O and CO2 features, although the latter molecule is seen at lower significance.

However, the significance of the dampening between spectral features in the morning and evening was less clear for the NE light-curve analysis. This approach produces the largest errors on the morning and evening spectra because this approach assumes some ignorance on the limb-darkening coefficients. As we show below, through light-curve experiments performed to study the robustness of our morning and evening spectra to assumptions on transit parameters, we deem this approach to be the most conservative, in terms of deriving differences between the morning and evening limbs, as very slight deviations from the true ‘underlying’ limb-darkening coefficients can give rise to false differences between morning and evening spectra, which can in turn be erroneously interpreted as an astrophysical effect in the exoplanet atmosphere. This is why we decided to perform inferences on the catwoman approach of NE to interpret the morning and evening spectra in the main text.

Robustness of morning and evening spectra to assumptions on transit parameters

Previous works that have studied the possibility of extracting morning and evening spectra directly from transit light curves have identified a number of possible degeneracies that might arise, and which could impact the derived spectra15,26,46. In particular, the degeneracy between the time-of-transit centre and limb asymmetries has been identified in previous works as the largest source preventing the performance of these detections in real data, with the use of precise wavelength-dependent transit light curves, such as the ones used in this work, being critical to lift it15,46. In addition, while limb-darkening has been shown to slightly decrease the detectability of limb asymmetries on simulated data26, any biases induced by fixing those coefficients have, to our knowledge, not been studied in detail in the literature. Finally, eccentric orbits have been shown to also give rise to asymmetric transit light curves47,48. Using the wrong assumption about the eccentricity of the orbit could thus, in turn, give rise to biases on morning and evening spectra, which are extracted by measuring light-curve asymmetries. We performed experiments to study those three systematic error sources to quantify their impact on our reported morning and evening spectra.

Robustness against no limb asymmetries

To define a null baseline robustness check against the catwoman methodology used in this work, we simulated noisy transit light curves using batman, which had the same input transit parameters as the white-light light-curve parameters used in our fits (that is, the ones from ref. 24, the same noise properties as the real data (including the visit-long slope) and transit depths that varied as a function of the wavelength matching the transit spectrum presented in ref. 10. We then fitted those light curves with a catwoman model, using the same approach as the one described above for the NE catwoman light-curve fits. As expected, we found that the extracted morning and evening spectra were consistent with each other, producing a null difference between them. The results of those simulations are shown in Extended Data Fig. 3a.

Robustness against the time-of-transit centre

To check the robustness of our spectra against using a fixed time-of-transit centre (obtained from ref. 24), we performed the same simulations as the ones described in the previous section. However, we used a time-of-transit centre 3σ larger than the one reported in ref. 24, which amounted to a time offset of 3.4 s. We then fitted those light curves with a catwoman model, which used the time-of-transit centre as a fixed parameter without this offset. We found that such an offset in timing had no measurable impacts on our morning and evening transit spectra, with the difference between them being consistent with zero. The results of those simulations are shown in Extended Data Fig. 3b.

Robustness against limb-darkening coefficients

We performed a similar experiment to the one described in the previous section, but modified the input limb-darkening coefficients to be offset by 0.01 from the fixed values, which were obtained following the methodology described above for NE’s catwoman transit light-curve fitting approach. We then fitted those light curves, but fixed the limb-darkening coefficients in our fit to the ones without those offsets. We found that these very small offsets on the limb-darkening coefficients had a measurable impact on the retrieved morning and evening spectra, giving rise to measurable morning and evening differences on the order of approximately 200−300 ppm when fixing those in the light-curve fitting procedure to the wrong values. The results from this simulation are presented in Extended Data Fig. 3c. The same experiment, but setting wide priors on these coefficients, as described in the NE catwoman light-curve fitting procedure above, allowed the input null difference between the evening and morning spectra (not shown) to be recovered. These experiments highlight that, while relative morning and evening spectral differences might be obtained by fixing the limb-darkening coefficients, even if they are slightly wrong, absolute spectral differences might not be robustly extracted in general. Even if aiming to obtain relative morning and evening spectral differences, in reality, limb-darkening offsets might be wavelength-dependent and thus might give rise to spurious signals and/or spectral features in the limb spectra. This was one of the main reasons we decided to present the results obtained from the NE catwoman light-curve fitting procedure in the main text—because it allows for limb-darkening coefficients to be significantly offset from the input theoretical model calculations. The limb-darkening coefficients retrieved from performing catwoman fits using the NE approach to our real NIRSpec/PRISM data are presented in Extended Data Fig. 4. Errors on the u1 coefficients ranged from 0.02−0.04, while errors on the u2 coefficients ranged from 0.03−0.06. Thus, offsets on the limb-darkening coefficients on the order of approximately 0.01, are indeed allowable by the data, and they are particularly likely in the 2.5–4.5 μm range for the linear (u1) coefficient of the quadratic law, which is where the retrieved limb-darkening coefficients deviate the most from the theoretical model predictions.

