Letter to the Editor

Tidal frequency dependence of the Saturnian k₂ Love number

¹ IMCCE, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Université, Univ. Lille, France
e-mail: valery.lainey@obspm.fr
² Canadian Institute for Theoretical Astrophysics, 60 St. George Street, Toronto, ON M5S 3H8, Canada
³ TAPIR, Mailcode 350-17, California Institute of Technology, Pasadena, CA 91125, USA
⁴ Department of Physics & Astronomy, Queen Mary University of London, Mile End Rd, London E1 4NS, UK
⁵ Department of Computer Science, Jinan University, Guangzhou 510632, PR China

Received: 16 February 2024
Accepted: 18 March 2024

Abstract

Context. Love numbers describe the fluid and elastic response of a body to the tidal force of another massive object. By quantifying these numbers, we can more accurately model the interiors of the celestial objects concerned.

Aims. We determine Saturn’s degree-2 Love number, k₂, at four different tidal forcing frequencies.

Methods. To do this, we used astrometric data from the Cassini spacecraft and a dynamical model of the orbits of Saturn’s moons.

Results. The values obtained for k₂ are 0.384 ± 0.015, 0.370 ± 0.023, 0.388 ± 0.006, and 0.376 ± 0.007 (1σ error bar) for the tidal frequencies of Janus–Epimetheus, Mimas, Tethys, and Dione.

Conclusions. We show that these values are compatible with a constant Love number formulation. In addition, we compared the observed values with models of dynamical tides excited in Saturn’s interior, also finding a good agreement. Future increases in the measurement precision of Love numbers will provide new constraints on the internal structure of Saturn.