In JWST/NIRSpec’s G395H observing mode, the incoming radiation gets dispersed over two detectors, NRS1 and NRS2. We integrated the time-series of stellar spectra from pixel column 300 to 2042 on the NRS1 and from pixel column 5 to 2010 on the NRS2 detectors to yield wavelength-integrated light curves for both detectors. The two light curves were then fit simultaneously. For the orbital parameters shared between both light curves, we adopted an eccentricity of zero, an argument of periapsis of 90◦ and a period of 1.27492504 days [47] and fit for the impact parameter (b) and semimajor axis normalized by the star’s radius (a/R∗). All other model parameters, the baseline coefficients c0 and c1 (Eq. 2), the partial phase curve parameters p0, p1 and p2, the transit radius coefficients (Ri/R∗in Eq. 1), t0 and the limb darkening coefficients were kept different between both light curves. For the limb darkening, we adopted a quadratic law with two free parameters (u1 and u2). The JWST/NIRISS white light curve was calculated by integrating the flux from detector column 33 to 2033 in the first grating order and fit in the same manner as the NIRSpec white light curve, but without the need to fit two independent light curves jointly.

We first fit the data from both instruments with a least-squares algorithm implemented into the lmfit package [48]. Then, we explored all fit parameters’ posterior probability distributions using the Markov chain Monte Carlo (MCMC) package emcee [49] and estimated the models’ Bayesian evidences using the nested sampling package dynesty [50]. In both sampling approaches, we included systematic noise terms (σsys) we added to the uncertainties of each integration (σp,i) in quadrature for determining the total uncertainty σ2 tot,i = σ2 p,i + σ2
(4)
sys
of each integration. This approach serves to fit for underestimated uncertainties in each light curve. For both sampling approaches, we adopted wide uniform priors for all model parameters (see Supplementary Table 1). In the MCMC, we use 500 walkers with 50,000 steps each of which we discard the first 20,000 steps as burn-in and thin the final samples by a factor of 100. The results of all fit parameters’ posteriors for both observations’ reductions are listed in Supplementary Tables 2, 3, 4 and 5. For the nested samplings, we used 500 live points. For model comparisons, we calculate all model fits’ Bayesian Information Criteria (BIC) from the MCMC samplings and their Bayesian evidences (Z) from the nested samplings. To calculate the statistical significances of the rotation-induced radius change delivered by the observations, we then calculate the differences in BIC (∆BIC) and the normal logarithm of the Bayes factors (ln(B)) of Mrot relative to Mtra which suggest conclusive detections in all observations and data reductions (see Extended Data Tables 1 and 2). We also compare Mrot with free R2/R∗with setting R2/R∗= 0, thus comparing two rotational light curve models with either a quadratic or a linear polynomial for the planet-to-star radius ratio as a function of time. In the NIRISS SOSS data, the light curve modeling approach with free R2/R∗is slightly preferred over the model with R2/R∗= 0 with ln(B) = 1.6 in the Firefly and ln(B) = 1.5 in the Fu reduction. In the NIRSpec G395H data, setting R2/R∗= 0 is slightly preferred over fitting for a free R2/R∗with ln(B) = 1.9 in Firefly and ln(B) = 1.2 in Eureka!. Thus, there is no indication to prefer either approach over the other [26] in all observations and data reductions.