Robustness against eccentricity

We repeated a similar experiment to the ones described above, but this time we set as an input batman model an eccentric orbit with parameters consistent at 3σ with the best-fit parameters presented in ref. 24, corresponding to an eccentricity and argument of periastron of e = 0.035 and ω = 10°. Our simulations, presented in Extended Data Fig. 3d, show that these set of values can indeed give rise to offsets between the morning and evening limbs, making the morning limb spectra larger than the evening limb spectra. We explored the range of (e, ω) allowed by the analysis presented in ref. 24 and found that the impact of these parameters always acted in the same direction to the WASP-39 b transit observations analysed in this work, with the values of e and ω allowed by the posterior distribution all potentially giving rise to larger morning depths than evening depths. With the morning and evening spectra reported in this work, we observed the opposite, however—larger evening depths than morning depths. This suggests that the absolute difference we observed between the morning and evening spectra in the NIRSpec/PRISM observations are, at worst, lower limits on the actual absolute depth difference between the morning and the evening limbs.

It is important to note, however, that a set of values of (e, ω) similar to the one used in our experiment would probably be unrealistically large, as secondary eclipse observations constrain e cos ω = 0.0007 ± 0.0017 (ref. 49), which would reject such an (e, ω) combination at more than 10σ. Given WASP-39 b’s eccentricity is consistent with zero, given data from different sources, which is, in turn, consistent with the relatively small circularization timescales for the planet, WASP-39 being an approximately 9-Ga star50, we suggest eccentricity offsets are a relatively minor effect for this system.

To test how the most up-to-date constraints on the properties of the system impacted our detection of the morning and evening differences in the transmission spectrum of WASP-39 b presented in this work, we re-ran a white-light light-curve fit similar to that in ref. 24, but assuming an eccentric orbit, and then let the posteriors of the transit parameters of this fit float as priors on our wavelength-dependant light-curve fits, instead of fixing those parameters, as was done in our nominal analysis. This new white-light light-curve fit was performed with two extra priors: (1) the constraint on e  cos  ω  =  0.0007 ±  0.0017 of ref. 49; and (2) a prior on the stellar density of WASP-39 b, obtained via the methodology outlined in refs. 51,52. This latter methodology first obtains stellar atmospheric parameters from high-resolution spectra, for which we used an average of three publicly available fibre-fed, extended range echelle spectrograph (FEROS) high-resolution spectra from PID 098.A-9007(A), obtained on 12 February 2017, which were reduced using the CERES pipeline53. This spectrum was given as input to the Zonal Atmospheric Stellar Parameters Estimator (ZASPE) code54, with which an initial set of stellar atmospheric parameters was obtained. Then, the available Gaia (G = 11.8867 ± 0.0020, BP = 12.3061 ± 0.0054, RP = 11.3258 ± 0.0031) and Two Micron All Sky Survey (2MASS) (J = 10.663 ± 0.024, H = 10.307 ± 0.023, K = 10.202 ± 0.023) photometry was combined with Gaia-derived distances (211.46 ± 2.35 pc, obtained via parallaxes using the methodology described in ref. 55) to obtain fundamental absolute stellar parameters using PARSEC isochrones56, with the spectroscopically derived stellar atmospheric parameters used as priors. This iterative procedure returns all the fundamental stellar parameters for the star. In particular, for WASP-39 b, we found R* = 0.897 ± 0.011 R⊙ and M* = 0.891 ± 0.033 M⊙, which, in turn, gave a stellar density of ρ* = 1,736 ± 121 kg m−3. We noted that those estimated stellar parameters were consistent with, and more precise than, those presented in the discovery paper of ref. 50.

