Issue |
A&A
Volume 676, August 2023
|
|
---|---|---|
Article Number | A21 | |
Number of page(s) | 6 | |
Section | Planets and planetary systems | |
DOI | https://doi.org/10.1051/0004-6361/202346352 | |
Published online | 01 August 2023 |
Relation between the moment of inertia and the k2 Love number of fluid extra-solar planets
1
Dipartimento di Fisica e Astronomia “Augusto Righi” (DIFA), Alma Mater Studiorum Università di Bologna,
Viale Berti Pichat 8,
40127
Bologna, Italy
e-mail: anastasia.consorzi2@unibo.it
2
Istituto Nazionale di Geofísica e Vulcanologia,
Via di Vigna Murata 605,
00143
Roma, Italy
Received:
8
March
2023
Accepted:
6
June
2023
Context. Tidal and rotational deformation of fluid giant extra-solar planets may impact their transit light curves, making the k2 Love number observable in the near future. Studying the sensitivity of k2 to mass concentration at depth is thus expected to provide new constraints on the internal structure of gaseous extra-solar planets.
Aims. We investigate the link between the mean polar moment of inertia N of a fluid, stably layered extra-solar planet and its k2 Love number. Our aim is to obtain analytical relations valid, at least, for some particular ranges of the model parameters. We also seek a general approximate relation useful for constraining N once observations of k2 become available.
Methods. For two-layer fluid extra-solar planets we explore the relation between N and k2 via analytical methods, for particular values of the model parameters. We also explore approximate relations valid over the entire range of two-layer models. More complex planetary structures are investigated by the semi-analytical propagator technique.
Results. A unique relation between N and k2 cannot be established. However, our numerical experiments show that a rule of thumb can be inferred that is valid for complex, randomly layered stable planetary structures. The rule robustly defines the upper limit to the values of N for a given k2, and agrees with analytical results for a polytrope of index one and with a realistic non-rotating model of the tidal equilibrium of Jupiter.
Key words: planets and satellites: interiors / planets and satellites: gaseous planets / planets and satellites: fundamental parameters
© The Authors 2023
Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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