Identifying deformed exoplanets with JWST and Ariel: A target selection metric for phase curve observations

Abstract: The shape of an exoplanet encodes fundamental information about its internal structure. For close-in giant planets, strong stellar tidal forces induce measurable deformations that can be probed through high-precision photometry. These deformations are quantified by the fluid Love numbers, which characterise a planet's response to external perturbations and are directly linked to its internal density distribution. In this work, we assess the potential of JWST and the future Ariel mission to constrain the Love numbers of hot Jupiters through full-orbit phase curve observations. To identify the most promising targets for this science case, we introduce a new detection metric, the deformation metric (D), which combines the expected deformation amplitude with the anticipated photometric signal-to-noise ratio. We apply this metric to the Ariel target list and identify WASP-33 b, WASP-76 b, and HAT-P-32 b as the three most favourable targets that currently lack Love number measurements. Using WASP-76 b as a benchmark case, we perform end-to-end retrieval simulations and show that a single continuous JWST phase curve observation can constrain the Love number $h_{2f}$ to a precision of $σ_{h_2f} \approx 0.09$, while a single Ariel visit could achieve $σ_{h_{2f}} \approx 0.18$. Such precision is likely sufficient for Love number measurements to provide meaningful constraints on planetary interior models and to distinguish between competing interior-structure scenarios, opening a new observational avenue for probing the deep interiors of exoplanets.