Atmospheric contribution to k22 (tidal Love number) in Hot Jupiters

The atmospheres of Hot Jupiters (HJs) are strongly shaped by the extreme day-to-night temperature contrasts that drive supersonic jet streams and global-scale circulation patterns. New observational techniques are beginning to provide constraints on both atmospheric wind velocities and planetary deformation, which is expected to be governed primarily by tidal forcing, planetary rotation, and the internal density structure.
However, sufficiently strong global-scale winds can redistribute enough mass to produce an additional dynamical deformation that may be comparable to, or even exceed, the contribution from the static interior structure. Here, we investigate this effect by calculating the lowest-order gravitational harmonic, J₂, which characterizes the planetary oblateness and, in the linear hydrostatic regime, is related to the degree-2 tidal Love number k₂₂
We estimate the contributions to J₂ from both the interior structure and the atmospheric jet streams. The dynamical contribution is calculated based on 3D circulation models spanning a broad HJ parameter space. We show that atmospheric mass anomalies associated with strong winds can significantly modify the expected deformation signal and may therefore be detectable with current and upcoming observations of HJs Love numbers.
Finally, we compare our predictions with existing measurements of tidal Love numbers for Ultra-HJs and explore the possibility of constraining the deep wind structure of exoplanet atmospheres from deformation measurements.