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A radial velocity analysis technique to determine planetary interiors via Love numbers

Presentation #302.05 in the session Giant Planet Interior Structure and Dynamics (Oral Presentation)

Published onOct 23, 2023
A radial velocity analysis technique to determine planetary interiors via Love numbers

The majority of the confirmed exoplanets have been identified either through transits or radial velocities surveys. Planets identified with both techniques are characterized by their mass and radius, providing an estimate of the mean density and giving a hint on the class of planet (e.g. distinguish a gas giant from a rocky planet). However, there is a degeneracy between the mean density and the planetary mass and radius (e.g. Valencia et al., 2013). The mean density alone cannot uniquely constrain the planetary composition and therefore its interior structure. The inner structure of exoplanets can be better constrained with the help of a third measurable parameter beyond mass and radius: the second-degree fluid Love number k2 (Love, 1911). It is highly sensitive to the thickness of the interior layers and is proportional to the concentration of mass towards the centre of the planet. Therefore it can be used to infer the internal structure of the body.

We will illustrate a method to analyze the radial velocity curve in the presence of periastron precession caused by general relativity and tidal interaction between the star and the planet. The latter can be linked to k2 (Kopal, 1959) and give a clue on the interior of the planet. We also study the effect of the rotationally and tidally distorted stellar shape on the radial velocity curves. This causes distortion in the shape of the RV curve as well, and leads to the presence of an apparent eccentric orbit. We will show that the correct estimate of this effect must be taken into account and some earlier studies overestimated its amplitude and significance. We will present our results when we applied our technique to the first exoplanetary systems. We will show evidence of periastron precession motion (Bernabò et al., submitted, 2023, Csizmadia et al., 2019) and the determination of the planetary Love number. Finally, we will discuss the meaning of the latter in the context of exoplanetary interiors.

References: Bernabò et al., Evidence for apsidal motion and detection of a co-moving companion star in the WASP-19 system, 2023, submitted to A&A, under review

Csizmadia et al., An estimate of the k2 Love number of WASP-18Ab from its radial velocity measurements, A&A, 623, A45, 2019

Kopal, Close Binary Systems, 1959

Love A. E. H., Some Problems of Geodynamics, 1911

Kopal, Dynamics of close binary systems, 1978

Valencia D., Guillot T., Parmentier V., Freedman R. S., Bulk composition of GJ 1214b and other sub-Neptune exoplanets, The Astrophysical Journal 775, 10, 2013

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