-0.3. We fix the gravitydarkening exponent β that governs what temperature difference a difference in surface gravity between the star’s equator and pole results in to 0.23 as varying it can cause it to run off towards physically unrealistic values [67]. Finally, we use Hamiltonian Monte Carlo with the NUTS sampler [68] in order to obtain posteriors on the parameters of interest. We also performed inference using the same priors but without the gravitydarkening map on the star as a comparison to a standard transit fit to examine the amplitude of a transit asymmetry the star’s gravity darkening induces.

TESS’s light curves confirm that WASP-121 A is measurably gravity-darkened, creating a transit asymmetry with an amplitude on the order of 100 ppm in the optical light curves between contact points 2 and 3 as well as upward residuals reaching up to ∼300 ppm during egress (see Extended Data Fig. 4). The posteriors of the planet’s and star’s inclination as well as the projected and true spin-orbit angles (see Supplementary Table 6) are consistent with previous radial-velocity observations of the system [47]. For the stellar rotation rate, we find (12.6 ± 0.19) % times the critical rotational velocity which is slightly lower than the (15−28) % estimated before [47] and thus suggests that the star’s rotation rate lies on the lower end of previous constraints. One possible reason for the small discrepancy between our result and the radialvelocity observation’s lower limit might be the star’s gravity-darkening exponent we fixed at β = 0.23. β can be lower than the value of β = 0.25 predicted theoretically [69], reducing the temperature contrast between stellar equator and pole for a given rotation rate. Thus, if WASP-121 A’s β were lesser than 0.23, our measured ω would be biased to smaller values which would be in line with our measurement being slightly lower than the Doppler tomography’s lower limit. Since the wavelength bands of TESS and JWST/NIRISS SOSS Order 1 overlap, the NIRISS SOSS light curve will also be affected by gravity darkening. Indeed, both the asymmetry between contact points 2 and 3 and the yet stronger upward residuals during egress caused by gravity darkening in TESS (see Extended Data Fig. 4) are clearly visible in the white light curve of NIRISS SOSS Order 1 (see middle rows of Fig. 1 and Extended Data Fig. 1). To examine, if the transit asymmetry observed with JWST/NIRSpec G395H’s NRS2 is consistent with WASP-121 A’s gravity darkening observed with TESS, we fit the JWST/NIRSpec G395H NRS2 data in the same manner as before, but with a maximum a-posteriors method. The stellar rotation rate required to fit the NRS2 light curve is ω = 19.8 % (see Supplementary Table 6) and thus, deviates from the TESS result by > 30σ. This demonstrates that gravity darkening of WASP-121 A is not sufficient for explaining the transit asymmetry observed with JWST/NIRSpec. Additionally, the gravity darkening model does not offer an explanation for the lack of a transit asymmetry in NRS1, if NRS2 were affected by gravity darkening as the transit asymmetry driven by gravity darkening would monotonically decreases as longer wavelengths are observed [64]. Therefore, in NRS2, gravity darkening must be a minor effect compared to WASP-121 b’s phase-dependent transmission spectrum as the symmetric NRS1 light curve demonstrates that gravity darkening has already dropped below a measurable level at that wavelength range (see Fig. 1 and Extended Data Fig. 1).