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HST/STIS capability for Love number measurement of WASP-121b

Data from transit light curves, radial velocity and transit timing observations can be used to probe the interiors of exoplanets beyond the mean density, by measuring the Love numbers $h_2$ and $k_2$. The first indirect estimate of $k_2$ for an exoplanet from radial velocity and transit timing variations observations has been performed by taking advantage of the years-spanning baseline. Not a single measurement of $h_2$ has been achieved from transit light curves, mostly because the photometric precision of current observing facilities is still too low. We show that the Imaging Spectrograph instrument on-board the Hubble Space Telescope could measure $h_2$ of the hot Jupiter WASP-121b if only few more observations were gathered. We show that a careful treatment of the noise and stellar limb darkening must be carried out to achieve a measurement of $h_2$. In particular, we find that the impact of the noise modelling on the estimation of $h_2$ is stronger than the impact of the limb darkening modelling. In addition, we emphasize that the wavelet method for correlated noise analysis can mask limb brightening. Finally, using presently available data, we briefly discuss the tentative measurement of $h_2 = 1.39^{+0.71}_{-0.81}$ in terms of interior structure. Additional observations would further constrain the interior of WASP-121b and possibly provide insights on the physics of inflation. The possibility of using the approach presented here with the Hubble Space Telescope provides a bridge before the high-quality data to be returned by the James Webb Space Telescope and PLATO telescope in the coming decade.