This new white-light light-curve fit gives posterior parameters that are, in turn, all consistent with the ones reported in ref. 24, notably, with a stellar density posterior of 1,705 ± 28 kg m−3, consistent at 1σ with the value of 1,699 ± 55 kg m−3 shown in that work (and much more constrained than our stellar density prior, showcasing this value as not dominated by it). The fit also put a limit on the eccentricity of WASP-39 b of e < 0.016 with 99% credibility (\(e\sin (\omega )=0.001{4}_{-0.0057}^{+0.0051}\); \(e\cos (\omega )=0.000{9}_{-0.0012}^{+0.0014}\)), a circular model still being preferred via the Bayesian evidence. As described above, we then used the posterior distributions of all the transit parameters of this eccentric model fit as priors for each wavelength-dependant light-curve fit using the catwoman NE methodology described above. We found a morning and evening transmission spectrum that is very similar to the one presented in Fig. 2, albeit with larger error bars—an increase dominated by the uncertainty on the eccentricity. This highlights the importance of having high-precision orbital parameters for systems when performing limb asymmetry detections and, in particular, good constraints on eccentricities and arguments of periastron. Despite these enlarged error bars, we still found an average evening-to-morning depth difference of 582 ± 188 ppm—a 3σ detection of the evening-to-morning depth effect presented in this work, even in this worst-case scenario. To further explore the impact of our orbital parameter estimation on our detection of inhomogeneous terminators on WASP-39 b, we ran experiments in which we artificially enlarged the error bars on the orbital parameters by 3-, 5- and 10-fold, for both circular (that is, e = 0) and eccentric (that is, free e  cos (ω) and e  sin (ω)) cases, and compared the average evening-to-morning depths for each case. We compared these differences both across the entire wavelength range and for wavelengths above 4 μm, where we saw the largest deviations in evening-to-morning depths. The results from our experiment are presented in Extended Data Fig. 2. As can be seen, for our circular case, error inflations of up to five times our reported error bars still support our detection of inhomogeneous terminators, whereas for the eccentric case, error inflations of up to three times only support this detection at wavelengths above 4 μm. These experiments highlight the dependency of the detection of this effect on the accuracy and precision of orbital parameters for WASP-39 b, which might also be the case for detecting the effect on other exoplanets. We noted, however, that these experiments provided an upper limit on the uncertainty on the evening-to-morning depth difference because the eccentricity should be wavelength-independent. In our case, however, we were fitting for eccentricity independently for each individual wavelength bin.

Robustness against white-light limb asymmetries

The white-light light-curve analyses performed in ref. 24 assumed a batman transit light-curve model. We left the transit parameters fixed in most of our wavelength-dependent light-curve fits to the NIRSpec/PRISM data. However, given our detection of limb asymmetries in this dataset, it could be that the posterior parameters in ref. 24 are biased, given no catwoman models were used to analyse the JWST data. We performed such fits leaving all the priors for the rest of the parameters unchanged and as described in ref. 24, but allowing for the JWST data to have asymmetric limbs through a catwoman model. We found all the transit parameters agreed within 1σ with respect to the values reported in ref. 24. However, the uncertainties in the time-of-transit centre, eccentricity and stellar density were larger by factors of approximately 1.5, 2 and 4 for the catwoman fits. When accounting for the constraints imposed by WASP-39 b’s secondary eclipse, described in the previous paragraph, however, all uncertainties but that of the stellar density were consistent between the analyses. This analysis suggests that the fact that ref. 24 did not use catwoman models to fit the JWST transit light curves is not a particularly important consideration in the case of WASP-39 b, in particular when referring to the constraints on the eccentricity and time-of-transit centre used in our wavelength-dependent fits.

