Retrieval of the fluid Love number $k_2$ in exoplanetary transit curves

Abstract

We are witness to a great and increasing interest in internal structure, composition and evolution of exoplanets. However, direct measurements of exoplanetary mass and radius cannot be uniquely interpreted in terms of interior structure, justifying the need for an additional observable. The second degree fluid Love number, $k_2$, is proportional to the concentration of mass towards the body's center, hence providing valuable additional information about the internal structure. When hydrostatic equilibrium is assumed for the planetary interior, $k_2$ is a direct function of the planetary shape. Previous attempts were made to link the observed tidally and rotationally induced planetary oblateness in photometric light curves to $k_2$ using ellipsoidal shape models. Here, we construct an analytical 3D shape model function of the true planetary mean radius, that properly accounts for tidal and rotational deformations. Measuring the true planetary mean radius is critical when one wishes to compare the measured $k_2$ to interior theoretical expectations. We illustrate the feasibility of our method and show, by applying a Differential Evolution Markov Chain to synthetic data of WASP-121b, that a precision $\le$ 65 ppm/$\sqrt{2min}$ is required to reliably retrieve $k_2$ with present understanding of stellar limb darkening, therefore improving recent results based on ellipsoidal shape models. Any improvement on stellar limb darkening would increase such performance.

Accepted for publication in The Astrophysical Journal

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• HST/STIS capability for Love number measurement of WASP-121b
• Tidal Response and Shape of Hot Jupiters
• Evidence of apsidal motion and a possible co-moving companion star detected in the WASP-19 system
• Stability and detectability of exomoons orbiting HIP 41378 f, a temperate Jovian planet with an anomalously low apparent density
• Post-Newtonian effects on some characteristic timescales of transiting exoplanets
• Constraining the oblateness of transiting planets with photometry and spectroscopy
• Tidal evolution of exoplanetary systems hosting Potentially Habitable Exoplanets. The cases of LHS-1140 b-c and K2-18 b-c
• The phase curve of the ultra-hot Jupiter WASP-167b as seen by TESS
• Retrieving interior properties of hot Jupiters with Love numbers and atmospheric measurements
• Exo-Geoscience Perspectives Beyond Habitability
• Relationship between the moment of inertia and the $k_2$ Love number of fluid extra-solar planets
• Exploring Exoplanet Dynamics with JWST: Tides, Rotation, Rings, and Moons
• Exploring the habitability and interior composition of exoplanets lying within the extended habitable zone
• Yuti: A General-purpose Transit Simulator for Arbitrary Shaped Objects Orbiting Stars
• Lie Group Theory of Multipole Moments and Shape of Stationary Rotating Fluid Bodies