Robustness of morning and evening spectra to planetary rotation

The framework and results presented above omit any impacts from planetary rotation during transit. If this were to be significant, the spectra observed at the very beginning of the transit event could be different from the spectra observed at the end. Assuming the exoplanet is tidally locked, the amount of rotation the planet undergoes (period of around 4.1 days) on timescales of the transit event (approximately 2.8 h) is on the order of approximately 10°, and calculations by Wardenier et al.57 suggest this might be too small for the detection of any signatures due to planetary rotation. To explore these constraints on our data, we performed the same light-curve analysis outlined above, but considering a different set of morning and evening depths during ingress rather than during egress. We found that during ingress, the mean morning-to-evening transit depth difference was −228 ± 187 ppm, and during egress, the difference was 344 ± 189 ppm. Both values are consistent with zero at 2σ, and thus we were unable to detect any differences between the morning and evening spectra during ingress and egress. We then joined those morning and evening depths, observed during ingress and egress, into a single total transit depth. When comparing the total transit depth during ingress to that of egress, we found a mean difference of 234 ± 144 ppm. This suggests that, while it is possible rotation effects are indeed important, they remain hard to detect with the quality of data at hand.

Robustness of morning and evening spectra to stellar rotation

Stellar rotation could, in principle, produce asymmetries in the transit light curves as the planet transits red- and blue-shifted regions of the star. WASP-39 b, however, has a very slow stellar rotation of 1.5 ± 0.6 km s−1 (ref. 50). In addition, JWST’s NIRSpec/PRISM’s resolution of about R = 100 suggests that such an effect should be small in the case of our observations. We performed calculations to determine how big such an effect would be on our observations and concluded that it would be below 1 ppm, even in the worst-case scenario of a stellar rotation speed at the 5σ limit imposed by the work of Faedi et al.50—that is, 4.5 km s−1.

Robustness of morning and evening spectra to stellar heterogeneities

Stellar heterogeneities (caused by, for example, spots and faculae) could, in principle, impact our ability to retrieve limb asymmetries from transit light curves. WASP-39, however, is a relatively quiet G-type star50. While photometric variability has been detected in Transiting Exoplanet Survey Satellite and Next Generation Transit Survey light curves with a low amplitude level of 0.06% in ref. 22—on the lower tail of the photometric variability observed in Kepler for G8-type stars like WASP-39 (ref. 58)—no evidence of spot-crossing events on the transit light curves of WASP-39 has been detected so far.

Unnoculted stellar heterogeneities, such as those modelled by the transit light-source effect58, would impact the limb spectra of the morning and evening in similar ways, and would thus be unable to give rise to the morning and evening differences observed in this work. Occulted cool or hot spots could, in principle, cause asymmetries in the transit light curve. These would, however, have to be larger than about 100 ppm in amplitude in the transit light curve at about 4 μm to give rise to the approximately 400 ppm differences we observed between the mornings and evenings (Fig. 1d). In turn, these should increase in amplitude for shorter wavelengths, which does not match the wavelength-dependence of the limb asymmetries observed in our work. In addition, any such features would be several times larger at optical wavelengths. However, although such features should be easily detectable, no such features were reported in the optical NIRSpec/PRISM light curves analysed in ref. 10.

Based on this, we suggest that stellar activity is unlikely to give rise to the morning and evening differences observed in this work.

Forward models and retrievals

ATMO model grid

We fitted the entire ATMO local condensation grid tailored to WASP-39 b, as introduced in ref. 28. These models included all the dominant species observed in the NIRSpec/PRISM spectrum of WASP-39 b, except for the sulfur species, which were marginally detected in this dataset10. To fit the morning and evening spectra, we took into consideration the fact that both are highly correlated, and thus used the log-likelihood framework introduced in ref. 26. To construct the morning and evening depth models, we simply took half the transit depth of a given ATMO model sampled for either the morning or evening limb spectra. Then, we tried all combinations of the models in the grid to fit the morning and evening limb depths. Given that there were 3,920 individual models for WASP-39 b in this grid, this resulted in over 15 million fits.

To bring those models to the observed transit depths in our data, we anchored the mean transit depth of both models to the average evening limb transit depth. This conserved any morning-to-evening transit depth offsets. This offset is, thus, the only free parameter in our model fits. Our set of best-fit models are all consistent with models on which the evening spectrum is hotter by about 200 K than the morning spectrum, spanning a wide range of possible cloud and haze properties. In terms of C/O ratios and metallicities, our best-fit models all produced similar C/O ratios for the morning and evening spectra in the range 0.3–0.6 and metallicities on the order of approximately 10× solar.

CHIMERA atmospheric retrievals

To perform a posterior exploration of the parameter space allowed by our observed morning and evening spectra, we decided to run atmospheric retrievals using the CHIMERA retrieval framework described in ref. 29 and modified in ref. 26 to handle morning and evening spectra. These models include all the dominant species observed in the NIRSpec/PRISM spectrum of WASP-39 b, except for the sulfur species, which were marginally detected in this dataset10. This framework performs chemically consistent modelling—that is, it performs chemical equilibrium calculations given the C/O ratios, metallicities and temperature/pressure profiles, which are combined with a prescription for clouds following the work of ref. 59. We used the same prior distributions introduced in ref. 26, the only modification being the prior on the temperature of the limbs, which we set to be a uniform prior of between 500 and 2,000 K for both the morning and evening limbs. Our atmospheric retrievals considered a common metallicity, fiducial 10-bar radius and parameters defining the temperature/pressure profile for the morning and the evening limbs, but considered different C/O ratios, vertical mixing and cloud-top properties for the morning and evening limbs.

The posterior distributions from our CHIMERA atmospheric retrievals—for which a set of posterior parameters are shown in Extended Data Fig. 5—constrained an evening temperature of \(106{8}_{-55}^{+43}\) K and a morning temperature of \(88{9}_{-65}^{+54}\) K, implying an evening-to-morning difference of \(17{7}_{-57}^{+65}\) K—a 3σ difference between the evening and morning limb temperatures, consistent with the findings from our ATMO best-fit grid model search described above. The rest of the parameters in our atmospheric retrievals were all consistent between the morning and evening limbs, suggesting that this temperature difference is one of the largest effects defining the difference between the morning and evening spectra. In particular, the C/O ratios were consistent with each other, with the evening limb having \({\rm{C}}/{\rm{O}}=0.5{8}_{-0.16}^{+0.13}\) and the morning limb having \({\rm{C}}/{\rm{O}}=0.5{7}_{-0.23}^{+0.17}\). Interestingly, while both limbs allowed for clouds, the cloud-top pressure in the evening limb was much more constrained than the pressure in the morning limb, the cloud-top pressure of the evening limb being located in our retrievals at approximately 1–10 mbar and the clouds in the morning limb being consistent with a wide range of possibilities. Notably, the posterior distributions presented in Extended Data Fig. 5 showcase how these cloud properties do not strongly define the morning and evening temperatures, probably stemming from the fact that these two properties are extracted both from the absolute depth difference between the morning and evening spectra and the amplitude of the H2O and CO2 features. For example, while the morning cloud-top pressure is consistent with a wide range of values, all those values are allowed within the relatively narrow temperature ranges for the morning and evening temperatures described above. In the case of the evening cloud-top pressure, which is much better defined, some slight correlations are observed with the temperatures, but again within well-constrained temperature values. Finally, the retrieved metallicity in our fits is consistent with a 10× solar metallicity—again, consistent with our best-fit ATMO models.

General circulation models

Condensate cloud model

The results from the cloud-microphysics model presented here were obtained by applying a kinetic cloud-formation model (consistent solution of nucleation of different species, growth and evaporation of mixed materials, gravitational settling, mixing, element conservation), coupled with the equilibrium gas-phase chemistry60,61 for 10× solar elemental abundances. We used one-dimensional (1D) pressure–temperature profiles as input, extracted from a cloud-free GCM simulation of WASP-39 b using ExpeRT/MITgcm62. The mixing timescale in the model was calculated based on the local vertical velocities from the GCM and scale height (see ref. 33). The mixing timescale was then multiplied by a factor of 100 (refs. 63,64). We noted that the GCM simulations were identical to those presented in ref. 32. The resulting cloud particle number densities, their mixed material compositions and mean particle sizes were used as input to calculate the local cloud opacity using the adapted version of petitRADTRANS65,66,67, employing the Landau, Lifshitz and Looyenga68,69 mixing prescription and Mie theory, using the publicly available Python code PyMieScatt70. The spectra from nine different latitudes (−86°, −68°, −45°, −23°, 0°, 23°, 45°, 68°, 86°) were then averaged at the evening and morning terminators, respectively.

Photochemical haze model

For modelling photochemical hazes, we used the haze model presented in ref. 35 in combination with SPARC/MITgcm71,72, which couples wavelength-dependent radiative transfer using the correlated-k method to a dynamical core based on primitive equations73. All numerical choices in the model are identical to the wavelength-dependent passive model presented in ref. 74, except that the planet parameters of WASP-39 b, a 10× solar metallicity and a temperature of the bottom-most layer of 4,154 K were assumed. The model treats hazes as passive tracers with constant particle sizes. Hazes are produced at low pressures on the dayside and destroyed at pressures greater than 0.1 bar. Particle sizes ranging from 1 to 1,000 nm were considered. The haze production rate then was adjusted to obtain a good match to the total (not terminator-resolved) transit spectrum. Particle sizes of 3 and 30 nm resulted in the best match to the transit spectrum. The spectrum shown in Fig. 3 uses a particle size of 30 nm and a haze production rate of 2.5 × 10−12 kg m−2 s−1 at the substellar point. The spectra generated with a particle size of 3 nm showed qualitatively similar, but smaller, differences between the morning and evening terminators.

Clear-atmosphere equilibrium and transport-induced disequilibrium chemistry models

To model the equilibrium and disequilibrium chemistry (in particular, the transport-induced quenching that occurs when chemical kinetics are coupled to atmospheric transport), WASP-39 b was simulated using the Met Office’s Unified Model75,76. This model’s dynamical core solves the non-hydrostatic, deep-atmosphere Navier–Stokes equations. Its radiative transfer code77,78,79 solves the two-stream equations using the correlated-k and equivalent extinction methods, including H2O, CO, CO2, CH4, NH3, HCN, Li, Na, K, Rb and Cs and collision-induced absorption due to H2–H2 and H2–He as sources of opacity, assuming clear-sky conditions and a 10× solar metallicity. Two different chemistry schemes were used. One was the chemical equilibrium scheme that computes a local chemical equilibrium using the Gibbs energy minimization, and the other was the chemical kinetics scheme that solves the ordinary differential equations describing the evolution of chemical species present in the reduced chemical network of ref. 80 to represent the disequilibrium thermochemistry (in the absence of photolysis), as implemented in refs. 34,81. To maintain stability, the model employs a vertical sponge, with a damping coefficient of 0.15 and a diffusion filter in the longitudinal direction with a coefficient of 3.83 × 10−2 (ref. 76).

Calculating morning and evening spectra

For the photochemical haze and clear-atmosphere models, we generated transmission spectra of WASP-39 b for the morning and evening terminators similarly to the method described in ref. 82. Briefly, we performed absorption-only, ray-striking radiative transfer through the input GCM at two orbital phases. We rotated the GCM by the phase angle at ingress and egress, respectively, in addition to interpolating the GCM onto an equal-altitude grid truncated at approximately 1 bar. For the Met Office’s Unified Model, chemical abundances were taken from the GCM output. For the SPARC/MITgcm photochemical haze model, the chemistry was interpolated from the FastChem83,84 equilibrium chemistry tables.

Our opacity sources included H2O (ref. 85), CH4 (refs. 86,87), CO (refs. 88,89), CO2 (ref. 90), C2H2 (ref. 91) and NH3 (refs. 92,93). We included the extinction (absorption and scattering out of the beam) from haze particles with Mie theory using PyMieScatt70, assuming homogeneous particles with their size set by the GCM input and a refractive index of soot94.

A note on 1D versus 3D transit-spectra calculations

We point out that spectra for the condensate cloud model were calculated using a 1D radiative transfer code with the classic mid-transit geometry due to the 1D nature of the microphysics model and the additional complexity of mixed-composition grains. By contrast, the spectra for the photochemical haze model and clear-atmosphere equilibrium and disequilibrium chemistry models were calculated using a 3D code that also correctly takes into account the change in geometry during ingress and egress through rotation. We noted that, in tests comparing the 1D and 3D geometries based on the model grid of ref. 95, the amplitude of the terminator differences changed. In some, but not all, cases, this led to stronger limb asymmetries if the full 3D geometry was considered (K.A. et al., manuscript in preparation). This could potentially bring the size of the observed differences into better agreement with the observations.